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3 years ago

Complete the square to transform the quadratic equation into the form (x – p)2 = q.

Mathematics

1 answer:

ryzh [129]3 years ago

7 0

The transformed equation is:

$(x-3)^2 = 23$

Step-by-step explanation:

We have to convert the equation in the form

$(x-p)^2 = q$

Given equation is:

$x^2-6x-8 = 6$

Adding 8 on both sides

$x^2-6x-8+8 = 6+8\\x^2-6x = 14$

In the given equation

a = x

b= ?

So,

$2.x.b = 6x\\b =\frac{6x}{2x}\\b = 3\\$

So 3^2 will be added on both sides

$(x)^2-6x+ (3) = 14+ (3)^2\\(x-3)^2 = 14+9\\(x-3)^2 = 23$

Hence,

The transformed equation is:

$(x-3)^2 = 23$

Keywords: Quadratic equation, transformation

Learn more about quadratic equation at:

#LearnwithBrainly

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Angle e measures 126LaTeX: ^\circ∘. What is the measure of LaTeX: \angle∠h?

Oksana_A [137]

Option C: 126° is the correct answer

Step-by-step explanation:

When two lines intersect, the four angles are formed. The angles vertically opposite with same vertex are called vertical opposite angles.

The opposite vertical angles are equal.

In the given figure, the pairs of vertically opposite angles are e,h and f,g.

Given

∠e = 126°

The measurement of e and h will be equal as they are vertically opposite

So,

m∠e = m∠h

m∠h = 126°

Hence,

Option C: 126° is the correct answer

Keywords: Vertical angles, lines

Learn more about angles at:

#LearnwithBrainly

6 0

3 years ago

Haley bought 8 pencils and 3 folders for $10.39. Nicole bought 5 pencils and 4 folders for $10.51. How much does a folder cost?

cupoosta [38]

Answer:

$1.89

Step-by-step explanation:

1) 8p+3f=$10.39

2) 5p+4f=$10.51

where p represents pencil & f represents folder.

multiply the first equation by 5 and the second equation by 8.

40p+15f=$51.95

40p+32f=$84.08

Subtract

17f=$32.13

f=$32.13/17 =$1.89

6 0

3 years ago

Read 2 more answers

Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performan

son4ous [18]

Answer:

(a-1) 22 rookies receiving a rating of 4 or better.

(a-2) 14 rookies received a rating of 2 or worse.

(b-1) Constructed below in explanation.

(b-2) 8% of total rookies received a rating of 5.

Step-by-step explanation:

We are provided the rating of Fifty pro-football rookies on a scale of 1 to 5 based on performance at a training camp as well as on past performance.

The frequency distribution constructed is given below:

Rating Frequency

1 4

2 10 where ranking of 1 indicate a poor prospect whereas

3 14 ranking of 5 indicate an excellent prospect.

4 18

5 4

(a-1) Rookies receiving a rating of 4 or better = Rating of 4 + Rating of 5

So, by seeing the frequency distribution 18 rookies received a rating of

4 and 4 rookies received a rating of 5.

Hence, Rookies receiving a rating of 4 or better = 18 + 4 = 22 rookies.

(a-2) Number of rookies received a rating of 2 or worse = Rating of 2 +

Rating of 1

So, by seeing the frequency distribution 10 rookies received a rating of

2 and 4 rookies received a rating of 1.

Hence, Rookies receiving a rating of 2 or worse = 10 + 4 = 14 rookies.

(b-1) Relative Frequency is calculated as = Each frequency value /

Total Frequency

Rating Frequency(f) Relative Frequency

1 4 4 / 50 = 0.08

2 10 10 / 50 = 0.2

3 14 14 / 50 = 0.28

4 18 18 / 50 = 0.36

5 <u> 4 </u> 4 / 50 = 0.08

$\sum f$ <u>= 50 </u>

Hence, this is the required relative frequency distribution.

(b-2) To calculate what percent received a rating of 5 is given by equation :

<em> x% of 50 = 4 </em> {Here 4 because 4 rookies received rating of 5}

x = $\frac{4*100}{50}$ = 8% .

Therefore, 8% of total rookies received a rating of 5.

5 0

4 years ago

First to answer well get brainliest!..<br> Plz

marta [7]

<h2>Answer: It is on the origin or quadrant I</h2>

3 0

3 years ago

For a Cosine function with amplitude =0.75 and period =10 , what is y(4) ?

frez [133]

We need to find a cosine function:

$y(x)=acos(bx) \\ \\ where: \\ \\ \left|a\right|=Amplitude \\ \\ Period=\frac{2\pi}{b}$

The amplitude represents half the distance between the maximum and minimum values of the function and the period goes from the x-value of one peak to the x-value of the next one. Therefore:

$a=0.75 \\ \\ b=\frac{2\pi}{10}=\frac{\pi}{5}$

Finally:

$\boxed{y(x)=0.75cos(\frac{\pi}{5}x)}$

And y(4) is:

$y(4)=0.75cos(\frac{\pi}{5}\times 4) \\ \\ \therefore \boxed{y(4)=-0.60}$

4 0

3 years ago

Read 2 more answers