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nikklg [1K]
2 years ago
8

A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in

commission for selling three suits and a pair of shoes. The next week, she earned $107 in commission for selling seven suits and two pairs of shoes. How much commission does she earn for selling each suit and each pair of shoes? Solve by substitution.
Mathematics
1 answer:
ahrayia [7]2 years ago
8 0
For this one you have to make the equations. And what I like to do is write it out, like this.One Week- $473 suits 1 shoes (pairs)
Another Week- $1077 suits 2 shoes (pairs)
Then I make/choose my variables.For suits, it's going to be x.And For shoes let's do y.(Or if you would like better you can do x and y, which ever works best for you)
Now for the equations:One Week,   47= 3x +1yAnother Week,   107= 7x + 2y
Now it's time for the Substitution! Your last problem had it easier because it was already in the form, y=mx+b, but since ours aren't we have to change it to y=mx+b.
One Week,  -0.33y + 15.67 =x Another Week,  -0.29y + 15.29 =x
Now you can use substitution. :)For y i got 9.5 or 9.50.For x, i got 12.34
So the answer is (9.5,12.34) or (12.34, 9.5)
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KatRina [158]

Answer:

y = 5

Step-by-step explanation:

1. This line is horizontal, because the y-coordinate never changes.

2. The equation for a horizontal line is y = (y-coordinate)

3. The y-coordinate is always 5, so the equation is y = 5.

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3 years ago
Multiply (5x^2 + x-4(x+2)
bagirrra123 [75]

Answer:

5x^2-3x-8

Step-by-step explanation:

So you will want this to be simplified.

expanding brackets is a great way of doing this

one you have expanded all brackets u get the answer above

:)

4 0
3 years ago
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is ce
lubasha [3.4K]
<h2>Answer:</h2>

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures 5\pi/12=75^{\circ}. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})

Finally, the exact value of the position of the rider after the carousel rotates 5\pi/12 radians is:

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

3 0
2 years ago
A computer company makes a rectangular screen with a The dimensions of the computer screen are modeled by diagonal of 20 inches.
Novosadov [1.4K]

Answer:

  x = 16

Step-by-step explanation:

The equation shown can be solved this way.

  x^2 +(x -4)^2 = 20^2

  x^2 +x^2 -8x +16 = 400

  2x^2 -8x -384 = 0

  x^2 -4x -192 = 0

  (x -16)(x +12) = 0

The positive solution is ...

  x = 16

_____

Since this makes use of the Pythagorean theorem, you've probably run across the 3-4-5 triangle. You often find scaled versions of it in algebra and geometry problems. Here, it is scaled by a factor of 4 to give a 12-16-20 triangle as half of the display screen.

The 3-4-5 triple is the only Pythagorean triple that is an arithmetic sequence. So, if the difference in side lengths is 4 and the diagonal is 5×4, you can be pretty certain that x = 4×4 and x-4 = 4×3.

6 0
2 years ago
21 POINTS!! Thank you so much!! There’s also things on my page worth lots points points as well! So if you could help with those
Art [367]

Answer:

Second one

third one

fifth one

last one

Step-by-step explanation:

Based on the x intercepts we can write

a(x+1)(x-5)

where a is some constant

solve for a by plugging in some coordinates

let's plug in (1,-8)

-8=a(1+1)(1-5)

-8= -8a

a=1

therefore the quadratic is (x+1)(x-5)

expand this

x²-4x-5

To find out where something is decreasing/increasing it's easiest to take the first derivative

x²-4x-5= 2x-4

set this equal to 0

2x-4=0

2x=4

x=2

Which means that our two intervals are

(-∞,2)U(2,∞)

plug in any values in the intervals to see whether or not the function is increasing/decreation

Let's plug in 0 for (-∞,2)

2(0)-4

-4

It's negative so it's decreasing on this interval

DO the same thing with the other one

let's plug in x=3

2(3)-4

2

this is positive so it's increasing on this interval

Go back to the critical value of x=2 and plug this into the equation to find the max/min

(2+1)(x-5)= -9

This is a minimum because the cofeccient for the degree is positive

For the limit one notice that we have a positive, even degree which means the end behavior is positive, positive

what this means is as x approaches negative infinity it's infinity

and as x approaches infinity it's infinity

6 0
2 years ago
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