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2 years ago

Solve this equation, pls. due today !!

Mathematics

1 answer:

Margarita [4]2 years ago

7 0

Answer:

1) c=100

2) x^4-40x^3+400x^2

Step-by-step explanation:

When I write ^# that means it's squared and has a number above it :)

You're welcome :)

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Explain how to find the vertex of 2x^2+12x+16

Elina [12.6K]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

Use $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2$

<h3>Answer: (-3, -2).</h3>

Other method:

$f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+16=2(9)-36+16=18-36+16=-2$

<h3>Answer: (-3, -2).</h3>

5 0

3 years ago

The expression 7kl – 3k(4k + 2l) is equivalent to:

koban [17]

Answer:

- 12k² + kl

Step-by-step explanation:

Given

7kl - 3k(4k + 2l) ← distribute parenthesis by - 3

= 7kl - 12k² - 6kl ← collect like terms

= - 12k² + kl

6 0

2 years ago

There are 63 students in a speech contest.Yesterday 1/3 gave a speech and today 2/3 of the remaining students gave their speech.

Paraphin [41]

Hey!

-----------------------------------------------

Solution:

Find 1/3 of 63.

63 / 3 = 21

21 students gave a speech today.

63 - 21 = 42

Find 2/3 of 42.

42 / 3 = 14

14 x 2 = 28

28 of the remaining students gave their speeches.

42 - 28 = 14

-----------------------------------------------

Answer:

14 students haven't given their speeches!

-----------------------------------------------

Hope This Helped! Good Luck!

7 0

2 years ago

Suppose in this semester, our Exam 1 average was about 86 with an SD of about 10. Suppose the correlation between our Exam 1 and

Oduvanchick [21]

Answer:

the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

Step-by-step explanation:

Given the data in the question;

mean X" = 86

SD σx = 10

Y" = 76

SD σy = 8.2

r = 0.6

Here, Exam 2 is dependent and Exam 1 is independent.

The Regression equation is

y - Y" = r × σy/σx ( x - x" )

we substitute

y - 76 = 0.6 × 8.2/10 ( x - 86 )

y - 76 = 0.492( x - 86 )

y - 76 = 0.492x - 42.312

y = 0.492x - 42.312 + 76

y = 0.492x + 33.688

Hence, the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492

And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688

4 0

2 years ago

Calculate the average daily balance with new purchases not included for the

USPshnik [31]

Answer: 510

Step-by-step explanation:

5 0

2 years ago