1)x+30=40
x=40-30
Answer :x=10
2)30-20+2x=10
10+2x=10
2x=0
Answer: x=0
3)3x-10+13=-2x+28
3x+3=-2x+28
3x+2x+3=28
3x+2x=28-3
5x=28-3
5x=25
x=5
4)13x-23-45=-7x+12
13x-68=-7x+12
13x+7x-68=12
13x+7x=12+68
20x=12+68
20x=80
x=4
5)2(x+4)=10x+24
2x+8=10x+24
2x-10x+8=24
2x-10x=24-8
-8x=24-8
-8x=16
x=-2
6)3(x-5)=1-(2x-4)
3x-15=1-(2x-4)
3x-15=1-2x+4
3x-15=5-2x
3x+2x-15=5
3x+2x=5+15
5x=5+15
5x=20
x=4
7)5x-10=15
5x=15+10
5x=25
x=5
8)x+4=x+6
4=6
no solution
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Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

Simplify. The denominator uses the difference of two squares pattern:

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

Split into two separate fractions:

Rewrite the two fractions:

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

Hence verified.
= 
The coefficients are 8 , 12, 6, 1
= 
The coefficients are 16, 96, 216, 216, 81
=
The coefficients are 27, 54,36 , 8
= x^4+4x^3y+6x^2y^2+4xy^3+y^4
The coefficients are 1, 4, 6, 4, 1
The angle of depression equals 32.
A way that you can solve this is by finding angle c. Angle C would be the same as the angle of depression because of alternate angles being congruent.
So you do the triangle angle sum theorem.
58+90+x=180
Simplify
148 +x=180
Subtract 148 from both sides
x=32
So Since angle c equals to 32 degrees, then the angle of depression is also 32 degrees.
The range of a data set is the greatest value minus the smallest value.
The greatest value here is 32, and the smallest value is 27: