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3 years ago

Can someone help me and explain what to do here?

Mathematics

1 answer:

Vesna [10]3 years ago

4 0

Answer:

∠STU = 69°

Step-by-step explanation:

The angle with vertex T is called an "inscribed angle." It intercepts arc SU. The relationship you are asked to remember is that the measure of the inscribed angle (T) is half the measure of the arc SU.

Point V is taken to be the center of the circle. The angle with vertex V is called a "central angle." It also intercepts arc SU. The relationship you are asked to remember is that the measure of the central angle (V) is equal to the measure of arc SU.

Using these two relationships together, we realize angle V is twice the measure of angle T:

∠SVU = 2×∠STU

18x +12° = 2(18x -57°) . . . . . . relationship between the marked angles

18x +12° = 36x -114° . . . . . eliminate parentheses

126° = 18x . . . . . . . . . . . add 114°-18x

∠STU = 18x -57° = 126° -57°

∠STU = 69°

_____

Additional comment

You may notice we did not solve for x. We only needed to know the value of 18x, so we stopped when we found that value. (Actually, we only need the value of 18x-57°. See below.)

Alternate solution:

(18x +12°) -(18x -57°) = 18x -57° . . . . . . . subtract 18x -57° from both sides of the first equation.

69° = 18x -57° . . . . . simplify. This is the answer to the problem.

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Veseljchak [2.6K]

Answer:

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Step-by-step explanation:

3 0

3 years ago

1. Find the value of x. A. 90 B. 80 C. 60 D. 45

tia_tia [17]

Answer:

A 90

Step-by-step explanation:

multiple ways to prove this.

e.g. since the angle between the two lines from the center of the circle to the 2 tangent touching points is 90 degrees (that is the meaning of these 90 degrees here as the angle of the circle segment defined by the 2 tangent touching points and the circle center), the tangents have the same "behavior" as tan and cot = the tangents at the norm circle at 0 and 90 degrees. they hit each other outside of the circle again at 90 degrees.

another way

imagine the two right triangles of the tangents crossing point to the circle center and the tangent/circle touching points.

the Hypotenuse of each triangle is cutting the 90 degree angle of the circle segment exactly in half (due to the symmetry principle). so the angle between radius side and Hypotenuse is 90/2 = 45 degrees.

that means also the angle of such a right triangle at the tangent crossing point is 45 degrees (as the sum of all angles in a triangle must be 180, we have the remainder of 180 - 90 - 45 = 45 degrees).

the angles of both right triangles at that point are the same, and so we can add 45+45 = 90 degrees for the total angle at the tangent crossing point.

8 0

3 years ago

Help me please. Help me please. Help me please.

Gnesinka [82]

A)
To be similar triangles have to have equal angles
triangle ZDB'
1)angle Z=90 degrees
triangle B'CQ
1) angle C 90 degrees

angle A'B'Q=90
DB'Z+A'B'Q+CB'Q=180, straight angle
DB'Z+90+CB'Q=180
DB'Z+CB'Q=90

triangle ZDB'
DZB'+DB'Z=180-90=90

DB'Z+CB'Q=90
DZB'+DB'Z=90
DB'Z+CB'Q=DZB'+DB'Z
2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )
3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.
so this triangles are similar by tree angles
b)
B'C:B'D=3:4
B'D:DZ=3:2
CQ-?
DC=AB=21
DC=B'C+B'D (3+4= 7 parts)
21/7=3
B'C=3*3=9
B'D=3*4=12
B'D:DZ=3:2
12:DZ=3:2
DZ=12*2/3=8
B'D:DZ=CQ:B'C
3:2=CQ:9
CQ=3*9/2=27/2

c)
BC=BQ+QC=B'Q+QC
BQ' can be found by pythagorean theorem

3 0

3 years ago

The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remainin

Goryan [66]

T divided by 2after each round

8 0

3 years ago

The Jaxon High School prom committee has 100 thumb drives to sell in a fundraiser. The function f(x) = 8x – 200 models their inc

Alina [70]

Answer:

25 = x

Step-by-step explanation:

Based on the equation we see that the thumb drives cost $200 which is why that is being subtracted. To calculate the break-even number of sales we need to make a total of 200 to cover the costs. We calculate this by matching the equation to 0 and solving for x...

0 = 8x - 200 ... add 200 on both sides

200 = 8x ... divide both sides by 8

25 = x

Finally, we can see that the committee will break even after selling 25 thumb drives which would make them $200 to cover all of their costs.

5 0

2 years ago