The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic centimeters.


A solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it is shown. The rectangular prism is 20 centimeters long, 5 centimeters wide, and 5 centimeters high. The rectangular prism-shaped-hole is 20 centimeters long, 2 centimeters wide, and 2 centimeters high.

The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The point given that lie on the line are mentioned below.

(0, 2) and (5, 8)

Then the equation of the line that passes through the points (0, 2) and (5, 8) will be given as,

(y - 2) = [(8 - 2) / (5 - 0)](x - 0)

y - 2 = (6/5)x

y = (6/5)x + 2

The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.

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Final answer:

To find the equation of the line passing through (0,2) and (5,8), we calculate the slope as 6/5 and use the y-intercept of 2 to write the equation as y = (6/5)x + 2.

Explanation:

To find an equation of the line that passes through the points (0,2) and (5,8), we need to calculate the slope and use one of the points to write the equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

First, let’s find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (8 - 2) / (5 - 0), which simplifies to m = 6 / 5. This is the slope of the line.

Now, we can use the slope and one of the points to find the y-intercept. Since the line passes through (0,2), we know that the y-intercept b is 2. Therefore, the equation of the line is y = (6/5)x + 2.

First choice: m^32n^16

Hope this helps!

Answer:

The correct answer would be m^32n^16.

Step-by-step explanation:

This is because when you have a power inside parenthesis multiplied by a power outside the parenthesis, you are simply going to multiply the numbers like so:

8 • 4 = 32

4 • 4 = 16

m^32n^16

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer:

I believe it is 7

Step-by-step explanation:

Answer:

903 1/8

Step-by-step explanation:

Just divide 7225 by 8. :) I put it in fraction form but decimal form is just 903.125. I hope this helps you out. :)

Answer:

its 903 with 1 left over

Answer:

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

Step-by-step explanation:

Succession can be understood as a sorted collection of values that respond to a general term or rule. We need to find if these numbers are in arithmetic progression or geometric progression.

In an arithmetic progression, every number is obtained as the previous number plus or minus a constant value called common difference. In a geometric progression, we get the next numbers as the previous one multiplied or divided by a constant value, called the common ratio.  

If we try to find a possible common difference between first and second terms we get:

[tex]2-(-3)=5[/tex]

If it was an arithmetic progression, third term should be

[tex]2+5=7[/tex]

Which is obviously not true. Now let's try to find a possible common ratio by dividing second by first term

[tex]r=\frac{2}{-3}=-\frac{2}{3}[/tex]

Testing our value to find the third term we get

[tex]a_3=2*(-\frac{2}{3})=-\frac{4}{3}[/tex]

Since we have more terms to test:

[tex]a_3=(-\frac{4}{3})*(-\frac{2}{3})=\frac{8}{9}[/tex]

The given value is just as predicted

The fourth term can be accurately predicted also:

[tex]a_4=(\frac{8}{9})*(-\frac{2}{3})=\frac{16}{27}[/tex]

Now we are sure it's a geometric progression, it can easily be stated the general term of the progression is

[tex]a_n=a_1*r^n \ n>=0[/tex]

[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]

Answer:

Step-by-step explanation:

B :because 11 pound in Ounces is 176

Answer:

6 units long.

Step-by-step explanation:

Given:

A polygon drawn on a graph.

In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.

Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.

Coordinates of A are [tex](x_1,y_1)=(-3, 4)[/tex] as seen in the graph.

Coordinates of B are [tex](x_2,y_2)=( 3, 4)[/tex] as seen in the graph.

Now, distance formula  for two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units[/tex]

Therefore, the horizontal line at the top is 6 units long.

Answer:

6 units long

Step-by-step explanation:

brainly patrol what is wrong with that

Answer:

exactly one

Step-by-step explanation:

1. subtract 2x from the equation 2x + y = 1

2. now you should have y= -2x + 1

3. then on the second equation subtract 4x from 4x + 2y = 2

4. now you should have 2y = -4x + 2

5. divide everything by 2

6. now you should have y = -2x + 1

7. since you got an exact answer on both of them then it is exactly one

There are 27 purple marbles

Step-by-step explanation:

Let p be the purple marbles

and

w be the white marbles

Then according to given statements

[tex]p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2[/tex]

Putting p = 4w-1 in equation 1

[tex]4w-1 +w = 34[/tex]

Adding one on both sides

[tex]5w-1+1 = 34+1\\5w = 35[/tex]

Dividing both sides by 5

[tex]\frac{5w}{5} = \frac{35}{5}\\w = 7[/tex]

Putting w = 7 in equation 2

[tex]p = 4(7)-1\\p = 28-1\\p = 27[/tex]

Hence,

There are 27 purple marbles

Keywords: Linear equation

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the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]

To find the fewest number of cars the employee must wash, we need to determine the minimum number of cars that will allow her to have at least $100 in spending money after saving $50.

