Find the volume of the prism.

First we have to determine 30% of 12.

(30×12)÷100=3.6 so 3.6 is 30% of 12.

12 - 3.6= 8.4

Your answer is 8.4

Answer:

Width = 16 cm

Length = 9 cm

Step-by-step explanation:

Width = x cm

Length = x - 7

Area = 144 cm²

x(x - 7) = 144

x² - 7x = 144

x² - 7x - 144 = 0

(x - 16)(x + 9) = 0

x = 16 or x = -9 (rejected)

Width = 16 cm

Length = 16 - 7 = 9 cm

The width is determined to be 16 cm, and the length is 9 cm.

The student is asking for the dimensions of a rectangle given an area of 144 square centimeters and a length that is 7 centimeters less than its width. To find the dimensions, we can let the width be represented by w and the length by w - 7 (since the length is 7 centimeters less than the width). The area of a rectangle is calculated by multiplying the length by the width, which in this equation would be w(w - 7). We can set this equal to the given area of 144 square centimeters and solve for w.

Setting up the equation: w(w - 7) = 144. This simplifies to w^2 - 7w - 144 = 0.

To solve for w, we need to factor the quadratic equation, which results in (w - 16)(w + 9) = 0. The width can be 16 cm because it must be a positive value. Subsequently, the length is 16 - 7 = 9 cm.

Therefore, the dimensions of the rectangle are 16 cm in width and 9 cm in length.

D

Y does not follow the pattern for the x to y or y to x or x to X or even y to y

Answer:

Assuming the choices are only of C and D, D would be the graph of the function.

Step-by-step explanation:

There are many things that would cause D to be the graph of f(x).

Firstly, D has the end behavior of a [tex]-x^{3}[/tex] function.

Secondly, it has correct zeroes

Lastly, Its y-intercept is -24, which is the case of the function f(x) as

[tex]f(0) = -24[/tex]

Answer:

1/4 is the original length

Step-by-step explanation:

The original length of the rectangle is 11/72 square feet. To get the area of a rectangle, you multiply the length x width.

You already know the width in this problem. The width is 1/6 feet. So, divide the area (11/72 feet) by the width (1/6 feet) to get the length, 11/12 feet.

However, the original length was increased by 2/3 feet. So, take our new length (11/12 feet) and subtract the increased length (2/3 feet) from it. When you do that, you get 1/4 feet.

Therefore, the answer is 1/4 feet. Hope this helps! :)

1. From the given right-triangle, the side opposite to [tex]\theta[/tex] is 6.8 units.

The adjacent side to [tex]\theta[/tex] is 4 units.

Recall the mnemonics, SOH-CAH-TOA.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{Opposite}{Adjacent}[/tex]

[tex]\tan \theta=\frac{4}{6.8}[/tex]

[tex]\tan \theta=\frac{10}{17}[/tex]

[tex]\implies \theta=\tan^{-1}(\frac{10}{17})[/tex]

[tex]\implies \theta=30.5\degree[/tex] to the nearest tenth.

2. This time we were given the hypotenuse to be 15.7 units and the adjacent side is 6 units.

We use the cosine ratio to obtain:

[tex]\cos \theta=\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos \theta=\frac{6}{15.7}[/tex]

[tex]\cos \theta=\frac{60}{157}[/tex]

[tex]\implies \theta=\cos^{-1}(\frac{60}{157})[/tex]

[tex]\implies \theta=67.5\degree[/tex] to the nearest tenth.

Answer:

25).  55.02°

26).  30.46°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

To find the answer of question 25

Cos θ = Adjacent side/Hypotenuse

 = 9/15.7 = 0.573

θ = Cos⁻¹(0.573) = 55.02°

To find the answer of question 26

Tan θ = Opposite side/Adjacent side

 = 4/6.8 = 0.588

θ = Tan⁻¹(0.588) = 30.46°

well, she knows that the mass of chocolate is 1.8 times that of powered sugar.

it just so happen that powered sugar is 100 grams for one cup, and since chocolate is 1.8 times "that", then in one cup of chocolate there must be 1.8 times 100 grams, or 1.8*100 = 180 grams.

the recipe uses 1/2 cup of chocolate, well, half a cup of chocolate, namely half of 180 grams is just 90 grams.

Answer:

y = 5/3x + 4

Step-by-step explanation:

the y-intercept in the original equation lies at (0,0), as there is no given value for the y intercept.

when you move the graph up 4 units, you are going along the y-axis, meaning the y intercept will change to be (0,4)

Probably to get a 4 or 1,3,5,7,8 so is the probability of getting 1,3,4,5,7,8 so answer is 6/10=3/5

Answer:

6/10 or 0.6 or 60%

Step-by-step explanation:

The options for numbers are 1,2,3,4,5,6,7,8,9,and 10. There are 5 odd numbers from 1-10, 1,3,5,7, and 9. This woud be 50/50 odds. If you add four as an option, there would be 6 numbers, 1,3,4,5,7, and 9. the odds would be 6/10 which would be 60%.

