-43 - 4r = 3 - 27r
Add 27r to both sides. -43 - 4r + 27r = 3 -27r + 27r or -43 + 23r = 3
Add 43 to both sides. -43 + 43 +23r = 3 + 43 or 23r = 46.
Divide both sides by 23 to get r by itself. 23r / 23 = 46 / 23 or r = 2
r = 2
Answer:
m<PTR = 140°
Step-by-step explanation:
First, find the value of x. To find the value of x, derive an equation which you'd use in solving for x.
m<PTQ = (x + 28)°
m<RTS = (2x + 16)°
m<PTQ = m<RTS (vertical opposite angles are congruent)
Therefore:
x + 28 = 2x + 16
Solve for x. Combine like terms
28 - 16 = 2x - x
12 = x
x = 12
Find m<PTQ
m<PTQ = (x + 28)
plug in the value of x
m<PTQ = 12 + 28 = 40°
m<PTR + m<PTQ = 180° (supplementary angles)
m<PTR + 40° = 180° (substitution)
m<PTR = 180 - 40 (subtracting 40 from each side)
m<PTR = 140°
Answer:
4 people name chocolate
Step-by-step explanation:
Let's first understand the given information.
The survey shows that 40 percent of a finite number of people name chocolate as their favorite flavor of ice cream. Because the survey is reporting a percentage, then 40% means that from 100 people 40 people name chocolate, while the others name a different type of flavor.
Dividing the total of people (100) by the ones who name chocolate (40) then we have:
100/40 = 2.5
Through the above equation we are actually expressing the following:
Total people = 2.5 * (people who name chocolate flavor)
Using this equation if we have now 12 people:
12 = 2.5 * (people who name chocolate flavor)
12/2.5 = (people who name chocolate flavor)
4.8 = people who chose chocolate flavor
Because we can't have 0.8 of a person, then if we have a sample of 12 people, we will expect that 4 of them name chocolate.
The length of the rectangular base is 9in
<h3>How to determine the value</h3>
It is important to note that the formula for determining the volume of a pyramid with rectangular base is expressed as;
Volume = lwh/3
Where;
- l is the length of the rectangular base of the pyramid
- w is the width of the rectangular base of the pyramid
- h is the height of the rectangular base of the pyramid
Given the value of the volume, width an height of the pyramid as 168, 7 and 8, we substitute the values, we have;
168 = l × 7 × 8/ 3
cross multiply
l × 7 × 8 = 168(3)
Find the product
56l = 504
To determine the length, divide both sides by 56, we get;
l = 504/ 56
l = 9In
Hence, the value is 9in
Learn more about volume here:
brainly.com/question/463363
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