Let's denote the number of cars she must wash as( x \).

Given:

- Earnings per car washed: $12

- Amount saved: $50

- Desired spending money: at least $100

Step 1: Calculate her earnings from washing cars:

The total earnings from washing cars will be ( 12x ) dollars.

Step 2: Calculate her spending money after saving:

She saves $50 of her weekly earnings, so her spending money will be her total earnings minus $50, which is \( 12x - 50 \) dollars.

Step 3: Write the inequality:

Since she wants to have at least $100 in spending money, we can write the inequality:

[tex]\[ 12x - 50 \geq 100 \][/tex]

This inequality states that her spending money after saving must be greater than or equal to $100.

Now, to solve for [tex]\( x \), we'll isolate \( x \)[/tex] on one side of the inequality.

Step 4: Solve the inequality:

[tex]\[ 12x - 50 \geq 100 \][/tex]

Add 50 to both sides:

[tex]\[ 12x \geq 150 \][/tex]

Now, divide both sides by 12:

[tex]\[ x \geq \frac{150}{12} \][/tex]

[tex]\[ x \geq 12.5 \][/tex]

Step 5: Interpret the result:

Since the number of cars washed must be a whole number (you can't wash half a car), the fewest number of cars she must wash to have at least $100 in spending money is 13.

So, the inequality representing the fewest number of cars she must wash is [tex]\( x \geq 13 \).[/tex]

The total number of college students was 17.94 million.

Step-by-step explanation:

Percentage of part time students = 34%

Number of part time students = 6.1 million

Let,

x be the total number of students

According to statement,

34% of x = 6.1 million

[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]

Dividing both sides by 0.34

[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]

The total number of college students was 17.94 million.

Keywords: percentage, division

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Answer:

place

Step-by-step explanation:

Answer:

The answer is " Place value"

Step-by-step explanation:

The place value determines the value of the digit in a number, based on its position.

A standard form number is divided into groups of three digits using commad. Each of these groups is called a period.

Answer:

Step-by-step explanation:

(0^209 + 1(209)/(209))^0 + 208

Answer:

22 people with red shirts and 10 people with yellow shirts

Answer:

[tex]\theta=205.298^o[/tex]

Step-by-step explanation:

We know

[tex]cos\theta=-.9041[/tex]

in the third quadrant [tex]180^o<\theta<270^o[/tex]

We use a scientific calculator to find the inverse cosine of -0.9041 to find

[tex]\theta=154.702^o[/tex]

Since this angle is not in the required quadrant we must find the other angle who has the same cosine. The required angle is equidistant from the found value from the 180 degrees angle, so our solution is

[tex]\theta=180^o+(180^o-154.702)=205.298^o[/tex]

===============================================

Explanation:

The x intercept is (-2,0) which is where the graph crosses the x axis.

The y intercept is (0,-6) which is where the graph crosses the y axis.

-----

Find the slope of the line through those two points

m = (y2-y1)/(x2-x1)

m = (-6-0)/(0-(-2))

m = (-6-0)/(0+2)

m = -6/2

m = -3

-----

The y intercept (0,-6) leads to b = -6

Both m = -3 and b = -6 plug into y = mx+b to get

y = mx+b

y = -3x+(-6)

y = -3x-6

-----

Now add 3x to both sides

y = -3x-6

y+3x = -3x-6+3x

3x+y = -6

-----

Lastly, multiply both sides by -2 so that the "-6" on the right hand side turns into "12" (each answer choice has 12 on the right hand side)

3x+y = -6

-2(3x+y) = -2(-6)

-2(3x)-2(y) = 12

-6x-2y = 12

which is what choice B shows.

Answer:

a^2 -6

Step-by-step explanation:

use ur basic knowing of equations

Answer:

The value of g(x) at x  = -3 is 18.

Step-by-step explanation:

Here, the given function is:

g(x) = - 5 x + 3

Now, for the value of x = -3 ,

g (-3) : Substitute the value of x  = -3 in g(x) , we get

g (-3)  =  -5 (-3) + 3

          =  15 + 3 = 18

or, g ( -3) = 18

Hence, the value of g(x) at x  = -3 is 18.

Answer:

[tex]-0.4(3x-2)+\frac{2x+4}{3}=0\ \textrm{for}\ x=4[/tex]

Step-by-step explanation:

Given:

The expression to evaluate is given as:

[tex]-0.4(3x-2)+\frac{2x+4}{3}[/tex]

The value of 'x' is 4.

Plug in 4 for 'x' in the above expression and simplify. This gives,

[tex]=-0.4(3(4)-2)+\frac{2(4)+4}{3}\\=-0.4(12-2)+\frac{8+4}{3}\\=-0.4(10)+\frac{12}{3}\\=-4+4\\=0[/tex]

Therefore, the value of the given expression for 'x' equal to 4 is 0.

The required value of the given expression is 0 when substituting the value of x = 4 into the expression.

The expression is given as follows:

-0.4(3x - 2) + (2x + 4) / 3

Let's evaluate the given expression for x = 4:

Expression = -0.4(3x - 2) + (2x + 4) / 3

Substitute x = 4 into the given expression:

Expression = -0.4(3 × 4 - 2) + (2 × 4 + 4) / 3

Expression = -0.4(12 - 2) + (8 + 4) / 3

Expression = -0.4(10) + 12 / 3

Expression = -4 + 12 / 3

Expression = -4 + 4

Expression = 0

Therefore, when x = 4, the value of the expression is 0.

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112 different area codes can be made.

Given, In a different plan for area codes, the first digit could be any number from 0 through 6 ,  

So, total 7 digits are possible for 1st place (i.e. 0 1 2 3 4 5 6)

The second digit was either 7 or 8,  

So, total 2 digits are possible for 2nd place (i.e. 7 8)

And the third digit could be any number except 0 or 6.  

So, total possible digits are 8 for 3rd place (i.e. 1 2 3 4 5 7 8 9)

With this plan, we have to find how many different area codes are possible?

[tex]\text { total possible combinations }=7 \text { possibilities for } 1 \text { st place } \times 2 \text { for } 2 \text { nd place } \times 8 \text { for } 3 \text { rd place }[/tex]

[tex]\text { Total possible area codes }=7 \times 2 \times 8=14 \times 8=112[/tex]

Hence, 112 different area codes can be made.

Answer:

Y- intercept is 5!

Answer:

x=2

Step-by-step explanation:

so if the bigger one is 16 and the other one is 4 that means you need to multiply 4 by 4 to get 16 so to find x you need to divide the 8 by 4 to find your answer

Answer:

x = 2

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x}{8}[/tex] = [tex]\frac{4}{16}[/tex] ( cross- multiply )

16x = 32 ( divide both sides by 16 )

x = 2

Answer:

see the explanation

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

The rule of the reflection of a point across the x-axis is equal to

(x,y) -----> (x,-y)

so

Verify each statement

1) Point (3,2) to (3,-2) is a reflection over the y-axis.

The statement is false

Because, is a reflection over the x-axis

A reflection over the y-axis will be

(3,2) -----> (-3,2)

2) A(1,3) to A'(-1,3) is a reflection over the y-axis

The statement is true

Answer:

Each girl gets 2/3 yd of ribbon.

Step-by-step explanation:

12 2/3=38/3

(38/3)/19

(38/3)(1/19)

(2/3)(1/1)=2/3

Answer:

V=349525.333*pi

Step-by-step explanation:

Volume of a sphere: V=(4/3)*pi*r^3 where r=radius.

r=64

V=(4/3)*pi*(64)^3=(4/3)(262144)pi=349525.333*pi

Answer:

Step-by-step explanation:

Let's first find the rate of increase for each period which is 3 months here.

According to the table at month [tex]x=0[/tex] value is [tex]2000[/tex]dollars and at month [tex]x=3[/tex] value is [tex]2012[/tex]dollars.

∴[tex]2012=2000(1+\frac{r}{100} )^1[/tex]

⇒[tex]1+\frac{r}{100} =\frac{2012}{2000}=1.006[/tex]

⇒[tex]r=0.006*100[/tex]

⇒[tex]r=0.6[/tex]%

Now the question is to find how long it will take for the investment value to increase 10 percent.

[tex]y=2000(1+0.006)^\frac{x}{3}[/tex]

[tex]2000(1+0.1)=2000(1.006)^\frac{x}{3}[/tex]

⇒[tex](1.006)^\frac{x}{3} =1.1[/tex]

⇒[tex]\frac{x}{3}=\frac{log(1.1)}{log(1.006)}[/tex]

⇒[tex]x=3(\frac{log(1.1)}{log(1.006)} )[/tex]

⇒[tex]x=47.7979126....[/tex]

∴at [tex]x=48[/tex] the value will slightly cross 10 percent increase.

