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3 years ago

Brainliest and 30 points please help

Mathematics

1 answer:

kolbaska11 [484]3 years ago

4 0

Answer:

22. Perimeter = 52 units

Area = 160 Square Units

23. Notation form : $2 \times 10^{5}$

Standard Form : 200000

Step-by-step explanation:

22.

The formula for perimeter is

P = 2 (length + Width )

= 2 ( 2x+3x+1)

= 2(5x+1)

The Formula for Area of a rectangle is

A= length x width

A= $2x \times (3x+1)$

A= $6x^2+2x$

Now we have to find the Perimeter and Area for x = 5

P = 2(5 x 5 +1)

P= 2(26)

P=52 units

A= 6 x 5 x 5 + 2 x 5

A= 150 + 10

A= 160 square units

23.

A. By using rule of exponents , we can determine that both the results will be same.

Miriam's calculation

$\frac{2.8 \times 10^{9}}{1.4 \times 10^{4}}$

$\frac{2.8}{1.4} \times 10^{9-4}$

$2 \times 10^5$

Priya's calculation

$\frac{2.8 \times 10^{2}}{1.4 \times 10^{-3}}$

$\frac{2.8}{1.4} \times 10^{2-(-3)}$

$2 \times 10^5$

Standard notation

$2 \times 10^5 = 200000$

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x = 6 feet.

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Answer:

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1. Write the equation of the piece-wise function graphed below.

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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

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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 $x \ge 0$

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