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navik [9.2K]
3 years ago
12

Simplify this expression: a + 2a + 3b - a - b

Mathematics
2 answers:
aniked [119]3 years ago
8 0
Simplified would be 2a+2b
LenaWriter [7]3 years ago
6 0
<span>a + 2a + 3b - a - b
combine like terms

= 2a + 2b
or
= 2(a+b)</span>
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What is the sum of the terms of the series (−1) + (−2) + (−3) + . . . + (−10)?
Murrr4er [49]
You can solve this problem by using the Gauss method. The Gauss method is a method where you can add the first and last numbers together, and then multiply by how many times that appears. Here, the sum of the first and last number is -11. In this sequence, it would appear ten times (since there are ten terms and the terms are used twice in every eleven). -11 * 5 is -55, so that means the answer to this question is -55. 
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3 years ago
Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A
alekssr [168]

Answer:

\theta_{CAB}=128.316

\theta_{ABC}=25.842

\theta_{BCA}=25.842

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}

AB= \sqrt{(-3-1)^2+(0-3)^2}=5

BC= \sqrt{(1-1)^2+(3-(-3))^2}=9

CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}

\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}

\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}

\theta_{CAB}=\arccos{-\dfrac{0.62}}

\theta_{CAB}=128.316

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}

\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)

\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)

\theta_{ABC}=\arcsin{0.4359}\right)

\theta_{ABC}=25.842

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

\theta_{BCA}=25.842

this can also be checked using the fact the sum of all angles inside a triangle is 180

\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180

25.842+128.316+25.842

180

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3 years ago
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You work at the peacock blue store 40 hours/week over five days at a rate of $10.25/hour. Deductions are fica (7.65%), federal w
Reptile [31]

210.69 is the answer.

Sorry for not explaining my work, in a bit of a hurry. I had this question back when i was in school.


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E E E E E? If I’m right please let me know
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2 years ago
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The answer is a = 0, b = -5, and c= 39.

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

<u>step 1</u> :

A quadratic equation means that it should have at least one squared term.

<u>step 2</u> :

The standard form is ax² + bx + c = 0.

<u>step 3</u> :

The solution to the quadratic equation is usually written in the form

x = (-b ± √(b2 − 4ac))/(2a)

where a = coefficient of x^2

           b = coefficient of x

          c = constant term

<u>step 4</u> :

The given equation is -5x +32.

∴ The answer is a = coefficient of x^2 = 0

                           b = coefficient of x = -5

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