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vovikov84 [41]
3 years ago
8

Triangle XYZ is equilateral with vertices located on circle W. Circle W is shown. Line segments W Y, W Z, and W X are radii. Lin

es are drawn to connect the points on the circle to form a triangle. Sides Z X, X Y, and Z Y are congruent. Which measurements are correct? Select two options. mArc X Y = 60° mArc Y Z = 120° mArc Z X = 180° m∠XWZ = 60° m∠YWZ = 120°

Mathematics
2 answers:
Ainat [17]3 years ago
6 0

Answer:

The answers are B & E

Step-by-step explanation:

Elis [28]3 years ago
4 0

Answer:

arc\ YZ=120^o

m\angle YWZ=120^o

Step-by-step explanation:

<u><em>The complete question in the attached figure</em></u>

we know that

An equilateral triangle has three equal sides and three equal interior angles (the measure of each interior angle is 60 degrees)

m\angle XYZ=m\angle YZX=m\angle ZXY=60^o

Remember that

The <u><em>inscribed angle</em></u> is half that of the arc it comprises

so

arc\ XY=arc\ YZ=arc\ ZX=2(60^o)=120^o

Remember that

<u><em>Central angle</em></u> is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

m\angle YWZ=arc\ YZ=120^o ----> by central angle

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Solve the following logarithmic equations.<br> log[(x^2 + 2x − 3)^4] = 0
saw5 [17]

Answer:

The solutions are x = 1.24 and x = -3.24

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log[(x² + 2x -3)⁴] = 0

Apply the logarithm property: log(xᵃ) = a log(x)

4 log[(x² + 2x -3)⁴] = 0

Divide by 4 both sides

log(x² + 2x -3) = 0

if log(x² + 2x -3) = 0, then  x² + 2x -3 = 1 because only log 1 = 0

x² + 2x -3 = 1

Subtract 1 at both sides of the equation

x² + 2x -4 = 0

Using the quadratic formula let´s solve this quadratic equation:

a = 1

b = 2

c = -4

x = [-b± √(b² - 4ac)]/2a

x =  [-2 + √(4 - 4(-4)·1)]/2 = 1.24

and

x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24

The solutions are x = 1.24 and x = -3.24

Have a nice day!

4 0
3 years ago
Point Z is the circumcenter of ΔTUV.
Vsevolod [243]

Answer:

32.8

Step-by-step explanation:

Since the angles given are 90 degrees and 57.2 you can add those together then subtract them from 180 to find the answer 32.8.

180 - 90 + 57.2 = 32.8

7 0
3 years ago
Read 2 more answers
A 600-ft tall building is represented by a 30-in. tall model.
alexdok [17]

\huge\boxed{19\ \text{inches}}

First, find the scale factor by dividing the first building's real-life height by its model height.

\frac{600}{30}=\frac{60}{3}=20

Now, we'll write an equation to find the model height of the second building.

r=20m

Here is an equation where r represents the real-life height of a building, 20 represents the scale factor, and m represents the model height of the same building.

Fill in the information we already know.

380=20m

Divide both sides by 20.

\frac{380}{20} = \frac{20m}{20}

\large{\boxed{19}}=m

So, the model height of the second building is 19 inches.

5 0
3 years ago
Every day Matilda's mom goes to the store and buys apples and oranges for $22. Then today she returned home with 5 apples and 4
BlackZzzverrR [31]

Answer: $1.82

Step-by-step explanation:

3 0
3 years ago
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating
natulia [17]

Answer:

V=25088π vu

Step-by-step explanation:

Because the curves are a function of "y" it is decided to take the axis of rotation as y

, according to the graph 1 the cutoff points of f(y)₁ and f(y)₂ are ±2

f(y)₁ = 7y²-28;  f(y)₂=28-7y²

y=0;   x=28-0 ⇒ x=28

x=0;   0 = 7y²-28 ⇒ 7y²=28 ⇒ y²= 28/7 =4 ⇒ y=√4 =±2

Knowing that the volume of a solid of revolution  V=πR²h, where R²=(r₁-r₂) and h=dy then:

dV=π(7y²-28-(28-7y²))²dy ⇒dV=π(7y²-28-28+7y²)²dy = 4π(7y²-28)²dy

dV=4π(49y⁴-392y²+784)dy integrating on both sides

∫dV=4π∫(49y⁴-392y²+784)dy ⇒ solving  ∫(49y⁴-392y²+784)dy

49∫y⁴dy-392∫y²dy+784∫dy =

V=4π( 49\frac{y^{5} }{5}-392\frac{y^{3}}{3}+784y ) evaluated -2≤y≤2, or 2(0≤y≤2), also

V=8\pi(49\frac{2^{5} }{5}-392\frac{2^{3} }{3}+784.2)  ⇒ V=25088π vu

8 0
3 years ago
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