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just olya [345]

3 years ago

14

I need help please 4x-6y=36 how to show my work please help it would mean a lot :)

1 answer:

andre [41]3 years ago

3 0

Answer:

Solving for x:

$x = \frac{3}{2} y + 9$

Solving for y:

$y = \frac{2}{3} x - 6$

Step-by-step explanation:

Please see the attached picture for full solution.

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Sophia is saving up money to buy a car that costs ______

earnstyle [38]

Answer:

Step-by-step explanation:

12 years, 10 months

7 0

3 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

or

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

Read 2 more answers

What is the distance between the two points (-8,-6) and (-2,4)?

MAVERICK [17]

Answer:

$\sqrt{136}$ = 11.66 units

Step-by-step explanation:

distance between 2 points (a,b) and (c,d) = $\sqrt{(a^{2}-c^{2} ) +(b^{2}-d^{2} ) }$

= $\sqrt{((-8)^{2}-(-2)^{2} ) + ((-6)^{2}-4^{2}) }$

= $\sqrt{136}$

= 11.66 units

6 0

3 years ago

What are the measures of Angles a, b, and c? Show your work and explain your answers.

Lyrx [107]

Answer:

(a, b, c) = (30°, 60°, 105°)

Step-by-step explanation:

Angle "a" and 30° are vertical angles, hence equal.

Angle "b" and angle "a" are complementary angles, so b = 90° -30° = 60°.

Angle "c" is supplementary to the one marked 75°, so is 180° -75° = 105°.

___

Angles "a" and "b" are complementary because the sum of angles in a triangle is 180° and the third angle in that triangle is 90°. Then ...

a+b = 180°-90° = 90°

___

75° and "c" are supplementary, because they are linear angles. The angle measure of a line is 180°, so that is their total measure.

6 0

3 years ago

Suppose the mean and standard deviation of the GPAs at Loyola are

Basile [38]

Answer:

Catherine's GPA is 2.48

Step-by-step explanation:

A z-score of 2.010 means that Catherine's GPA is 2.01 standard deviations above the mean. Therefore, Catherine's GPA is $\bar{x}+2.01\sigma=1.963+2.01(0.257)\approx2.48$

3 0

2 years ago