Answer:
x = 200
Step-by-step explanation:
1/5x – 2/3y = 30
substitute in y
1/5x - 2/3(15) = 30
multiply
1/5x - 10 = 30
isolate the variable
1/5x = 40
multiply each side by 5
x = 200
Answer:
0, π
Step-by-step explanation:
cos x sin x = sin x
cos x sin x - sin x = 0
sin x (cos x - 1) = 0
sin x = 0, x = 0, π
cos x - 1 = 0
cos x = 1, x = 0
So answers: 0, π
First we can find the perimeter of the given rectangle
P=2L+2W (L=length and W=width)
P=2*3+2*4
P=6+8
P=14
So now we want to come up with a different combination of numbers that would give up a perimeter of 14. We know that 14 is divisible by 2 so let's make out width 2. If we plug in 2 as the width and 14 as the perimeters, we can solve for length
14=2L+2*2
14=2L+4
10=2L (subtract 4 from both sides)
L=5
So the dimensions are 5 units and 2 units
Hope this helps!
X=3
Let's solve your equation step-by-step.
−
|
x
−
4
|
+
2
=
−
2
x
+
7
Step 1: Add -2 to both sides.
−
|
x
−
4
|
+
2
+
−
2
=
−
2
x
+
7
+
−
2
−
|
x
−
4
|
=
−
2
x
+
5
Step 2: Divide both sides by -1.
−
|
x
−
4
|
−
1
=
−
2
x
+
5
−
1
|
x
−
4
|
=
2
x
−
5
Step 3: Solve Absolute Value.
|
x
−
4
|
=
2
x
−
5
We know either
x
−
4
=
2
x
−
5
or
x
−
4
=
−
(
2
x
−
5
)
x
−
4
=
2
x
−
5
(Possibility 1)
x
−
4
−
2
x
=
2
x
−
5
−
2
x
(Subtract 2x from both sides)
−
x
−
4
=
−
5
−
x
−
4
+
4
=
−
5
+
4
(Add 4 to both sides)
−
x
=
−
1
−
x
−
1
=
−
1
−
1
(Divide both sides by -1)
x
=
1
x
−
4
=
−
(
2
x
−
5
)
(Possibility 2)
x
−
4
=
−
2
x
+
5
(Simplify both sides of the equation)
x
−
4
+
2
x
=
−
2
x
+
5
+
2
x
(Add 2x to both sides)
3
x
−
4
=
5
3
x
−
4
+
4
=
5
+
4
(Add 4 to both sides)
3
x
=
9
3
x
3
=
9
3
(Divide both sides by 3)
x
=
3
Check answers. (Plug them in to make sure they work.)
x
=
1
(Doesn't work in original equation)
x
=
3
(Works in original equation)
