To solve this, use the ‘completing the square’ strategy.
Leave a space to make the first two values a perfect square.
y=(x^2-2x___)-3
Divide -2 by 2 and square that number to put in the blank. Then subtract that number from outside.
y=(x^2-2x+1)-3-1
Simplify!
y=(x-1)^2-4
It is in vertex form now ;)
Please make my brainliest ,’-)
In order to do this you need a system of equations. One equation is going to be about the numbers of people, the other is going to be about the money: what it costs for each type of person and the total amount of money earned. Money and numbers of people are 2 different things so they have to be in 2 different equations. We know that there were children and adults that went to the park and that the total NUMBER of people is 220. That means that adults plus children equal 220 people total. Or, in equation form, a + c = 220. Now the money part. Each child costs 2.25, so the cost of a child is 2.25c; each adult costs 6.20, so the cost of an adult is 6.20a. The total amount of money earned was 890. That equation is 2.25c + 6.20a = 890. Solve the first equation for a: a = 220 - c. Now sub in that value for a in the money equation, like this: 2.25c + 6.20(220-c) = 890. Solve this for c. 2.25c+1364-6.2c = 890. Combine like terms to get -3.95c = -474. Divide both sides by 3.95 to get that c = 120. There were 120 children out of the 220 people that attended. That means that there were 220-120 adults, or 100 adults. There you go!
Answer:
1,281
Step-by-step explanation:
6^4 is 1,296 subtract 15 you get 1,281
Answer:
-x^2-2xy-3x
Step-by-step explanation:
a. The volume of prism 1 is 8346.562 ft³
b. The surface area of the white eraser is 13 cm²
The question has to do with scale factor
<h3>What is scale factor?</h3>
Scale factor is the ratio of two similar quantities
<h3>a. How to find the volume of Prism 1.</h3>
Since
- Prism 1 has a surface area of A = 289 ft² and
- Prism 2 has a surface area of A' = 529 ft².
Let
- L be the length of side of prism 1 and
- L' the length of side of prism 2
We have that scale factor = A/A'
Also,
A/A' = (L/L')²
L/L = √(A/A') = √( 289 ft²/ 529 ft²) = √0.49 = 0.7
Since
- prism 1 has a volume of V and
- prism 2 has a volume of V' = 24334 ft³. We have that
V/V' = (L/L')³
So, V = (L/L')³V'
So, substituting the values of the variables into the equation, we have
V = (L/L')³V'
V = (0.7)³24334 ft³
V = 0.343 × 24334 ft³
V = 8346.562 ft³
So, the volume of prism 1 is 8346.562 ft³
<h3>b. How to find the surface area of the white eraser?.</h3>
Since
- The white eraser has volume of V = 2 cm³ and
- The yellow eraser has volume of V' = 16 cm³.
Let
- L be the length of side of white eraser and
- L' the length of side of yellow eraser
We have that scale factor = V/V'
Also, V/V' = (L/L')³
L/L = ∛(V/V')
= ∛( 2 cm³/16 cm³)
= ∛(1/8)
= 1/2
Since
- White eraser has a surface area of A and
- Yellow eraser has a surface area of A = 52 cm² . We have that
A/A' = (L/L')²
So, A = (L/L')²A'
So, substituting the values of the variables into the equation, we have
A = (L/L')²A'
A = (1/2)²52 cm²
A = 1/4 × 52 cm²
A = 13 cm²
So, the surface area of the white eraser is 13 cm²
Learn more about scale factor and surface area here:
brainly.com/question/26161002
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