Answer:
Subtract 12 from both sides of the equation
Step-by-step explanation:
Solve for x:
12+x=15
-12 -12
x = 3
Brainlist please.
Answer:
D) Subtract 12 from both sides of the equation.
To solve for x in the equation 12 + x = 15, we need to isolate the variable x on one side of the equation. We can do this by subtracting 12 from both sides of the equation, which gives:
12 + x - 12 = 15 - 12
x = 3
Therefore, the solution for x is 3.
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The total 460 cards are sold on Mothers day.
Given that, Bob's gift shop sold a record number of cards for Mother's Day.
One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day.
Let the number of cards sold on mothers day be x.
Here, 10% of x =46
10/100 ×x= 46
10x=4600
x=460
Therefore, total 460 cards are sold on Mothers day.
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On Monday 149 people each bought 1 CD at a music store. On Tuesday 263 people each bought 1 All the CDs cost $9. What was the total amount paid for the CDs on these two days?
Answer:
Step-by-step explanation:
On Monday, the total amount paid for CDs = 149 * $9 = $1341
On Tuesday, the total amount paid for CDs = 263 * $9 = $2367
Therefore, the total amount paid for CDs on these two days = $1341 + $2367 = $3708.
5
Select the correct answer,
Solve the following inequality for %.
z-9≤2(9)
O A. X=<9
OB. X> =11
OC. x<-7
OD. x<10
Answer:
1) -4<x<-2
2) x<-7 or x75
3) 2<x<7
4) x<-5 or x<6
5) x<-8 or x74
Step-by-step explanation:
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 less than or equal to x less than or equal to 3
The correct list of functions ordered from 0 ≤ x ≤ 3 is:
h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x
Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.
For f(x) = x^2, the slope between x = 0 and x = 3 is:
[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]
For g(x) = 2x + 1:
[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]
For h(x) = sin(x):
[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279
For k(x) = e^x, the slope between x = 0 and x = 3 is:
[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076
Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:
[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]
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--The complete Question is, Consider the following four functions:
f(x) = x^2
g(x) = 2x + 1
h(x) = sin(x)
k(x) = e^x
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --
Use point-slope form to write the equation of a line that passes through the point (16,−14) with slope 1.
The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
What is meant by equation?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.
What is meant by slope?
Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.
According to the given information
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:
y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30
So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.
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dont understand what m supposed to do at the radius = diameter/2 part
Step-by-step explanation:
Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle
Ahanu jumped 1,050 times. Rolando jumped 1,080 times. How many fewer jumps did Ahanu do than Rolando?
Answer:
Step-by-step explanation:
the fewer jumps=the jumps Ronaldo did - the jumps Ahanu did
= 1080-1050
= 30
What happens when the function f(x) = 2 sin(2) is transformed by the rule g (w) = - f(x)?
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
O f(x) is reflected over the y-axis.
O f(x) is reflected over the x-axis.
• f(x) is compressed toward the y-axis by a factor of 1/2 and is reflected over the y-axis
Answer:
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
Step-by-step explanation:
The function f(x) = 2sin(2x) has an amplitude of 2 and a period of π/2. When we apply the rule g(w) = - f(x), we are reflecting the graph of f(x) over the x-axis and then taking its opposite. This means that the amplitude of g(w) will still be 2, but the graph will be reflected and stretched away from the x-axis by a factor of 2.
I hope it helps you
why does an angle formed by a tngent and a chord have the same measure as an insribed angle that intercepts the same arc
An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.
When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.
This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.
Now, consider an inscribed angle that intercepts the same arc as the chord.
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.
Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.
Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.
Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.
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What is the power of the hypothesis test, using the decision rule given above, if the population mean amount of mercury is 11.5 micrograms per ounce? Give your answer to 4 decimal places.
The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.
To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.
Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.
A hypothesis test for the population mean amount of mercury in a certain type of fish.
Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.
If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.
This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
The hypothesis test, it is impossible to calculate the power.
It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.
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Suppose a charity received a donation of 29.9 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds?
Simplify.
Remove all perfect squares from inside the square roots. Assume
�
xx and
�
zz are positive.
