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3 years ago

Which expression is exactly equivalent to 5a + 3b + 4 + 7a + 9 ?

Mathematics

2 answers:

Cloud [144]3 years ago

7 0

Answer:

Step-by-step explanation:

5a+3b+4+7a+9=

=12a+3b+13

allsm [11]3 years ago

6 0

Expression 2
12a+3b+13

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1The volumes of two similar prisms are 972 cm3 and 36 cm3. The surface area of the larger prism is 594 cm2.

diamong [38]

Answer:

Part 1)

The scale factor of the smaller prism to the larger prism is 3

The scale factor of the larger prism to the smaller prism is 1/3

Part 2) The surface area of the smaller prism is 66 square centimeters

Step-by-step explanation:

Part 1) What is the scale factor for the similar figures?

we know that

If two figures are similar, then the ratio of their volumes is equal to the scale factor raised to the cube

Let

z ----> the scale factor

x ---> volume of the larger prism

y ---> volume of the smaller prism

$z^3=\frac{x}{y}$

we have

$x=972\ cm^3\\y=36\ cm^3$

substitute

$z^3=\frac{972}{36}$

Simplify

$z^3=27\\z=3$

therefore

The scale factor of the smaller prism to the larger prism is 3

The scale factor of the larger prism to the smaller prism is 1/3

Part 2) What is the surface area of the smaller prism?

we know that

If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared

Let

z ----> the scale factor

x ---> surface area of the larger prism

y ---> surface area of the smaller prism

$z^2=\frac{x}{y}$

we have

$x=594\ cm^2$

$z=3$

substitute

$3^2=\frac{594}{y}$

solve for y

$y=\frac{594}{9}=66\ cm^2$

therefore

The surface area of the smaller prism is 66 square centimeters

6 0

3 years ago

The cost of a salad bar is $4 per pound graph it

Virty [35]

X y
1 = 4
2 = 8
3 = 12
4 = 16
X = pounds
y = price

3 0

3 years ago

PLEASE HELP ME !!!!

Viefleur [7K]

Answer:

y = 17/2

Step-by-step explanation:

7y − 4 = 9y + 13 − 4y

Simplify both sides of the equation.

7y - 4 = 5y + 13

Subtract 5y from both sides.

2y - 4 = 13

Add 4 to both sides.

2y = 17

Divide both sides by 2.

y = 17/2

I hope this helps! Feel free to ask any questions!

3 0

3 years ago

2(x+y)=23-2y <br>6x-7=20-5y

slavikrds [6]

Answer:

the solution is (-1/2, 6).

Step-by-step explanation:

Next time, please share the instructions.

Start by carrying out the indicated multiplication:

2x + 2y = 23 - 2y

Consolidate l ike terms: combine 2y and -2y: result: +4y on the left side:

2x + 4y = 23

Let's solve this system using elimination by substitution. Multiply 2x + 4y = 23 by -3 to obtain a -6x term:

-3(2x + 4y = 23) = -6x - 12y = -69. Now combine this result with the second equation:

-6x - 12y = -69

6x + 5y = 20 + 7

-------------------------

- 7y = -42

Dividing both sides by -7, we get y = 6. Subbing 6 for y in the 2nd equation, we get:

6x = 27 -5(6), or

6x = 27 - 30 = -3

Then x = -3/6, or x = -1/2

and the solution is (-1/2, 6).

3 0

3 years ago

Find the simple interest and the total amount after three years.

Ahat [919]

Answer:

A = $ 14,596.99

A = P + I where

P (principal) = $ 11,750.00

I (interest) = $ 2,846.99

Step-by-step explanation:

5 0

4 years ago