$\bf 32^{2c}=8^{c+7}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5\\ 8=2\cdot 2\cdot 2\\ \qquad 2^3 \end{cases}\implies (2^5)^{2c}=(2^3)^{c+7} \\\\\\ 2^{5(2c)}=2^{3(c+7)}\implies \stackrel{\textit{if the bases are the same, then so are the exponents}}{5(2c)=3(c+7)\implies 10c=3c+21} \\\\\\ 7c=21\implies c=\cfrac{21}{7}\implies c=3$

3 0

2 years ago

Read 2 more answers

Cami goes scuba diving. She descends 18 feet in 3 minutes. Which expressions represent the average rate at which Cami’s position

julsineya [31]

Answer:

6 ft/min

Step-by-step explanation:

Theres a neat trick to note; whenever you say per think of it as a fancy word for divide, because the label is always gonna be a/b (a per b)

Therefore,

the rate of feet per minute will be the feet divided by the minutes;

18 feet in 3 minutes = 18/3 ft/min

Therefore the rate is 6 feet per minute.

IF you need an explanation on what average rate implies:

Note; the word average is not prudent to answer as its extraneous, however if there was more data like "Cami descends 18 ft in 3 min and Nami descends 9 ft in 3 minutes; whats the average rate at which they descend" then you'd have to add the two rates up and divide by two.

Hope this helps :)

7 0

2 years ago

Greek architects considered a rectangle whose length was approximately 1.6 times its width to be the most visually appealing. fi

Oliga [24]

Let
x-------------> the length of a rectangle
y-------------> the width of a rectangle
we know that
x+y=130-----------> equation 1
and
x=1.6y--------------> equation 2

I substitute 2 in 1
(1.6y)+y=130-------------> 2.6y=130------------> y=130/2.6------> y=50 ft
x=1.6y--------> x=1.6*50---------> x=80 ft

the answer is
the length is 80 ft
the width is 50ft

3 0

2 years ago

Please help i need answers for my assignment

SashulF [63]

Answer:

1) $14, 2) please see explanation below 3) please see explanation below

Step-by-step explanation:

a) about $15-$1

b) Higher, because the estimate lowered the price that is being subtracted.

c) 15-1=14

Pedro has about $14 left over.

a) 3 is the closes because to solve this question you divide 100.8 by 35. The product is 2.88, thus supporting that 3 is the closes answer.

b) 8 is the closes because to solve this question you divide 49.2oz by 6. The product is 8.2.

c) 0.04 is the closes because to solve this question you divide 20 by 0.78, resulting in 0.039.

a) 2.49 times 6 = 14.88

His parents spent $14.88 on goodie bags

b) 150 divided by 8 = 18.75

His parents spent $18.75 per hour for the bounce house.

c) 14.88 + 18.75 = 33.63 and 182.53 - 33.63 = 148.90

His parents spent $148.90 on his birthday party excluding the goodie bags and bounce house

HOPE THIS HELPS <33333

-Silver

8 0

2 years ago