Solve the system of equations below using a method of your choosing.
help please
Answers
The solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).
The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.
Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.
To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.
Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:
2x + 5 = 13
y = 3x^2 - 2x + 7
4a + 2b - 3c = 10
Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.
Substitute the value of y in the second equation with the expression for y from the first equation:
2x + 3(4x-22) = 4
Simplify and solve for x:
2x + 12x - 66 = 4
14x = 70
x = 5
Substitute the value of x in the first equation to solve for y:
y = 4(5) - 22
y = -2
Therefore, the solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.
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Related Questions
Given f(x)=x^2+9 and g(x) =-x-7, find (f+g)(x).
Answers
Answer:
x^2 - x + 2.
Step-by-step explanation:
Answer:
x² - x + 2
Explanation
Work out using the given functions to set up and simplify (f + g) (x)
a cone-shaped container is oriented with its circular base on the top and its apex at the bottom. it has a radius of 12 inches and a height of 8 inches. the cone starts filling up with water. what fraction of the volume of the cone is filled when the water reaches a height of 2 inches?
Answers
Fraction of the volume of the cone = 1/4 0r 0.25
Volume of a coneA cone is a solid that has a circular base and a single vertex.
To calculate its volume, you need to multiply the base area (area of a circle: π × r²) by height and by 1/3:
volume = (1/3) × π × r² × h
Volume of the cone using radius 12inches and height 8inches =
(1/3) × π × 12² × 8
= 0.6981inches³
Volume of the cone using radius 12inches and height 2inches =
(1/3) × π × 12² × 2
= 0.17453inches³
in order to find the fraction filled with water, we use the
Volume of 2inches/Volume of 8 inches.
0.17453/0.6981
= 0.25 or 1/4
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the platinum charges 30$ membership fee plus a 6$ per video game similarly,the bronze packaging fee and an additional cost for every video game downloaded x the graph represents the total cost y,of the bronze package
Answers
Total cost of the bronze package = Membership fee + Cost per video game
Total cost of the bronze package = 30$ + (6$ x Number of video games downloaded)
Total cost of the bronze package = 30$ + 6$y
Therefore, the equation for the graph is y = (Total cost - 30$) / 6$
Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
Answers
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = [tex]-2^{3}[/tex] - 6 = -14
g(2) = [tex]2^{3}[/tex] - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3[tex]x^{2}[/tex]
g'(-2) = 3[tex]-2^{2}[/tex] = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
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Three boats start cruising around a small island starting at the same time and from the same location, and following the same route. The first boat is going 5km / h * r the second boat is going 4km / h * r and the third boat is going 3km / h * r One full circle around the island is 2 km. In how many minutes will all three boats next meet at the starting location?
PLEASE HELP QUICK
Answers
In 120 minutes, all the three boats will next meet at the starting location. The solution has been obtained by using the concept of least common multiple.
What is least common multiple?
Least Common Multiple is abbreviated as LCM. The smallest multiple shared by two or more different numbers is referred to as the least common multiple.
We are given that three boats start cruising around a small island starting at the same time and from the same location, and following the same route.
They take one full circle around the island which is 2 km.
First boat:
It covers 5 km in 60 minutes.
So, it will cover 2 km in 60/5 * 2 = 24 minutes
Second boat:
It covers 4 km in 60 minutes.
So, it will cover 2 km in 60/4 * 2 = 30 minutes
Third boat:
It covers 3 km in 60 minutes.
So, it will cover 2 km in 60/3 * 2 = 40 minutes
Now, taking the LCM of 24, 30 and 40, we get 120.
Hence, in 120 minutes all the three boats will next meet at the starting location.
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2) Lou plans to go to a beauty salon. She sees this special offer. treatments (£31. facial) (£29 leg wax) (£35 massage) (£27. manicure) (£13 eyelash tint) book any 3 treatments get 25% off the total cost Lou wants to book a massage and 2 other different treatments. She has £60 to spend on the treatments. Work out the total cost of the 3 treatments using the special offer for Lou. Remember to write down the 3 treatments.