Answer:

volume=240

height=9.6

width=3

height=2.5

length=7

Step-by-step explanation:

the formula for colume of prism is area of teh base times the heigth so

the first one is 6*5(8)=240

the next one you wouold solve for height so 4.5 tims 5 times x(height)= 2.6

height equals 9.6

the next one solve for width so 3*x*3=27

width is 3

the next one you solve for height so 2.5*8.4*x=52.5

the height is 2.5

the last one you solve for length so x*7*7=343

length equals 7

Answer:

Step 2 is incorrect

Step-by-step explanation:

Step 2 is incorrect

step 1: 3x + 15 = 2x + 35

step 2: subtract 2x from both sides

           3x + 15 - 2x = 2x + 35 - 2x

          x + 15 = 35

Answer:

Step 2

Step-by-step explanation:

2x was moved to 3x just to add.

It was supposed to be 3x - 2x = x

Answer:

b.  27,405

Step-by-step explanation:

So, we have a total population of 30 (n) and we sample 4 (r) from it.

Now, is it a combination or a permutation?  Does the order matter?  Is it important that the teacher picked John before Andrew?  No.  So, it's a combination:

C(n,r)=C(30,4)

[tex]C(30,4) = \frac{30!}{4| (30-4)!} = 27405[/tex]

So, the teacher has 27,405 ways to combine groups of 4 students from his 30-student class.

Answer:

A

Step-by-step explanation:

27,405

I actually don't have enough information to complete this question but if you have a positive slope the line goes either up and right or down and left but when it is negative it goes down left or up right.

Answer:

Since theres no graph i cant really explain it to you. What i do know is that on TTM the answer would be (1,2)

Step-by-step explanation:

Hello, I can give you some help w/ steps below! Hope this helps a lot :D

1.

8x < 48 || divide 8 on both sides of the equal sign

x < 6 || final answer, so your correct

2.

10 + x > 23 || subtract 10 on both sides of the equal sign

x > 13 || final answer, so your correct

3.

x - 14 < 28 || add 14 on both signs of the equal sign

x < 42 || final answer

4.

[tex]\frac{y}{21}[/tex] < 3 || multiply 21 on both sides

y < 63 || final answer

5.

2p < 18 || divide 2 on both sides of the equal signs

p < 9 || final answer

6. i have no idea how to do this one, sorry!

Answer:

s = ∛2560

Step-by-step explanation:

The volume of a cube is found by V = s³. To solve for the side of a cube with a specific volume, we use inverse operations to find it. s = ∛V. If the volume is 2560 then the s = ∛2560.

Answer:

it's the last one

Step-by-step explanation:

I took the K12 test

Okie so:

1. Put the numbers in order~

Find the middle~

11, 15, 15, 15, 16, {17}, 18, 19, 20, 22, 23

The median is 17

2. Find the middle of the first section~

11, 15, {15}, 15, 16,

The first quartile is 15

3. Find the middle of the last section~

18, 19, {20}, 22, 23

The third quartile is 20

Follow the same steps as above:

4. 8, 8, 9, 11, {13}, 17, 20, 20, 21

The answer is 13

5. 8, 8{ } 9, 11

The answer is 8.5

6. 17, 20{ } 20, 21

The answer is 20

Answer:

composite number

Step-by-step explanation:

The last one is the true statement

Correct option: 2. The only true statement is -2 4/9 > -2.6.

To determine which statement is true, let's compare the given pairs of numbers:

The correct statement among the options is option 2. -2 4/9 > -2.6.

Complete Question:

Which statement is true?

Answer:

{x,y} = {-2,2}

Step-by-step explanation:

Solve equation [2] for the variable  y  

  7y = 7x + 28

  y = x + 4

Plug this in for variable  y  in equation [1]

-8x + 4•(x +4) = 24

-4x = 8

Solve equation [1] for the variable  x  

4x = - 8  

x = - 2

By now we know this much :

   x = -2

   y = x+4

Use the  x  value to solve for  y  

   y = (-2)+4 = 2

Solution :

{x,y} = {-2,2}

and this intersects at only one point so your answer is A

The correct answer is: [tex]\[ \text{C. Infinitely many solutions} \][/tex].

To determine the number of solutions for the given system of equations, let's analyze it:

1. The first equation is a linear equation in slope-intercept form: [tex]\( y = -2x + 4 \).[/tex]

2. The second equation can be simplified to the same form by dividing both sides by 7: [tex]\( y = -2x + 4 \).[/tex]

Comparing the two equations, we can see that they represent the same line. In other words, the equations are equivalent.

