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3 years ago

Solve 4x − 2(x + 1) = 3x + 10. −12 12 −8 8

2 answers:

8 0

Original Equation: 4x - 2(x+1) = 3x + 10

Step 1: Use Distributive Property
4x - 2x - 2 = 3x + 10

Step 2: Combine Like Terms
2x - 2 = 3x + 10

Step 3: Solve
2x - 2 = 3x + 10
- 2x -2x
--------------------------------
-2 = x + 10
-10 -10
------------------------
-12 = x

erastovalidia [21]3 years ago

4 0

The Answer is, x = -12. I check and it is correct. I also just took the test and is correct.

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Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake,

Sholpan [36]

Answer:

12 times 5=60 not 70

Step-by-step explanation:

12(5+2y)=4y-(5-9y

60+24y=4y-5-9y

60+24y=-5y-5

29y+60=-5

29y=-65

y=-65/29 or y= about -2.38

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5 0

2 years ago

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Save me the headache

maxonik [38]

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

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

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

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

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

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

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3 years ago

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How many five-digit codes can be made if the first number cannot be a 0 or a 1 and no numbers can repeat?

Makovka662 [10]

Answer:

24,192.

Step-by-step explanation:

The first number must be one of 2,3,4,5,6,7,8 or 9. That is 8 possibilities.

The number of permutations of the other 4 numbers is 9P4

= 9! / (9-4)!

= 3024

Now we multiply by the 8:

3024 * 8

= 24,192.

6 0

3 years ago

6r-2(r+8)=11<br> Solve equation

pav-90 [236]

$6r-2(r+8)=11\ \ \ \ |\text{use distributive property}\\\\6r-2(r)-2(8)=11\\\\6r-2r-16=11\ \ \ \ \ |+16\\\\4r=27\ \ \ \ \ |:4\\\\r=6.75$

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3 years ago

A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (6, 5). What is

OLga [1]

Answer:

The vector joining the ship to the rock is t= 7 i + 5 j

The direction is 0.9505 radians east of north.

Step-by-step explanation:

The position vector of the ship:

r= 1 i + 0 j

The position vector of the ship:

s= 6 i + 5 j

The vector joining the ship to the rock is:

t = r + s

t = (1 i + 0 j) + (6 i + 5 j)

t = 7 i + 5 j

The bearing of the rock to the ship is:

Θ= $\frac{ \pi}{2} - arctan (\frac{5}{7})$ = 0.9505 radians

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3 years ago