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3 years ago

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1. Use a property of exponents to write (3b)⁵ as a product of powers. 2. What is the width of the rectangle written as an expone

ntial expression? - Area: 10⁴ m² - Length: 10³ m

1 answer:

motikmotik3 years ago

8 0

Answer:

Step-by-step explanation:

1. (3b)^5

= (3b)^2 * (3b)^3.

2. Width = area / length

= 10^4 / 10^3

= 10^(4-3)

= 10 m.

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago

10 points! doing brainliest! Do all 3<br><br><br>

faltersainse [42]

Answer:

12) $\frac{7}{3} = \frac{b}{18}$

$3b = 126$

$\frac{3b}{3} = \frac{126}{3}$

$b = 42$

13) $\frac{3.6}{m} = \frac{1.2}{3.6}$

$1.2m = 12.96$

$\frac{12m}{12} = \frac{12.96}{12}$

$m = 10.8$

14) $\frac{16}{10} = \frac{n + 2}{5}$

$80 = 10n + 20$

$80 - 20 = 10n +20 -20$

$60 = 10n$

$\frac{60}{10} = \frac{10n}{10}$

$n = 6$

7 0

3 years ago

Evaluate 10% of 5000

Oduvanchick [21]

Answer:

500

Step-by-step explanation:

that is the procedure above

7 0

3 years ago

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FILL in the blanks with appropriate answers:

PSYCHO15rus [73]

Answer:i dunno

Step-by-step explanation:

ya

4 0

3 years ago

If angle A is (2x+8) degrees and Angle B is (2x+8) and A and B are supplementary angles....what is measurement of angle B?

atroni [7]

<h3>Supplementary Angles:</h3>

Angles which adds up to 180°.

<h3>Given:</h3>

A = 2x + 8

B = 2x + 8

<h3>To Find:</h3>

The measurement of B.

<h3>Solution:</h3>

A + B = 180°

or, 2x + 8 + 2x + 8 = 180°

or, 4x + 16 = 180°

or, 4x = 180 - 16 = 164°

or, x = 164/4 = 41°

<h2>Answer:</h2>

B = 2x + 8 = 2(41) + 8 = 82 + 8 = 90°

<u>B</u><u> </u><u>=</u><u> </u><u>9</u><u>0</u><u>°</u>

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3 years ago

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