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3 years ago

How many different ways can you make 50 cents if you have 1 quarter, 5 dimes, and 10 nickels?

Mathematics

1 answer:

german3 years ago

5 0

Answer: There are 10 different ways!

Explanation:

You need to find non-negative numbers N, D, and Q so that:

5N + 10D + 25Q = 50

N + 2D + 5Q = 10

Q = 0 , 1 , 2

If Q = 1, then you have:

N + 2D = 5

Q = 1 , D = 2 , N = 1

Q = 1 , D = 1 , N = 3

Q = 1 , D = 0 , N = 5

N + 2D = 10

This gives the last solutions:

Q = 0 , D = 5 , N = 0

Q = 0 , D = 4 , N = 2

Q = 0 , D = 3 , N = 4

Q = 0 , D = 2 , N = 6

Q = 0 , D = 1 , N = 8

Q = 0 , D = 0 , N = 10

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Question 8 The product of – x2 + 5x – 1 and a monomial is 4x2 20x + 4. What is the monomial? ОА 4. B 4X С -4 -47

Scrat [10]

Answer: -4

Step-by-step:

-x^2+5x-1 x _ = 4x^2-20x+4

4x^2-20x+4 / -x^2+5x-1

In the blank the answer would be -4 which is the monomial.

6 0

3 years ago

Write an equation that goes through (8,1) and is perpendicular to 2y + 4x =12

Serggg [28]

Answer:

2y -x + 6 = 0

Step-by-step explanation:

Here a equation and a point is given to us and we are interested in finding a equation which is perpendicular to the given equation and passes through the given point .

The given equation is ,

$\sf \longrightarrow 2y + 4x = 12 \\$

$\sf \longrightarrow 4x + 2y = 12$

Firstly convert this into slope intercept form , to find out the slope of the line.

$\sf \longrightarrow 2y = -4x +12\\$

$\sf \longrightarrow y =\dfrac{-4x+12}{2}\\$

$\sf \longrightarrow y =\dfrac{-4x}{2}+\dfrac{12}{2}\\$

$\sf \longrightarrow \red{ y = -2x + 6 }$

Now on comparing it to slope intercept form which is y = mx + c , we have ,

m = -2

And as we know that the product of slopes of two perpendicular lines is -1 . So the slope of the perpendicular line will be negative reciprocal of the slope of the given line. Therefore ,

$\sf \longrightarrow m_{\perp}=\dfrac{-1}{-2}=\red{\dfrac{1}{2}}$