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3 years ago

What expression represents the measure of angle x?

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

5 0

An isosceles triangle is a triangle that has 2 equal sides and 2 equal angles.

side XY = side XZ
∠Y = ∠Z
Since ∠Y = a° then ∠Z = a°

Because interior angles of a triangle sum up to 180°, we simply need to find the difference between 180° and the 2 known angles to solve for the measure of angle X.

∠X = 180° - 2a°

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How many ounces of 50% alcohol solution must be mixed with 80 ounces of a 20% alcohol solution to make a 40% alcohol solution?

Paraphin [41]

X = amount of 50% solution
y = total amount after mixing

Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.

We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80

next, apply the percentages to get an equation for the amount of alcohol:

0.4 y = 0.5 x + 16

Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240

8 0

2 years ago

HELP WITH THESE QUESTIONS PART 2.

polet [3.4K]

Answer: (a) IV (b) positive (c) $\frac{\pi}{4}$ (d) C (e) $\sqrt{2}$

Step-by-step explanation:

a) $\frac{15\pi}{4}$ - $\frac{8\pi}{4}$ = $\frac{7\pi}{4}$ , which is located in Quadrant IV per the Unit Circle.

b) sec is $\frac{1}{cos}$ . Cos is the x-coordinate. The x-coordinate inQuadrant IV is positive.

c) the reference angle is the angle from $\frac{7\pi}{4}$ to 2π = $\frac{\pi}{4}$

d) since the angle is below the x-axis and the reference angle is $\frac{\pi}{4}$ , then the angle is equal to $-sec(\frac{\pi}{4}$ )

e) sec = $\frac{1}{cos}$ ⇒ sec $\frac{7\pi}{4}$ = $\frac{2}{\sqrt{2} }$ = $\frac{2}{\sqrt{2} }$ $(\frac{\sqrt{2}} {\sqrt{2}})$ = $\frac{2\sqrt{2} }{2}$ = $\sqrt{2}$

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Answer: (a) $\frac{3\pi}{2}$ (b) (0, -1) (c) A (d) -1

Step-by-step explanation:

a) $\frac{11\pi}{2}$ - $\frac{4\pi}{2}$ = $\frac{7\pi}{2}$ - $\frac{11\pi}{2}$ = $\frac{3\pi}{2}$

b) $\frac{3\pi}{2}$ is on the Unit Circle at (0, -1)

c) sin = $\frac{opposite}{hypotenuse}$ which equals $\frac{y}{r}$ on the Unit Circle.

d) sin is the y-coordinate. sin $(\frac{3\pi}{2})$ = -1

6 0

3 years ago

Please help!!!! No explanation needed Help is appreciated

Elodia [21]

Answer:

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3 years ago

What is 420/1000 in simplest form

balandron [24]

The answer would be 21/50. If you have numbers with a few zeros you can cross one of the top amd bottom until you reach the other numbers, if that makes sense. You can changd 420/1000 to 42/100. Then just keep dividing it by a numner that goes evenly into both the numerator and denominator.

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3 years ago

The king who retains power by tradition of allegiance ensures that a religious doctrine is enforced as government policy. Which

vaieri [72.5K]

Answer:

The answer is C.This country has both a democracy and a theocracy

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3 years ago