Answer: 1unit.
Step-by-step explanation:
Area of the rectangle
A = length × width
Since the area = 20 and the width is x and the length is x + 1.
We now substitute for the values in the above formula and solve for x
20 = x × x + 1
20 = x( x + 1 ), we now open
20 = x² + x , then re arrange.
x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means
Here, I am going to solve using factorization by grouping
x² + x - 20 = 0
x² + 5x - 4x - 20 = 0
x( x + 5 ) - 4( x + 5 ) = 0
( x + 5 )( x - 4 ). = 0
Therefore, the solution for x will be
x = -5 or 4, but x can not be -5 ( negative), so x = 4.
Now the difference between width and the length can easily be calculated from the above,
Width = 4 (x) , and length = 5 (4 + 1),
Now difference will be
5 - 4 = 1unit.
Answer:
Equation: 
Solve for n: n = 112
Step-by-step explanation:
To first set up the equation, you need to look at the verbal description and translate into numbers and operations:
'three fourths a number' = 
'plus 8' = + 8
'is' =
'20 less' = - 20
'the number' = n
Put the expressions together:
'three fourths a number plus 8': 
'20 less than the number': n - 20
Set them equal to each other and solve:
Add 20 to both sides: 
Subtract 
from both sides: 
Multiply both sides by 
: 
Solve for n: n = 112
First you have to multiply 2x33 which is 66 then you have to add 1 which is 67 so the answer would be 67/2 I don’t know about the percent sign though
Answer:
Step-by-step explanation:
IQR is the difference between Q3 and Q1
<u>According to the top box plot:</u>
<u>The IQR is:</u>
Okay, so your first one, number six. You have two shapes there, a cone and a circle. Now you have a full cone and a half of a circle. Let's start with the cone. The formula for the volume of a cone is πr²h/3. You have your height, that is 12, so get your paper out and plug that in. H = 12. Now, your radius is where it gets a bit tricky. Have you ever heard of the Pythagorean theorem? It's a²+b²=c². Look at the cone, but look at it like it's a two-dimensional shape. You see the triangle in the middle, ignore the rest and pretend it's only that triangle. You now have a right triangle, You know your height is 12, and by looking at the triangle adjacent to it, and know it's equal, you know that your hypotenuse (the longest side of your triangle) is 15. So plug that into the Pythagorean theorem. Now you have 12²+b²=15². Use algebra to work that out, and you're left with 9. So your radius is 9. Now plug that into your volume of a cone equation. The volume of the cone is about 1017.88. Now find the circle or sphere. The formula is 4/3πr³. Just plug in your radius and get your answer, which is 3053.63. Now cut that in half, as you've only got half a circle. Now you've got 1526.82. Now add that to the volume of your cone, and you've got your final answer. 2544.7, or about that. I used π on a calc, and not 3.14, so it might be a little different.
Do you think you can do the next one? Just look at your triangle in there. You've already got one side and a hypotenuse, so plug it into the Pythagorean theorem and get your last side. Then look at the little marks on there and you can see if places are the same. If you need help with it don't hesitate to ask. I'm staying up all night anyway. Homeschooled and behind, so I'm not going anywhere.
