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4 years ago

Find the measure of angle Z.

Mathematics

1 answer:

Keith_Richards [23]4 years ago

5 0

<u>Answer:</u>

Angle Z = 117°

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

We are given a figure with a triangle with two known angles and one unknown angle. That unknown angle further extends to form a straight line and we are to find that exterior angle z.

We know that the sum of all three angles of a triangle is 180°. So the third unknown angle of the given triangle will be = 180 - (45 + 72) = 63°.

We also know that angles on one side of a straight line always add to 180°.

Therefore, angle z = 180 - 63 = 117°.

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Ivahew [28]

Answer:

1. 24

2. 4 with power 5 (4⁵)

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3 years ago

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Reil [10]

Answer:

$\sqrt[8]x = x^\frac{1}{6}$

Step-by-step explanation:

Given:

$\sqrt[6] x$

Required

Represent as an exponent

In indices, we have:

$\sqrt[n]x = x^\frac{1}{n}$

By comparison:

$\sqrt[8]x = \sqrt[n]x$

$n = 8$

Apply this law to the given expression:

We have:

$\sqrt[8]x = x^\frac{1}{6}$

3 0

3 years ago

Determine the x-intercept and y-intercept of the following linear equations

Blizzard [7]

Answer:

Step-by-step explanation:

the x intercept takes coordinate (x,0)

the y intercept takes coordinate (0,y)

x intercept y intercept

40: x+y=5 (5,0) (0,5)

x=0 , y=5, when y=0 x=5

41: x-y=5 (5,0) (0,-5)

x=0, -y=5 then y=-5, when y=0, x=5

42: 3x+4y=12 (4,0) (0,3)

x=0, 4y=12⇒y=12/4⇒y=3

y=0, 3x=12⇒x=12/3⇒x=4

43: 2x+3y=6 (3,0) (0,2)

x=0 , 3y=6⇒y=6/3=2

y=0 ,3y=6 ⇒ y=6/3 ⇒y=2

44: 3x+4y=-24 (-8,0) (0,-6)

x=0 , 4y=-24⇒y=-24/4 ⇒ y=-6

y=0 , 3x=-24⇒ x=-24/3⇒x=-8

45: 1/3x+2/3y=5/6 (5/2,0) (0,5/4)

x=0 , 2/3 y=5/6 ⇒12y=15 ⇒ y=15/12 ⇒y=5/4

y=0 , 1/3 x=5/6 ⇒6x=15 ⇒x=15/6 ⇒x=5/2

46: x=-2 (-2,0) no y intercept

it is vertical line , there is no y intercept

47: y=15 no x intercept (0,15)

horixzontal line, no x intercept

48: 3x-7y=8 (8/3,0) (0,-8/7)

x=0 , -7y=8 ⇒y=-8/7

y=0 , 3x=8 ⇒x=8/3

7 0

4 years ago

Find the measure of line segment TU. Assume that lines which appear to be tangent to the circle are tangent.

Sedaia [141]

Given:

A figure of a circle. A secant SU and a tangent SR is drawn to the circle from the external point S.

To find:

The measure of the line segment TU.

Solution:

According to the secant tangent segment theorem, the square of tangent is equal to the product of secant and external segment of the secant.

Using secant tangent segment theorem, we get

$SR^2=SU\times ST$

$(40)^2=(32+2x-2)\times (32)$

$1600=(30+2x)(32)$

$1600=960+64x$

Subtract both sides by 960.

$1600-960=64x$

$640=64x$

Divide both sides by 64.

$\dfrac{640}{64}=x$

$10=x$

Now, the measure of the line segment TU is:

$TU=2x-2$

$TU=2(10)-2$

$TU=20-2$

$TU=18$

Therefore, the correct option is C.

6 0

3 years ago

Plz help me this is a final!!!

Marat540 [252]

Answer: (a) 10 (b) 1. 10 2. -10 (c) 1. 10 2. 10

Step-by-step explanation:

6 0

3 years ago