A formula for finding SA, the surface area of a rectangular prism, is
SA = 2(ab + ac + bc), where a, b, and c represent the lengths of the edges of the prism. What is the surface area of this prism if a = 12 inches, b = 6 inches, and c = 4 inches?

A. 240 in. 2
B. 248 in. 2
C. 288 in. 2
D. 258 in.2

Answer:

Option (b)

Step-by-step explanation:

Let the points represented by the given table lie on a line.

And the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Let the points lying on the line are (0, -2) and (3, -3)

Slope of the line 'm' = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{-2-(-3)}{0-3}[/tex]

m = [tex]\frac{-2+3}{0-3}[/tex]

m = -[tex]\frac{1}{3}[/tex]

y-intercept 'b' = (-2)

Equation of the line is,

y = [tex]-\frac{1}{3}x-2[/tex]

This equation matches with equation given in option (b).

Option (b) will be the answer.

Answer:

∠ BOJ and ∠BOE

Step-by-step explanation:

A central angle is an angle whose vertex is at the centre of the circle.

The 2 sides of the angle are radii from the opposite ends of an arc.

∠ BOJ and ∠ BOE are therefore central angles

Answer:

A = 35 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 10)(7)

A = 35 cm^2

Answer:

lines n and o are parallel lines

Step-by-step explanation:

Answer:

x = -2  x = 2  (irrational numbers)

Step-by-step explanation:

Answer: See below

Note: If the length and width does not match the picture, then just flip the numbers. I cannot guarantee the area is 100% correct because you did not provide a picture. If the top/bottom of the trapezoid is 27, 62, and the left/right of the trapezoid is 30, then the area below is correct. If the picture shows the opposite then but 30 into a and b.

Step-by-step explanation:

Though you did not attach a picture as described in the problem, we will have to try our best to work with what you gave us.

I am assuming the lengths are the lines on the left and right of the trapezoing and the widths are the lines on the top and bottom of the trapezoid.

A.

To find the perimeter, you add the lengths and widths.

P=30+30+27+63=150 ft

To find the area, you use the formula [tex]A=\frac{a+b}{2} h[/tex]. The a and b represent the bases or in this case, the widths.

[tex]A=\frac{27+63}{2} (24)[/tex]

[tex]A=1080 ft^2[/tex]

B.

The frame has to do with the area of the glass because the frame surrounds the outside of the glass. The surrounding of the glass would be the perimeter.

The glass would be the area because the area covers everything inside the frame.

Answer:

A: When you add all of the sides, you get 150 as the perimeter.

B: The frame has to do with the area of the glass. The frames surround the outside of the glass. This would be the perimeter. The glass would be the area.

Answer:

48 students in science

Step-by-step explanation:

Let r = students in robots club

s = students in science club

r+s = 84

s = r+12

Substitute the second equation into the first

r+(r+12) = 84

Combine like terms

2r+12 = 84

Subtract 12 from each side

2r = 84-12

2r = 72

Divide by 2

r = 72/2 = 36

We need to find s

s = r+12

s = 36+12

s = 48

There are 48 students in the science club

Answer:

first one take 1.5$ and the second one take 1.86$

Step-by-step explanation:

x + y = 3.36 --> the boys are splitting $3.36

x = 3y - .12 --> one boy received $.12 less than 3 times as much as the other

--> substitute the second equation for the x in the first equation

(3y - .12) + y = 3.36 --> combine like terms

4y - .12 = 3.36 --> add .12 to both sides of the equation

4y = 3.48 --> divide both sides by 4

y = .87

the other boy gets $0.87

substitute into x = 3y - 12

x = 3(.87) - .12

x = 2.61 - .12

x = 2.49

the first boy gets $2.49

Answer:

1/4 cup of sugar

Step-by-step explanation:

Answer:1/4

Step-by-step explanation:

1/2 divided by 2 = 1/4

Answer:

50%

Step-by-step explanation:

since talks is one side and heads is one side both together equal 100% so half aka heads would be 50%

Answer:

He started the day with 7.65

Step-by-step explanation:

Assuming at the beginning of yesterday he had a balance of x

He will be charged 34 dollars since he went negative

x- 3.75 -12.07 - 34 =-42.17

Combine like terms

x -49.82 = -42.17

Add 49.82 to each side

x -49.82+49.82 = -42.17+49.82

x = 7.65

Answer:

x=-5/2

Step-by-step explanation:

4 x^2 +20 x +25 = 0

x^2+5x=-25/4

(b/2)^2=(5/2)^2

x^2+5x+25/4=0

(x+5/2)^2=0

x=-5/2

(Hope this helps)

Answer:

12 nickels, 9 quarters, 15 dimes

Step-by-step explanation:

Let's call the number of nickels n, the number of dimes d, and the number of quarters q. Now, we can set up the following equations:

n+d+q=36

q=n-3

d=q+6

Now, we can do some substitution:

d=(n-3)+6=n+3

Plugging this into the first equation, you get:

n+(n+3)+(n-3)=36

3n=36

n=12

There are twelve nickels, meaning that there are 9 quarters and 15 dimes. Hope this helps!

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

(x - 3)(x + 9) = -27

Expand the brackets:

x^2 + 9x - 3x - 27 = -27

Simplify:

x^2 + 6x - 27 = -27

+ 27 to both sides

x^2 + 6x = 0

Factorise:

x(x + 6)

The solutions are x = 0, x = -6

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Answer: If you would like to solve (x – 3)(x + 9) = –27, you can do this using the following steps:

(x – 3)(x + 9) = –27

x^2 + 9x - 3x - 27 = -27

x^2 + 6x - 27 + 27 = 0

x^2 + 6x = 0

x * (x + 6) = 0

1. x = 0

2. x = -6

The correct result would be x = 0.

