Write 75 as a product of primes. Use index notation when giving your answer.

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Answer:

The volume of this composite figure is 312 cubic inches.

Step-by-step explanation:

Volume of pyramid:

[tex] \frac{1}{3} ( {6}^{2} )(5) = \frac{1}{3} (36)(5) = \frac{1}{3} (180) = 60[/tex]

Volume of rectangular prism:

[tex]12(3)(7) = 252[/tex]

Volume of composite figure:

[tex]60 + 252 = 312[/tex]

Answer: A. 15 miles.

Step-by-step explanation: Did the math 22, 33 and got A. 15 miles.

Answer:

Yes, the sequence is an arithmetic sequence

Step-by-step explanation:

Notice that each consecutive number is being added by the next odd number up:

0+3=3

3+5=8

8+7=15

15+9=24

24+11=35

We can represent this as the arithmetic sequence [tex]a_n=n(n+2)[/tex]

From the description of the function as we can see in the question, the function is a quadratic function.

The term quadratic function refers to a type of function that is obtained from the equation ax^2+ bx + c =0.

A function in which as the domain values approach infinity, the range values approach infinity and as the domain values approach negative infinity, the range values approach infinity is a quadratic function.

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Answer: 54 degrees

Step-by-step explanation:

Since AZ is tangent to circle V, it forms a 90 degree angle with the circle. If you compare XW with AZ, you can see they are perpendicular to each other. Angle W has already been found, and it's 36 degrees.

So if you subtract 90 by 36, it gives you YWZ, 54 degrees.

Answer: Slope: 3

x-intercept(s): [tex](-\frac{1}{3} , 0)[/tex]

y-intercept(s): [tex](0,1)[/tex]

The linear equation is 3x + 5y = 75. Then the value of A, B, and C will be 3, 5, and 75 respectively.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equation of a line is given as

y = mx + c

where m is the slope and c is the constant.

Then we have

y = (-3/5)x + c

The line is passing through (25, 0). Then we have

25 = c

Then we have

y = (-3/5)x + 25

On simplifying, we have

5y = -3x + 75

3x + 5y = 75

Then the value of A, B, and C will be 3, 5, and 75 respectively.

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Answer:

Based on hint and given formula, we can complete the problem. The question asks for square feet of grass so we know that we are solving for the area, A. It also tells us the height (looking downward) of the field is 75 ft,h, while the two bases are 125 ft and 81 ft (b1 and b2). So we can solve the equation. A = 75((125+81)/2) A = 75(206/2) A = 75(103) A = 7725 The area of the field is 7725 square feet.

Step-by-step explanation:

The equivalent equations of the trapezoid are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The formula for the area of a trapezoid can be rearranged in different ways to express the same relationship between the height, the bases, and the area.

Here are a few equivalent equations:

h = 2A / (b₁ + b₂) (solve for h)

b₁ = 2A / h - b₂ (solve for b₁)

b₂ = 2A / h - b₁ (solve for b₂)

A = (b₁ + b₂) x h / 2 (multiply both sides by 2 and divide by h)

These equations can be used interchangeably to calculate the area, height, or base of a trapezoid, depending on which variables are known or given.

Thus,

The equivalent equations are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

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Answer:

Step-by-step explanation:

(-3*4)^2 = (-12)^2 = 144

Answer:

22/24-18/24

Step-by-step explanation:

Convert each low number to the factor
1/3 * 4 = 4/12 which has the same denomanator as 7/12
And the same for 1/2 * 4 = 4/8 which has the same denominator as 2/8
Then you add both with both,
Next you convert both of them to the same denominator and the closest number will be 24 then yousubtract and voila.

Question:
(7/12+1/3)−(1/2+2/8)

Answer:

Fraction Form:
1/6

Decimal Form:

0.16

Hope this helps.

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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]

             ❖ A number y increased by 5 is at least -21.

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

          ❖ First, if you come across the word "increased" it means we

    "increase" a number, or add something to that number, like

y increased by 5 [tex]\longmapsto[/tex] [tex]\sf{y+5}[/tex]

Now, we are also given that this expression is at least -21, which means it can't be -21; it can be -21 or it can be greater than -21.

So we have

[tex]\longmapsto\sf{y+5\geq -21}}[/tex]

Solving for y

[tex]\longmapsto\sf{y\geq -21-5}[/tex]

[tex]\longmapsto\sf{y\geq -26}[/tex]

So the values of y greater than or equal to -26 will make this inequality true.

 [tex]\rule{300}{1}[/tex]

Answer:

y >= - 26

Step-by-step explanation:

your equation at first looks like this

y + 5 >= -21

then you subtract 5 to both sides

y >= -26

Answer:

The answer is option C

Step-by-step explanation:

The solution is in the image

Answer: 68850

Step-by-step explanation:

interest = 765000(3/100x3)

= 68850

if your finding total cost add 765000 + 68850 = 833850

The rate of change of the linear function whose graph passes through points (-5, -2) and (-2, 6) is: 2.7.

The rate of change of a linear function is given as change in y over change in x.

