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Daniel [21]
3 years ago
13

Deangelo has $7 worth of dimes and quarters in a jar. He has 7 more quarters than dimes.

Mathematics
2 answers:
Aleksandr [31]3 years ago
4 0
Deangelo has 15 dimes and 22 quarters

Hope this helps
svlad2 [7]3 years ago
3 0
D=number of dimes
q=number of quarters

let's count everything in cents
dimes are worth 10 cents
quarters are worth 25 cents

10d+25q=700
divide both sides by 5
2d+5q=140


he has 7 more quarters than dimes
q=7+d
subsitute 7+d for q in other equation

2d+5q=140
2d+5(7+d)=140
2d+35+5d=140
7d+35=140
minus 35 both sides
7d=105
divide both sides by 7
d=15

sub back

q=7+d
q=7+15
q=22


22 quarters and 15 dimes
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I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.
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Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

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Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

 of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

   represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

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(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

     is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ m = \frac{285-340}{4-0}=\frac{-55}{4}

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

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(c) The linear equation form is y = mx + c, where m is the slope and c is

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∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

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∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

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- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

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=============================================

Work Shown:

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