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Juli2301 [7.4K]

3 years ago

10

If two lines are parallel and cut by a transversal, then the corresponding angles are congruent. What is the converse of this po

stulate?

1 answer:

FromTheMoon [43]3 years ago

5 0

If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

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The number of chickens (c) is four times as many the number of horses

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Answer:

D

Step-by-step explanation:

Number of chickens (c) is = 4 times number of horses (4h). c = 4h

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So, since the polygons are similar, they will share a scale factor.

The dilation is a reduction.

SF= preimage/image

SF=48/40

SF= 1.2

To find the value of x, multiply 20 by 1.2, so:

20(1.2)=24

Thus, x = 24

Now, to check if the sides are proportional (this will determine if the polygons are, in fact, similar.)

24/20=1.2
48/40=1.2

BTW, the missing side measure for the image is 40 since 48 is its corresponding side, and 48/1.2 (SF) is 40.

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Suppose you roll two number cubes. What is the probability of getting:

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What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline min

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Answer:

Value of expression in single logarithm is $\log_3\left(2z^2\right)$ .

Step-by-step explanation:

Given expression is,

$2\left(\log_3\left(8\right)+\log_3\left(z\right)\right)-\log_3\left(3^4-7^2\right)$

Now using logarithmic rule to solve the expression as follows,

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$\log_c\left(a\right)+\log_c\left(b\right)=\log_c\left(ab\right)$

Therefore,

$2\log_3\left(8z\right)-\log_3\left(3^4-7^2\right)$

Applying power rule of logarithmic,

$a\log_c\left(b\right)=\log_c\left(b^a\right)$

Therefore,

$\log_3\left(\left(8z\right)^2\right)-\log_3\left(3^4-7^2\right)$

$\log_3\left(\left(64z^2\right)\right)-\log_3\left(3^4-7^2\right)$

Applying quotient rule of logarithmic,

$\log_c\left(a\right)-\log_c\left(b\right)=\log_c\left(\frac{a}{b}\right)$

Therefore,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{3^4-7^2}\right)$

Simplifying,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{81-49}\right)$

$\log_3\left(\dfrac{\left(64z^2\right)^2}{32}\right)$

$\log_3\left(2z^2\right)$

Therefore value of expression is $\log_3\left(2z^2\right)$

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