Vera's location after three hours is thus 2,100 feet above sea level.
What is division?Division is a basic arithmetic operation used to find how many times one number (the divisor) is contained within another number (the dividend). The result of a division operation is the quotient. Division is often represented using the symbol "÷" or "/". Sometimes division results in a remainder, which is the amount left over after dividing as much as possible. Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is used in a wide variety of mathematical and real-world contexts, such as sharing equally, calculating rates, and solving equations.
Here,
To find Vera's location after three hours of climbing down the mountain, we first need to convert three hours into minutes. There are 60 minutes in one hour, so three hours is:
3 hours x 60 minutes/hour = 180 minutes
Vera descends at a rate of five feet per minute, so after 180 minutes, she will have descended:
180 minutes x 5 feet/minute = 900 feet
3,000 - 900 = 2,100
Therefore, Vera's location after three hours is 2,100 feet above sea level.
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Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -1/4 (multiplicity 2) and 2/3 (multiplicity 1) and with f(0)=2.
f(x)=?
Answer:
Step-by-step explanation:
To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:
f(x) = A(x + 1/4)^2(x - 2/3)
where A is a constant that we need to determine to satisfy the condition f(0) = 2.
To find A, we substitute x = 0 into f(x) and set the result equal to 2:
f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2
Solving for A, we find that A = -54.
Therefore, the polynomial f(x) is:
f(x) = -54(x + 1/4)^2(x - 2/3)
A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?
A one-sample t-interval for a population mean
Robin Nest's average daily sales were $1,644 based on credit sales and net receivables.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Average daily sales are the estimated amount of sales made daily in a year.
It can be found by the formula:
= Net credit sales / Number of days in the period
Solving gives:
= 600,000 / 365 days
= $1,644
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The complete question is given below.
Robin's Nest had net credit sales for the current period of $600,000 and average net receivables were $50,000. What is Robin's Nest's average daily sales
write the equation of the line that goes through the point and has the given (4,1); slope=2 Write all final answers in slope-intercept form.
Answer: y = 2x - 7
Step-by-step explanation:
Slope-intercept form is y=mx+b
m = slopeb = y-interceptSubstitute variables with their given values.
y = 2x + b
In order to find the y-intercept, or b, we can plug the point provided, (4,1) , into y = 2x + b and solve for b.
1 = 2(4) + b
1 = 8 + b
-7 = b
Now we can put the y-intercept into the equation, and get y = 2x - 7 .
CAN SOMEONE HELP WITH THIS QUESTION?✨
The correct sketch is B
What is the liquid range of water?The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.
This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.
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A one-terabyte external hard drive is on sale at a 21% discount. If the original price was $347, what is the sale price?
(Type a whole number or an exact decimal. If the decimal does not terminate round to the two decimal places)
Answer:
the sale price of the one-terabyte external hard drive is $274.13.
Step-by-step explanation:
To find the sale price of the one-terabyte external hard drive, we can use the following formula:
Sale price = Original price - Discount amount
where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.
Substituting the given values into the formula, we get:
Discount amount = 0.21 * $347 = $72.87
To find the sale price, we subtract the discount amount from the original price:
Sale price = $347 - $72.87 = $274.13
Therefore, the sale price of the one-terabyte external hard drive is $274.13.
Select the correct answer from each drop-down menu.
Consider right triangle ABC.
A triangle ABC has right angle at B is shown. Base AB has length labeled 40 units. Height BC has length labeled 9 units, and hypotenuse AC has length 41 units.
Answer:
By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
How to get the measures of the other two sides of the right triangle?
Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
sin(a) = (adjacent cathetus)/(hypotenuse).
tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
hypotenuse = AC
opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
Step-by-step explanation:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Read the following sentence.
The grizzly bear ambled across the meadow, uprooting logs in search of the delicious grubs that tunneled beneath
Which words belong in the blank?
O her
O it
O him
them
Answer: it
Step-by-step explanation:
Jamaica from Jammin' Candles is trying to arrange 40 candles on a table. She wants them arranged as close to a square shape. Which way should she arrange the candles?
2 rows of 20 candles
10 rows of 4 candles
5 rows of 8 candles
4 rows of 10 candles
The 5th term of a geometric sequence is 729 and the 10th term
is 3. Find the 12th term. Round to the nearest thousandth if
necessary, or answer as a fraction in the form a/b.
