Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
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<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
Hey there!!
Remember : R = range and f ( x ) = y and y = range
R : { 5 , 6 , 7 , 8 }
( 1 ) 5 = 1 x / 2 + 4
... 5 - 4 = x / 2
... 1 = x / 2
... x = 2 = ( 2 , 5 )
( 2 ) 6 = x / 2 + 4
... 2 = x / 2
... x = 4 = ( 4 , 6 )
( 3 ) 7 = x / 2 + 4
... 3 = x / 2
... x = 6 = ( 6 , 7 )
( 4 ) 8 = x /2 + 4
... 4 = x/2
... x = 8 = ( 8 , 8 )
Hope my answer helps!
Answer:
The determinant of the matrix for the the pineapple cake is 4,350. the price of one pineapple cake is 3,520
The determinant of the matrix for the chocolate cake is 5,075 . the price of the chocolate cake is 4,414
Answer:
5) Regular decagon. 6) Yes.
Step-by-step explanation:
Number 6 is yes bc the interior angles of a triangle have to equal 180, and 1+2+177 equals 180.
Answer:
900 calories
Step-by-step explanation:
First you have to find the unit rate, how many calories are there in ONE cracker? To find that you have to divide 60 ÷ 12 = 5 and to check with the other one, 75 ÷ 15 = 5
So, one cracker is 5 calories. Now, how many calories are in 180 crackers? You multiply, 180 x 5 = 900
That means there are 900 calories in 180 crackers.
Hope that helps and have a great day!
