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2 years ago

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triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third

angle is 30 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

1 answer:

aev [14]2 years ago

7 0

Please find attached photograph for your answer. Hope it helps. Please do comment

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Is the product of 3/6×5/4 equal to the product of 3/4×5/6? Explain how<br>you known.

nekit [7.7K]

Changing the order of the denominator doesn’t change the product. 4•6=24 and 6•4=24 again.

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3 years ago

Read 2 more answers

56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

It takes 8 workers 12 days to build a wall work out how many days it would take 3 workers to complete the same job

MissTica

Answer: 4.5 days or 4 1/2 days

Step-by-step explanation: We can use cross product property, to solve this. Workers to Days remember that

6 0

3 years ago

9x - y = 15 2x + 8y = 28

faust18 [17]

9x - y = 15
2x + 8y = 28

Use the substitution method.
Solve for y in the first equation.

9x - y = 15
-y = 15 - 9x
y = -15 + 9x

Now plug in y into the second equation.
2x + 8(-15 + 9x) = 28
2x - 120 + 72x = 28
74x - 120 = 28
74x = 148
x = 2

Plug x back into the rewritten first equation.
y = -15 + 9(2)
y = -15 + 18
y = 3

x = 2, y = 3

5 0

3 years ago

How do I find angle a?

vfiekz [6]

The slope of the line is 2/3, so the angle is arctan(2/3) ≈ 33.69°.

8 0

3 years ago