Answer:
Step-by-step explanation:
Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.
We know that the 5th term is 729, so:
a * r^4 = 729
10th term is 3, so:
a * r^9 = 3
r^5 = 3/729
r^5 = 1/243
r = (1/243)^(1/5)
r = 1/3
a * (1/3)^4 = 729
a = 3^7
Therefore, the sequence is:
3^7, 3^6, 3^5, 3^4, 3^3, ...
The 12th term is:
3^2 = 9
the average rate of change of g(x)=-3x^(3)+3 from x=-3 to x=3 .
On solving the provided question we can say that The average rate equation of change of g(x) from x = -3 to x = 3 is -27.
What is equation?A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.
Average Rate of Change = (g(b) - g(a)) / (b - a)
In this case, [tex]g(x) = -3x^3 + 3[/tex], and we need to find the average rate of change from x = -3 to x = 3.
So, we plug in the values of a=-3 and b=3 into the formula:
Average Rate of Change =[tex](g(3) - g(-3)) / (3 - (-3))[/tex]
[tex]= (-3(3)^3 + 3) - (-3(-3)^3 + 3)) / (6)\\= (-81 + 3) - (81 + 3)) / 6\\= (-78 - 84) / 6\\= -162 / 6\\= -27[/tex]
The average rate of change of g(x) from x = -3 to x = 3 is -27.
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WILL VOTE 75 POINTSSS
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
cos θ
1 + cos θ
1 − cos θ
sin θ + tan θ
Answer:
The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".
Answer:
1 - cos θ
Step-by-step explanation:
Please Someone smart help me with this!!
a) The linear function is defined as follows: y = 1 - 0.2x.
b) The slope and the intercepts are interpreted as follows:
The slope indicates that the power decreases by 20% per hour.The x-intercept indicates that the battery lasts 5 hours.The y-intercept indicates that the battery power is at 100% when you turn on the laptop.c) The battery power is at 75% after 1.25 hours.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The graph touches the y-axis at y = 1, hence the intercept b is given as follows:
b = 1.
From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:
m = -1/5
m = -0.2.
Hence the function is:
y = -0.2x + 1.
The battery power is of 75% = 0.75 when y = 0.75, as follows:
0.75 = -0.2x + 1
0.2x = 0.25
x = 0.25/0.2
x = 1.25 hours.
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help i need to fisinsh some work for my geometry class because teacher is mean
Answer:
5pi (use the pi character button on your screen)
Step-by-step explanation:
Arc length formula is the shortest formula in all of all math!
Arc length = r•theta
r is the radius. In your question, it is 6.
"theta" is the angle in radians, which was given in your question as 5pi/6.
Fill in these given values to the formula.
Arc length
= r • theta
= 6 • 5pi/6
Simplify (the 6's cancel)
= 5pi
Given f(x) = x ^ 2 + 3x and g(x) = 2x ^ 2 find (f g) (- 1) .
Type answer only in the box.
Answer:
-4
Step-by-step explanation:
You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².
ProductThe product of the functions is the product of their values for each value of x.
(f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)
(f·g)(-1) = -4
PRE-CALCULUS:
Hi! Not really sure how to go about this problem..please help!
Answer:
6
Step-by-step explanation:
the numerator of the fraction is
6(t+h) +1 -(6t +1) = 6h
so the fraction is 6h/h =6
Middle school students were asked whether they receive an allowance and whether they have a cell phone. The results are shown in the table.
cell phone No cell phone
Allowance 45 21
NO Allowance 35 49
What is the approximate percent of total students that receive no allowance and do not have a cell phone?
The outlined content above was added from outside of Formative.
23%
33%
47%
49%
The approximate percent of total students that receive no allowance and do not have a cell phone is this:
C. 47%
How to get the approximate percentageFirst, we are given some figures that stand for the number of students who receive no allowance and have no cell phones. We have to calculate the total number of students as follows:
45 + 21 + 35 + 49 = 150
The number of students who receive no allowance = 49
The number of students who have no cell phones =21
So, the percentage is = The Total number of students that receive no allowance and have no cell phones / Total number of students.
= 49 + 21 = 70
70/150 × 100
= 46.6%
Approximately this is 47%.
