Which is the equation of the given line?
Question options:
A. x = –2
B. y = –2x
C. x = 2
D. y = –2

Answer:

He would run 4.5 miles in 42 minutes if the rate is the same!

Step-by-step explanation:

Answer:

\(x = 1.2\)

See Attachment for Graph

Step-by-step explanation:

Given

\(y = -x + 4\)

\(y = 4x - 2\)

Required

Determine the point of intersection

To do this, we simply equate both expressions of y

i.e.

\(-x + 4 = 4x - 2\)

Solve for x

\(-x - 4x = - 2 - 4\)

\(-5x = -6\)

Divide through by -5

\(x = \frac{-6}{-5}\)

\(x = \frac{6}{5}\)

\(x = 1.2\)

Hence, the point of intersection is 1.2

Answer: 5 weeks

Explanation:

To find out when both siblings will have the same amount of money in their savings accounts, we need to solve the system of equations:

y = 10x + 25

y = 5x + 50

We can set the two equations equal to each other and solve for x:

10x + 25 = 5x + 50

5x = 25

x = 5

Therefore, after 5 weeks, both siblings will have the same amount of money in their savings accounts. So the answer is 5 weeks.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

For more such question on function. visit :

https://brainly.com/question/11624077

#SPJ8

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

For more related questions on time spent:

https://brainly.com/question/28263820

#SPJ8

Check the picture below.

The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

Learn more on circles ;https://brainly.com/question/14868497

#SPJ1

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

Learn more about Tangent Ratio on:

question

#SPJ1

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

For more related questions on minimum profit:

https://brainly.com/question/32510275

#SPJ8

The values of L that will maximize the profit are 0 and -200

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

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

Read more about functions at

https://brainly.com/question/32616074

#SPJ1

Answer:

y = (-5x + 12)/-7

Step-by-step explanation:

5x - 7y = 12

-7y = -5x + 12

I now divide both sides by -7.

y = (-5x + 12)/-7

Answer:

Ther are 9 ways !!!

Step-by-step explanation:

Answer:

The Greatest Common Factor, the GCF, is the biggest ("greatest") number that will divide into (that is, the largest number that is a factor of) both 2940 and 3150. On the other hand, the Least Common Multiple, the LCM, is the smallest ("least") number that both 2940 and 3150 will divide into.

Have a good day

The answer of the given question on the listing the critical numbers is  the critical numbers as x = 3, 6, and 9. and the function has an absolute maximum at x = 9. and the function has an absolute minimum at x = 2.

an absolute maximum occurs at the highest point on the graph of a function over its entire domain. It can be a local maximum or a global maximum, depending on whether there are any other points in the domain that have higher function values. Finding the absolute maximum of a function is important in optimization problems, where we want to find the maximum or minimum value of a function subject to certain constraints.

Based on the graph provided, we can approximate the critical numbers as x = 3, 6, and 9.

To determine whether there is relative maximum, relative minimum, absolute maximum, or absolute minimum at each critical number, we need to examine  behavior of function near each critical number.

At x = 3, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

At x = 6, the function has a relative minimum, since the graph changes from decreasing to increasing at that point.

At x = 9, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

Since the graph increases without bound as x approaches 10 from the left, but approaches a finite value as x approaches 10 from the right, the function has an absolute maximum at x = 9.

Since the graph decreases without bound as x approaches 2 from the right, but approaches a finite value as x approaches 2 from the left, the function has an absolute minimum at x = 2.

To know more about Function visit:

https://brainly.com/question/10500042

#SPJ1

Answer:

It's C, I just wrote it out.

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

for such more question on line

https://brainly.com/question/24644930

#SPJ8

Answer:

Step-by-step explanation:

We know that the sides in a square are equal length. We also know that you have to multiply length by width to get area. So if we know that the length of one side is 16 feet then all we have to do if multiply 16 by 16. Hence why the answer is 256 square feet of carpet.

The number can be used to get rid of all fractions is 12

The equation is given as:

6 - 3/4x + 1/3 = 1/2x + 5

The denominator of the fractions are:

4, 3 and 2

The LCM of 4, 3 and 2 is 12

So, we have:

12 * [6 - 3/4x + 1/3] = 12 * [1/2x + 5]

Evaluate the products

72 - 9x + 12 = 6x + 60

Hence, the number can be used to get rid of all fractions is 12

Read more about fractions at:

https://brainly.com/question/11562149

#SPJ1

I'll answer this question in a bit, I am busy with some other things right now.

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

Learn more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ8

Answer:

\(y - 20 = 24(x - 3)\)

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, has the following format:

\(y - y_0 = m(x - x_0)\)

In which the point is \((x_0,y_0)\) and the slope is m.

(3, 20)

This means that \(x_0 = 3, y_0 = 20\). So

\(y - y_0 = m(x - x_0)\)

\(y - 20 = m(x - 3)\)

Slope:

The slope is the derivative of the function at the point:

The function is:

\(y = x^3 - 3x + 2\)

The derivative is:

\(y^{\prime}(x) = 3x^2 - 3\)

At the point, we have that \(x = 3\). So

\(m = y^{\prime}(3) = 3*3^2 - 3 = 27 - 3 = 24\)

So the equation to the tangent line to the curve a the point is:

\(y - 20 = 24(x - 3)\)

Answer:2^7 ≠ 7^2

Step-by-step explanation:

2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2

The only factor is 2

7^2 = 7 * 7

The only factor is 7

Comparing the factors when written as a repeated multiplication,

2^7 and 7^2 have no common factor :

2^7 = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128

7^2 = 7 * 7 = 49

Answer:

false

Step-by-step explanation:

How many gallons of a 10% solution. Would need to be added to a 20% solution to obtain 50 gallons of a 30% solution?

2.How many gallons of milk containing 4% fat is mixed with milk containg 1% fat to obtain a 15 gallon mixture containing 2% fat?

Eric jogs for 45 minutes.

Speed is measured as the ratio of distance to the time in which the distance was covered.

We have,

Eric walked and jogged and the total distance combined:

= 5.25 miles

Distance walked = 1.5 miles

The distance jogged:

= 5.25 - 1.5

= 3.75 miles

Now,

Speed = 5 miles per hour

We can write it as:

1 hour = 5 miles

We need to find 3.75 miles.

Multiply 3.75/5 on both sides.

(3.75 / 5)  x 1 hours = 3.75 miles

0.75 hour = 3.75 miles.

This means 45 minutes to jog for 3.75 miles.

Thus Eric jogs for 45 minutes.

Learn more about speed here:

https://brainly.com/question/28224010

#SPJ1

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

According to the information provided, 4.5 litres of red paint and 1400 ml of blue paint are required to manufacture the paint mixture.

Red paint requires 3/4 x 6 = 9/2 = 4.5 litres.

To know more about Litres visit:

https://brainly.com/question/25546396

#SPJ1