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Two angles of a triangle ABC measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures 13 units, what is the sum of the lengths of the two remaining sides? Express your answer as a decimal to the nearest tenth.

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∠A = 30º        ∠B = 45º       a = 13

b + c = 43.499 units  

when we factor, we get 2*x+2*12=2x+24

start by converting 3 2/3 into a proper fraction -> 11/3

12*11/3=44

start by converting 2 1/2 into a proper fraction -> 5/2

20*5/2=50

set up the equation 0.6x=18 where x is the number of people at the playground

divide both sides by 0.6 to get 30 people at the playground

15-5=10

2n=10

n=5

distribute and combine like terms to get -x=11

then divide both sides by 1 to get x=-11

now you do the checking. :)

hint: rewrite the equation with a denominator. 

61/7=8 R5 so the answer is 8

this is simply 10*2/3=20/3

Chocolate used for frosting: 2/5 * 16 = 32/5.

Chocolate used for brownies: 3/5 * 16 = 48/5

Difference: 48/5 - 32/5 = 16/5.

Answer: 16/5 more ounces.

[ABC] = 180 square units

[DEF] = ¹/₄ [ABC]  = 45 square units

[DEF] : [ABC] = 1 : 4

∠ABC = tan^-1(AC / AB)

BC = sqrt(AB² + AC²) = √801

ΔABC inradius  r = 5.349

ΔABC circumradius   R = 14.151

2/3 of 10 = 2/3 * 10 = 20/3. 20/3 = 6.666...

Hello, Guest!

Your question is no good!!!            [ABC] cannot be more than 200 !!!

If [ABC] = 200 then the perimeter is 40 + 5√32  

Line 1: Slope = 2. Y-Intercept = 3. Equation: y = 2x + 3. When y = 2, x = -1/2.

Line 2: Slope = -1. Y-Intercept = -3. Equation: y = -x - 3. When y = 2, x = -5.

Line 3: Given. When y = 2, x = 1.

Line 4: Given. When y = 2, x = 1.

Line 5: Slope = 2. Y-Intercept = -3. Equation: y = 2x - 3. When y = 2, x = 5/2.

-1/2 + -5 + 1 + 1 + 5/2 = -1

Hope this helps!

The coefficient of the x^2 term is -4-7+x = -10

The coefficient of the xy term is 3+4-1 = 6

The coefficient of the y^2 term is -1+6-2 = 3

Therefore the final polynomial is 

\(\boxed{-10x^2 + 6xy + 3y^2}\)

Find the slope of (5,5) and (3,1). That is equal to rise/run = -4/-2 = 2.

y = 2x + c

Plugin the information given: 5 = 2(5) + c

Solve: 5 = 10 + c -> c = -5

Equation: y=2x-5

Plugin the information: y = 2(-6)  - 5

Solve: y = -12  - 5 -> y = -17

C = 17

Remainder:

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

7 x 5 = 35

7 x 6 = 42

7 x 7 = 49

7 x 8 = 56

7 x 9 = 63

61 is between 56 and 63.

Answer: 8 R5

Decimal:

61/7 = 8.71428571...

oop i got it-- 

its 5

The ratio is (3 + sqrt(6))/(2*pi), so a + b + c = 3 + 6 + 2 = 11.

That sum is equal to \(\frac{83(84)}{2}=83(42)\). Since 83 is prime, and it is greater than 42, it must be the biggest prime divisor. Therefore, 83 is the answer.

1. Guest was almost right, but he/she forgot to multiply by 2 when squaring the binomial. So the answer is 12.

2. \((r-s)^2 = r^2-2rs+s^2\). By Vieta's formulas, \(r+s = \frac{-6}{-1} = 6\), and \(rs = \frac{2}{1} = 2\) so \((r+s)^2= r^2+2rs+s^2 = 6^2=36\). Now just subtract \(4rs=8\) from 36 to get what we want, so the final answer is 28. 

3. Divide \(3x^2-4x+15=0\) by 3 to get \(x^2 - \frac{4}{3}x + 5 = 0\). Therefore, the ordered pair is \((\frac{-4}{3}, 5)\)

So the surface area formula is \(A=2πrh+2πr^2\).

So you plug 3 for r and 82 for h.

You should get around 1602.21.

For part B, I'm kinda confused. When you said 2 layers, do you mean that each layer is 1 full jar of special paint? Once you respond I can try to help more.

it's not right :/ but thx for trying