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3 years ago

Write 2 equationsand show your workPLZ HELP ME ASAP I NEED HELP

Mathematics

1 answer:

Grace [21]3 years ago

7 0

<h2>Explanation:</h2><h3>Part A.</h3>

You are asked to define variables that "model the situation" without being told what you care about in the situation. For that purpose, the variables you have chosen, ...

d = number of coins
q = their total value

are completely appropriate. Your choice will give rise to two equations, already solved:

d = 90 . . . . . . . . the equation for the amount of coins
q = 17.55 . . . . . . the equation for the value of the coins

___

However, that is not going to be helpful for Part B.

In Part B, you're asked for the <em>number of quarters</em>. You might expect that choosing a variable to represent this quantity would be helpful, and you'd be right. For a variety of reasons, choosing another variable to represent the <em>number of dimes</em> is also helpful. Now, we have the definitions

let q = the number of quarters in Dylan's bank
let d = the number of dimes in Dylan's bank

The corresponding system of equations is ...

q + d = 90 . . . . . the number of coins Dylan has
0.25q +0.10d = 17.55 . . . . the value of the coins Dylan has

_____

Since you're only interested in the number of quarters, it can be convenient to choose a solution method that focuses only on the q variable. Here, we'll multiply the first equation by -0.10 and add the result to the second equation. That eliminates d and gives an equation only in q.

-0.10(q +d) +(0.25q +0.10d) = -0.10(90) +(17.55)

0.15q = 8.55 . . . . . simplify

8.55/0.15 = q = 57 . . . . . . divide by the coefficient of q to find the solution

Dylan has 57 quarters in his bank.

=====

<em>Comment on "this situation" problems</em>

As you have discovered, modeling a particular "situation" needs to be informed by the aspect(s) of the situation that you care about. Many modern math texts ask for a model of "this situation" without bothering to tell you that crucial piece of information.

I find it unfortunate, and not particularly instructive in good critical thinking practice or problem solving technique.

Here, we found it helpful to read ahead for clues as to what the problem is really about. That will often be a helpful approach.

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Jules has 1200 and is spending 40 per week. kelsey has 400 and is saving 50 a week. in how many weeks, will jules and kelsey hav

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After x weeks:
Jules will have: 1,200 + 40 x.
Kelsey will have: 400 + 50 x.
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50 x - 40 x = 1,200 - 400
10 x = 800
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Answer: In 80 weeks they will have the same amount of money.

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3 years ago

Read 2 more answers

Solve the right triangle ABC, with Cequals90degrees. Aequals58.3degrees, cequals24.8 ft

horsena [70]

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

The hypotenuse of the triangle is b and a , c are its legs
sin(A) = $\frac{a}{b}$
sin(C) = $\frac{c}{b}$
$b=\sqrt{a^{2}+c^{2}}$
The sum of the measures of the two acute angles A and C is 90°

∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = $\frac{a}{c}$

∵ c = 24.8 feet

∴ sin(58.3) = $\frac{a}{24.8}$

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = $\frac{b}{c}$

∵ c = 24.8 feet

∴ sin(31.7) = $\frac{b}{24.8}$

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Learn more:

You can learn more about solving the triangle in brainly.com/question/12985572

#LearnwithBrainly

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3 years ago

Solve the equation by completing the square m^2+6m-77=-5

Grace [21]

Maybe you thought about this:
m^2+6m-77+5=0 => m^2+6m-72=0 => m^2+ 2*3*m+3^2-3^2-72=0
=> m^2+2*3*x+3^2= (m+3)^2 this is the complete square of the binomial, we will still keep it =>
(m+3)^2 -9 -72=0 => (m+3)^2 - 81 = 0 => (m+3)^2 - 9^2 = 0
Now we got the difference squares, it mean a^2 - b^2 = (a-b) (a+b)
In according to this => (m+3-9) (m+3+9) = 0 =>
(m-6) (m+12)=0 => m-6=0 or m+12=0 => m1=6 or m2= -12 !!!!
Are you satisfied with this solution?

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