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nikitadnepr [17]
3 years ago
13

The angle measurements in the diagram are represented by the following expressions.

Mathematics
2 answers:
Anna11 [10]3 years ago
7 0
<h3><u>Answer:</u></h3>

x = 12°

<h3><u>Step-by-step explanation:</u></h3>

Since both lines are parallel.

Using alternate angle property!

= > Angle A = Angle B

= > 5 x - 15 = 2 x + 21

= > 5 x - 2 x = 21 + 15

= > 3 x = 36

= > x = 12

Therefore, the value of x is 12°.

valkas [14]3 years ago
3 0

Answer:

45°

Step-by-step explanation:

A and B are Alternate exterior angles and congruent, thus

5x - 15 = 2x + 21 ( subtract 2x from both sides )

3x - 15 = 21 ( add 15 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

Thus

∠ A = 5x - 15 = 5(12) - 15 = 60 - 15 = 45°

∠ B = 2x + 21 = 2(12) + 21 = 24 + 21 = 45°

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Miguel spent a total of $60 at the grocery store. Of this amount , he spent $18 on fruit. What percentage of the total did he sp
Paraphin [41]

Answer:

30%

Step-by-step explanation:

A percent can be found by dividing the part by the whole, or

part/whole

In this case, the part is the amount he spent on fruit. The whole is the total amount he spent.

amount spent on fruit/ total amount spent

He spent $18 on fruit, and $60 in total.

$18/ $60

Divide 18 by 60

18/60

0.3

Convert 0.3 to a decimal by multiplying by 100 or moving the deicaml place two spots to the right.

0.3*100=30

0.3--> 3.0 --> 30

30%

He spent 30% on fruit.

4 0
3 years ago
12% of 72 is what number ?
valina [46]
The best thing to do here is to find 1%, then multiply this by 12.
72/100= 0.72
0.72*12= 8.64
Therefore, 12% of 72 is 8.64
Hope this helps :)
6 0
3 years ago
Read 2 more answers
The weight of 10,000 identical samples of a substance is 100 pounds. What is the weight of 10 samples?
Misha Larkins [42]
The answer to the problem is .1
7 0
4 years ago
If A+B+C=<img src="https://tex.z-dn.net/?f=%5Cpi" id="TexFormula1" title="\pi" alt="\pi" align="absmiddle" class="latex-formula"
seraphim [82]

Answer:

a + b + c = \pi \\  =  > c=  \pi - a - b \\  <  =  >  \tan(c)  =  \tan(\pi - a - b)  =  -\tan(a + b)

Step-by-step explanation:

we have:

\tan(a)  +  \tan(b)  +  \tan(c)  \\  =  \tan(a)  +  \tan(b)  -  \tan(a + b)  \\  =  \tan( a)  +  \tan(b)  -  \frac{ \tan(a) +  \tan(b)  }{1 -  \tan(a)  \tan(b) }  \\  =  \frac{ ( \tan(a) +  \tan(b)  ) \tan(a) \tan(b)  }{ \tan(a) \tan(b)  - 1 } (1)

we also have:

\tan(a)  \tan(b)  \tan(c)  \\  =  -  \tan(a)  \tan(b)  \tan(a + b)  \\  =  \frac{ -(\tan( a  )   + \tan(b) ) \tan(a)  \tan(b) }{1 -  \tan(a)  \tan(b) }  \\  =  \frac{( \tan(a)  +  \tan(b)) \tan(a)   \tan(b) }{ \tan(a) \tan(b)  - 1 } (2)

from (1)(2) => proven

5 0
3 years ago
What is the justification for each step in the solution of the equation?
Alexandra [31]

For this case we have the following equation:

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

If we multiply both sides of the equation by 3 we get:

2x-1 = 6 (x + 2) ---> Multiplication Property of Equality

Applying the distributive property we have:

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Adding 1 on both sides of equality we have:

2x-1 + 1 = 6x + 12 + 1\\

2x = 6x + 13 ---> Addition Property of Equality

Subtracting 6x on both sides we have:

-6x + 2x = 6x-6x + 13\\

-4x = 13 ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

\frac{-4x}{-4}= \frac{13}{-4}\\

x = -\frac{13}{4}---> Division Property of Equality


5 0
3 years ago
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