Answers
The total cost for each combination with the special offer would be:
Massage, leg wax, and manicure: £68.25
Massage, facial, and eyelash tint: £59.25
Massage, leg wax, and eyelash tint: £57.75
How to find the total cost?We can try out the different possibilities and calculate the total cost of each.
Let's start by listing the prices of the treatments she's interested in:
Massage: £35
Facial: £31
Leg wax: £29
Manicure: £27
Eyelash tint: £13
Now, we can try out the different combinations of 3 treatments and calculate their total cost:
Massage, facial, and leg wax:
Total cost = £35 + £31 + £29 = £95
With 25% off, the cost would be £71.25, which is over Lou's budget of £60, so this combination is not possible.
Massage, facial, and manicure:
Total cost = £35 + £31 + £27 = £93
With 25% off, the cost would be £69.75, which is still over Lou's budget of £60, so this combination is also not possible.
Massage, leg wax, and manicure:
Total cost = £35 + £29 + £27 = £91
With 25% off, the cost would be £68.25, which is within Lou's budget of £60. Therefore, this combination is possible.
Massage, facial, and eyelash tint:
Total cost = £35 + £31 + £13 = £79
With 25% off, the cost would be £59.25, which is within Lou's budget of £60. Therefore, this combination is also possible.
Massage, leg wax, and eyelash tint:
Total cost = £35 + £29 + £13 = £77
With 25% off, the cost would be £57.75, which is within Lou's budget of £60. Therefore, this combination is also possible.
From the above calculations, we can see that Lou can choose from three possible combinations of treatments that fit within her budget and qualify for the special offer:
Massage, leg wax, and manicure
Massage, facial, and eyelash tint
Massage, leg wax, and eyelash tint
The total cost for each combination with the special offer would be:
Massage, leg wax, and manicure: £68.25
Massage, facial, and eyelash tint: £59.25
Massage, leg wax, and eyelash tint: £57.75
Therefore, Lou can choose any of the above combinations and pay the corresponding total cost to enjoy the special offer.
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What is the area of a square if the base is 4 m in the height is 4 m
Answers
The area of the square according to the dimensions of base and height is 16 m².
The square is a shape with equal sides. Thus, the base and height of this shape is always equal. Now when we have the measurements of its side, we can calculate the area of the square. The formula for the same is -
Area = side²
Keep the value in formula to find the value of are of square
Area of square = 4²
Taking square on Right Hand Side of the equation
Area of square = 16 m²
Thus, the area of square is 16 m².
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How Long Is 500 Minutes In Hours And Minutes?
Answers
500 minutes are equal to 8 hours and 20 minutes.
Time is a valuable commodity that we must use wisely. We measure it in seconds, minutes, hours, days, weeks, months, and years. It is important to be able to convert time units so that we can manage our schedule efficiently.
To convert minutes to hours, we need to divide the number of minutes by 60, which is the number of minutes in an hour. Therefore,
500 minutes ÷ 60 minutes/hour = 8.33 hours
However, this answer is in decimal form, which is not a typical way to represent time. We want to express it in hours and minutes.
To do so, we will use the fact that there are 60 minutes in an hour. Therefore, we can multiply the decimal part of the answer by 60 to get the remaining minutes.
0.33 hours x 60 minutes/hour = 20 minutes
So, 500 minutes is equivalent to 8 hours and 20 minutes.
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how to find point of inflection
Answers
To find a point of inflection, take the second derivative of the function, set it equal to zero and solve for x, and verify the point by checking the sign of the second derivative on either side of the point.
Follow these steps to locate a point of inflection:
Take the function's second derivative. The derivative of the first derivative is the second derivative. This will give you the concavity of the function.Put the second derivative to zero and find x. This will show you where the concavity changes.At this stage, check to see if the sign of the second derivative changes. The point is a point of inflection if the second derivative is positive to the left of the point and negative to the right of the point. The point is not an inflection point if the sign of the second derivative does not change.Check the concavity of the curve on each side of the point to verify it.It is a point of inflection if the curve shifts from concave up to concave down at the point. It is also a point of inflection if it transitions from concave down to concave up.
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What is the conversion of 54c to fahrenheit?
Answers
54 degrees Celsius is equivalent to 129.2 degrees Fahrenheit.