72
�
3
�
3
=
72x
3
z
3
=square root of, 72, x, cubed, z, cubed, end square root, equals
By simplifying the given square root , we get Simplified Root : 6 xz • [tex]\sqrt{(2xz) }[/tex]
how can we simplify roots ?Factor 72 into its prime factors
72 = 23 • 32
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
36 = 22 • 32
Factors which will remain inside the root are :
2 = 2
To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
6 = 2 • 3
At the end of this step the partly simplified square root looks like this:
6 • [tex]\sqrt{ (2x3z3) }[/tex]
Simplify the Variable part of the square root
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
[tex]\sqrt{(x8)}[/tex]=x4
[tex]\sqrt{ (x^6)}[/tex]=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
[tex]\sqrt{ (x5)}[/tex]=x2•[tex]\sqrt{x}[/tex]
[tex]\sqrt{ (x^7)}[/tex]=x-3•[tex]\sqrt{x}[/tex]
Applying these rules to our case we find out that
[tex]\sqrt{ (x3z3)}[/tex] = xz • [tex]\sqrt{(xz) }[/tex]
Combine both simplifications
[tex]\sqrt{ (72x3z3)}[/tex] = 6 xz •[tex]\sqrt{(2xz) }[/tex]
Simplified Root :
6 xz • [tex]\sqrt{(2xz) }[/tex]
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Add or Subtract then complete the chart
The simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.
The constant term is the term without a variable, in this case, 4 is the constant term.
What is polynomial?
A polynomial is a mathematical expression that consists of variables and coefficients
To simplify the polynomial, we need to combine like terms. We have:
(4x² - 3x + 10) + (-9x² + 4x - 6)
= 4x² - 3x + 10 - 9x² + 4x - 6 (distributing the negative sign)
= (4x² - 9x²) + (-3x + 4x) + (10 - 6) (grouping like terms)
= -5x² + x + 4 (combining like terms)
Therefore, the simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.
In the polynomial -5x² + x + 4, the degree is 2, the leading coefficient is -5, and the constant term is 4.
The degree of a polynomial is the highest power of the variable in the polynomial, in this case, x² has the highest power of 2.
The leading coefficient is the coefficient of the term with the highest power of the variable, in this case, -5 is the coefficient of the x² term, so it is the leading coefficient.
The constant term is the term without a variable, in this case, 4 is the constant term.
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An athlete has decided to track how many minutes they exercise each day. During the first day, the athlete exercised for 30 minutes. For each day after that, the athlete increased their exercise time by 3 minutes. Which equation in point-slope form models the number of minutes the athlete exercises, y, based on the day, x?
A: y-30=3(x-1)
B: y+30=3(x+1)
C: y-1=3(x-30)
E: y+1=3(x+30
The initial exercise time is 30 minutes, so the y-intercept of the line is 30. The athlete increases their exercise time by 3 minutes each day, which means the slope of the line is 3. The correct answer is option: A.
We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the first day's exercise time as our point, we get (1, 30) as our (x1, y1) values. Substituting these values into the point-slope form and simplifying, we get y - 30 = 3(x - 1), that is option A. Hence option A is correct.
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The central train station in a large city is located at the intersection of tracks A, B, and C as shown below. pls pls pls respond now!!!!
a.) The position of the train moving from station A to station B after 10 minutes 20 km east
b.) The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin is 50 km west
c.) The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin is 80 km west
How do we know?we have that:
Railway station - A B C
Distance(km) - 0 30 60
Starts from A , train reaches B be in 15 minutes
Starts from A , train reaches C be in 30 minutes
a.)
If A is origin
As train covers 30km = 15 minutes
⇒ 15 minutes = 30 km
1 minute = km
⇒ 10 minutes = 2×10 = 20 km
The position of the train moving from station A to station B after 10 minutes = 20 km east
b.)
If B is origin then , the position of the train moving from station A to station B after 10 minutes = 30 + 20 = 50 km west
c.)
