MATHEMATICS HIGH SCHOOL

What is f(x) = 7x2 + 42x written in vertex form?

Answers

Answer 1

Answer:

Answer:

$\boxed{\boxed{y = 7(x+3)^2-63}}$

Step-by-step explanation:

The general vertex form of parabola is,

$y=a(x-h)+k$

where,

(h, k) is the vertex of the parabola.

The given function is,

$\Rightarrow f(x) = 7x^2 + 42x$

$\Rightarrow y = 7x^2 + 42x$

$\Rightarrow y = 7(x^2 + 6x)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2$

$\Rightarrow y = 7(x+3)^2-7\cdot 9$

$\Rightarrow y = 7(x+3)^2-63$

This is vertex form the given function.

Answer 2

Answer: Hello,

y=7x²+42x
==>y=7(x²+2*3*x+9)-63
==>y=7(x+3)²-63

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Round the mixed number to the nearest whole or half. 8 4/27

lius has 5 over 8 quart of grape juice he pours the same amount in each 5 glasses which equation represents the fraction of a quart of grape juice n that is in each glass

Answers

so we have to divide 5/8 into 5 equal segments.

5 5
-- ÷ ---
8 1

in order to divide fractions we need to flip the second fraction and change the sign from a divition sign to a multiplication sign

5 1 5
-- × --- = ---
8 5 40

now we just simplify 5/40 is equal to 1/8

each glass gets 1/8 of a quart

Emily and Rachel had lunch at the mall. Emily ordered two slices of pizza and three cookies and her bill was $8. Rachel ordered one slice of pizza and four cookies and her bill was $9. What was the price of one slice of pizza? What was the price of one cookie?

Answers

Answer:

one slice of pizza: $1

one cookie: $2

Step-by-step explanation:

Emily: two pizzas (1+1)+three cookies (2+2+2)= 8

Rachel: one pizza (1)+four cookies (2+2+2+2)= 9

can i plz get brainilest? :)

Answer:

piza 1 buck

cooky 2 bucks

Step-by-step explanation:

i did not look at the other answer...

lol i copied the other answer

A, B & C lie on a straight line. BD = CD. ∠ BCD = 70° and ∠ BAD = 10°. Work out x

Answers

Answer:

x= 100

Step-by-step explanation:

straight line = 180⁰

180-(70+10)= 100

Which expression is a difference of squares with a factor of 5x − 8?25x2 − 16
25x2 + 16
25x2 − 64
25x2 + 64

Answers

Answer:

option (3) is correct.

$25x^2-64$

Step-by-step explanation:

Given : factor 5x − 8

We have to choose an expression out of given option that is a difference of squares with a factor of 5x − 8

Using algebraic identity $a^2-b^2=(a+b)(a-b)$

a difference of squares is written mathematically as $a^2-b^2$

Since one factor is 5x − 8

using identity stated above other factor has be 5x+8

Thus $(5x+8)(5x-8)$

On simplify , we get

$(5x+8)(5x-8)=(5x)^2-8^2=25x^2-64$

Thus, option (3) is correct.

a2 - b2 = (a-b)(a+b)

(5x-8)(5x+8) = 25x2 - 64

answer: 25x2 - 64

A system of equations has no solution.If y=8x +7 is one of the equations,which could be the other equation has no solution.If y=8x +7 is one of the equations,which could be the other equation

Answers

Answer:

The other line is y= 8x - 7

Step-by-step explanation:

The given equation in two variable is

y= 8x ± 7

The two equations in two variables are:

Ax + By +C=0

P x + Q y +R=0

Now, the condition that these two equations has no solution is if;

A/P = B/Q ≠ P/R

Another condition is in terms of line , if the two lines have same slope.

For example, y= ax + b and , y = ax + p are two lines having same slope means they are parallel, that is they will never intersect.

If the line is , y = 8x + 7, the other line will be, y= 8x - 7

Answer: Y = 8X - 7

Step-by-step explanation:

A system of equations with no solution, means the two lines are parallel to each other.

If parallel to each other, they will have common gradient but different intercept.

How do you solve 10(3^x) = 810 ?

Answers

3^x = 810/10
3^x = 81
Since 81 has a perfect fourth power of 3, which is 3*3*3*3 = 3^4 = 81
3^x = 3^4
You can easily remove the similar bases (which is 3) and bring down the exponent.
x = 4

- - To Start, Divide both sides by 10

$(10(3^x))/(10) = (810)/(10)$

- - Solve For The Exponent:

$3^(x) =81$

- - Now use log to solve:

$log(3x)=log(81)$

$x*(log(3))=log(81)$

$x= (log(81))/(log(3))$

$x=4$

~Hope this helps

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