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marusya05 [52]
3 years ago
14

Complete the table. Original Price Percent of Discount Sale Price $ 5% $57

Mathematics
1 answer:
mario62 [17]3 years ago
6 0

Answer:

I think it is $54.15 sorry if wrong

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Austin is on the swim team. Each week he swims a total of 3000 meters. How many kilometers does he swim each week?
marishachu [46]

Answer:

3 km

Step-by-step explanation:

<em>(NOTE: One kilometer is 1000 meters)</em>

Divide 3000 by 1000 to get 3

8 0
3 years ago
1. Write the equation of the piece-wise function graphed below​.
DaniilM [7]

Problem 4

<h3>Answer:</h3>

f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}

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

Work Shown:

The left line goes through (-2,0) and (0,4)

The slope of this line is

m = (y2-y1)/(x2-x1)

m = (4-0)/(0-(-2))

m = (4-0)/(0+2)

m = 4/2

m = 2

The y intercept is b = 4

Since m = 2 and b = 4, this means y = mx+b turns into y = 2x+4. This portion is only done when x < 1. Note the open circle at the endpoint of this portion. So we do not include x = 1 as part of this piece.

---

The line on the right side goes through (1,-2) and (2,-1)

Slope

m = (y2-y1)/(x2-x1)

m = (-1-(-2))/(2-1)

m = (-1+2)/(2-1)

m = 1/1

m = 1

The y intercept is b = -3. You can see this if you extend the line until it crosses the y axis.

Alternatively, plug in (x,y) = (1,-2) and m = 1 into y = mx+b to find that b = -3

So y = mx+b turns into y = 1x+(-3) or just y = x-3

We combine both parts to end up with f(x) = \begin{cases}2x+4 \text{ if } x < 1\\x-3 \text{ if } x \ge 1\end{cases}

This is only graphed when x \ge 1 (note the closed or filled in circle for the endpoint of this portion).

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

Problem 5

Answer:

<h3>f(x) = \frac{1}{2}|x+3| is the absolute value function</h3><h3>while this is the piecewise function</h3>

f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\

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

Work Shown:

y = |x| .... parent function

y = |x+3| ... shift 3 units to the left

y = (1/2)*|x+3| .... vertically compress by factor of 1/2

f(x) = (1/2)*|x+3|

------

Break that down into a piecewise function

when x < -3, then y = -(1/2)(x+3)

when x \ge -3, then y = (1/2)(x+3)

I'm using the rule that y = |x| turns into y = -x when x < 0 and y = x when x \ge 0

So that is how we get f(x) = \begin{cases}-\frac{1}{2}(x+3) \text{ if } x < -3\\\frac{1}{2}(x+3) \text{ if } x \ge -3\end{cases}\\as the piecewise function.

8 0
3 years ago
Read 2 more answers
Equation don't has three time much money than his brother who has 25.
mash [69]
First think out the equation, once you've done that multiply 3 by 25 to get 75
5 0
3 years ago
Find -2/3 divided by 4/6<br> -1<br> 4/9<br> -9/4<br> 1
nalin [4]

Answer:

-1

Step-by-step explanation:

The given expression is:

-\frac{2}{3}\div \frac{4}{6}

We multiply by the reciprocal to get:

-\frac{2}{3}\times \frac{6}{4}

We factor so that we can cancel easily:

-\frac{2}{3}\times \frac{3\times 2}{2\times 2}

Cancel the common factors to get:

-\frac{1}1}\times \frac{1\times 2}{1\times 2}

This simplifies to:

-1

6 0
3 years ago
Read 2 more answers
The perimeter of a rectangle is 36 meters. If the length of the rectangle is 10 meters, what is the width (in meters)?
Dmitry [639]
The width is 8. The length is 10 so 10+10 equals 20. You subtract 20 from 36 you get 16. 16/2 is 8. If you add 8+8+10+10 you get 36.
8 0
2 years ago
Read 2 more answers
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