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k0ka [10]
2 years ago
10

What is the equation for the line with a slope of -3 that passes through the

Mathematics
1 answer:
Naya [18.7K]2 years ago
8 0
The answer in the last one
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The ratio of Luke's age to Jack's age is 3:2. If Luke is 36, how old is Jack?
melamori03 [73]

Answer:

Jack is 24

Step-by-step explanation:

Luke : jack

3            2

We know like is 36

3*12 = 36, so we need to multiply by 12

Luke : jack

3*12     2*12

36          24

8 0
2 years ago
Read 2 more answers
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
If two sides of a triangle are 5 and 7 inches longer than the third side and the perimeter measures 21, find the length of each
aleksandr82 [10.1K]
Hello

x
x +5 
x + 7

x + x + 5 + x + 7 = 21 
3 x = 21 - 12
3 x = 9
x = 3 

3 , 5 et 7 pouces
7 0
3 years ago
The perimeter of a square garage door is 16 yards. How long is each side of the garage door?
Andre45 [30]

Answer:

each side will be 4

Step-by-step explanation:

since a square has 4 sides the equation will be 16÷4

8 0
2 years ago
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Will mark brainliest pls answer
alukav5142 [94]
Y =0.5x +2 The y-intercept is found by the coordinates (0,2) and the change is 0.5
4 0
2 years ago
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