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3 years ago

What does the quadratic function f(x)=x^2-10x+9 look like when it is rewritten in the form f(x) = a (x-h) + k

Mathematics

1 answer:

Tatiana [17]3 years ago

6 0

ANSWER

When $f(x)=x^2-10x+9$ is written in the form $f(x)=a(x-h)^2+k$ , it looks like $f(x)=(x-5)^2-16$

EXPLANATION

To write $f(x)=x^2-10x+9$ in the form $f(x)=a(x-h)^2+k$ , we have to complete the squares.

We add and subtract half the coefficient of $x$ square.

$f(x)=x^2-10x+(-5)^2-(-5)^2+9$

The first three terms of the function is now a perfect square.

$f(x)=(x-5)^2-25+9$

We now simplify rto obtain,

$\Rightarrow f(x)=(x-5)^2-16$

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A bag is filled with 100 marbles that are all the same size and shape each marble has one color the number of marbles in a color

Svetlanka [38]

Answer: 21/100

Step-by-step explanation:

Number of green marbles = 21

Number of blue marbles = 35

Number of red marbles = 18

Number of yellow marbles = 26

Total number of marbles = 100

The probability of choosing a free marble will be:

= Number of green marbles / Tot number of marbles

= 21 / 100

4 0

3 years ago

Joe is considering taking out along with the principal of $15,500 From one of two banks. Bank A charges and interest rate of 6%,

ki77a [65]

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total cost of the loan at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount taken as loan.

Considering bank A's offer

From the information given,

P = $15500

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

t = 8 years

Therefore,

A = 15500(1 + 0.06/12)^12 × 8

A = 15500(1 + 0.005)^96

A = 15500(1.005)^96

A = $25019.2

The interest paid is

25019.2 - 15500 = $9519.2

Considering bank B's offer

From the information given,

P = $15500

r = 6.5% = 6.5/100 = 0.065

n = 12 because it was compounded 12 times in a year.

t = 7 years

Therefore,

A = 15500(1 + 0.065/12)^12 × 7

A = 15500(1 + 0.0054)^84

A = 15500(1.0054)^84

A = $24366

The interest paid is

24366 - 15500 = $8866

The interest that would by paid on bank B's offer is lower than that of bank A and the duration of the loan offer from bank B is shorter than that of bank A.

Therefore,

Bank A gives you more time to pay up the loan and you end up paying more interest

Bank gives you lesser time to pay up the loan and you end up paying lesser interest.

3 0

3 years ago

a video game has 35 levels in it if you beat 5 of the levels what is the ratio of levels left to the levels that have been beate

marta [7]

We have 35 - 5 = 30 levels left to beat.

The question is asking us for the levels left to beat, to the ones that already have been beaten:

30 : 5

Simplified;

6 : 1

8 0

3 years ago

Please help im stuck on this question

VARVARA [1.3K]

Answer:

(12,0)

Step-by-step explanation:

slope m=

$\frac{54-36}{27-22} =\frac{18}{5}$

$y-36=\frac{18}{5}(x-22)\\\\5y-180=18x-396\\\\y=\frac{18x}{5} -\frac{46}{5}$

$0=\frac{10}{5}x-\frac{46}{5}\\\\x=\frac{216}{18} =12$

hope it helps...

have a great day

7 0

3 years ago

X² - xy = 0<br> x + y = 1

wolverine [178]

Answer:

(0, 1 ) and ( $\frac{1}{2}$ , $\frac{1}{2}$ )

Step-by-step explanation:

Given the 2 equations

x³ - xy = 0 → (1)

x + y = 1 → (2) ( subtract x from both sides )

y = 1 - x → (3)

Substitute y = 1 - x into (1)

x² - x(1 - x) = 0

x² - x + x² = 0

2x² - x = 0 ← factor out x from each term on the left side

x(2x - 1) = 0

Equate each factor to zero and solve for x

x = 0

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = $\frac{1}{2}$

Substitute these values into (3) for corresponding values of y

x = 0 : y = 1 - 0 = 1 ⇒ (0, 1 )

x = $\frac{1}{2}$ : y = 1 - $\frac{1}{2}$ = $\frac{1}{2}$ ⇒ ( $\frac{1}{2}$ , $\frac{1}{2}$ )

3 0

3 years ago