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castortr0y [4]
3 years ago
14

A collection of dimes and quarters has a total value of five dollars and contains 29 coins. How much of each kind of coin are th

ere in the collection.
Mathematics
1 answer:
Feliz [49]3 years ago
4 0

Answer:

15 dimes and 14 quarters.

Step-by-step explanation:

Let q represent number of quarters and d represent number of dimes.

We have been given that a collection of dimes and quarters contains 29 coins. We can represent this information in an equation as:

q+d=29...(1)

q=29-d...(1)

We know each dime is worth $0.10 and each quarter is worth $0.25.

We are also told that the total value of coins is $5. We can represent this information in an equation as:

0.25q+0.10d=5...(2)

Upon substituting equation (1) in equation (2), we will get:

0.25(29-d)+0.10d=5

7.25-0.25d+0.10d=5

7.25-0.15d=5

7.25-7.25-0.15d=5-7.25

-0.15d=-2.25

d=\frac{-2.25}{-0.15}

d=15

Therefore, there are 15 dimes in the collection.

Upon substituting d=15 in equation (1), we will get:

q=29-d\Rightarrow 29-15=14

Therefore, there are 14 quarters in the collection.

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Can a chord also be classified as a radius?
klemol [59]
No.

A chord is a straight segment that joins two points of the circumference. It starts at a point in the circumference and ends at other point in the circumference.

The radius goes from the center of the circle (which is not on the circumference) to one point of the circumference.

The diameter is a chord (the largest chord possible); but not the radius.
5 0
3 years ago
Read 2 more answers
The Kellys are saving up to go on a family vacation in 2 years. They invest $3200 into an account with an annual interest rate o
ryzh [129]

Answer:

$3,273.14

Step-by-step explanation:

-We first calculate the effective interest rate of 1.13% compounded daily:

i_m=(1+i/m)^m-1\\\\=(1+0.0113/365)^{365}-1\\\\=0.011363909

#Now, we calculate the compounded amount after 2 years using this rate:

A=P(1+i)^n\\\\=3200(1.011363909)^2\\\\\\=3273.14

Hence, the compounded amount after 2 years is $3,273.14

6 0
2 years ago
You are fundraising for the schools track team by selling clothing. The first day, you sell 13 t-shirts and 17 pairs of shorts f
Anastasy [175]

Answers:

one t-shirt costs  $10

one pair of shorts costs  $15

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

Explanation:

x = cost of one t-shirt

y = cost of one pair of shorts

13x+17y = 385 is the first equation because 13x represents the money you get from selling 13 shirts, and the 17y represents the amount you get from selling 17 shorts. The total 13x+17y is given to be $385

The second equation is 13x+12y = 310 for similar reasoning, but this time you sell 12 shorts this time and you get $310 in revenue.

The system of equations we have is:

\begin{cases}13x+17y = 385\\13x+12y=310\end{cases}

There are a few ways to solve this system. Possibly the quickest method is to note that the 13x shows up twice, so we can subtract straight down to eliminate the x terms

So,

  • 13x-13x becomes 0x or just 0, and the x terms go away.
  • 17y-12y becomes 5y
  • 385-310 becomes 75

After those three subtractions, we have the equation 5y = 75 which solves to y = 15 after dividing both sides by 5. This means the cost of one pair of shorts is $15

Plug this y value into any equation involving x and y, and solve for x

13x+17y = 385

13x+17(15) = 385

13x+255 = 385

13x = 385-255

13x = 130

x = 130/13

x = 10

Therefore, each t-shirt costs $10

-----------------

To help verify the answer, plug (x,y) = (10,15) into each equation. We should end up with a true result after simplifying both sides.

Start with the first equation

13x+17y = 385

13(10)+17(15) = 385

130+255 = 385

385 = 385

We get a true result which confirms the first equation.

Repeat for the second equation.

13x+12y = 310

13(10)+12(15) = 310

130+180 = 310

310 = 310

Both equations are true so (x,y) = (10, 15) has been fully confirmed.

6 0
2 years ago
At the market, 2.4 pounds of carrots cost $1.68 and 1.8 pounds of broccoli cost $1.53. How much more does 1 pound of broccoli co
Greeley [361]

For calculating that, you have to find the unit rate first;

2.4 pound carrot = $1.68

1 pound carrot = $1.68/2.4 = $0.7

1.8 pound broccoli = $1.53

1 pound broccoli = $1.53/1.8 = $0.85

So, it would be = $0.85 - $0.7 = $0.15

SO, YOUR ANSWER IS $0.15

5 0
3 years ago
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statemen
xeze [42]
Hey there!

It seems your problem is simply trying to rewrite the sentence.

Let's rewrite our sentence, from the phrase after the comma to the phrase before the comma.
Essentially, we are just flipping the sentence structure.

It should be this:
The two angles are complementary if the sum of the two angles are 90 degrees.

Let's take a good look at our answers.

A.) There are two angles.
While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.

B.) The sum of two angles is 90 degrees.
This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.

C.) The angles are complementary.
This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.

D.) Angles are complementary if their sum is 90 degrees.
This is an accurate statement, and provides details to support it's claim, also rewriting the original sentences into one properly. This answer choice is correct.

Your answer is D.)

I hope this helps!
8 0
3 years ago
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