The cups of popcorn that the boys eat in all is 5 1/4 cups.
<h3>How to illustrate the information?</h3>
From the information, Toby, Tyler, and Tim got hungry and decided to share a bag of popcorn and each boy ate 1 3/4 cups of popcorn.
It should be noted that the total popcorn and hat was eaten will be:
= Fraction eaten by each person × Number of people
= 1 3/4 × 3
= 7/4 × 3
= 21/4
= 5 1/4
This illustrates the concept of multiplication of fractions.
Learn more about fractions on:
brainly.com/question/17220365
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Answer:
3 and 9
if f(x)=x^2+13 and g(x)=12x-14
Step-by-step explanation:
So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).
So we want to find when f(x)=g(x) for x.
f(x)=g(x)
![x^2+13=12x-14](https://tex.z-dn.net/?f=x%5E2%2B13%3D12x-14)
Let's get everything to one side.
Subtracting 12x and adding 14 to both sides.
![x^2+13+14-12x=0](https://tex.z-dn.net/?f=x%5E2%2B13%2B14-12x%3D0)
I'm going to reorder the left hand side and also simplify the 13+14 part:
![x^2-12x+27=0](https://tex.z-dn.net/?f=x%5E2-12x%2B27%3D0)
Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.
Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.
So the factored form of our equation is
![(x-3)(x-9)=0](https://tex.z-dn.net/?f=%28x-3%29%28x-9%29%3D0)
Since the product is 0, then at least one of the factors must be 0.
So we want to solve both x-3=0 and x-9=0.
x-3=0 can be solved by adding 3 on both sides. This gives us x=3.
x-9=9 can be solved by adding 9 on both sides. This gives us x=9.
The intersection of f and g happens at x=3 or x=9.
Answer:
(2X100000)+(7X10000)+(6X1000)
Step-by-step explanation:
BO = 2 * GR
x+3 = 2 (3x-1)
x + 3 = 6x - 2
6x - x = 3+2
5x = 5
x = 1
so GR = 3x - 1 = 3(1) - 1 = 3 - 1 = 2
answer: GR = 2
Answer:
Option (A)
Step-by-step explanation:
One side of the given triangle is a diameter of the semicircle given.
Measure of the diameter = 10 units
Total area of the semicircle = ![\frac{1}{2}\pi (r^{2})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%28r%5E%7B2%7D%29)
= ![\frac{1}{2}\pi (5)^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cpi%20%285%29%5E2)
= 39.27 square units
Area of the right triangle = ![\frac{1}{2}(\text{Base})(\text{Height})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BBase%7D%29%28%5Ctext%7BHeight%7D%29)
= ![\frac{1}{2}(6)(8)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%286%29%288%29)
= 24 square units
Area of the shaded region = Area of the semicircle - Area of the right triangle
= 39.27 - 24
= 15.27 square units
≈ 15 square units
Therefore, option (A) will be the answer.