24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter

From the diagram given in the question, we are asked to find the missing length indicated.

We can see from the diagram that the right triangles are similar, so the ratio of hypotenuse to short leg is the same for all.

So,

x/900 = (1600 + 900)/x

Let's cross multiply:

x² = 900(2500)

let's take square of both sides:

x = √(900) * √(2500)

x = 30(50)

x = 30 * 50

x = 1500

Therefore, the missing length is 1500

Answer:

bottom one

Step-by-step explanation:

Lets make a picture of our problem:

where h denotes the height of the box.

We know that the volume of a rectangular prism is

Since the volume must be 8 cubic centimeters, we have

Then, the height function is equal to

On the other hand, the function cost C is given by

that is,

which gives

By substituting the height result from above, we have

which gives

Now, in order to find minum cost, we need to find the first derivative of the function cost and equate it to zero. It yields,

which is equivalent to

by moving x squared to the left hand side and the number 8 to the right hand side, we have

Therefore, by substituting this value in the height function, we get

therefore, by rounding to the neastest hundredth, the height which minimize the cost is equal to 1.97 cm

The said statement is true.

A power has two parts, a base and an exponent.

Example

The answer is TRUE

Same side interior angles are angles on the same side of the transversal line, inside the two lines intersected.

<5 is an interior angle, on the same side as <3.

On The left side of the bisector line.

Adam had $200

He spent $75 on clothes and $55 on video game

The total money spent by Adam is

The amount left with Adam is

Then his mom gave him $20

The total amount of money Adam have now is

Hence, the answer is $90

Step-by-step explanation:

A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,

so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.

Therefore the degrees will a nonagon have rotational symmetry

Hene the correct answer is Option B

Given,

The expression is,

Required:

The graph of the line.

The interval notation is [-3, infinity).

The line of the inequality is,

Hence, the graph of the line is obtained.

The meaning of estimate is approximately calculating an answer to check its accuracy.

Approximate calculation:

Approximate value means the value that is close to this number, less than it, as close as possible, and with a requested level of precision.

For example, the approximate value of π is 3.14

Given,

Here we have the word estimate.

Now, we have to find the meaning of it.

Estimate value means to find a value that is close enough to the right answer, usually with some thought or calculation involved.

For example, let us consider Alex estimated there were 10,000 sunflowers in the field by counting one row then multiplying by the number of rows. Here we doesn't have the exact value instead of that we take the approximate value to identify the number. This process is called estimation.

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We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:

therefore, 45 percent of 240 is 108

Answer:

0.4384 < p < 0.5049

Explanation:

The confidence interval for the population proportion can be calculated as:

Where p' is the sample proportion, z is the z-score related to the 95% level of confidence, n is the size of the sample and p is the population proportion.

Now, we can calculate p' as the division of the number of voters of favor approval by the total number of voters.

Additionally, n = 865 and z = 1.96 for a 95% level of confidence. So, replacing the values, we get:

Therefore, the confidence interval for the true proportion is:

0.4384 < p < 0.5049

Answer:

To solve the system of two linear inequalities graphically,

For step 1,

Draw a line 4x+6y=24

Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.

Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,

Similarly for the inequality,

It covers the region right side of the line x=2,

we get the siolution region as the intersecting region of both inequality which defined in the graph as,

Dark blue shaded region is the required solution set for the given inequalities.

We have the following equation

y = -x + 8

this equation is writen in slope intercept form

y = mx + b

where m is the slope

From the above, we can see that the slope is m = -1

The question is given as

To solve, we need to make (x + yi) the subject of the formula.

To do so, we move 6i to the right-hand side of the equation:

Therefore, OPTION A is correct.

Answer:

(x + yi)= 2-6i

Step-by-step explanation:

Complex numbers

(x + yi) +6i = 2

Subtract 6i from each side

(x + yi) +6i -6i = 2-6i

(x + yi)= 2-6i

SOLUTION

Let us solve the simultaneous equation

using elimination

To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.

So to make the y's different, I will multiply the second equation by a -1. This becomes

So, now we can eliminate y, doing this we have

Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have

So, x = 1 and y = -2

Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,

Now, we will put y = x - 3 into the other equation, which is equation 1, we have

So, substituting x for 1 into equation 1, we have

Substituting x for 1 into equation 2, we have

Now, for graphing,

Congruent Shapes

Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),

All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.

The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.

Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is

xm = (-6+4)/2 = -1

Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:

xm = (-8+6)/2 = -1

For the points R(-4,-6) and D(2,-6):

xm = (-4+2)/2 = -1

For the points Q(-9,-4) and D(8,-4):

xm = (-9+8)/2 = -0.5

Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent

For both shapes to be congruent, the coordinates of Q should have been (-10,-4)

we have the formula

we have

R=9.2

I0=1

substitute in the given equation

I=1,584,893,192.46

Given:

Find-:

Sol:

Use integration then:

The function value at x = 2 is:

The function value at x = 5

Function value at x = 8

For a line to be parallel to another line, the slope will be the same

1st equation:

Since the slope of the first line = 2/5, the slope of the second line will also be 2/5

We would insert the slope and the given point into equation of line to get y-intercept of the second line:

The equation for the line that passes through (-7, 6) and parallel to line 2x - 5y - 8 = 0:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

C = 10N + 700

Step 02:

functions:

C = total cost

N = number of copies

Domain:

number of copies produced

{0, 1, 2, 3, .... 100}

Range:

cost of publishing book (in dollars)

{700, 710, 720, 730, ... 1700}

That is the full solution.

Answer:

seven less than the quotient of two and a number squared increased by six

7 -  (2/n²)  + 6

nine times the difference of a number cubed and three; 9(n³-3)

eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7

twice the difference of a number cubed and eight;  2 n³- 8

Step-by-step explanation:

It is given that the boy owns 6 pairs of pants, 8 shirts, 2 ties, and 3 jackets.

It is also given that he must wear one of each item.

Recall the Fundamental Counting Principle:

The same is valid for any number of events following after each other.

Hence, the number of different outfits he can wear by the counting principle is:

Evaluate the product:

The number of different outfits he can wear is 288.

You have the following sequence for the population of the rabbits:

6, 18, 54, ...

The explicit formula for the previous sequence is obtained by considering the values of n (1,2,3,..) for the first terms of the sequence.

You can observe that the explicit formula is:

a(n) = 6·3^(n - 1)

in fact, for n=1,2,3 the result is:

a(1) = 6·3^(1 - 1) = 6·3^0 = 6

a(2) = 6·3^(2 - 1) = 6·3^1 = 18

a(3) = 6·3^(3 - 1) = 6·3^2 = 6·9 = 54

which is consistent with the given sequence 6, 18, 54, ...

In the given figure,

The pair of alternate interior angle is,

Every parallel line would have the same slope because the slope formula is Δy/Δx and the difference would be the same, so the slope for the line with the given points would be -1/6, or roughly 0.167.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel.

A line's steepness can be determined by looking at its slope. In mathematics, slope is determined by dividing the change in y by the change in x. Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

Here the coordinates are (-6,0) and (0,-1)

ΔX = 0 – -6 = 6

ΔY = -1 – 0 = -1

Slope (m) =ΔY/ΔX

=-1/6

= -0.16666666666667

≈-0.167

The slope for the line with the given points would be -1/6, or roughly 0.167, because the slope formula is Δy/Δx and the difference would be the same for every parallel line.

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Given:

Let's factor using synthetic division.

Equate the divisor to zero:

x - 5 = 0

x = 5

List all terms of the polynomial: 1, -7, 2, 40

Palce the numbers representing the divisor and dividend into a long division-like configuration

To factor using synthetic division, we have:

Therefore, the factored expression is:

The zeros are also the roots of the polynomial.

The zeros of a polynomial are all the x-values that makes the polynomial equal to zero,

To find the zeros, equate each afctor to zero:

(x - 4) = 0

x = 4

(x + 2) = 0

x = -2

Thus, the zeros are:

x = 4, -2

ANSWER:

Solution:

Consider the following expression:

Remember that The factorial function is defined by the product:

thus, according to this definition, the given expression can be expressed as:

now, simplifying the previous expression we obtain:

we can conclude that the correct answer is:

Since the sum of angles in a triangle is 180°, it follows that;

Since line segment AB is parallel to the line segment CD, it follows from the Corresponding angles theorem that:

Therefore, The req

Step 1. We will start by making a diagram of the situation.

Since the length of the rectangle is twice the width, if we call the width x, then the length will be 2x as shown in the diagram:

Step 2. One thing that we know about the rectangle is its perimeter:

This perimeter has to be the result of the sum of all of the sides of the rectangle:

Step 3. Solve the previous equation for x.

In order to solve for x, the first step is to combine the like terms on the left-hand side:

The second step to solve for x is to divide both sides of the equation by 6:

Simplifying:

Step 4. Remember from the diagram from step 1, that x was the width of the rectangle:

and the length was 2x, so we multiply the result for the with by 2:

And these are the values for the width and the length.

Answer:

The width is 60yd

The length is 120yd

Solution

The picture below is the solution to the problem

Brief explanantion

From the data given, It is obvious that:

Minimum = 2

Maximum =

The total number of the data is 3, so the number 7th term is the median

Thus,

Median = 8

To find Q1

Q1 is between the third and fourth term

Therefore, Q1 is

Similarly, to find Q3

Q3 is between the tenth and the eleventh term

Therefore, Q3 is