Answer:

2 years ago :/

Step-by-step explanation:

Final answer:

To find the dimensions of a rectangle with an area of 24 sq. inches and a perimeter of 50 inches, we set up a system of linear equations and solve for the length and width. The dimensions are found to be either 24 inches by 1 inch or 1 inch by 24 inches.

Explanation:

The question given by a student involves finding the dimensions of a rectangle given its area and perimeter. Given the area (24 sq. inches) and the perimeter (50 in.), we can set up two equations to solve for the length and width:

Area = length imes width = 24 sq. inches

Perimeter = 2 imes (length + width) = 50 inches

We can divide the perimeter by 2 to get the sum of the length and width:

25 = length + width

Since we have two equations, this forms a system of linear equations which we can solve simultaneously. First, assume the length is the larger dimension and let us represent it by 'L' and the width by 'W'. We have:

L imes W = 24

L + W = 25

To solve for L and W, we can use substitution or elimination methods. Let's assume we solve for W in terms of L using the first equation, W = 24/L, and then we substitute it into the second equation:

L + 24/L = 25

Multiplying both sides by L to clear the fraction, we get:

L² + 24 = 25L

Then we rearrange the terms to set the equation to zero:

L² - 25L + 24 = 0

Now we can factor this quadratic equation to find the values of L:

(L - 1)(L - 24) = 0

So, L can be either 1 inch or 24 inches. If L is 24 inches, then W will be 1 inch (since 24 imes 1 = 24), and if L is 1 inch, then W will be 24 inches. Either way, the dimensions that satisfy both the area and perimeter equations are 24 inches by 1 inch.

The dimensions of the rectangle are [tex]\( {24 \text{ inches} \text{ by } 1 \text{ inch}} \)[/tex].

To find the dimensions of the rectangle, let's denote the length by l and the width by w.

Given:

1. The area of the rectangle is 24 square inches:

[tex]\[ l \cdot w = 24 \][/tex]

2. The perimeter of the rectangle is 50 inches, which gives us the equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Let's solve these equations step by step.

From the perimeter equation:

[tex]\[ 2l + 2w = 50 \][/tex]

Divide the entire equation by 2 to simplify:

[tex]\[ l + w = 25 \][/tex]

Now we have two equations:

[tex]\[ l + w = 25 \]\[ l \cdot w = 24 \][/tex]

Let's solve for l and w using substitution or elimination.

From ( l + w = 25 ), we can express l as:

[tex]\[ l = 25 - w \][/tex]

Substitute [tex]\( l = 25 - w \)[/tex] into [tex]\( l \cdot w = 24 \)[/tex]:

[tex]\[ (25 - w) \cdot w = 24 \][/tex]

Expand and rearrange the equation:

[tex]\[ 25w - w^2 = 24 \]\[ w^2 - 25w + 24 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula [tex]\( w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \)[/tex], where ( a = 1 ), ( b = -25 ), and ( c = 24 ):

[tex]\[ w = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4 \cdot 1 \cdot 24}}}}{{2 \cdot 1}} \]\[ w = \frac{{25 \pm \sqrt{{625 - 96}}}}{2} \]\[ w = \frac{{25 \pm \sqrt{{529}}}}{2} \]\[ w = \frac{{25 \pm 23}}{2} \][/tex]

So, we get two possible values for w:

[tex]\[ w = \frac{{25 + 23}}{2} = 24 \]\[ w = \frac{{25 - 23}}{2} = 1 \][/tex]

Now, find l for each value of w:

1. If ( w = 24 ):

 [tex]\[ l = 25 - 24 = 1 \][/tex]

2. If ( w = 1 ):

[tex]\[ l = 25 - 1 = 24 \][/tex]

The ratio 6 to 2 is equivalent to the ratio 3 to 1, obtained by dividing both the numerator and denominator of the ratio by their greatest common divisor, which is 2.

To find a ratio equivalent to 6 to 2, you simplify the ratio by dividing both numbers by their greatest common factor. In this case, the greatest common factor is 2, so 6 ÷ 2 = 3 and 2 ÷ 2 = 1. Therefore, the equivalent ratio is 3 to 1.

The ratio 6 to 2 can be simplified by dividing both numbers by their greatest common divisor, which is 2. Therefore, 6 divided by 2 is 3, and 2 divided by 2 is 1. This simplification shows that the ratio 6 to 2 is equivalent to 3 to 1. Ratios compare two quantities and can be expressed in several forms such as fractions, with a colon, or using the word "to". An equivalent ratio maintains the same proportional relationship between its components, just like how 6:2 has the same proportional relationship as 3:1.