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4 years ago

Find the solution of this system of equations 2x-2y=-12 4x-7y=-15

1 answer:

6 0

2x - 2y = -12
- 2y = -2x - 12
y = x + 6

4x - 7 (x + 6) = -15
4x - 7x - 42 = -15
-3x - 42 = -15
-3x = 27
x = -9

y = -9 + 6
y = -3

(-9 , -3) is the solution

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I’m so confused I need help please!!

shutvik [7]

Answer:

5. 9 8. $2\sqrt{10}$

Step-by-step explanation:

a²+b²=c²

so for #5 12²+b²=15²

144+b²=225 (subtract 144 from both sides)

b²=81

b=9

For #8

9²+b²=11²

81+b²=121 (subtract 81 from both sides)

b²=40

b= $\sqrt{40}$

$\sqrt{40}$ =

$2\sqrt{10}$

6 0

3 years ago

Read 2 more answers

Dobby the house-elf has dropped all his socks on the floor in the middle of the night! He has 30 red socks, 22 gold socks and 14

Semenov [28]

Only 4 because the only way he cant get a pair is if he picks up a different colour to the previous sock, so by the fourth he will have picked up at two of at least one colour

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3 years ago

WILL GIVE 30 points a scatter plot and a possible line of best fit is shown is the line of best fit accurate for the data shown

Romashka [77]

I think It is 2. it makes the most sense to me

5 0

3 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

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3 years ago

What will your balance be on an investment of $7000 at 2% for 4 years compounded annually.

e-lub [12.9K]

Your balance would be 35, I think

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3 years ago