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4 years ago

15

Solve each equation. check you solution. (7t - 2) - (-3t + 1) = -3(1 - 3t)

1 answer:

Lynna [10]4 years ago

5 0

(7t-2) - (-3t+1) = -3*(1-3t)
First distribute:
7t-2+3t-1 = -3+9t
Now get all the terms with 't' on the same side by subtracting/adding:
7t+3t-9t = -3+2+1
Combine the terms:
1t=0
t=0

Check:
Plug in 0 for t and see if both sides of the equation come out the same:
Does (7(0)-2) - (-3(0)+1) = -3(1-3(0)) ?
(-2) - (1) = -3(1) ?
-3 = -3 ?
Yes! It works, so t=0!

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Mars2501 [29]

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3 years ago

Shelley has a collection of dimes, nickels and quarters that is worth $5.25. There are a total of 48 coins. If there are 7 more

Mumz [18]

Answer:

25 dimes

Step-by-step explanation:

Given

Coins: Nickels (N), Quarters (Q) , and Dimes (D)

$0.05 = 1 nickel, $0.10 = 1 dime and $0.25 = 1 quarter

So, the amount implies:

$0.05N + 0.10D + 0.25Q = 5.25$

The number of coin implies:

$N + D + Q = 48$

and

$N = 7 + Q$

Required

Determine the number of Dimes

$0.05N + 0.10D + 0.25Q = 5.25$

$N + D + Q = 48$

$N = 7 + Q$

Substitute 7 + Q for N in the first and second equation

$0.05N + 0.10D + 0.25Q = 5.25$

$0.05(7 + Q) + 0.10D + 0.25Q = 5.25$

$0.35 + 0.05Q+ 0.10D + 0.25Q = 5.25$

Collect Like Terms

$0.10D + 0.25Q+0.05Q = 5.25 - 0.35$

$0.10D + 0.30Q = 4.90$ ----- (1)

$N + D + Q = 48$

$7 + Q + D + Q = 48$

Collect Like Terms

$D + Q + Q= 48 - 7$

$D + 2Q= 41$

Make Q the subject

$2Q = 41 - D$

$Q = \frac{41}{2} - \frac{D}{2}$

$Q = 20.5 - 0.50D$

Substitute 20.5 - 0.50D for Q in (1)

$0.10D + 0.30Q = 4.90$

$0.10D + 0.30(20.5 - 0.50D) = 4.90$

$0.10D + 0.30*20.5 - 0.30*0.50D = 4.90$

$0.10D + 6.15 - 0.15D = 4.90$

$0.10D - 0.15D = 4.90 - 6.15$

$-0.05D = -1.25$

Solve for D

$D = \frac{-1.25}{-0.05}$

$D = 25$

<em>Hence, there are 25 Dimes</em>

4 0

3 years ago

Find the sum. Enter your answer in lowest terms.<br> 7/20 + 3/9

AlekseyPX

7/2+3/9=
(7+3)+(0.2+0.9)=
10+1.1=11.1

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4 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Let S = {4, 6, 8} and T = {3, 5, 7}. Use the set roster notation to write each of the following sets, and indicate the number of

allochka39001 [22]

Answer:

See explanation

Step-by-step explanation:

<u>Definition:</u> $S\times T=\{(s,t)|s\in S,\ t\in T\}$

<u>Given:</u> $S=\{4,6,8\},\ T=\{3,5,7\}$

1. Find $S\times T:$

$S\times T=\{(4,3),(4,5),(4,7),(6,3),(6,5),(6,7),(8,3),(8,5),(8,7)\}$

There are 9 elements.

2. Find $T\times S:$

$T\times S=\{(3,4),(3,6),(3,8),(5,4),(5,6),(5,8),(7,4),(7,6),(7,8)\}$

There are 9 elements.

3. Find $S\times S:$

$S\times S=\{(4,4),(4,6),(4,8),(6,4),(6,6),(6,8),(8,4),(8,6),(8,8)\}$

There are 9 elements.

4. Find $T\times T:$

$T\times T=\{(3,3),(3,5),(3,7),(5,3),(5,5),(5,7),(7,3),(7,5),(7,7)\}$

There are 9 elements.

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3 years ago