Terms that have the same variable part are called like terms. Like terms can be added or subtracted to form a single term.
1.
16x - 4x = -48
First, combine the like terms 16x and -4x.
12x = -48
Now divide both sides by 12.
x = -4
2.
7m - 5 - 13m = 25
First, combine the like terms 7m and -13m.
-6m - 5 = 25
Now add 5 to both sides.
-6m = 30
Divide both sides by -6.
m = -5
3.
12.25 = 0.5q + 3.75
Subtract 3.75 from both sides.
8.5 = 0.5q
Multiply both sides by 2.
17 = q
q = 17
4.
2(2x - 4) + x = 7
Distribute the 2.
4x - 8 + x = 7
Combine 4x and x.
5x - 8 = 7
Add 8 to both sides.
5x = 15
Divide both sides by 5.
x = 3
5.
8 = 3(3x + 8) - x
Distribute the 3.
8 = 9x + 24 - x
Combine 9x and -x.
8 = 8x + 24
Subtract 24 from both sides.
-16 = 8x
Divide both sides by 8.
-2 = x
x = -2
Answer:
The polar coordinates are as follow:
a. (6,2π)
b. (18, π/3)
c. (2√2 , 3π/4)
d. (2, 5π /6)
Step-by-step explanation:
To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .
To calculate r, we use Pythagorean theorem:
r =
---- (1)
To calculate the θ, first we will find out the θ
' using the inverse of cosine as it is easy to calculate.
So, θ
' =
cos
⁻¹ (x/r)
If y ≥ 0 then θ = ∅
If y < 0 then θ = 2
π − ∅
For a. (6,0)
Sol:
Using the formula in equation (1). we get the value of r as:
r = 
r = 6
And ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (6/6)
∅ =cos
⁻¹ (1) = 2π
As If y ≥ 0 then θ = ∅
So ∅ = 2π
The polar coordinates are (6,2π)
For a. (9,9/
)
Sol:
r = 9 + 3(3) = 18
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (9/18)
∅ = cos
⁻¹ (1/2) = π/3
As If y ≥ 0 then θ = ∅
then θ = π/3
The polar coordinates are (18, π/3)
For (-2,2)
Sol:
r =√( (-2)²+(2)² )
r = 2 √2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (-2/ 2 √2)
∅ = 3π/4
As If y ≥ 0 then θ = ∅
then
θ = 3π/4
The polar coordinates are (2√2 , 3π/4)
For (-√3, 1)
Sol:
r = √ ((-√3)² + 1²)
r = 2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ ( -√3/2)
∅ = 5π /6
As If y ≥ 0 then θ = ∅
So θ = 5π /6
The polar coordinates are (2, 5π /6)
We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:

Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:

Now, we have our final range: -5 < x < 9
Where’s the cone? Is there a picture of a cone? I can’t really solve this, I’m sorry if I bother you
Answer:
D. reflection across a vertical line
Step-by-step explanation:
Reflection is basically a mirror image. Since you can see that the first triangle is flipped over to get the second one, this is a reflection.
It is not a vertical translation; this means that the triangle shifted up or down.
It is not a horizontal translation, this means that the triangle shifted left or right.
It is not a rotation about point A either, this would have meant that the triangle spun around.