A temperature unit developed from the SI (International System of Units) is the Celsius (symbol: °C).
Prior to the adoption of the metric system, the Fahrenheit (symbol: °F) was a commonly used measurement of temperature.
Add 1.8 to the °C temperature.
To this number, add 32.
This is the response in degrees Fahrenheit.
To convert 54 degrees Celsius to Fahrenheit,
You can use the formula:
°F = (°C × 9/5) + 32
where °F is the temperature in Fahrenheit,
°C is the temperature in Celsius.
Substituting 54 for °C, we get:
°F = (54 × 9/5) + 32
°F = (486/5) + 32
°F = 97.2 + 32
°F = 129.2
Therefore, 54 degrees Celsius is equivalent to 129.2 degrees Fahrenheit.
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Does the following equation show a linear or nonlinear function? Linear Nonlinear y=-2x³-6
Answers
The equation y = -2x³ - 6 represents a nonlinear function.
What is linear function and nonlinear function?
The highest for linear functions is only one, whereas nonlinear functions have more.
The equation y = -2x³ - 6 represents a nonlinear function because the highest power of x, which is 3, is greater than 1. In general, a function is considered linear if it can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the equation cannot be written in that form because of the presence of x³, which makes the relationship between x and y nonlinear.
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. Molly travels 90km to get home after work. She leaves at 6pm and arrives home at 7:30pm.
Calculate her average speed in km per hour
Answers
Answer:
60 Kilometers per hour
Step-by-step explanation:
To solve for how long it took Molly to get home, we can use this equation:
7:30 - 6 = 1:30So, Molly took an hour and 30 minutes, or 90 minutes to travel 90km.
To get the number of km she traveled every hour, we can use this equation:
90 × [tex]\frac{2}{3}[/tex] = 60Why do we multiply by 2/3?
We multiply by [tex]\frac{2}{3}[/tex] because if we need to figure out the average speed for every hour (60) we need to convert 90 to 60, and to do that we multiply the 90 by [tex]\frac{2}{3}[/tex].
Therefore, Molly travels 60km every hour.
At a football game, a vender sold a combined total of 124 sodasand hot dogs the number of sodas sold was three times the number of hot dogs sold find the number of sodas and the numbers of hot dogs sold
Answers
Step-by-step explanation:
x = number of sold sodas
y = number of sold hot dogs
x + y = 124
x = 3y
so,
3y + y = 124
4y = 124
y = 31
x = 3y = 3×31 = 93
there were 93 sodas and 31 hot dogs sold.
the annual income for independent sales representatives in the united states is thought to be highly right-skewed with a mean equal to $144,300 and a standard deviation of $32,450. given this information, if a sample of 36 independent sales representatives is selected, what is the probability that the mean of the sample will exceed $130,000?
Answers
Answer: $275,000
Step-by-step explanation:
Larissa is helping plan the campus Spring Fling, which is a variety of fun competitions, games, and activities the last day of school. It is held outside, so she is going to have a booth with a sports drink served in cone-shaped paper cups. The cone-shaped paper cups have a diameter of 7 cm and a height of 12 cm, but Larissa is going to use a height of 10 cm when calculating the volume of each cup because she is not going to fill the cup to the top. Larissa is able to purchase the sports drink in economy cans that are cylindrical, with a diameter of 15 cm and a height of 30 cm. The cans are completely full. Larissa wants to purchase enough cans of the sports drink to have 900 servings of the sports drink. A serving is the volume Larissa calculated for the cone-shaped cup. What is the minimum number of cans of the sports drink that Larissa should purchase? Responses A 26 cans26 cans B 22 cans22 cans C 6 cans6 cans D 105 cans
Answers
Answer:
Step-by-step explanation:
Firgure is out your self
From the given data, the answer is option B, 22 cans. Larissa should purchase minimum 22 cans of sport drink.
First, we need to calculate the volume of each cone-shaped cup using the given dimensions:
Radius of the cone = diameter / 2 = 7 cm / 2 = 3.5 cm
Height of the cone = 10 cm
Using the formula for the volume of a cone, we get:
Volume of each cone-shaped cup = (1/3) x π x radius² x height
Volume of each cone-shaped cup = (1/3) x π x (3.5 cm)² x 10 cm
Volume of each cone-shaped cup ≈ 128.68 cm³
Next, we need to calculate the total volume of sports drink needed for 900 servings:
Total volume of sports drink needed = 900 x 128.68 cm³
Total volume of sports drink needed ≈ 115811.2 cm³
Now, we need to calculate the volume of one economy can of sports drink using the given dimensions:
Radius of the can = diameter / 2 = 15 cm / 2 = 7.5 cm
Height of the can = 30 cm
Using the formula for the volume of a cylinder, we get:
Volume of one can of sports drink = π x radius² x height
Volume of one can of sports drink = π x (7.5 cm)² x 30 cm
Volume of one can of sports drink ≈ 5309.73 cm³
Finally, we can divide the total volume of sports drink needed by the volume of one can of sports drink to find the minimum number of cans Larissa should purchase:
Minimum number of cans of sports drink = Total volume of sports drink needed / Volume of one can of sports drink
Minimum number of cans of sports drink = 115811.2 cm³ / 5309.73 cm³ = 21.83
Since we need to purchase whole cans, the minimum number of cans Larissa should purchase is 22.
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Select the correct answer.
If f(x) = 3x + 2 and g(x) = 2x - 2, what is (f- g)(x)?
O A.
OB.
X + 4
OE.
X-2
O C. X
O D. 5x-2
X-4
Answers
Answer:
A
Step-by-step explanation:
(f - g )(x)
= f(x) - g(x)
= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1
= 3x + 2 - 2x + 2 ← collect like terms
= x + 4
The value of the function (f-g)(x) is x+4.
What is a function?A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).
Given are two functions, f(x) = 3x+2 and g(x) = 2x-2, we need to find the value of (f-g)(x)
So,
(f-g)(x) = f(x) - g(x)
= 3x+2 - (2x-2)
= x+4
Hence, the value of the function (f-g)(x) is x+4.
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The graph of f(x)=x^2 was translated 2 units to the right to create the graph of function g. Write an equation in vertex form to represent function g.
Answers
The equation in vertex form to represent the translation is
f(x) = (x - 2)^2
How to write the translation equationThe parent equation is as follows f(x) = x^2
The translation of 2 units to the right is achieved by subtracting 2 from the equation the squaring all the values. This is written as
f(x) = (x - 2)^2
The vertex form of quadratic equation is of the form
y = a(x - h) + k
comparing with the equation shows that
a = 1
h = 2
k = 0
and hence the equation is already in vertex form
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Can someone help me on this?
Answers
The correct linear equation for the table is,
⇒ y = - 5x - 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The table is shown in figure.
Now, Let two points from the table are (4, - 22) and (3, - 17).
Hence, Equation of linear function is,
⇒ y - (- 22) = (- 17 - (-22)) / (3 - 4) (x - 4)
⇒ y + 22 = (5/- 1) (x - 4)
⇒ y + 22 = - 5 (x - 4)
⇒ y + 22 = - 5x + 20
⇒ y = - 5x + 20 - 22
⇒ y = - 5x - 2
Thus, The correct linear equation for the table is,
⇒ y = - 5x - 2
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Name two measures of the variation of a distribution, and state the conditions under which each measure is preferred for measuring the variability of a single data set. A. The mean is preferred when the data is relatively symmetric B. The standard deviation is preferred when the data is relatively symmetric C. The median is preferred when when the data is relatively symmetric D. The standard deviation is preferred when there are many data points E. The interquartile range is preferred when the data is strongly skewed or has outliers. F The interquartile range is preferred when there are few data points G. The z-score is preferred when there are many data points H. The median is preferred when the data is strongly skewed or has outliers.
Answers
Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
Measures of the variation of a distribution:
Measures of the variation of distribution are used to quantify the spread or dispersion of the data points in the distribution.
Variance:The variance is a measure of the variation of distribution that represents how spread out the data points in a distribution are from the mean.
A higher variance indicates that the data points are more spread out, while a lower variance indicates that they are more tightly clustered around the mean.
