All categories

3 years ago

Which constant term should be used to complete the square? x^2-5x+__=7

1 answer:

7 0

The constant term should be (-5/2)^2 or (5/2)^2 or 25/4. This constant term comes from taking the coefficient on the x^1 term, halving it, and then squaring it.

You might be interested in

If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Lelechka [254]

Answer:

$\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }$

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

$f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)$

So we can say that

$a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}$

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

$(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab$

and we can notice that

$a^2+b^2=(a+b)^2-2ab$ so

$(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab$

it comes

$x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}$

multiply by 3

$3x^2-20x+2*16+5=3x^2-20x+37$

4 0

3 years ago

What is the value of f(g(1))

jeka57 [31]

Answer: 1

Step-by-step explanation:

All you had to do was multiply g by 1 so f(g(1)) as a value is 1

8 0

3 years ago

1. Given the following relation, determine the inverse relation.

gayaneshka [121]

Answer:

1. a

2. $f^{-1} (x)=\frac{x}{2} +2$

Step-by-step explanation:

1. Since there is one value of y for every value of x in (−1,0),(−4,5),(3,2),(−3,5), this relation is a function.

2. To find the inverse, interchange the variables and solve for y.

$f^{-1} (x)=\frac{x}{2} +2$

5 0

2 years ago

A dog walker earns $10 plus $3 per dog. What equation represents this model?

xxTIMURxx [149]

10+3x Or 3x+10.
This is because he gets 10 dollars add it to the 3 he gets per dog. The per dog is X as you don’t know how many dogs he gets

6 0

2 years ago

The chart given here lists the amount of rainfall received in centimeters in each month. By how much is the combined rainfall re

wlad13 [49]

It is B:23 centimeters 54+56=110. 63+70=133 133-110= 23c

4 0

3 years ago