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2 years ago

3.find the measure of each missing angle

Mathematics

2 answers:

olga nikolaevna [1]2 years ago

8 0

Answer:

3 is 180-74 = 106

4: 53+106+x=180 x=21

Maurinko [17]2 years ago

6 0

Answer:

Angle 1= 69

Angle 2= 37

Angle 3= 106

Angle 4= 21

Step-by-step explanation:

(Angle 2) The box in the corner is a 90-degree angle. So, 90-53=37

(Angle 1) Now that you have angle 2, add 37+74. You get 111. Subtract 180 and 111.

The answer for angle one is 69.

(Angle 3) Since it is a line, the two angles combined are 180 degrees. 180-74= 106.

(Angle 4) Now that you have angle 3, add 106 and 53. You will get 159. 180-159= 21

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Answer:

28) E

31) D

32) B

26) E

Step-by-step explanation:

Question 28

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Given:

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Question 31

Vertical Parabola Equation: $y=\dfrac{1}{4p}(x-h)^2+k$

where

vertex: (h, k)
focus: (h, k + p)
directrix: y = k - p

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If the focus is (9, 27) and the directrix is at y = 11,

then the y-coordinate of the vertex will be: (27 - 11)/2 + 11 = 19

So the vertex is (9, 19)

Also, y-coordinate of focus: 19 + p = 27 ⇒ p = 8

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Question 32

Horizontal Parabola Equation: $x=\dfrac{1}{4p}(y-k)^2+h$

where

vertex: (h, k)
focus: (h + p, k)
directrix: x = h - p

The vertex of the parabola is at equal distance between focus and the directrix.

If the focus is (-1, 15) and the directrix is at x = -4,

then the x-coordinate of the vertex will be: (-1 + 4)/2 = -2.5

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Also, -2.5 - p = -4 ⇒ p = 1.5

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Question 26

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She's correct, but not for the right reasons. The sum of any two rational numbers is rational, but simply giving one example of that being the case isn't enough. In fact, Andrea could have done billions of similar cases and always found that there was one case she hadn't tested. What we need here is a proof, and here it is.

Let's say we have two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$ , where a, b, c, and d are all integers. Adding the two numbers together, we find that their sum is

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Since the sum or product of any two integers is always another integer, we know that both ad + cb and bd are integers, and since the definition of a rational number is a ratio of two integers, we can say with 100% certainty that $\frac{ad+cb}{bd}$ is rational, which means that the sum of any two rational numbers is also rational.

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