All categories

2 years ago

1. Given that 4x²- 16x + 15 = a(x-p)²+ q for all values of x.

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

8 0

Answer:

a = 4, p = 2, q = - 1

Step-by-step explanation:

Expand the right side of the identity, then compare the coefficients of like terms with those on the left side.

a(x - p)² + q ← expand (x - p)² using FOIL

= a(x² - 2px + p²) + q ← distribute parenthesis

= ax² - 2apx + ap² + q

Compare coefficients of x² term

a = 4

Compare coefficients of x- term

- 2ap = - 16, that is

- 2(4)p = - 16

- 8p = - 16 ( divide both sides by - 8 )

p = 2

Compare constant terms

ap² + q = 15 , that is

4(2)² + q = 15

16 + q = 15 ( subtract 16 from both sides )

q = - 1

Thus a = 4, p = 2, q = - 1

You might be interested in

Please anyone help me on this question

vazorg [7]

Answer:

a) 60

b) 0.24

c) 150

Step-by-step explanation:

a) P(green) = ⅕

Expected no. = 300 × ⅕

= 60

b) total = 300

P(purple) = 72/300

= 6/25 = 0.24

c) P(blue) = 45/300

= 3/20 = 0.15

Expected no.: 1000 × 0.15

= 150

5 0

2 years ago

I need help sorry for bothering everyone. Two supporting reasons are missing from the proof. Complete the proof by dragging and

attashe74 [19]

Since ∠2=60° = ∠8 so it will also be 60 °
the sum of the both are 60°+∠7=180°
∠7= 180°- 60° = 120°

6 0

2 years ago

Read 2 more answers

A surveyor is studying a map of the community and is using vectors to determine the distance between two schools. On the map, th

guajiro [1.7K]

<h2>C. components: (-28,-25), actual distance about 37.54 meters</h2>

5 0

2 years ago

Read 2 more answers

Five consecutive odd integers whose sum is 85

Katen [24]

Answer:

13,15,17,19,21

Hope I helped! ☺

7 0

2 years ago

Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00

Tatiana [17]

Answer:

The principal must be = $8991.88

Step-by-step explanation:

Formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount after 't' years.

P is the principal amount

n is the number of times interest is compounded each year.

r is the rate of interest.

Here, we are given that:

Amount, A = $15000

Rate of interest = 13 % compounded quarterly i.e. 4 times every year

Number of times, interest is compounded each year, n = 4

Time, t = 4 years.

To find, Principal P = ?

Putting all the given values in the formula to find P.

$15000 = P(1 + \frac{13}{400})^{4\times 4}\\\Rightarrow 15000 = P(1 + 0.0325)^{16}\\\Rightarrow 15000 = P(1.0325)^{16} \\\Rightarrow 15000 = P \times 1.66817253\\\Rightarrow P = \dfrac{15000}{1.66817253}\\\Rightarrow P \approx \$8991.88$

So, <em>the principal must be = $8991.88</em>

4 0

2 years ago