Answer:
1. The domain for the number of fruit cups is 0 minimum and 20 maximum.
[0 < x < 20].
2. [10 < y < 70]
Step-by-step explanation:
1. The domain is 0 to 20 because there are 20 people total who will each have a fruit cup
2. The range is $10 to $70 because the minimum price is $10 without any fruit cups and $70 when there are 20 fruit cups.
Answer:
<h2>C. G(x) = (x - 1)² - 3</h2>
Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
Look at the picture.
The graph of F(x) shifted 1 unit to the right and 3 units down.
Therefore the equation of the function G(x) is
![G(x)=(x-1)^2-3](https://tex.z-dn.net/?f=G%28x%29%3D%28x-1%29%5E2-3)
Answer:
B. 6 7/10
Step-by-step explanation:
We solve the above y by carrying out addition.
The quarts of Lemonade she made is calculated as:
1 2/5 quarts of syrup + 5 3/10 quarts of water
= 1 + 5 + (2/5 + 3/10)
Lowest common denominator = 10
= 6 ( 4 + 3/10)
= 6 7/10 quarts of Lemonade
Mrs Olive made 6 7/10 quarts of Lemonade
For the given triangle, the value of x equals 30.9892 units.
Step-by-step explanation:
Step 1:
In the triangle, the angle is 40°, the opposite side has a length of 26 units, the adjacent side has a length of x units while the hypotenuse is not given.
To determine the value of x, we determine the value of the tan of the given triangle.
To calculate the tan of angle A we divide the opposite side's length by the the adjacent side's length.
![tan A = \frac{oppositeside}{adjacent side}.](https://tex.z-dn.net/?f=tan%20A%20%3D%20%5Cfrac%7Boppositeside%7D%7Badjacent%20side%7D.)
Step 2:
The length of the opposite side = 26 units.
The length of the adjacent side = x units.
![tan A = \frac{oppositeside}{adjacent side}, tan 40 = 0.8390, tan A = \frac{26}{x} .](https://tex.z-dn.net/?f=tan%20A%20%3D%20%5Cfrac%7Boppositeside%7D%7Badjacent%20side%7D%2C%20tan%2040%20%3D%200.8390%2C%20tan%20A%20%3D%20%5Cfrac%7B26%7D%7Bx%7D%20.)
![0.8390 = \frac{26}{x} , x = \frac{26}{0.8390} = 30.9892.](https://tex.z-dn.net/?f=0.8390%20%3D%20%5Cfrac%7B26%7D%7Bx%7D%20%2C%20x%20%3D%20%5Cfrac%7B26%7D%7B0.8390%7D%20%3D%2030.9892.)
So x measures 30.9892 units.
Answer:
a=1 or a=5/6
Step-by-step explanation:
I'm going to attempt to factor 6a^2-a-5
a=6
b=-1
c=-5
Find two numbers that multiply to be a*c and add to be b.
a*c=-30 =-6(5)
b=-1 =-6+5
So replace -a with -6a+5a in the expression we started with
6a^2-6a+5a-5
now we factor by grouping
6a(a-1)+5(a-1)
(a-1)(6a-5)
Now let's solve the equation:
(a-1)(6a-5)=0
So a=1 or a=5/6