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larisa86 [58]
3 years ago
6

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.

<h3>How to find x?</h3>

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

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

brainly.com/question/11832081

#SPJ1

5 0
1 year ago
In Bobby’s school, math grades for the year are calculated from assignments, tests and a final exam. Assignments count 30%, test
jarptica [38.1K]

Answer:

A) Bobby's overall grade is 70.4%

Step-by-step explanation:

To solve this problem we must calculate the percentages each grade represents from the overall grade. Therefore:

assignment = 85*30% = 85*30/100 = 25.5%

tests = 72*20% = 72*20/100 = 14.4%

exam = 61*50% = 61*50/100 = 30.5%

total = assignment + tests  + exam

total = 25.5 + 14.4 + 30.5 = 70.4

Bobby's overall grade is 70.4%. Therefore the correct answer is A).

7 0
3 years ago
I need help with this question
Novay_Z [31]

Answer:

$ \frac{\sqrt{3} - 1}{2\sqrt{2}} $

$ \frac{-(\sqrt{3} + 1)}{2\sqrt{2}} $

$ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $

Step-by-step explanation:

Given $ \frac{11 \pi}{12} = \frac{3 \pi}{4} + \frac{\pi}{6} $

(A) $ sin(\frac{11\pi}{12}) = sin (\frac{3 \pi}{4}  + \frac{\pi}{6}) $

We know that Sin(A + B) = SinA cosB + cosAsinB

Substituting in the above formula we get:

$ sin (\frac{3\pi}{4} + \frac{\pi}{6}) = \frac{1}{\sqrt{2}} . \frac{\sqrt{3}}{2} + \frac{-1}{\sqrt{2}}. \frac{1}{2} $

$ \implies \frac{1}{\sqrt{2}} (\frac{\sqrt{3} - 1}{2}) = \frac{\sqrt{3} - 1}{2\sqrt{2}}

(B) Cos(A + B) = CosAcosB - SinASinB

$ cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}}) $

$ \implies \frac{-1}{\sqrt{2}}. \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} . \frac{1}{2} $

$ \implies cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}) $

$ = \frac{-(\sqrt{3} + 1)}{2\sqrt{2}}

(C) Tan(A + B) = $ \frac{Sin(A +B)}{Cos(A + B)} $

From the above obtained values this can be calculated and the value is $ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $.

3 0
3 years ago
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