Step-by-step explanation:
Remember to isolate the variable for each question. Note the equal sign, what you do to one side, you do to the other.
1) 4 + x = 8
Subtract 4 from both sides
4 (-4) + x = 8 (-4)
x = 8 - 4
x = 4
D) x = 4 is your answer
2) -2x ≤ 6
Note that when dividing or multiplying a negative number, you must flip the sign. Isolate the variable (x).
(-2x)/-2 ≤ (6)/-2
x ≥ 6/-2
x ≥ -3
A & B are the same, so you'll have to ask the teacher which one was supposed to have a negative 3
3) Remember to do the opposite of PEMDAS. First subtract, then multiply. Again, isolate the variable (x).
x/2 + 3 = 5
x/2 + 3 (-3) = 5 (-3)
x/2 = 5 - 3
x/2 = 2
(x/2)(2) = 2(2)
x = 2 * 2
x = 4
A) x = 4 is your answer
4) Remember to do the opposite of PEMDAS. First subtract, then divide. Again, isolate the variable (x).
7x + 6 = 20
7x + 6 (-6) = 20 (-6)
7x = 20 - 6
7x = 14
(7x)/7 = (14)/7
x = 14/7
x = 2
D) x = 2 is your answer
5) You are solving for x. Note that there are two variables, however, you don't need to worry too much about the second variable (<em>a</em>), just know that you cannot combine (using addition or subtraction) a number with variable and a constant (a number without).
First, subtract 8a from both sides:
2x + 8a (-8a) = 10 (-8a)
2x = 10 - 8a
Next, divide 2 from both sides to isolate the variable (x):
(2x)/2 = (10 - 8a)/2
x = (10)/2 (-8a)/2
x = 5 - 4a
D) x = 5 - 4a is your answer
~
Given, the surface area of a sphere is =
The formula to find the surface area of a sphere =
Where, r is the radius of the sphere.
As the surface area of the sphere given, we can equate it with the formula.
So we can write the equation as,
To find r, first we have to move 4 to the right side by dividing it to both sides. We will get,
Now to find r, we have to move to the right side, by dividing it to both sides. We will get,
Now to find r, we will take square root to both sides.
So we have got the radius of the sphere = 9cm.
Now the formula to find the volume of the sphere =
Now plugging in the value of r we will get,
Volume =
=
=
=
=
=
So the required volume of the sphere =
I can’t really see the answer choices
Answer:
The ratio of the length of DE and the length of BC = 1/4
Step-by-step explanation:
From the figure we can see two sectors
<u>To find the length of BC</u>
The sector ABC with radius r and central angle 2β
BC = (2πr)( 2β/360)
= 4πrβ/360
<u>To find the length of DE</u>
The sector ADE with radius r/2 and central angle β
DE = (2πr/2)( β/360)
= πrβ/360
<u>To find the ratio of DE to BC</u>
DE/BC =πrβ/360 ÷ 4πrβ/360
= πrβ/360 * 360/ 4πrβ
=1/4