If a car is going 100 Miles Per Hour, how many miles does the car go in one hour?
PLEASE HELP THIS IS VERY HARD!!!

The equation of the line satisfying the given conditions. It passes through (1,6); parallel to the line y = 9x - 4 is y = 9x - 3.

To find an equation of the line that satisfies the given conditions, we need to use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

Since the line we are looking for is parallel to the line y = 9x - 4, it will have the same slope, which is 9. Therefore, the equation of the line we are looking for will be y = 9x + b.

Now, we need to find the value of b. We can do this by plugging in the given point (1,6) into the equation and solving for b:

6 = 9(1) + b
6 = 9 + b
b = -3

So the equation of the line that satisfies the given conditions is y = 9x - 3.

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a) approximately 7.64% of all bags sold are underweight.

b)  the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

a) To find the fraction of all bags sold that are underweight, we need to find the area under the normal distribution curve to the left of 5 ounces. Using the standard normal distribution, we can calculate the z-score:

z = (5 - 5.1) / 0.07 = -1.43

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -1.43 is 0.0764. Therefore, approximately 7.64% of all bags sold are underweight.

b) To find the probability that none of the 5 bags in a bargain pack is underweight, we need to find the probability that each individual bag is not underweight. Using the result from part (a), the probability that one bag is underweight is approximately 0.0764. Therefore, the probability that none of the 5 bags is underweight is:

(1 - 0.0764)⁵ = 0.5595

Rounding to four decimal places, the probability that none of the 5 bags is underweight is approximately 0.5595 or 55.95%

c) To find the probability that the mean weight of the 5 bags is below the stated amount of 5 ounces, we need to use the sampling distribution of the mean. The mean of the sampling distribution is the same as the population mean, 5.1 ounces. The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size:

s = 0.07 / √(5) = 0.0313

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0313

= -3.19

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -3.19 is approximately 0.0007.

Therefore, the probability that the mean weight of the 5 bags is below 5 ounces is approximately 0.0007 or 0.07%

d) To find the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces, we need to use the sampling distribution of the mean again. The mean of the sampling distribution is still 5.1 ounces. The standard deviation of the sampling distribution is:

s = 0.07 / √(20)

= 0.0157

The z-score for a sample mean of 5 ounces is:

z = (5 - 5.1) / 0.0157
= -6.37

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -6.37 is essentially 0.

Therefore, the probability that the mean weight of a 20-bag case of potato chips is below 5 ounces is very close to 0.

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The best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.

The value of stocks in a certain new startup company is being modeled by the function S(t), where t is in years since the company going public in 2015. The given information about the value of the company's stocks is S′(5)=0 and S′′(t)>0 for 5 ≤ t ≤ 6.

The derivative S′(t) represents the rate of change of the value of the company's stocks with respect to time. Therefore, S′(5)=0 means that the rate of change of the value of the company's stocks at t=5 is zero, or in other words, the value of the company's stocks is not changing at t=5. This indicates that the value of the company's stocks has reached a local maximum or minimum at t=5.

The second derivative S′′(t) represents the rate of change of the first derivative S′(t) with respect to time. Therefore, S′′(t)>0 for 5 ≤ t ≤ 6 means that the rate of change of the first derivative S′(t) is positive for 5 ≤ t ≤ 6, or in other words, the first derivative S′(t) is increasing for 5 ≤ t ≤ 6. This indicates that the value of the company's stocks is increasing at an increasing rate for 5 ≤ t ≤ 6.

the best interpretation of the given information about the value of the company's stocks is that the value of the company's stocks has reached a local minimum at t=5 and is increasing at an increasing rate for 5 ≤ t ≤ 6.

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If a poisson process rate was 1.5 (15 events in 10 min) with a mean of 0.387, then

a) p(no events for 3 min) - 0.0498

b) p(1 event in 1 min) - 0.3347

c) p(>= 1 event in 1 min) - 0.7769

d) uncertainty for a, b, c - For a), σ = 1.732 and for b) and c), σ = 1.225

A Poisson process is a stochastic process that counts the number of events in a given time interval. It is characterized by two parameters: the rate, λ, which is the average number of events in a given time interval, and the mean, μ, which is the average number of events in the entire process.

a) The probability of no events in 3 minutes is given by the Poisson probability mass function:

P(X = 0) = (λt)^0 * e^(-λt) / 0! = e^(-λt)