If C is the origin then , the position of the train moving from station A to station B after 10 minutes = 60 + 20 = 80 km west
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#possible complete question:
Three railway stations, A, B, and C, are situated on a straight railway route. Station B is at 30 km in the east from station A and station C is at 60 km in east from station A. A train, with a constant average velocity, starts from A and reaches B in 15 minutes, and reaches C in 30 minutes. Assuming that station A is the origin, find the following:
a. The position of the train moving from station A to station B after 10 minutes.
b. The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin.
c. The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin.
In the picture below Pac-Man, from the video game PAC-MAN, is shown eating ghosts. In the pictare his mouth is open 60° and the radius of the circle is 13 mm, What is the area of the Pac-Man, to the nearest tenth mm"?
The solution of Circle and angle problem is the area of the Pac-Man, to the nearest tenth mm" is 131.8 mm²
what is circle and angle ?A circle is a geometric shape that is defined as the set of all points in a plane that are equidistant from a fixed point called the center.
An angle is a measure of the amount of turn between two lines that share a common endpoint, called the vertex of the angle.
According to given informationTo find the area of the Pac-Man, we need to find the area of the sector that represents its mouth and subtract the area of the triangle formed by the two radii and the chord of the sector.
First, we need to find the length of the arc that represents the mouth of Pac-Man. The formula for the length of an arc is:
L = (θ/360) x 2πr
Where L is the length of the arc, θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14.
Plugging in the values we have:
L = (60/360) x 2π(13)
L = 4.29 mm
Next, we can find the area of the sector that represents the mouth of Pac-Man. The formula for the area of a sector is:
A = (θ/360) x πr²
Where A is the area of the sector, θ is the central angle in degrees, and r is the radius of the circle.
Plugging in the values we have:
A = (60/360) x π(13)²
A = 141.37 mm^2
Finally, we need to find the area of the triangle formed by the two radii and the chord of the sector. We can use the formula for the area of a triangle:
A = (1/2) x base x height
The base of the triangle is the chord of the sector, which is equal to twice the radius multiplied by sin(θ/2):
base = 2r x sin(θ/2)
base = 2(13) x sin(30)
base = 13 mm
The height of the triangle is equal to half the length of the chord times cos(θ/2):
height = (1/2) x (L/2) x cos(θ/2)
height = (1/2) x (4.29/2) x cos(30)
height = 1.47 mm
Plugging in the values we have:
A = (1/2) x 13 x 1.47
A = 9.53 mm²
Therefore, the area of the Pac-Man (sector minus triangle) is approximately:
A = 141.37 - 9.53
A = 131.84 mm²
Rounded to the nearest tenth, the area of the Pac-Man is 131.8 mm²
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Camile realizes she is charged more based on the volume of the box and not the weight which box would fit her requirements and be the best choice to save her on shipping cost? Explain your reasning
To save on shipping costs, Camile should choose a box that is lightweight and has a small volume.
Why should Camile choose a box that is lightweight and has a small volume?This is because she has realized that she is charged based on the volume of the box and not the weight.
Therefore, a smaller volume box would cost her less than a larger volume box of the same weight.
For example, if Camile needs to ship a 5-pound item, she should choose a smaller box with a volume that is just enough to fit the item, rather than a larger box with more empty space. This is because the larger box would have a greater volume, and therefore, incur a higher shipping cost even though it weighs the same as the smaller box.
In summary, when selecting a box to save on shipping costs, it is important to consider both weight and volume. Camile should choose a box that is lightweight and has a smaller volume to reduce her shipping costs.
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One of the parking lot lights at a hospital has a motion detector on it, and the equation (x + 10)2 (y−8)2=16 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the parking lot light and be detected? Responses a. 2 ft b. 4 ft c. 9 ft d. 256 ft
The greatest distance, in feet, a person could be from the parking lot light and be detected is 4 ft. So, correct option is B.
The equation (x + 10)^2 + (y−8)^2=16 describes a circle with center (-10,8) and radius 4. The distance from the center of a circle to any point on its circumference is equal to the radius. Therefore, the greatest distance a person could be from the parking lot light and still be detected is equal to the radius of the circle, which is 4 feet.
This means that any point on the circumference of the circle with a distance of 4 feet or less from the center (-10,8) would be within the range of the motion detector.
Option (a) 2 feet is too small and would fall inside the circle, meaning the person would not be detected. Option (c) 9 feet and option (d) 256 feet are too large and fall outside the circle, meaning the person would also not be detected.
Therefore, the correct answer is option (b) 4 feet.
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If 2. 2 liters of gas is inhaled at 18°C and is heated to 38°C in the lungs, what is the new volume of the gas?
The new volume of the gas is 2.35 liters.
To solve this problem, we can use the formula for Charles's Law:
V1/T1 = V2/T2
We are given that V1 = 2.2 liters, T1 = 18°C, and T2 = 38°C. We need to find V2.
First, we need to convert the temperatures to Kelvin. To convert Celsius to Kelvin, we add 273.15:
T1 = 18°C + 273.15 = 291.15 K
T2 = 38°C + 273.15 = 311.15 K
Now we can plug in the values and solve for V2:
V1/T1 = V2/T2
2.2/291.15 = V2/311.15
V2 = (2.2/291.15) * 311.15
V2 = 2.35 liters (rounded to two decimal places)
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Please Help :))) If DE| |AB, by the Side Splitter Theorem, ...
If DE| |AB, by the Side Splitter Theorem, We can conclude that DE is parallel to AB if and only if CD/DA = CE/EB or x/y = z/w.
What is Side Splitter Theorem?The Side Splitter Theorem is a geometric theorem that relates the lengths of the sides of a triangle and the segments formed when a line is drawn parallel to one of the sides of the triangle.
Specifically, if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.
In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the lengths of the segments it divides on the other two sides are proportional to the lengths of those sides.
If DE is parallel to AB, then by the Side Splitter Theorem, we have:
CD/DA = CE/EB
Substituting the given variables, we get:
x/y = z/w
We can also use the fact that triangles CDE and ABC are similar, which implies that their corresponding sides are proportional. Specifically, we have:
CD/AB = CE/AC = DE/BC
Substituting the given variables and using the fact that CD = x, DA = y, CE = z, and EB = w, we get:
x/(y+w) = z/(x+z)
Cross-multiplying both equations, we get:
xy + xw = yz + xz
Simplifying, we get:
x(w+z) = yz
Dividing both sides by wz, we get:
x/y = z/w
Which is the same as the equation we obtained using the Side Splitter Theorem.
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PS is the midsegment of the trapezoid QRTU.
If PS = 36 and QR = 48, what is TU?
T
R
S
TU =
U
P
Q
The length of segment TU is given as follows:
TU = 24 units.
How to obtain the length of segment TU?The length of segment TU is obtained applying the trapezoid midsegment theorem, which states that the length of the midsegment of the trapezoid is equals to the mean of the length of the bases of the trapezoid.
The parameters for this problem are given as follows:
Midsegment PS = 36.Bases TU = x and QR = 48.Hence the length of TU is obtained as follows:
36 = (x + 48)/2
x + 48 = 72
x = 24.
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Ken ran from one corner of a field to the opposite corner, a distance of 85 meters. Then he ran along its length, a distance of 77 meters. How wide is the field?
Answer:
24 meters
Step-by-step explanation:
We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.
Using Pythagoras' theorem, we can write:
w^2 + 77^2 = 85^2
Simplifying this equation gives:
w^2 = 85^2 - 77^2
w^2 = 576
Taking the square root of both sides gives:
w = sqrt(576)
w = 24
Therefore, the width of the field is 24 meters 1.
I hope this helps!
A large Ferris wheel has a diameter of 90 meters and the top of the wheel is 102 meters above the ground. The Ferris wheel has 36 passenger capsules spaced evenly along the wheel. The diagram below shows 10 of the Ferris wheel capsules arranged such that the center of the wheel is at point C, the capsule at point M is at the same height as the center of the wheel, and the capsule at point T is at the very top of the wheel.
The height of the center of the Ferris wheel 51 m.
The height of capsule M is 51 m and the height of capsule T is 102 m.
What is the height of the wheel?
Using this information, we can calculate the height of the center of the Ferris wheel, the height of capsule M, and the height of capsule T.
Height of the center of the Ferris wheel:
The center of the Ferris wheel is the midpoint of its diameter. Therefore, the height of the center of the Ferris wheel is half of the height of the top of the wheel above the ground.
Height of center of Ferris wheel = 102 meters / 2 = 51 meters.
Height of capsule M:
Since capsule M is at the same height as the center of the Ferris wheel, the height of capsule M is also 51 meters.
Height of capsule T:
Since capsule T is at the very top of the Ferris wheel, its height above the ground is equal to the height of the top of the Ferris wheel above the ground.
Height of capsule T = 102 meters.
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HELP ME AND I'LL GIVE YOU 100 POINTS!!! ANSWER IT HONESTLY PLS!!!
Find the area, in square inches, of the composite figure.
12 in.
2 in.
3 in.
3 in.
25 in.
looks somewhat like what my problem looks like but with the numbers I listed
Four out of 5 freshmen study algebra. How many study
algebra in a class of 400?
Answer:
4/5 ×400
0.8 × 400
=320 freshmen study algebra.
I had used fraction method.
PLEASE HELP! SHOW WORK AND EXPLAIN ON HOW YOU GOT THE ANSWER! I WILL MARK YOU BRAINLIEST IF YOU DO!
Katie's claim can be represented by the equation: a² ¢= 4(1/2ab) + b²
How to explain the equationKatie's claim can be represented by the equation:
Outer square area = Sum of areas of four triangles + Inner square area or mathematically, a² = 4(1/2ab) + b²
where "a" and "b" are the lengths of the legs of the right triangle and "a²" represents the area of the outer square, while "b²" represents the area of the inner square.
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Answer Immeditely Please
The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units
What are similar triangles?Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.
The similar triangles are; ΔABD, ΔBCD, ΔACB
∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)
[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]
4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16
4 × 16 = 64 = [tex]\overline{BD}[/tex]²
[tex]\overline{BD}[/tex] = √(64) = 8
The length of the segment [tex]\overline{BD}[/tex] = 8 units
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5) Danielle goes shopping for yoga pants. The promotion at the
store is if you buy 8 pairs for $98. How much would Danielle pay
if she bought 5 pairs with the same promotion?
Add or subtract then complete the chart.
A simplification of the polynomial is -c³ + 2c² - 9c + 1.
The degree of the polynomial is equal to 3.
The leading coefficient of the polynomial is equal to -1.
The constant of the polynomial is equal to 1.
What is a polynomial function?In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as the following:
Multiplication (product)AdditionSubtractionNext, we would subtract the two (2) given polynomials as follows;
Expression = (c³ + 2c² - 5c) - (2c³ + 4c - 1)
Expression = c³ + 2c² - 5c - 2c³ - 4c + 1
By rearranging the given polynomials by combining like terms, we have;
Expression = -c³ + 2c² - 9c + 1
Where:
The degree = 3.
The leading coefficient = -1.
The constant = 1.
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For the line y = 1 — 4x, create a table to show the values of x and y where x is from -2 to 2.
Answer:
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To create a table for the line y=1-4x from x=-2 to x=2, we substitute in each x value into the equation, solve for y, and display these pairs in a table. The pairs are (-2, 9), (-1, 5), (0, 1), (1, -3), and (2, -7).
Explanation:
The equation of the line is y = 1 - 4x. To create a table showing the values of x and y where x is from -2 to 2, we need to substitute each value of x into the equation, solve for y, and then organize the results in a table.
When x = -2, y = 1 - 4*(-2) = 1 + 8 = 9When x = -1, y = 1 - 4*(-1) = 1 + 4 = 5When x = 0, y = 1 - 4*0 = 1When x = 1, y = 1 - 4*1 = 1 - 4 = -3When x = 2, y = 1 - 4*2 = 1 - 8 = -7
So, the table representing these values would look like this:
x y
-2 9
-1 5
0 1
1 -3
2 -7
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