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The number of people who survived the Titanic based on class and gender is in the table below. Suppose a person is picked at random from the survivors. Female Male Total 193 1st 134 59 2nd 194 25 119 3rd 80 58 138 Total 308 142 450 a) What is the probability that a survivor was male? b) What is the probability that a survivor was in the 2nd class? c) What is the probability that a survivor was a male, given that the person was in the 2nd class? d) What is the probability that a survivor was a male and in the 2nd class? e) What is the probability that a survivor was a male or in the 2nd class?
a) The probability that a survivor was male is:
142/450 = 0.315
b) The probability that a survivor was in the 2nd class is:
119/450 = 0.264
c) The probability that a survivor was a male, given that the person was in the 2nd class is:
25/119 ≈ 0.210
d) The probability that a survivor was a male and in the 2nd class is:
25/450 ≈ 0.056
e) The probability that a survivor was a male or in the 2nd class is:
P(male or 2nd class) = P(male) + P(2nd class) - P(male and 2nd class)
= 142/450 + 119/450 - 25/450
= 236/450
= 0.524
study the graph to see how grasshoppers of three different body colors survive predation by blue jays in a mostly green environment. grasshopper numbers are shown before and after blue jays preyed on them. which statements are supported by the data in the table? choose three correct answers.
The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.
What is a bar graph?
Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
We are given a graph showing grasshopper numbers before and after blue jays preyed on them.
From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.
Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.
Hence, the statement A and statement B are supported by the data in the table.
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Given the equation of a line in standard form, determine the slope, y-intercept, and
sketch the line.
x-3y = -9
The slope of x - 3y = -9 is, m = 1/3, while the y-intercept (b) is 3.
The sketch of x - 3y = -9 is shown below.
How to Determine the Slope and Y-intercept of the Equation of a Line?To determine the slope and y-intercept of the line given by the equation x - 3y = -9, we can rewrite it in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can solve for y:
x - 3y = -9
-3y = -x - 9
y = (1/3)x + 3
Now we can see that the slope of the line is m = 1/3, and the y-intercept is b = 3.
To sketch the line, we can use the slope and y-intercept. We can start by plotting the y-intercept (0,3) on the y-axis. From there, we can use the slope of 1/3 to find additional points on the line. For example, if we move 3 units to the right along the x-axis, we can move up 1 unit (since the slope is 1/3) to get another point on the line, which is (3,4). We can repeat this process to find more points on the line and then connect them to sketch the line.
The sketch is shown below in the attachment.
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The ratio of games lost to games won by
netball team is 2:3. The team has won 18
games How many games did they lose.
Answer:12
Step-by-step explanation:
A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. How can he use this information to choose a location? Can you develop a quantitative approach to do this?
Criteriia Weight 1 2 3 4
Raw material availability 0.15 G P OK VG
Infrastructure 0.1 OK OK OK OK
Transportation cost 0.35 VG OK P OK
Labor relations 0.2 G VG P OK
Quality of life 0.2 G VG P OK
VG = Very good
G = Good
OK = Acceptable
P = Poor
The best option is Location 2, which you can determine by adding up the points for each site using the information below.
What is meant by reflect?An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. Every point in one figure is equal distance from every corresponding point in the other, and this is what is meant when one figure is said to reflect the other.Reflection is a type of transformation that reverses a shape in a mirror line, also known as a line of reflection, such that each point is the same distance from the mirror line as its mirrored point. For instance, Triangle P has Triangle Q as a reflection on the line x = 4 x = 4 x = 4. Representing the reverse of a figure, a reflection is a change.The complete question is:
A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Use the information below to calculate total points for each location and choose the best option. Round your answers to two decimal places.
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25 POINTS PLEASE EXPLAIN ANSWER
the graph of f(x)=cos(x) is transformed into a new function, g(x), by stretching it horizontally by a factor of 6 and shifting it 5 units down. what is the equation of the new function g(x)?
Answer:
To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:
g(x) = cos((1/6)x)
To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:
g(x) = cos((1/6)x) - 5
So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.
