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blagie [28]
3 years ago
8

A local boys club sold 136 bags of mulch and made a total of $521. It sold two types of mulch: hardwood for $4.00 a bag and pine

bark for $3.75 a bag. How many bags of each kind of mulch did it sell ?
Mathematics
1 answer:
Anni [7]3 years ago
4 0

Answer: 14.32

Step-by-step explanation:

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What is the value of x?<br> A. 6<br> B. 5<br> c. 4<br> D.3
Mumz [18]

Answer:

D

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments which are proportional to the other 2 sides, that is

\frac{BC}{AC} = \frac{BD}{AD} , substitute values

\frac{4}{3} = \frac{x}{2.25} ( cross- multiply )

3x = 9 ( divide both sides by 3 )

x = 3 → D

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
Simplify the expression(a4−6a2b2+ b4)−(−2a4+5a2b2+ 3b4) and hence, find its value for a = 2and b = −1.
ELEN [110]

Answer:

(a) 3a^4 - 11a^2b^2 -2b^4

(b) 3a^4 - 11a^2b^2 -2b^4= 2

Step-by-step explanation:

Given

(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)

Solving (a): Simplify

(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)

Open brackets

a^4 - 6a^2b^2+ b^4 +2a^4-5a^2b^2- 3b^4

Collect Like Terms

a^4 +2a^4- 6a^2b^2-5a^2b^2+ b^4 - 3b^4

Simplify Like Terms

3a^4 - 11a^2b^2 -2b^4

Solving (b): Simplify when a = 2 and b = -1

3a^4 - 11a^2b^2 -2b^4

3*(2)^4 - 11*(2^2)*(-1)^2 -2*(-1)^4

3 * 16 - 11 * 4 * 1 - 2 * 1

48 - 44 - 2

= 2

Hence:

3a^4 - 11a^2b^2 -2b^4= 2

4 0
2 years ago
How do you write 140% as a fraction?
riadik2000 [5.3K]
% means out of a hundred. So, 140% should be 140/100.
8 0
3 years ago
Read 2 more answers
Chris is 6 feet tall. To find the height of a tree, he measures his shadow and the tree's
Ket [755]

Answer:

click the the photo to see better

Step-by-step explanation:

6 0
2 years ago
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