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2 years ago

Use the figure to find the measures of the numbered angles. a 107 b mm

Mathematics

1 answer:

sveticcg [70]2 years ago

6 0

Angle 1 is 107
Angle 2 is 73

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Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

8 0

2 years ago

Please help me, I am completely lost...

charle [14.2K]

5 is the answer, you are welcome.

8 0

3 years ago

Given y = 3x + 1 State the quadrants in which this graph is in. (Use the numbers 1-4)

FrozenT [24]

I have no clue man or woman

3 0

3 years ago

Please help ill give brainiest answer!

eduard

1. First of all, this is a isosceles triangle, meaning measurement I=58°, which makes it way easier to find T.

$58 + 58 + x = 180$

$116 + x = 180$

$x = 64$

1. m{t}°=64 m{I}°=58

2. This one is easy because algebra is the key.

$100 - x + 30 + 4x + 7x = 180$

Add like-terms.

$130 +10x = 180$

$10x = 50$

$\frac{50}{10} = x = 5$

x=5

The only thing that confuses me is the y. Is it 7xy, y as a side, or what? Feel free to reply

8 0

2 years ago

Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2

Ghella [55]

Answer: (b) x = -2/3

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

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x = -2

x = -2/3

8 0

2 years ago

Use the figure to find the measures of the numbered angles. a 107 b mm​

Use the figure to find the measures of the numbered angles. a 107 b mm