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2 years ago

The number that is twice as much as five more than a number a? Simplify the answer.

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

8 0

Let us assume the unknown number is n.

Given statement " The number that is twice as much as five more than a number a."

Twice of a is = 2 times of a= 2a.

Now, it is said twice of that number of 5 more than a.

So, we can set an equation as

Subtracting a from both sides, we get

2a - a = a-a +5

a = 5.

<h3>Therefore, unknown number a is 5.</h3>

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Which shows one way to determine the factors of 12x3 – 2x2 + 18x – 3 by grouping?

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

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Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

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The third angle is 14 more than the second

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And remember that the sum of these three angles must be equal to 180.

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Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

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Combine like terms;

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Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

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Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

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