The venom of Conus geographus is extremely toxic to humans. The neurotoxins of the cone shell are small peptides of fewer than 30 amino acids that target the neuronal communication sequence to achieve paralysis. The normal prey of geographus are small fish. Envenomation in humans leads to a wide range of symptoms. Sixty percent of the victims experience intense pain, 75% experience swelling around the wound, and 40% have both symptoms. (a) Draw an appropriate Venn diagram for these data (b) Are the two symptoms independent of each other? (c) What is the probability that the victim will experience at least one of these symptoms? (d) If a victim experiences swelling, what is the probability he will also have intense pain? (e) What is the probability that a victim will experience pain but not swelling? (f) What is the probability that a victim will not experience either symptom?
Therefore , the solution of the given problem of probability comes out to be probability of not experiencing either symptom is 0.05.
What precisely does the probability method suggest?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.
Here,
To determine if the two symptoms are independent, we need to check if the probability of one symptom changes depending on whether the other symptom is present or not.
P(pain | swelling) = 40% / 75% = 0.533
P(pain | no swelling) = 20% / 25% = 0.8
Since the conditional probabilities are not equal, the two symptoms are dependent.
(c) The probability that the victim will experience at least one of these symptoms is the probability of experiencing pain, swelling, or both. This can be calculated as:
P(pain or swelling) = P(pain) + P(swelling) - P(pain and swelling)
= 60% + 75% - 40%
= 95%
So the probability of experiencing at least one of these symptoms is 95%.
(d) The probability that a victim will have intense pain given that they have swelling is the conditional probability:
P(pain | swelling) = 40% / 75%
= 0.533
So the probability of having intense pain given that there is swelling is 0.533.
(e) The probability that a victim will experience pain but not swelling can be calculated as:
P(pain and no swelling) = P(pain) - P(pain and swelling)
= 60% - 40%
= 20%
So the probability of having intense pain without swelling is 20%.
(f) The probability that a victim will not experience either symptom is the complement of the probability of experiencing at least one symptom:
P(neither pain nor swelling) = 1 - P(pain or swelling)
= 1 - 0.95
= 0.05
So the probability of not experiencing either symptom is 0.05.
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1. Kylie and Matt are driving out of town, leaving from the same house indifferent cars. Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie begins traveling. Kylie drives at a rate of 50 miles per hour.
Part A.
The system of equations represents the distance y, from the starting point of each driver x minutes after Kylie starts driving.
y=40x +50
y= 50x
Graph the system in the coordinate plane and label each line with the driver it represents
PART B
Describe the situation in which Kylie and MAtt are travelling but are never the same distance from starting point at the same time. Write a system of equations to model the situation. How many solutions does the system have? Explain your reasoning.
SOLUTION:
Answer:
PART A:
The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.
Here is Matt's equation:
y = 40x + 50
The y-intercept of this equation is 50, while the slope is 40.
Here is Kylie's equation:
y = 50x
The slope of this equation is 50, and the y-intercept is 0. | /
| /
| /
| /
| /
-----|------------------
| / \
|/ \
/-------------\
0 1 2 3 4 5 6 x-axis
The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.
PART B:
When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:
(Matt's distance) y=40x+50
Kylie's distance is given by y = 50(x – 20).
Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.
We can set the two equations equal to one another to determine how many solutions this system has:
40x + 50 = 50(x - 20) (x - 20)
40x + 50 = 50x - 1000\s100 = 10x
x = 10
This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
PART A:
The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.
Here is Matt's equation:
y = 40x + 50
The y-intercept of this equation is 50, while the slope is 40.
Here is Kylie's equation:
y = 50x
The slope of this equation is 50, and the y-intercept is 0. | /
| /
| /
| /
| /
-----|------------------
| / \
|/ \
/-------------\
0 1 2 3 4 5 6 x-axis
The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.
PART B:
When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:
(Matt's distance) y=40x+50
Kylie's distance is given by y = 50(x – 20).
Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.
We can set the two equations equal to one another to determine how many solutions this system has:
40x + 50 = 50(x - 20) (x - 20)
40x + 50 = 50x - 1000\s100 = 10x
x = 10
This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.
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PLEASE HURRY
A. Plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane.
B. Find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y). The point (2,0) will go to the ordered pair___.
C. What do you notice about x^2+y^2=4 and x^2+y^2=1? The small circle is a __ of the larger one using the origin as a center and a scale factor of __.