Step-by-step explanation:

Answer:

P=1440

Step-by-step explanation:

"P is 90 more than Q."

P=Q+90

"20% of P is equal to 1/3 of Q."

1/5(P)=(1/3)Q

From the first equation, we have that P=Q+90.

Thus, we can substitute any P's for Q+90's!

The second equation becomes 1/5(Q+90)=(1/3)Q

Distribute the 1/5 and 1/3 to get (1/5)Q+180=(1/3)Q

Subtract 1/5 Q from both sides.

You should get 180= (2/15)Q

Multiply both sides by 15/2 to get 1350=Q.

Given Q, we can easily solve for P.

Remember the first equation- P=Q+90

Then substitute in 1350 for Q.

So we have P=1350+90

Finally, we have P=1440

Answer:

(x-6)^(2)=y+7

Step-by-step explanation:

Answer:

[tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

Step-by-step explanation:

Given

[tex]16b^2c^{12} - 0.25[/tex]

Required

Factor Completely

Follow the steps below;

Rewrite 0.25 as a fraction

[tex]16b^2c^{12} - \frac{25}{100}[/tex]

Simplify fraction to lowest term

[tex]16b^2c^{12} - \frac{1}{4}[/tex]

Expand [tex]16b^2c^{12}[/tex]

[tex]4^2b^2c^{6*2} - \frac{1}{4}[/tex]

[tex](4bc^{6})^2 - \frac{1}{4}[/tex]

Expand [tex]\frac{1}{4}[/tex]

[tex](4bc^{6})^2 - \frac{1}{2}*\frac{1}{2}[/tex]

[tex](4bc^{6})^2 -( \frac{1}{2})^2[/tex]

From laws of product of two squares

[tex]a^2 - b^2 = (a+b)(a-b)[/tex]

So,

[tex](4bc^{6})^2 -( \frac{1}{2})^2[/tex] is equivalent to

[tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

The expression cannot be factorized any further;

Hence, the factor of [tex]16b^2c^{12} - 0.25[/tex] is [tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

Answer:

13) x=4, y=0

15) x= -3, y=1

Step-by-step explanation:

13. Label the 2 equations.

y= x-4 -----(1)

-4x -6y= -16 -----(2)

From (2): -2x -3y= -8 -----(3)

(divide by 2 throughout)

Subst. (1) into (3):

-2x -3(x-4)= -8

-2x -3x +12= -8 (expand)

-5x= -8 -12 (simplify, constant to 1 side)

-5x= -20 (simplify)

x= 4 (divide by -5 throughout)

subst. x=4 into (1):

y= 4 -4

y= 0

15. x= y -4 -----(1)

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

subst. (1) into (2):

-2(y-4) +3y= 6

-2(y) -2(-4)= 6 (expand)

-2y +8= 6

-2y= 6 -8 (bring constant to 1 side)

-2y= -2

y= 1 (divide by -2 throughout)

subst. y=1 into (1):

x= 1 -4

x= -3

Answer:

7(14)-11=87

2(14)-3=25

5(14)-2=68

Step-by-step explanation:

Ight Homie, lemme help you out.

To start, add (7x-11) + (2x-3) + (5x-2)

That should get you (14x-16)

Then set up the equation

14x-16=180

180 is the sum of the triangle angles. (if i said that right)

Then solve for x

14x-16=180

     +16   +16

14x=196                Divide

((14x)/14)=196/14

x should equal 14.

Then replace x with 14

7(14)-11=87

2(14)-3=25

5(14)-2=68

I hope this helps. Stay safe Homie!

Answer:

1017.8

Step-by-step explanation:

the area of the circle is A = pi r^2

Solution,

P={7,8,12,19}

Q={12,15,17,19}

P U Q={7,8,12,19} U { 12,15,17,19}

={ 7,8,12,15,17,19}

P-Q={7,8,12,19}-{12,15,17,19}

={7,8}

Hope it helps

Good luck on your assignment

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The Answer To Your Question Is:

A

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Answer:

A

Step-by-step explanation:

Thats the correct definition

Answer:

1

Step-by-step explanation:

7x-1+2x-1=7

9x=9

x=1

Answer:

x=1

Step-by-step explanation:

RS + ST = RT

7x-1 + 2x-1 = 7

Combine like terms

9x-2 = 7

Add 2 to each side

9x-2+2 = 7+2

9x= 9

Divide by 9

9x/9 = 9/9

x = 1

Answer:

x = 20

KPL =  64

JPL =  116

Step-by-step explanation:

A linear pair adds to 180 degrees

2x+24  + 4x+ 36 = 180

Combine like terms

6x+60 = 180

Subtract 60 from each side

6x = 120

Divide by 6

6x/6 = 120/6

x = 20

KPL = 2x+24 = 2*20+24 = 40+24 = 64

JPL = 4x+36 = 4*20 +36 = 80+36 = 116

KPL = 64

x = 20

JPL =  116

Step-by-step explanation:

Linear = 180

2x+24  + 4x+ 36 = 180

Must combine like terms ( 2x and 4x)

6x+60 = 180

Isolate x by subtracting 60

6x = 120

Divide by 6 to simplify

6x/6 = 120/6

x = 20

KPL = 2x+24 = 2*20+24 = 40+24 = 64

JPL = 4x+36 = 4*20 +36 = 80+36 = 116

Answer:

Addition

Step-by-step explanation:

The first step in solving 4x-3=5 is to add 3 to both sides. This demonstrates the addition property of equality, since adding a number to both sides of an equation balances it.

Answer:

none because there is no 7

Answer:

6

Step-by-step exp

Answer:

6

Step-by-step explanation: