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3 years ago

Given 1 = 123° and 8 = 7z + 11. What is the value of z, if lines a and b are parallel?

Mathematics

2 answers:

Murljashka [212]3 years ago

7 0

Answer:

z = 16

Step-by-step explanation:

Since a and b are parallel lines, then

∠ 1 and ∠ 8 are Alternate exterior angles and are congruent, thus

7z + 11 = 123 ( subtract 11 from both sides )

7z = 112 ( divide both sides by 7 )

z = 16

Serga [27]3 years ago

3 0

Answer:

z=16

Step-by-step explanation:

We know for sure that since A and B are parallel that 1, 4, 5, and 8 are equal.

So then the equation is simply 123=7z+11---> 7z=112----> z=16

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My friend sets out walking at a speed of $3$ miles per hour. I set out behind her $5$ minutes later at $4$ miles per hour. When

r-ruslan [8.4K]

Answer: The answer is 0.25 miles.

Step-by-step explanation: Given that my friend started walking at a speed of 3 miles per hour and I started 5 minutes after him at a speed of 4 miles per hour. We need to find the number of miles my friend travelled when I started walking.

Since I started 5 minutes after than my friend, so we are to find the distance travelled by my friend in 5 minutes.

In 1 hour, i.e., 60 minutes, distance travelled by my friend = 3 miles.

In 1 minute, distance travelled by my friend is

$\dfrac{3}{60}=\dfrac{1}{20}~\textup{miles}.$

Therefore, distance travelled by my friend in 5 minutes will be

$\dfrac{1}{20}\times 5=\dfrac{1}{4}=0.25~\textup{miles}.$

Thus, the answer is 0.25 miles.

3 0

3 years ago

Read 2 more answers

Which of these numbers is between 5/6 and 1?<br> (A) 4/5 <br> (B) 4/7 <br> (C)6/7

djverab [1.8K]

Two basic ways in which to do this problem:

1. Find and apply the LCD.

2. Convert all of the given numbers to their decimal form, to 2 or 3 places only.

Try #2 first:

5/6 = 0.83

4/5 = 0.80 is not between 5/6 and 1. Reject it.
4/7 = 0.57 Reject
6/7 = 0.86 This is between 5/6 and1. This is the answer.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%

Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since $4^{x} + 6^{x} = 9^{x}$ ,

Dividing through by 4ˣ, we have

$\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }$

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

$y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}$

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

$y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618$