PLEASE HURRY
Answer:
Step-by-step explanation:
A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:
For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).
For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)
B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:
(1/2x,1/2y) = (1/22, 1/20) = (1,0)
Therefore, the point (2,0) will go to the ordered pair (1,0).
C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.
Solve the quadratic equation for x. What is one of the roots?
3x2 − 14x − 5 = 0
please any help would be nice!!!
The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.
According to given information :Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have
[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]
Therefore, the two roots of the quadratic equation in exact square root form are:
[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]
Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.
What is quadratic equation ?A quadratic equation is a second-degree polynomial equation in one variable of the form:
[tex]ax^2 + bx + c = 0[/tex]
where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.
The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.
The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:
[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]
where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).
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Which of the following equations has no real solutions?
OA. 10(x-6) = 10x - 60
OB.10(x+6)= 10(x + 10)
OC. 10x-6=60x-6
OD. 10x-610x6
Answer:
10x-610x6
The equation 10x-610x6 has no real solutions because it cannot be solved for any value of x. The left side of the equation is 10x-6, and the right side is 10x+6. Since the left side is greater than the right side, no value of x can make the equation true.
Graph the equation on the coordinate plane
y=-1/2x
Select two points on the line to graph the line
A graph of the linear equation y = -1/2(x) in slope-intercept form is shown in the image attached below.
What is a proportional relationship?In Mathematics, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
Next, we would use an online graphing calculator to plot the given linear function as shown in the graph attached below.
In conclusion, the slope of this linear function is equal to -1/2 and it represents a proportional relationship.
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Jeremy’s work is below. Determine whether or not he has simplified the ratio 8in/3in correctly. Justify your answer.
The solution is, the total surface area is 92 sq. inches.
What is total surface area?Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.
here, we have,
Total paper required = total surface area
Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],
Where 'l' is the length, 'b' is the breadth and 'h' is the height
For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]
=2[24 + 6 + 16]
=2[46]
= 92 sq. inches
Hence, The solution is, the total surface area is 92 sq. inches.
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The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can
hold no more than 120 people. The drama club must make a minimum of $670 from
ticket sales to cover the show's costs. Also, they can sell at most 30 student tickets
and a minimum of 80 adult tickets. If a represents the number of student tickets sold
and y represents the number of adult tickets sold, write and solve a system of
inequalities graphically and determine one possible solution.
Number of Inequalities: 3
From the graph of system of linear inequality there may be other possible solutions, but (20, 100) is one that satisfies all the given constraints.
What are the equations of inequalityLet's first define our variables and their corresponding constraints:
Let a be the number of student tickets sold.
Let y be the number of adult tickets sold.
The total number of tickets sold cannot exceed 120, so we have the constraint
a + y ≤ 120 ...eq(i)
The minimum revenue required is $670, so we have the constraint 4a + 8y ≥ 670...eq(ii)
The drama club can sell at most 30 student tickets, so we have the constraint a ≤ 30.
The drama club must sell a minimum of 80 adult tickets, so we have the constraint y ≥ 80.
The last inequality is
y ≥ 80
To solve these inequalities graphically, we will plot the lines for each constraint on a coordinate plane and shade the region that satisfies all the inequalities. The shaded region will represent all possible combinations of student and adult tickets that meet the constraints.
First, let's plot the line for the a + y ≤ 120 constraint. We can rewrite this as y ≤ -a + 120 and plot the line y = -a + 120 on the coordinate plane:
The shaded region for this constraint is below the line and includes the origin.
Next, let's plot the line for the 4a + 8y ≥ 670 constraint. We can rewrite this as y ≥ (-1/2)a + 83.75 and plot the line y = (-1/2)a + 83.75 on the same coordinate plane:
The shaded region for this constraint is above the line.
Now, let's plot the constraint a ≤ 30. We can draw a vertical line at a = 30:
The shaded region for this constraint is to the left of the line.
Finally, let's plot the constraint y ≥ 80. We can draw a horizontal line at y = 80:
The shaded region for this constraint is above the line.
To find a possible solution, we need to find the point where all four shaded regions overlap. This point represents a combination of student and adult tickets that satisfies all the constraints. One such point is (20, 100), which means the drama club can sell 20 student tickets and 100 adult tickets to meet their requirements and raise at least $670 in revenue.
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