Where t is the time interval (3 minutes), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 0) = e^(-1.5 * 3) = 0.0498

b) The probability of 1 event in 1 minute is given by the Poisson probability mass function:

P(X = 1) = (λt)^1 * e^(-λt) / 1! = λt * e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X = 1) = 1.5 * e^(-1.5) = 0.3347

c) The probability of at least 1 event in 1 minute is given by the complement of the probability of no events:

P(X >= 1) = 1 - P(X = 0) = 1 - e^(-λt)

Where t is the time interval (1 minute), and λ is the rate (1.5 events per minute). Plugging in the values gives:

P(X >= 1) = 1 - e^(-1.5) = 0.7769

d) The uncertainty for each of the probabilities is given by the standard deviation of the Poisson distribution:

σ = sqrt(λt)

For a), the standard deviation is:

σ = sqrt(1.5 * 3) = 1.732

For b) and c), the standard deviation is:

σ = sqrt(1.5 * 1) = 1.225

Therefore, the uncertainty for each of the probabilities is given by the standard deviation.

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Answer:

Let's first define our variables:

Let x be the number of students in each van and bus.

Using substitution:

From the problem, we know that:

High School A rented 8 vans and 8 buses, with a total of 240 students. So we can write the equation:

8x + 8x = 240

High School B rented 4 vans and 1 bus, with a total of 54 students. So we can write the equation:

4x + 1x = 54

Now, we can solve for x in one of the equations and then substitute that value into the other equation to solve for the other variable. For example, let's solve for x in the second equation:

5x = 54

x = 10.8

Now, we can substitute this value of x into the first equation to solve for the number of students in each van and bus for High School A:

8x + 8x = 240

8(10.8) + 8(10.8) = 172.8

So each van and bus for High School A has 10.8 students in it.

Using elimination:

We can rewrite the equations we used above in standard form:

8x + 8y = 240

4x + y = 54

We can eliminate y by multiplying the second equation by -8 and adding it to the first equation:

8x + 8y = 240

-32x - 8y = -432

-24x = -192

x = 8

Now, we can substitute this value of x into either equation to solve for y:

4(8) + y = 54

y = 22

So each van and bus for High School A has 8 students in it and each van and bus for High School B has 22 students in it.

Using graphing:

We can graph the two equations on the same coordinate plane and find the point where they intersect, which represents the solution:

8x + 8y = 240

4x + y = 54

To graph these equations, we can first solve for y in each equation:

y = -x + 30

y = -4x + 54

Then, we can plot these two lines on the same coordinate plane and find their intersection:

(6, 24)

So each van and bus for High School A has 6 students in it and each van and bus for High School B has 24 students in it.

we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.

To prove the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A), we can use the following steps:

Step 1: Use the identity sin^2(A) + cos^2(A) = 1 to express sin^4(A) in terms of cos^4(A).

sin^4(A) = (1 - cos^2(A))^2

Step 2: Expand the expression on the right hand side.

sin^4(A) = 1 - 2cos^2(A) + cos^4(A)

Step 3: Rearrange the terms to get the expression on the left hand side.

sin^4(A) - cos^4(A) = 1 - 2cos^2(A)

Step 4: Verify that the expression on the left hand side is equal to the expression on the right hand side.

1 - 2cos^2(A) = 1 - 2cos^2(A)

Therefore, the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) is proven to be true.

In conclusion, we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.

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Answer:

1 3/4

Step-by-step explanation:

To turn 7/4 into a mixed number, you have to look at the numerator and the denominator. 4 can go into 7 once (with 3 left over), so it would be 1 and 3/4

Hence, the shape is rectangular prism with the dimensions 10mm, 8mm, and 8mm has a surface area of 448mm2.

We must first calculate the surface area of each face of a rectangular prism with 10mm, 8mm, and 8mm measurements before adding them all up.

The top and bottom faces, which are both rectangles with measurements of 10 mm by 8 mm, are first measured for area:

Area of the top and bottom faces is equal to 2 (10 x 8 mm) or 160 mm2.

The area of the front and back faces, which are both rectangles measuring 10 mm by 8 mm, is then determined: Area of the front and back faces is equal to 128mm2 (8mm x 8mm).

The area of the two side faces, which are both rectangles with dimensions of 10 mm by 8 mm, is then determined: Area of the side sides is equal to 2 (10mm x 8mm) = 160mm2.

