The graph shows f(x) = |x – h| + k. What is the value of h?

allsm [11]

Answer:

See explanation

Step-by-step explanation:

16. Two parallel lines are cut by transversal. Angles with measures $(6x+20)^{\circ}$ and $(x+100)^{\circ}$ are alternate exterior angles. By alternate exterior angles, the measures of alternate exterior angles are the same:

$6x+20=x+100\\ \\6x-x=100-20\\ \\5x=80\\ \\x=16$

Then

$(6x+20)^{\circ}=(6\cdot 16+20)^{\circ}=116^{\circ}\\ \\(x+100)^{\circ}=(16+100)^{\circ}=116^{\circ}$

17. Two parallel lines are cut by transversal. Angles with measures $(2x+12)^{\circ}$ and $(3x-22)^{\circ}$ are alternate interior angles. By alternate interior angles, the measures of alternate interior angles are the same:

$2x+12=3x-22\\ \\2x-3x=-22-12\\ \\-x=-34\\ \\x=34$

Then

$(2x+12)^{\circ}=(2\cdot 34+12)^{\circ}=80^{\circ}\\ \\(3x-22)^{\circ}=(3\cdot 34-22)^{\circ}=80^{\circ}$

18. Two parallel lines are cut by transversal. Angles with measures $(6x-7)^{\circ}$ and $(5x+10)^{\circ}$ are alternate exterior angles. By alternate interior angles, the measures of alternate exterior angles are the same:

$6x-7=5x+10\\ \\6x-5x=10+7\\ \\x=17$

Then

$(6x-7)^{\circ}=(6\cdot 17-7)^{\circ}=95^{\circ}\\ \\(5x+10)^{\circ}=(5\cdot 17+10)^{\circ}=95^{\circ}$

19. The diagram shows two complementary angles with measures $2x^{\circ}$ and $56^{\circ}$ . The measures of complementary angles add up to $90^{\circ},$ then

$2x+56=90\\ \\2x=90-56\\ \\2x=34\\ \\x=17$

Hence,

$2x^{\circ}=2\cdot 17^{\circ}=34^{\circ}$

Check:

$34^{\circ}+56^{\circ}=90^{\circ}$

20. Angles $\angle 1$ and $\angle 2$ are vertical angles. By vertical angles theorem, vertical angles are congruent, so

$m\angle 1=m\angle 2\\ \\5x+7=3x+15\\ \\5x-3x=15-7\\ \\2x=8\\ \\x=4$

Hence,

$m\angle 1=(5x+7)^{\circ}=(5\cdot 4+7)^{\circ}=27^{\circ}\\ \\m\angle 2=(3x+15)^{\circ}=(3\cdot 4+15)^{\circ}=27^{\circ}$

21. $\angle 5$ and $\angle 8$ are supplementary. The measures of supplementary angles add up to $180^{\circ},$ so

$m\angle 5+m\angle 8=180^{\circ}\\ \\3x-40+7x-120=180\\ \\10x-160=180\\ \\10x=180+160\\ \\10x=340\\ \\x=34$

Therefore,

$m\angle 5=(3x-40)^{\circ}=(3\cdot 34-40)^{\circ}=62^{\circ}\\ \\m\angle 8=(7x-120)^{\circ}=(7\cdot 34-120)^{\circ}=118^{\circ}\\ \\62^{\circ}+118^{\circ}=180^{\circ}$

7 0

2 years ago

2) The triangles are similar. Find the similarity ratio of the first triangle to the 1 point

USPshnik [31]

Given:

Triangles FRI and DAY are similar.

To find:

Similarity ratio

Solution:

<em>If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.</em>

Here, FR and DA are corresponding sides.

$$\Rightarrow \frac{FR}{DA} =\frac{4}{6}$

Cancel the common factors of 4 and 6, we get

$$\Rightarrow \frac{FR}{DA} =\frac{2}{3}$

⇒ FR : DA = 2 : 3

⇒ ΔFRI : ΔDAY = 2 : 3

Similarity ratio of the first triangle to the second triangle is 2 : 3.

7 0

3 years ago

Is that right? <br><br> Please help

kondaur [170]

Answer:

yes x = 16

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is

133 = x + 117 ( subtract 117 from both sides )

16 = x

8 0

3 years ago

Nandeville and Henningsburg are 75 miles apart. On a map, the two cities are 5 inches apart. How many miles does 1 inch represen

soldier1979 [14.2K]

Answer:

5 miles

Step-by-step explanation:

because when u divide 10 and 2 you will get 5

6 0

2 years ago

3 -6 12 4 20 ? what is the answer to this pattern

Lapatulllka [165]

Answer:

subtract 9

add 18

subtract 8

add 16

6 0

2 years ago