The figure shows a square plot of land in tiny town. The diagonal line represents a new road that was recently built. How long is the new road? Round the nearest tenth if necessary.


A. 9 miles


B. 18 miles


C. 10.7 miles


D. 12.7 miles

The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;

(a) f(0) = 1

(b) f(0) = 12

(c) f(0) = -2

Part of the question appears missing. From a similar question online, we have;

(a) A table of values;

x: -1, 0, 1, 2, 3

y: 7, 1, 6, -3, -4

Taking the function, f(x) = y, we have;

From the above values in the table, when x = 0, y = f(0) = 1

Therefore;

(b) y = 12 - 2•x²

Taking the function, f(x) = y, we have;

At x = 0, y = f(0) = 12 - 2 × 0² = 12

Therefore;

(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)

Let f(x) = a•x² + b•x + c, represent the function, we have;

f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c

f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c

f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c

Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;

a = 1, b = -4, c = -2

Which gives;

f(x) = x² - 4•x - 2

Therefore;

f(0) = 0² + 4×0 - 2 = -2

Which gives;

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Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

To find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.

To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).

This gives us:

1 part of the ratio = 1225 / 35 = 35

To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.

For the part that corresponds to 8, we have:

8 parts of the ratio = 8 x 35 = 280 items

For the part that corresponds to 27, we have:

27 parts of the ratio = 27 x 35 = 945 items

Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

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Answer:

There are 12 sections on the spinner, and out of the 12 sections, 5 of them are red.

If he spins the spinner 48 times, he should expect 5x4, or 20 of the spins to land on red.

Let me know if this helps!

Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

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Answer:

101.9

Step-by-step explanation:

Because to find the mean, you need to add up all the numbers. Then divide by the amount of numbers you added.

Answer:

?

Step-by-step explanation:

Answer:

3.Ans
4 is the thousands place value in the number 524,897,123.

The value of the digit 4 would be 4,000,000.

Calculation: 4 x 1,000,000 = 4,000,000


4.Ans

The product of (6*5)*10^3 is 3000. This product has 3 zeroes.

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Answer:

6+5*(10-8)=16

Step-by-step explanation:

Using BODMAS multiplication takes precedence over addition and subtraction so as it stands it would be calculated as 6 + (5*10) - 8. To get the answer 16 it would be 6 + 5(10 - 8) Solving the brackets first, this gives 6 + (5*2) which gives 16.

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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The line's equation in the form of a point-slope is y + 7 = 7 (x + 1).

A mathematical description of the steepness as well as the direction of a line is its slope, commonly referred to as its gradient. Despite the lack of obvious justification, the letter "m" is frequently used to represent slope. Though it is written as "y = mx + b" and "y = mx + c," respectively.

Slope:

slope = y2 - y1 / x2 - x1.

Slope halt the form:

y = mx + b.

Slope develop at a point.:

y - y1 = m ( x - x1) ( x - x1)

Common Form. Ax + By = C.

x - axis. the graph's horizontal axis.

y - axis. the graph's vertical axis.

intercept with X. the location where a line crosses the x axis at an angle.

intercepting at Y.

An equation for a line is denoted by the formula: y - y0 = m(x-x0), where m is the slope of the line and (x0, y0) is any point on the line.

Using the coordinates (-1, -7) and (1, 7), calculate the slope:

m = 7 + 7 / 1 + 1m = 7.

Substitute the slope and (-1, -7) in the formula to obtain:

y - (-7) = 7 (x-(-1))=> y + 7 = 7 (x+ 1)

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Answer:

\(b=3\sqrt{13}\)

Step-by-step explanation:

Segment Addition Postulate:

\(\bar{PY}=\bar{MP}+\bar{MY}\)

Substitute MP = 4, MY = 9 into PY = MP + MY:

\(\bar{PY}=4+9\)

Calculate PY = 4 + 9:

\(\bar{PY}=13\)

Representing same angles:

\(cos A = leg adjacent to <A/hypotenuse:

\(cos(Substitute DY = b, PY = 13 into cos (<DYP)=DY/PY:

\(cos(Substitute <DYP=<DYM into cos(<DYP)=b/13:

\(cos(cos A=leg adjacent to <A/hypotenuse:

\(cos\left(Substitute DY=b, MY=9, cos(<DYM)=b/13 into cos (<DYM)=MY/DY:

\(\frac{b}{13}=\frac{9}{b}\)

Calculate b/13=9/b:

\(b=3\sqrt{13}\)

I hope this helps you :)

Answer:

c

Step-by-step explanation:

The answer would be (C) 20.

Answer:

The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.

In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.

Option B, 12.5, is the correct answer.

Step-by-step explanation:

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

The correct question is;

Joey borrows $2400 from his grandfather and pays the money back in monthly payments of $200.

a. Write a linear function that represents the remaining money owed L(x) after x months.

b. Evaluate L(10) and interpret the meaning in the context of this problem.

A) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey still owes his

grandfather after 10 months.

B) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey has paid his

grandfather after 10 months.

C) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey has paid his

grandfather after 10 months.

D) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey still owes his

grandfather after 10 months.

Answer:

A) L(x) = 2400 - 200x

B) Option D is correct

Step-by-step explanation:

A) We are told that Joey borrowed 2400.

Now he pays back in installments of 200 every month.

Thus for x number of months he would have paid 200x.

Thus,the linear function that represents the remaining money owed is;

L(x) = 2400 - 200x

B) L(10) = 2400 - (200 * 10)

L(10) = 2400 - 2000

L(10) = 400

Thus, after 10 months, Joey is owing 400.

So, looking at the given options, the correct one is option D.

Answer:

reflection of the axis y=4

Step-by-step explanation:

becuase it is reflected on itself

Answer:

Reflect Triangle A by the line y = 4

Step-by-step explanation:

The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.

Answer:

x = 11.2

Step-by-step explanation:

Since, ΔPQR ~ ΔVST,

By the property of similar triangles, corresponding sides of these triangle will be proportional.

\(\frac{PQ}{VS}=\frac{QR}{ST}\) ---------(1)

Since, scale factor = \(\frac{\text{Dimension of the image figure}}{\text{Dimension of the original}}\)

\(\frac{2}{5}\) = \(\frac{PQ}{VS}\)

Therefore, from equation (1)

\(\frac{2}{5}=\frac{x}{28}\)

x = \(\frac{28\times 2}{5}\)

x = 11.2

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The contraposition statement is true in all applicable cases, we can conclude that the original statement is also true. Therefore, if n2 is divisible by 3, then n is divisible by 3.

To prove that if n2 is divisible by 3, then n is divisible by 3, we will use contraposition, the quotient remainder theorem, and cases.

First, we will use contraposition to restate the original statement. The contraposition of "if n2 is divisible by 3, then n is divisible by 3" is "if n is not divisible by 3, then n2 is not divisible by 3."

Next, we will use the quotient remainder theorem to divide n by 3. According to this theorem, we can write n as 3q + r, where q is the quotient and r is the remainder. There are three possible cases for the value of r: 0, 1, or 2.

Case 1: r = 0
In this case, n is divisible by 3, so this case does not apply to the contraposition statement.

Case 2: r = 1
In this case, n = 3q + 1, so n2 = (3q + 1)2 = 9q2 + 6q + 1. This expression is not divisible by 3, so the contraposition statement is true in this case.

Case 3: r = 2
In this case, n = 3q + 2, so n2 = (3q + 2)2 = 9q2 + 12q + 4. This expression is not divisible by 3, so the contraposition statement is true in this case.

Since the contraposition statement is true in all applicable cases, we can conclude that the original statement is also true. Therefore, if n2 is divisible by 3, then n is divisible by 3.

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Answer:

Yes

Step-by-step explanation:

y-8= -8(x-2)  ==> solve for y

y = -8(x - 2) + 8  ==> add 8 on both sides to isolate y

y = (-8 * x - 2(-8)) + 8  ==> distribute -8 to x and -2 using the distribution

                                         property

y = (-8x - (-16)) + 8 ==> simplify

y = (-8x + 16) + 8  ==> subtracting by a negative number is equivalent to

                               adding by a positive number.

y = -8x + 16 + 8

y = -8x + 24  ==> Degree of x in the equation is 1, so the function is linear

Answer:

$1.03

Step-by-step explanation:

7/8 = 0.875

then

43 7/8 = 43.875%

43.875/100 = 0.43875

2.35 * 0,43875 = 1.031

Round to the neares cent:

1.03

Step-by-step explanation:

\(43 \frac{7}{8} \% \: of \: 2.35 \\ \frac{351}{8} \% \: of \: 2.35 \\ \frac{351}{8 \times 100} \times 2.35 \\ \frac{824.85}{800} = \boxed{\$1.0310625}\)

Answer:

A

Step-by-step explanation:

Slope = (change in y)/ (change in x)

          = (-1 - 4)/ (8 - 3)

          = -5/5

          = -1

Answer:

105 cm³

Step-by-step explanation:
i think lol

Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : \(f(x) = ( 25 - x^{2} )\)

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               \(Area = \int\limits^{maxX}_ {minX} \, f(x)dx\)

               \(Area = \int\limits^5_ {-5} \, (25-x^{2} )dx\)

Hence, Option A correctly calculates the area of the graph given.

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Answer:

1. 15 to 21 = 21 - 15 / 15 = 0.4*100% = 40%

2. 12 teachers to 48 teachers = 48 - 12/48 = 0.75 * 100% = 75%

3. 80 pencil to 120 pencil = 120 - 80 / 80 = 0.5*100% = 50%

4. 40 cans to 70 cans = 70 - 40 / 70 = 0.43 * 100% = 43%

On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

he diameter of the ball bearings varies according to a distribution that is approximately Normal

mean 11.5 mm and standard deviation 0.05 mm

the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm

Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

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12. MORT

13. MNR

14. SDT

15. MOSR