We add up the areas of all the faces to determine the overall surface area:

Whole surface area equals the sum of the areas of the top and bottom faces, the front and back faces, and the side faces.

Surface area total = 160 mm2 + 128 mm2 + 160 mm2

448 mm2 is the total surface area.

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The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

What are algebraic expressions?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and arithmetic operations (such as addition, subtraction, multiplication, and division). It can also include exponents, roots, and other mathematical symbols.

Algebraic expressions are used to represent mathematical relationships and to solve problems in various areas of mathematics, science, and engineering. Examples of algebraic expressions include 3x + 5, 2y - 7, and 4x² - 3xy + 2.

A. The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.

B. The expression that is equivalent to m + m + m + m that is the sum of two terms is 2m + 2m, where 2m is one term and the other term is also 2m.

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Answer:

2/3 (-9+3) simplifies to 2/3 (-6) which is equal to -4.

Step-by-step explanation:

To simplify 2/3(-9+3), we need to start by simplifying the expression inside the parentheses, which is -9+3=-6. Therefore, we can rewrite the expression as 2/3(-6).

Now we can apply the distributive property of multiplication over addition/subtraction to simplify further. This property states that a(b+c) = ab + ac. So, 2/3(-6) can be written as:

2/3 x -6 = 2/3 x (-1 x 6) = 2/3 x (-1) x 6 = -2/3 x 6

Now we just need to multiply -2/3 by 6, which gives us -12/3 or -4. Therefore, 2/3(-9+3) simplifies to -4.

The equation of the function is f(x) = 1/2cos(x)

From the question, we have the following parameters that can be used in our computation:

The sinusoidal graph

The sinusoidal graph is a cosine function

The parent function of a cosine function is

y = cos(x)

Based on the points on the graph, we can see that the graph is shrinked by 2

Mathematically, this is represented as

f(x) = 1/2y

So, we have

f(x) = 1/2cos(x)

Hence, the function is f(x) = 1/2cos(x)

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The speaker has a volume of about 34.67 cubic inches.

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. The several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the question:

The following formula can be used to determine a pyramid's volume:

V = base area * height * (1/3)

Since the speaker in this instance is shaped like a triangular pyramid, we can use the base area of 13 square inches and the height of 8 inches to calculate the volume.

When the values are added to the formula, we obtain:

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Hence, the speaker's volume is roughly 34.67 cubic inches.

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Answer:

112m

Step-by-step explanation:

The area of the given  Parallelogram is 112 m².

given that the parallelogram in fig.. We splits this parallelogram in three parts, that is, first is triangle ,second is square and third is again a triangle.

Since, the area of triangle:

[tex]\mathrm{Area\ of\ triangle}=\frac{1}{2}[/tex] × base × height

and the [tex]\mathrm {Area\ of\ Square}=[/tex] width × height.

Here in triangle, base=6 and height=8

[tex]\mathrm {Area\ of\ Square}=[/tex]

therefor the [tex]\mathrm{Area\ of\ triangle}=\frac{1}{2}[/tex]×6×8

                                               =24m².

Here in square,  width=8 and height=8

therefore the [tex]\mathrm {Area\ of\ Square}=[/tex] 8×8

                                               =64m².

Area of first split, that is, triangle is 24 m².

Area of second split, that is, square is 64 m².

Area of third split, that is, again a triangle is 24 m².

Total area= 24+64+24

                 =112 m².

Therefor the total area of parallelogram is 112 m².

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As a result, the park's estimated area, calculated using a trapezoidal sum with three equally spaced subintervals, is 50 square miles.

A quadrilateral with at least one set of parallel edges is known as a trapezoid. The bases and legs of a trapezoid are referred to by their parallel and non-parallel edges, respectively. The space between the bases of a trapezoid measured perpendicularly is its height. A = (1/2)h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the two bases, is the formula for a trapezoid's area.

given

By calculating the function's average at the left and right ends of the subinterval, it is possible to determine the height of each trapezoid.

A1 = (1/2) * (base1 + base2) * height

= (1/2) * (2 + 2) * 9 = 18 is the area of the first trapezoid.

A2 = (1/2) * (base1 + base2) * height

= (1/2) * (2 + 2) * 11 = 22 is the formula for the area of the second trapezoid.

