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allochka39001 [22]
2 years ago
5

Find all the unknown angle measures in the diagram. Justify your answer for each angle measure.

Mathematics
1 answer:
Jet001 [13]2 years ago
4 0

Answer:

∠1 is 90° because it is a right angle

To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;

x + 90 + 30 = 180

x + 120 = 180

-120        -120

x = 60, ∠2 = 60°

Angle 5 is vertical to angle 1 which equals 90 degrees, and <u>vertical angles are congruent</u> meaning that they measure the same degrees so therefore ∠5 = 90°

Angles 4 and 40° are <u>vertical</u> to angle 2 which measures 60 degrees;

40 + x(where x equals angle 4) = 60

-40       -40

x = 20, ∠4 = 20°

Specified earlier, angles <u>40° and 4 are equal to 60°</u>, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.

So we set up the equation;

40 + 20(angle four) + x = 90

60 + x = 90

-60       -60

x = 30, ∠3 = 30°

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slamgirl [31]

Answer:

A. 2 factors: 5 and (6+4x)

B. 5: 1 term  

(6+4x): 2 terms

C: The coefficient is 4

Step-by-step explanation:

The factors are the parts of expression separate by multiplications, so there are 2 factors: 5 and (6+4x)

The terms of each factor are the terms separate by the sign + or -. So the term of the factor 5 is 1 and the terms of the factor (6+4x) are 6 and 4x

The coefficient of the variable term is the number that is beside the variable. The coefficient of x is 4.

4 0
3 years ago
If f(x)=x+7 and g(x)= 1 divided by x-13, what is the domain of (f•g)(x)?
andrew11 [14]
<h2>Hello!</h2>

The answer is:

The domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

<h2>Why?</h2>

This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.

Composite function is equal to:

f(g(x))=(f\circ} g)(x)

So, the given functions are:

f(x)=x+7\\\\g(x)=\frac{1}{x-13}

Then, composing the functions, we have:

f(g(x))=\frac{1}{x-13}+7\\

Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.

If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.

So, the domain of the function is all the real numbers except the number 13:

Domain: (-∞,13)∪(13,∞)

Have a nice day!

5 0
3 years ago
*select all that apply
Stels [109]
The answer to the question is the first, third and fifth
4 0
3 years ago
Which coordinates will best represent point K′?
mina [271]

Answer:

C. (6,2)

Step-by-step explanation:

(-2,-3) becomes (-2+8, -3+5), (6,2)

6 0
2 years ago
A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 8 bags and spend $37, how many
Andrew [12]

Answer:

  • 6 3-lb bags
  • 2 1-lb bags

Step-by-step explanation:

Let x represent the number of 3-lb bags purchased. Then the total purchase was ...

  $2(8 -x) +$5.50(x) = $37

  16 +3.50x = 37 . . . . . . . . . divide by $, collect terms

  3.50x = 21 . . . . . . . . . . . . . subtract 16

  21/3.50 = x = 6 . . . . . . . . divide by the coefficient of x

You bought 6 3-lb bags of peanuts and 2 1-lb bags.

4 0
3 years ago
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