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olasank [31]
3 years ago
15

Part A: Solve A = (x + 23) for x. (4 points) Part B: Determine the value of x when A = 108. (2 points) Part C: Solve -np - 90 &g

t; 30 for n. Show your work. (4 points)
Mathematics
1 answer:
Galina-37 [17]3 years ago
7 0
<span>Part A: Solve A = (x + 23) for x.

A = x + 23

=> A - 23 = x + 23 - 23

=> A - 23 = x

=> x = A - 23 <------- answer

Part B: Determine the value of x when A = 108

Replace the value of A in the expression x = A - 23

x = 108 - 23 = 75

x = 75 <------- answer

Part C: Solve -np - 90 > 30 for n.

-np - 90 > 30

=> -np + np - 90 >30 +  np

=> - 90 > 30 + np

=> -90 - 30 > 30 - 30 + np

=> -120 > np

=> np < - 120 <----- answer
</span>
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For the right triangles below, find the exact values of the side lengths b and d.
Ivanshal [37]

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached below;

According to the first triangle, taking 30° as the reference angle, the opposite side of the triangle will be 5 and the adjacent will be the unknown side "b"

According to SOH, CAH, TOA;

tanθ = opposite/adjacent (using TOA)

Given;

θ = 30°, opposite = 5 and adjacent = b

tan30° = 5/b

b = 5/tan30°

b = 5/(1/√3)

b = 5*√3/1

b = 5√3

According to the 45° triangle, the opposite side of the triangle will be d and the hypotenuse will be 7

Using SOH;

sinθ = opposite/hypotenuse

Given;

θ = 45°, opposite = d and adjacent = 7

sin45° = d/7

d = 7sin45°

d = 7(1/√2)

d = 7/√2

Rationalize 7/√2

= 7/√2*√2/√2

=7√2/2

Hence the value of d is 7√2/2

7 0
3 years ago
5x – 12y – 17 = 0<br> 1*9(x + 2) - (y + 1) + 3 = 0
valentina_108 [34]

Answer: x=\frac{12y+17}{5}

y=\frac{-5x+17}{-12}

x=\frac{y-20}{9}

y=9x+20

Step-by-step explanation:

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (plus 12y from both sides)

5x=12y+17 (divide 5 from everything)

x=\frac{12y+17}{5}

5x-12y-17=0 (plus 17 from both sides)

5x-12y=17 (minus 5x from both sides)

-12y=-5x+17 (divide everything by -12)

y=\frac{-5x+17}{-12}

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (plus y to both sides)

9x=y-20 (divide 9 from both sides)

x=\frac{y-20}{9}

1*9(x+2)-(y+1)+3=0 (distribute 9 to x and to 2) (distribute -1 to y and to 1)

1*9x+18-y-1+3=0 (times 9x by 1)

9x+18-y-1+3=0 (combine like terms)

9x-y+20=0 (minus 20 from both sides)

9x-y=-20 (minus 9x from both sides)

-y=-9x-20 (divide -1 from everything)

y=9x+20

3 0
3 years ago
Help me with this please, thank you
Hoochie [10]

Answer:

2x + x + 90 = 180

3x + 90 = 180

3x = 90

x = 30°

2(30)= 60°

8 0
3 years ago
(+×9)(×-2) can some one solve it
marshall27 [118]
X2 - 2x + 9x - 18
X2 + 7x - 18
4 0
3 years ago
3x-7x=12x how would u solve this?
Ipatiy [6.2K]

Answer:

Because theres nothing to solve for x is all real numbers

Step-by-step explanation:

There is no way to solve it as theres nothing to solve for. You just plug in the x's with any number you want and it still will be there

4 0
3 years ago
Read 2 more answers
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