Given the points:

(-5, -2) and (-2, 6)

Change in y = 6 -(-2) = 8 units

Change in x = -2 -(-5) = 3 units

Rate of change = 8/3 = 2.7.

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Answer: 43

Step-by-step explanation: subsitute -2 into x

4(-2)^2 - 7(-2) + 13 = 43

Answer: [tex]\frac{7}{16}[/tex]

Step-by-step explanation: Distance to school = [tex]\frac{7}{10}[/tex] mile

Distance covered = [tex]\frac{5}{8}[/tex] of [tex]\frac{7}{10}[/tex]

                      = [tex]\frac{5}{8}[/tex] x [tex]\frac{7}{10}[/tex]

                       = [tex]\frac{35}{80}[/tex]

                      = [tex]\frac{7}{16}[/tex]

The equation of the circle is given as (x-h)² + (y-k)² = r². Then the value of y will be ± √5/3.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h, k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The equation of the circle has the center at the origin and the radius is one unit. Then we have

x² + y² = 1

The point P = (-2/3, y) lies on the unit circle. Then the value of y will be

(-2/3)² + y² = 1

y² = 1 - 4/9

y² = 5/9

y = ± √5 / 9

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Answer:

Its a linear function as there is a common difference of -9.

Step-by-step explanation:

x  y      Difference

1   4    

2  -5      -9

3 -14      -9

4 -23     -9

5 -32     -9

For a difference in x of we have a difference in y  of -9.

Answer:

  23.6 ft

Step-by-step explanation:

In the right triangle, an acute angle, the hypotenuse, and an adjacent side are marked. We went to know the length of the adjacent side. The trig relation involved is ...

  Cos = Adjacent/Hypotenuse

__

Filling in the given information, this relation tells us ...

  cos(29°) = x/(27 ft)

Solving for x, we get ...

  x = (27 ft)cos(29°) ≈ 23.614 ft

The value of x is about 23.6 ft.

Considering the definition of probability,  the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]

The multiplication rule or product rule allows you to find the probability that event A and event B occur at the same time.

Two events A and B are dependent if the occurrence of one affects the occurrence of the other. For dependent events, the multiplication rule states that:

P(A∩B)= P(A)× P(B|A) (where P(B|A) indicates “the probability of ‘B’ having occurred ‘A’)

In this case, you know:

The probability that the first movie selected is an comedy movie and the second movie is a action film.

Once the first movie is selected, there are no longer 6 movies available. There are only 5, because one of the options is eliminated. So the occurrence of the first event affects the second event and the events are dependent.

Then, the probabilty can be calculated A:

Probability= [tex]\frac{3}{6}[/tex]× [tex]\frac{3}{5}[/tex]

Probability= 0.3= 30%

Finally, the probability that the first movie selected is an comedy movie and the second movie is a action film is 30%.

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Answer:

x= 3

x= -2

Step-by-step explanation:

x^2-x=6

x^2-x-6=0

find which 2 numbers when multiplied give -6 and

when added give -1

they are -3 and 2

(x-3)(x+2)

x= 3

x= -2

Answer:

[tex]2\frac{1}{5}[/tex]

Step-by-step explanation:

The 11 gals of water are equally split up into 5 tanks, so divide 11 by 5.

[tex]\frac{11}{5}[/tex] then simplifies into [tex]2\frac{1}{5}[/tex]

Answer: On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the right of the line is shaded.

Step-by-step explanation:

x = # of stools = 20

y = # of recliners = 50-20 = 30

Answer:

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

Answer:

values

x=17

AT = 49 units

OG = 21 units

Answer:

The second one is the correct answer

Step-by-step explanation:

There are more mammals on the list than birds and fish combined.

Answer:

x = 15

∠AOB = 15°

∠BOC = 165°

Step-by-step explanation:

Angles on a straight line add up to 180°

[tex]\sf \implies \angle AOB + \angle BOC=180[/tex]

Substitute the given expressions for the angles:

[tex]\sf \implies (2x - 15) + 11x = 180[/tex]

Collect and combine like terms:

[tex]\sf \implies 2x +11x- 15=180[/tex]

[tex]\sf \implies 13x- 15=180[/tex]

Add 15 to both sides:

[tex]\sf \implies 13x- 15+15=180+15[/tex]

[tex]\sf \implies 13x=195[/tex]

Divide both sides by 13:

[tex]\sf \implies \dfrac{13x}{13}=\dfrac{195}{13}[/tex]

[tex]\sf \implies x=15[/tex]

Now substitute the found value of x into the expressions for each angle:

[tex]\sf \implies \angle AOB =2(15)-15=15^{\circ}[/tex]

[tex]\sf \implies \angle BOC =11(15)=165^{\circ}[/tex]

Using the distance formula, each side of the park is 13 units long

The vertices of the park are given as:

(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).

The length of each side is calculated using the following distance formula:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Using any consecutive points, we have:

[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]

Hence, each side of the park is 13 units long

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Answer:

(6.5,-6)

Step-by-step explanation:

(7+6)÷2= 6.5

(-5+-7)÷2=-6