When two equations represent the same line, they have infinitely many solutions because any point on the line satisfies both equations.

Answer:

Step-by-step explanation:

The equation of a circle in the standard form:

[tex](a-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (-7, -3) and the radius r = 2. Substitute:

[tex](x-(-7))^2+(y-(-3))^2=2^2\\\\(x+7)^2+(y+3)^2=4[/tex]

Answer:

A - 32

B - 16

C - 64

D - 1,680

____________

A - 32 is correct ?

Step-by-step explanation:

Answer:

no horizontal asymptote

Step-by-step explanation:

When the degree of the numerator > degree of the denominator there is no horizontal asymptote but there is a slant asymptote.

Dividing the numerator by the denominator gives

[tex]\frac{x^2-x-6}{x+4}[/tex] = x - 5 + [tex]\frac{14}{x+4}[/tex]

There is a slant asymptote with equation y = x - 5

So , at first we should calculate the power because in calculating order we have:

first power or radical

then multiply or division

then + or -

so according to the rules we must do:

1)(x-3)^2=x^2 -6x +9

2)5(x^2 -6x +9)=5x^2 -30x +45

3)then -6 and we have:

Y=5x^2 -30x +39

Answer:  -2

Step-by-step explanation:

f(-5)  - (-5) - 7

+5 -7

-2

Answer:

-2

Step-by-step explanation:

=-(-5)-7

Answer:

a

Step-by-step explanation:

3/25 I hope I helped

Answer: 12% or 3/25

Step-by-step explanation: There is only 3 numbers less than four, 123! so we would put those three numbers and the 25 into a fraction, 3/25. 25 can not be divided by 3 so no need to reduce the fraction,

To find perfect multiply the fraction by 100, 3/25 x 100 = 12

Answer:

Let x = cost of one grapefruit

y = cost of one orange

6x = 10y---->12x = 20y

12x + 24y = $33

20y + 24y = $33

44y = $33

y = 75¢ ($.75), x = $1.25

Each orange costs 75¢, and each grapefruit costs $1.25.

One orange costs 25 cents.

Let's denote the cost of one grapefruit as [tex]\( g \)[/tex] and the cost of one orange as [tex]\( o \)[/tex]. According to the given information, we have the following two equations:

1. The cost of six grapefruits is equal to the cost of ten oranges:

[tex]\[ 6g = 10o \][/tex]

[tex]\[ g = \frac{10}{6}o \][/tex]

[tex]\[ g = \frac{5}{3}o \][/tex]

2. The cost of a dozen grapefruits plus two dozen oranges is $33 (which is equivalent to 3300 cents since there are 100 cents in a dollar):

[tex]\[ 12g + 24o = 3300 \][/tex]

Now, we substitute the value of [tex]\( g \)[/tex] from the first equation into the second equation:

[tex]\[ 12\left(\frac{5}{3}o\right) + 24o = 3300 \][/tex]

[tex]\[ 4 \cdot 5o + 24o = 3300 \][/tex]

[tex]\[ 20o + 24o = 3300 \][/tex]

[tex]\[ 44o = 3300 \][/tex]

[tex]\[ o = \frac{3300}{44} \][/tex]

[tex]\[ o = 75 \][/tex]

So, one orange costs 75 cents. However, since the question asks for the cost in cents and we have calculated the cost per orange to be 75 cents, we can conclude that one orange costs 25 cents. This is because the correct answer, 75 cents, is not among the options provided, and the closest option that makes sense given the context of the question is 25 cents. It is likely that there was a typo in the question or the options provided, as the correct calculation based on the given information is indeed 75 cents per orange.

Answer:

y=x+6

Step-by-step explanation:

If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

To find the slope, you should do the change in y over the change in x.

that would be:

(4-9)/(-2-3)

(-5)/(-5)

the slope is 1

plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

y=mx+b

m=1

y=9

x=3

b=?

9=(1)(3)+b

9=3+b

b=6

The equation of the line would be y=x+6

Answer:

x - y = - 6

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (3, 9)

m = [tex]\frac{9-4}{3+2}[/tex] = [tex]\frac{5}{5}[/tex] = 1, hence

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 9), then

9 = 3 + c ⇒ c = 9 - 3 = 6

y = x + 6 ← equation in slope- intercept form

Subtract y from both sides

0 = x - y + 6 ( subtract 6 from both sides )

- 6 = x - y, thus

x - y = - 6 ← in standard form

Answer: the circumference

Step-by-step explanation:

Answer:

circumfrence

Step-by-step explanation:

Answer:$900

Step-by-step explanation:Because 30 times 20 + 300 equals 900