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Sauron [17]
3 years ago
14

A jar containing only dimes and quarters contains a total of 54 coins. The value of all the coins in the jar is $9.15. Solve by

elimination to find the amount of dimes and quarters that are in the jar.
Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

Answer: the jar contains 29 dimes and 25 quarters.

Step-by-step explanation:

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

The worth of a quarters is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

Let x represent the number of dimes contained in the jar.

Let y represent the number of quarters contained in the jar.

A jar containing only dimes and quarters contains a total of 54 coins.. This means that

x + y = 54

The value of all the coins in the jar is $9.15. This means that

0.1x + 0.25y = 9.15 - - - - - - - - - - - 1

Substituting x = 54 - y into equation 1, it becomes

0.1(54 - y) + 0.25y = 9.15

5.4 - 0.1y + 0.25y = 9.15

- 0.1y + 0.25y = 9.15 - 5.4

0.15y = 3.75

y = 3.75/0.15 = 25

x = 54 - y = 54 - 25

x = 29

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The function g(x) = p sin x +q, where p>0, has a maximum value of 10 and a minimum value of -4. Find the value of p and of q.
tester [92]

Answer: p=7, q=3

Step-by-step explanation:

The midline of the function is

\frac{10-4}{2}=3 \implies q=3

This means that to obtain a maximum of 10, when \sin x reaches it's maximum, 1, g(x)=p+q=10 \implies p=7

7 0
2 years ago
At the store, you buy a backpack for $30.42, a binder for $9.89 and a combination lock for $5.75. If you give the cashier $50.00
Shkiper50 [21]

Answer:

$3.94

Step-by-step explanation:

$30.42 + $9.89 + $5.75 = £46.06

$50.00 - $46.06 = $3.94

7 0
3 years ago
Read 2 more answers
what are the coordinates of the orthocenter of △ABC with vertices at A(1, 2), B(1, 6), and C(5, 6)?
iren2701 [21]
(1,6)
This should help for future problems
<span>https://www.mathportal.org/calculators/analytic-geometry/triangle-calculator.php</span>
6 0
3 years ago
Read 2 more answers
13.
Artist 52 [7]

Answer:

5 units

Step-by-step explanation:

An isosceles triangle is a triangle with two legs that have the same length. The perimeter of a triangle is the sum of the lengths of all sides of the triangle. Now taking this into account, we know that:

2L + B = 14 units

Where:

L is the measure of one leg

B is the measure of the base

Since two legs are the same and the base is 1 less, this means the measure of each leg would be:

B = L -1

Now we have two equations:

2L + B = 14 units

B = L- 1

We plug one equation into the other and make 1 equation:

2L + (L-1) = 14 units

Get rid of the parentheses:

2L + L - 1 = 14

Combine like terms:

3L - 1 = 14

Add 1 to both sides of the equation:

3L - 1 + 1 = 14 + 1

3L = 15

Divide both sides by 3:

3L/3 = 15/3

L = 5

So the length of a leg is 5 units

Let's check!

B = L - 1

B = 5 - 1

B = 4

Then we use that to solve for the perimeter:

2L + B

2(5) + 4

10 + 4 = 14

7 0
3 years ago
Explain how to use the vertex and the value of “A” to determine the range of an absolute value function. PLEASE HELP!!
Thepotemich [5.8K]

Answer:

First, a absolute value function is something like:

y = f(x) = IxI

remember how this work:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that I0I = 0.

And the range of this function is all the possible values of y.

For example for the parent function IxI, the range will be all the positive reals and the zero.

First, if A is the value of the vertex of the absolute function, then we know that A is the maximum or the minimum value of the function.

Now, if the arms of the graph open up, then we know that A is the minimum of the function, and the range will be:

y ≥ A

Or all the real values equal to or larger than A.

if the arms of the graph open downwards, then A is the maximum of the function, and we have that the range is:

y ≤ A

Or "All the real values equal to or smaller than A"

5 0
3 years ago
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