Rewrite the function by completing the square.
f(x)=x^2+20x+40
Answers
f(x)=x²+20x+40
To complete the square, the same value needs to be added to both sides.
f(x)+?=x²+20x+?+40
Now i make the same thing in different forms ok
To complete the square x²+20x+100=(x+10)² add 100 to the expression
f(x)+?=x²+20x+100+40
Is the same ok you can choose which way you can do
x²+20x+?
write the expression as a product with the factor 2 and x
x²+2x×x10+?
x²+2×x×10+?
Since 10 is part of the middle term, add 10² to the expression
x²+2×x×10+10²
Calculate the product
x²+20x+10²
or evaluate the power
x²+20x+100
f(x) +?=x²+20x+100+40
Since 100 was added to the right - hand side, also add 100 to the left hand side
f(x)+100=x²+20x+100+40
Using a²+2ab+b²=(a+b)², factor the expression
f(x)+100=(x+10)²+40
------------------
x²+20x+100
Write the expression as a product with the factors x and 10
x²+2×x×10+100
Write the number in the exponential form with an exponent of 2
x²+2×x×10+10²
Using a²+2ab+b²=(a+b)² factor the expression
(x+10)²
--------
f(x)+100=(x+10)²+40
Move constant to the right-hand side and change its sign
f(x)=(x+10)²+40-100
Calculate the difference
40-100
Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger
-(100-40)
Subtract the numbers
-60
Answer:f(x)=(x+10)²-60
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Final answer:
To rewrite the function f(x) = x² + 20x + 40 by completing the square, we find half the coefficient of the x term, square it, subtract the constant term in the original equation from this squared result, then rewrite the function as (x+10)^2 - 60.
Explanation:
When you're asked to rewrite the function by completing the square, there are certain steps to follow. We start with the function f(x) = x² + 20x + 40.
- First, take the coefficient of the x term (in our case, 20) and divide it by 2. This would yield 10.
- Next, square the result from step 1. That is 10² = 100.
- Subtract the constant term in the original equation from the squared result i.e. 100 - 40 = 60.
- Finally, the equation takes this form: f(x) = (x+10)² - 60.
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Answers
100% - 30% = 70%
The price is not needed
Final answer:
Miguel paid 70% of the original price for the bicycle. The original price was calculated as approximately $175 by dividing the price Miguel paid ($122.50) by 70% (the remaining percentage after the 30% discount).
Explanation:
Miguel paid $122.50 for a bicycle which was discounted by 30%. So, the $122.50 represents the 70% of the original price (because 100% - 30% = 70%). To find out what 100% (the original price) is, we need to perform a calculation where we divide the price paid by Miguel ($122.50) by 70% (in decimal format, that's 0.70).
The formula would structure as below:
Original Price = Price Paid / Percentage of Original Price Paid
Substituting in the values provided, the equation would be:
Original Price = $122.50 / 0.70
Following through with this calculation, we find that the original price of the bicycle was approximately $175. Therefore, Miguel paid 70% of the original price, as that's the remaining percentage after the 30% discount.
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Answers
Step-by-step explanation:
We know that this particularly line can be named as :
- JK ←→
- LM ←→
This give us the following information :
- The line passes through the points J and K
- The line passes through the points L and M
One statement we can make is :
The points J , K , L and M are aligned. So the line passes through the points J , K , L and M.
We also know that given a line there are infinite planes that contain the line.
Given that the points J , K , L and M belong to the same line, we can state that :
There are infinite planes that contain the points J , K , L and M.
Answers
Answer:
y = -3x + 6
Step-by-step explanation:
Equation of straight line is given by,
y = mx + b
m = slope of the line
b = y-intercept
From the graph attached,
m =
=
= -3
y intercept 'b' = 6
Therefore, equation of the line will be,
y = -3x + 6
distributive property
commutative property
associative property
inverse property
Answers
Answer:
commutative property
Step-by-step explanation:
Either order or way you put the numbers, it will be the same answer.
ANSWER and I will give you brainiliest
Answers
Answer:
2000
Step-by-step explanation:
If 3 days = 600 we need to know what 1 day is so we do 600 / 3
600 / 3 = 200
Then multiply 200 by 10 to find 10 days
200 * 10 = 2000
10 days = 2000
There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 0, negative 20 and 4, 10.