The third trapezoid's area is given by

A3 = (1/2) * (base1 + base2) * (1/2) * (2 + 2). * 10

= 10

The three trapezoids' combined areas make up the entire area under the curve, which roughly corresponds to the size of the park:

A total = A1 + A2 + A3 

= 50

As a result, the park's estimated area, calculated using a trapezoidal sum with three equally spaced subintervals, is 50 square miles.

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Answer:

slope is undefined

Step-by-step explanation:

We have 2 coordinates (-4,0) and (-4,1)

Slope m = (y2 - y1)/(x2 - x1) = (1 - 0)/(-4 - -4) = 1/0 or undefined

The undefined slope is the slope of a vertical line

The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,

Measurement error, Random variation and Sampling error.

Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.

Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.

Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.

For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.

Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.

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Answer: The plane traveled 15838.5 feet from point A to point B.

1. 1920 Beetle Population

Beetle Type #Beetles #Beetle % Frequency

BB 22 22/86 ≈ 0.26

bb 14 14/86 ≈ 0.16

Bb 50 50/86 ≈ 0.58

2. 2020 Beetle Population

Beetle Type #Beetle % Frequency

BB 0 0/14 = 0

bb 14 14/14 = 1

Bb 0 0/14 = 0

3. Gene pool for the beetle population: The gene pool for the beetle population consists of the two alleles for the coloration gene, which are represented by "B" (dominant allele) and "b" (recessive allele).

4. Allele frequency for the 1920 Homozygote dominant Beetle population:

5. The allele frequency for the heterozygote population in 2020 is B = 0 and b = 1.

6. Yes, the beetle population experienced evolution because the allele frequencies changed from 1920 to 2020.

For question 1 and 2 above, The % frequency for each beetle type was calculated by dividing the number of beetles of that type by the total number of beetles in the population, and then multiplying the result by 100 to get a percentage.

For example, in the 1920 beetle population, the frequency of BB beetles was calculated as follows:

% Frequency of BB = (# of BB beetles / Total # of beetles) x 100

% Frequency of BB = (22 / 86) x 100

% Frequency of BB ≈ 25.58 or 26% (rounded to the nearest whole number)

Similarly, the % frequency for bb and Bb beetles in the 1920 population were calculated as:

% Frequency of bb = (14 / 86) x 100 ≈ 16%

% Frequency of Bb = (50 / 86) x 100 ≈ 58%

The same process was used to calculate the % frequency for the 2020 beetle population.

4. The frequency of the dominant allele (B) in the 1920 population is the sum of the number of copies of B (from BB and Bb beetles) divided by the total number of alleles (2x the total number of beetles).

Frequency of B = (22 + 50/2) / (86x2) ≈ 0.55

5. Allele frequency for the 2020 heterozygote beetle population:

Since only the frequency of the heterozygote (Bb) is given, the frequency of both alleles (B and b) can be calculated as follows:

Frequency of b = 1 - Frequency of B = 1 - 0 = 1

Frequency of B = frequency of Bb / 2 = 0 / 2 = 0

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Answer:

c

Step-by-step explanation:

1 2/3 = 5/3 = 20/12

3 1/4 = 13/4 =39/12

In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.

How is area determined?

The length of the other leg of the right triangle can be determined using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where the hypotenuse is c and the triangle's legs are a and b.

We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:

[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]

[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]

Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:

[tex](1/2) * Base * Height = Area[/tex]

We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:

Area: (1/2) * 4 feet * 4 square feet (3)

= 8sqrt(3) square feet

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Answer:

4.2 represents the initial height of the ball.

Step-by-step explanation:

h(x) = -16x² + 24x + 4.2

At x = 0, h(0) = 4.2

4.2 represents the initial height of the ball.

Answer:

To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:

0 = -(x+7)(x+4)

This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:

x+7 = 0 => x = -7

x+4 = 0 => x = -4

Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.

Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.

To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:

0 = -(x-3)

This equation will be true if (x-3) = 0, which gives us:

x-3 = 0 => x = 3

Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.

Step-by-step explanation:

Answer:

x-intercepts can be found below

Step-by-step explanation:

The equation:

[tex]y=-(x+7)(x+4)[/tex]

Can also be written as:

[tex]y=-1(x+7)(x+4)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x+7=0, x=-7[/tex]

[tex]x+4=0, x=-4[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](-7,0)[/tex]

[tex](-4,0)[/tex]

The equation:

[tex]y=-(x-3)[/tex]

Can also be written as:

[tex]y=-1(x-3)[/tex]

In order to find the x-intercepts, we must set each of the factors equal to 0.