The variance is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Standard deviation:Standard deviation is a measure that shows how the spread or dispersion of a set of data points from the mean.
The standard deviation can tell us how tightly or loosely the data points are clustered around the mean. A smaller standard deviation indicates that the data points are tightly clustered, while a larger standard deviation indicates that the data points are more spread out.
The standard deviation is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Some of the measures of the variation of distribution are Range, Interquartile range, Coefficient of variation, etc.
Therefore,
Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
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Jess travels 196km to visit her cousins. She leaves home at 8:00am and arrives there are
11:15am. Calculate her average speed in km per hour to the nearst whole number.
Answers
Time is measured is km per hour
196km
3hrs and 15 minutes = 3.25 hours
196 / 3.25 = 60 km / hour
What is the conversion of 47kg in lbs ?
Answers
The conversion mass value of the kilograms to pounds is given by
( 103.635 ) pounds.
Kilograms and pounds are units which represents one of the standard unit form help us to measure mass.Standard formula which relates these two quantities of mass are represented as :
One kilogram is equal to 2.205 pounds
After substituting the standard relation between the kilograms and the pounds we get the required value,
1 kilogram = 2.205 pounds
⇒ 47 kilograms = ( 47 ) × ( 2.205 ) pounds
⇒ 47 kilograms = ( 103.635 ) pounds
Therefore, the converted value of 47 kilograms into the pounds is written as ( 103.635 ) pounds.
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Relatively easy, maths word problem. Please make sure to include working out and try your best to give the correct answer and not a blank space just to get points.
Answers
Answer:
68
Step-by-step explanation:
Looking at the pattern of what is given for the bottom section. I can count two sections as being 6 blocks and then between those sections I would count 4 blocks. This would be true for the bottom and the top. The middle holding up the top and the bottom would need 4 more blocks for each "pillar"
2(6 + 6 + 4 + 4) + 4(4) = 56
If I use that same patter with the new structure
2(7 + 7 + 5 + 5) + 4(5) = 68
Answer:
68
Step-by-step explanation:
We know that a cube has 8 corners. So that's 8 cubes just for the corners. We also know that a cube has 12 edges. An edge can be calculated by subtracting 2 from the side length. Since the side length is 7 cubes long, the edge length is 5 cubes long. The total number of cubes is:
N = (number of corner * cubes per corner) + (number of edges * cubes per edges)
[tex]N = (8 * 1) + (12 * 5) = 8 + 60 = 68[/tex]
Can someone please help me?
Answers
The value of x is 20, and the measures of the angles are:
H = 58°
I = 71°
J = 51°
How to find the value of x?We know that the sum of the interior angles of a triangle is always equal to 180°, and here we know that the measures are:
H = 3x - 2
I = 4x - 9
J = 3x - 9
Then we can write the linear equation:
3x - 2 + 4x - 9 + 3x - 9 = 180
And solve that for x.
10x - 20 = 180
10x = 180 + 20
10x = 200
x = 200/10 = 20
Then the measures of the angles are:
H = 3x - 2 = 3*20 - 2 = 58
I = 4x - 9 = 4*20 - 9 = 71
J = 3x - 9 = 3*20 - 9 = 51
So the correct option is C.
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how many milligrams are in milliliters
Answers
The density of water is 1 gram per milliliter, which means that 1 milliliter of water weighs 1000 milligrams (1 gram).
Milligrams (mg) and milliliters (ml) are two different units of measurement used for different purposes. Milligrams are used to measure mass or weight, while milliliters are used to measure volume or capacity.
The conversion between milligrams and milliliters depends on the density of the substance being measured. The density is a measure of the amount of mass per unit of volume.
In general, the conversion between milligrams and milliliters is not straightforward and requires knowing the density of the substance being measured. However, for liquids with a density of approximately 1 gram per milliliter, 1 milliliter is equivalent to 1000 milligrams.
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what is the solution of 3+ x-2/x-3 ≤ 4
Answers
im positive the answer is x<3
Mr. Brown wants to place a water heater that has a volume of 100 liters and a diameter of 40 cm into a strong-box. Will the water heater fit in the strong-box if it has a width of 45 cm and a height of 90 cm? Use П as 3.14.
Answers
Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.
what is cylinder ?The cylindrical, which is frequently a lobed solid, comprises one of the most simple curvature geometric forms. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinders" is also used to refer to an infinitely curved surface in a number of modern domains of topology and geometries. A "cylinder" is a two half object made up of curved surfaces with circle tops and bases. A cylinder is a two half solid figure with two bases that are both similar circles connected at its height, which is controlled by the separation of the legs from the center. Cans of iced drinks and the wicks from toilet paper are example of cylinders.
given
r = d/2 = 40/2 = 20 cm
v = pi *r*r*h
100 = 3.14 * 20*20 *h
100 = 1256*h
h = 0.08 cm
strong box = surface area of cuboid = 45 * 90
= 4050 cm2
surface area of water heater = A=2πrh+2πr2=2·π·20·0.08+2·π·202
≈2523.3
Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.
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40% of an amount is $4 find the full amount
Answers
The full amount is $10.
According to given information :Let x be the full amount.
We know that 40% of the amount is equal to $4, so we can set up the equation:
0.4x = 4
To solve for x, we can divide both sides by 0.4:
x = 4 ÷ 0.4
x = 10
Therefore, the full amount is $10.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and operations that are grouped together. It can be a simple expression, like "2 + 3", or a more complex one, like "(x + 3) / (y - 2)".
Expressions can be evaluated to produce a result, but they are not necessarily equations, since they don't always include an equal sign. They can also be used as components in larger expressions or equations.
For example, the expression "2x + 3y" can be used as part of the equation "2x + 3y = 12" to represent a relationship between x and y, or it can be used as part of a larger expression, like "(2x + 3y) / 5".
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A series of isosceles triangles are drawn between two red line segments.
a
= 22°.
Answers
The value of x found using the properties of the isosceles triangle is 92°.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Although this triangle's two sides are equal, the base of the triangle is the side that is not equal.
Given a = 22°
Since it is an isosceles triangle, a = 1 = 22°
One of the properties of a triangle is that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Here ∠2 is the exterior angle of the first isosceles triangle.
So ∠2 = ∠1 + a = 22 + 22 = 44°
Now∠ 3 = ∠2 = 44°
∠x = 180 - (∠2+∠3) = 180 - (44+44) = 92°
∠4 = 180 - (x+∠1) = 180 - (92+22) = 66°
∠5 = ∠4 = 66°
∠y = 180 - 66 -66 = 48°
∠6 = 180 - ∠y - ∠3 = 180 - 48 - 44 = 88°
∠7 = ∠6 = 88°
∠x = 180 - ∠7 = 180- 88 = 92°
Therefore the value of x found using the properties of the isosceles triangle is 92°.
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At a hockey game, a vender sold a combined total of 172 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answers
Therefore , the solution of the given problem of linear equation comes out to be 129 sodas were sold.
What exactly is a linear equation?The formula y=mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.
Here,
Let's start by defining some variables. Let s be the number of sodas sold and h be the number of hot dogs sold.
We know from the problem that:
s + h = 172 (the total number of sodas and hot dogs sold)
s = 3h (the number of sodas sold is three times the number of hot dogs sold)
We can substitute the second equation into the first equation to eliminate s and get an equation in terms of h:
3h + h = 172
4h = 172
h = 43
So, 43 hot dogs were sold. We can then use the second equation to find the number of sodas sold:
s = 3h = 3(43) = 129
Therefore, 129 sodas were sold.
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Consider the toss of a pair of dice what is the probability that the total number of dots appearing on top is 7
Answers
The probability of rolling a 7 with a pair of dice is 1/6. This is because there are six possible combinations that add up to 7.
Each of these combinations has an equal probability of occurring, so the probability of rolling a 7 is 1/6. (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
To explain further, when two dice are rolled, there are 36 possible outcomes, each with an equal probability of occurring. Of the 36 outcomes, 6 of them will result in the total number of dots appearing on top being 7. Since 6 out of 36 outcomes result in a 7, the probability of rolling a 7 is 6/36 or 1/6. This means that if two dice are rolled 36 times, there is a 1 in 6 chance that the total number of dots appearing on top will be 7 at least once.
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