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2 years ago

Evaluate: 2a + 7b for a = 5 and b = 3

Mathematics

2 answers:

Schach [20]2 years ago

7 0

Answer:

Step-by-step explanation:

Substitute the values for the variables.

$2(5)+7(3)\\10+21\\31$

jonny [76]2 years ago

3 0

hello,

substitute in the numbers

2(5) + 7(3)

10 + 21

= 31

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A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

6 0

3 years ago

Help!! It's question 14

Leona [35]

Answer:

200/120 = 5/3

5/3 x 3 = 5 oz

you can also do it this way:

3/120 = x/200

x = 600/120 = 5

5 0

3 years ago

A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits on

egoroff_w [7]

Answer: The probability that the number made up of the first two digits on the clock is less than 25 is 1.

Step-by-step explanation:

The probability of an event is a number which describe the chances of the event will happen.

We know that on digital clock, the first two digits always show as number less that 25.

Therefore, the event that the number made up of the first two digits on the clock is less than 25 is certain. [Since An event that is certain to happen has a probability of 1.]

Hence, the probability that the number made up of the first two digits on the clock is less than 25 is 1.

4 0

3 years ago

Really Easy, Help pleaseee

Dima020 [189]

1 minute = 0.25km

Step-by-step explanation:

divide both numbers that were given by 8. 8÷8 is 1 and 2÷8 is 0.25.

5 0

2 years ago

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Can someone explain 15-20? I really need help and it's due tomorrow. Thank you in advance!

zubka84 [21]

15-20 is -5. If you put 15 on a number line and go back twenty spaces you land on -5 hope this helps.

7 0

3 years ago

Read 2 more answers