[tex]-1=0[/tex]

[tex]x-3=0, x=3[/tex]

The x-intercepts are:

[tex](0,0)[/tex]

[tex](3,0)[/tex]

Answer:

Here is a table showing the relationship between the number of coins collected and the total points earned:

Number of coins (c) Total points (p)

0 0

1 20

2 35

3 50

4 65

5 80

6 95

7 110

8 125

9 140

10 155

To graph these ordered pairs, we can plot the number of coins collected (c) on the x-axis and the total points earned (p) on the y-axis. Then we can plot each ordered pair as a point on the graph and connect the points with a line. The resulting graph should show a linear relationship between c and p, with a slope of 15 and a y-intercept of 0.

Analyzing the graph, we can see that as the number of coins collected increases, the total points earned also increases at a constant rate. This suggests that collecting coins is an important part of the game, as it significantly increases the player's total score. Additionally, the slope of the line (15) tells us that each additional coin collected is worth 15 points, while reaching the next level is worth only 5 points.

Answer: Since lines l and m are parallel, we can use the fact that corresponding angles are congruent. Therefore:

m∠1 = m∠6 (corresponding angles)

m∠6 + m∠2 = 180° (supplementary angles, as angles 6 and 2 form a straight line)

m∠2 = m∠7 (corresponding angles)

m∠3 = m∠7 (alternate interior angles)

m∠1 + m∠4 = 180° (supplementary angles, as angles 1 and 4 form a straight line)

m∠3 + m∠4 = 180° (supplementary angles, as angles 3 and 4 form a straight line)

We know that m∠1 = 63°, so we can use the equations above to find m∠6 and m∠7:

m∠1 = m∠6, so m∠6 = 63°.

m∠6 + m∠2 = 180°, so m∠2 = 180° - m∠6 = 180° - 63° = 117°.

m∠2 = m∠7, so m∠7 = 117°.

m∠3 = m∠7, so m∠3 = 117°.

m∠1 + m∠4 = 180°, so m∠4 = 180° - m∠1 = 180° - 63° = 117°.

m∠3 + m∠4 = 180°, so m∠3 + 117° = 180°, which means m∠3 = 63°.

Therefore, the measures of the angles are:

m∠1 = 63°

m∠2 = 117°

m∠3 = 63°

m∠4 = 117°

m∠6 = 63°

m∠7 = 117°

Step-by-step explanation:

The line passes through the x-axis at the point (13/2, 0).

To find where the line passes through the x-axis, we need to find the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, so the y-coordinate of this point will be 0.

We can use the slope-intercept form of a line, y = mx + b, to find the x-intercept. First, we need to find the slope of the line, m. The slope is given by the formula:
m = (y2 - y1)/(x2 - x1)

Plugging in the given points, we get:

m = (5 - 1)/(-1 - 5)

m = -2/3

Now we can plug in one of the points and the slope into the equation to solve for the y-intercept, b:
1 = -2/3(5) + b
b = -13/3

So the equation of the line is:
y = -2/3x + 13/3

To find the x-intercept, we set y to 0 and solve for x:
0 = -2/3x + 13/3
x = 13/2

So the line passes through the x-axis at the point (13/2, 0).

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The inequalities shown by the graph are y < 3, x > -1, x < 3, and y >-2.

The given graph has four lines showing different inequalities.

One undotted line is parallel to the x-axis and is at y = 3. The shaded region is below y = 3

Hence, the inequality will be y < 3

Another dotted line is parallel to the x-axis and is at y = -3. The shaded region is above y = -2

Hence, the inequality will be y > -2

Another dotted line is parallel to the y-axis and is at x = -1. The shaded region is to the right of x = -1

Hence, the inequality will be x > -1

Another dotted line is parallel to the y-axis and is at x = 3 The shaded region is to the left of x = 3

Hence, the inequality will be x < 3

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It takes approximately0.082 seconds for the eraser to hit the student in the head.

The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.

First, we will set h(t) equal to 3 and rearrange the equation:

-16t^(2)+35t+6=3

Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0

Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))

Simplifying further, we get:
t= (-35±√(1417))/(-32)

Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27

Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.

Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.

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Answer:

No solution

Step-by-step explanation:

Use the given functions to set up and simplify f(9)

Answer:

How are we supposted to do your homework if we dont have a picture or explanation of it??

Step-by-step explanation: