solve for c, express your answer in simplest and exact form
a=9(b+c)
To solve for c, we need to isolate it on one side of the equation. Let's start by distributing 9 to (b+c):
a = 9b + 9c
Next, subtract 9b from both sides of the equation to move it to the right side:
a - 9b = 9c
Now, divide both sides of the equation by 9 to solve for c:
c = (a - 9b)/9
Therefore, the solution for c is (a - 9b)/9.
solve for u
Q=1/8(u+w+v)
To solve for u, we need to isolate it on one side of the equation. Let's start by multiplying both sides of the equation by 8 to get rid of the fraction:
8Q = u + w + v
Next, subtract w and v from both sides of the equation to isolate u:
8Q - w - v = u
Therefore, the solution for u is 8Q - w - v.
In a small rectangular wallet photo, the width is 6cm less than the length. If the border (perimeter) of the photo is 20cm, find the length and width.
Part 1 of 2
The length of the rectangular photo is
.
Part 2 of 2
The width of the rectangular photo is
.
Part 1 of 2:
Let's denote the length of the rectangular photo as L. According to the problem statement, the width is 6cm less than the length, so the width can be expressed as L - 6.
Part 2 of 2:
The border, which represents the perimeter of the photo, is given as 20cm. The formula for the perimeter of a rectangle is 2L + 2W, where L represents the length and W represents the width. We can set up the equation as follows:
2L + 2(L - 6) = 20
Simplifying the equation:
2L + 2L - 12 = 20
4L - 12 = 20
4L = 32
L = 8
Therefore, the length of the rectangular photo is 8cm.
Substituting this value into the width formula L - 6:
W = 8 - 6
W = 2
Therefore, the width of the rectangular photo is 2cm.
The perimeter of a triangle is 20ft. One side is 5ft longer than the shortest side. The third side is 3ft longer than the shortest side. Find the lengths of all the sides.
Part 1 of 3
The length of the shortest side is
.
Part 2 of 3
The length of the largest side is
.
Part 3 of 3
The length of the remaining side is
.
Part 1 of 3:
Let's denote the length of the shortest side as x.
Part 2 of 3:
According to the problem, one side is 5ft longer than the shortest side. So, the length of this side can be expressed as x + 5.
Part 3 of 3:
The third side is 3ft longer than the shortest side. So, the length of the third side can be expressed as x + 3.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 20ft.
Therefore, we can set up the equation as follows:
x + (x + 5) + (x + 3) = 20
Simplifying the equation:
3x + 8 = 20
3x = 12
x = 4
So, the length of the shortest side is 4ft.
Substituting this value into the expressions for the other two sides:
The length of the largest side = x + 5 = 4 + 5 = 9ft.
The length of the remaining side = x + 3 = 4 + 3 = 7ft.
Therefore, the lengths of all the sides are:
Shortest side: 4ft
Largest side: 9ft
Remaining side: 7ft.
Two angles are complementary. One angle is 8 degrees less than the other angle. Find the measures of the angles.
Let's denote one angle as x degrees.
Since the two angles are complementary, the other angle can be expressed as 90 degrees minus x degrees.
According to the problem statement, one angle is 8 degrees less than the other angle, so we can set up the following equation:
x = (90 - x) - 8
Now we can solve for x:
x = 90 - x - 8
2x = 82
x = 41
Therefore, one angle measures 41 degrees.
To find the measure of the other angle, we can subtract 41 from 90:
90 - 41 = 49
So, the other angle measures 49 degrees.
In summary, one angle measures 41 degrees and the other angle measures 49 degrees.
Sorry I meant 18 less not 8 less
No problem. Let's solve the problem with the given correction.
Let's denote one angle as x degrees.
Since the two angles are complementary, the other angle can be expressed as 90 degrees minus x degrees.
According to the problem statement, one angle is 18 degrees less than the other angle, so we can set up the following equation:
x = (90 - x) - 18
Now let's solve for x:
x = 90 - x - 18
2x = 72
x = 36
Therefore, one angle measures 36 degrees.
To find the measure of the other angle, we can subtract 36 from 90:
90 - 36 = 54
So, the other angle measures 54 degrees.
In summary, one angle measures 36 degrees and the other angle measures 54 degrees.
Two angles are supplementary. One angle is four times as large as the other angle. Find the measures of the angles.
Let's denote one angle as x degrees.
Since the two angles are supplementary, the other angle can be expressed as 180 degrees minus x degrees.
According to the problem statement, one angle is four times as large as the other angle, so we can set up the following equation:
x = 4(180 - x)
Now let's solve for x:
x = 720 - 4x
5x = 720
x = 144
Therefore, one angle measures 144 degrees.
To find the measure of the other angle, we can subtract 144 from 180:
180 - 144 = 36
So, the other angle measures 36 degrees.
In summary, one angle measures 144 degrees and the other angle measures 36 degrees.