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1 year ago

Solve the following quadratic by completing the square. y = x2 - 6x +2

Mathematics

1 answer:

Nana76 [90]1 year ago

4 0

Answer: $3 \pm \sqrt{7}$

Step-by-step explanation:

$1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}$

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Give the properties for the equation -2x 2 - y + 10x - 7 = 0.

Sladkaya [172]

Given:

The quadratic equation is

$-2x^2-y+10x-7=0$

To find:

The vertex of the given quadratic equation.

Solution:

If a quadratic function is $f(x)=ax^2+bx+c$ , then

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

We have,

$-2x^2-y+10x-7=0$

It can be written as

$-2x^2+10x-7=y$

$y=-2x^2+10x-7$ ...(i)

Here, $a=-2,b=10,c=-7$ .

$\dfrac{-b}{2a}=\dfrac{-10}{2(-2)}$

$\dfrac{-b}{2a}=\dfrac{-10}{-4}$

$\dfrac{-b}{2a}=\dfrac{5}{2}$

Putting $x=\dfrac{5}{2}$ in (i), we get

$y=-2(\dfrac{5}{2})^2+10(\dfrac{5}{2})-7$

$y=-2(\dfrac{25}{4})+\dfrac{50}{2}-7$

$y=\dfrac{-50}{4}+25-7$

$y=\dfrac{-25}{2}+18$

On further simplification, we get

$y=\dfrac{-25+36}{2}$

$y=\dfrac{11}{2}$

So, the vertex of the given quadratic equation is $\left(\dfrac{5}{2},\dfrac{11}{2}\right)$ .

Therefore, the correct option is A.

3 0

2 years ago

|v|>3 solution to the inequality on the number line

Andrew [12]

On a number line, v would be all the numbers to the left of -3 (for example, |-4|=4 which is greater than 3) and all the values to the right of positive 3. Since it can't equal 3, v=-3 and v=3 are not included on the number line.

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3 years ago

Which one is the word form of 3 x 5/6

Maslowich

Three times five sixths

3 0

2 years ago

Read 2 more answers

Farmer grey has 10 chicks. He has 3 more chicks than farmer brown. Which sentence shows how many chicks farmer brown has?

Paha777 [63]

Answer: is 7

Because 3+7 is 10

3 0

2 years ago

You deposit $200 every quarter for 12 years into a sinking fund that pays 2.25% interest compounded annually. What is the future

anzhelika [568]

Answer:

$16,974.57

Step-by-step explanation:

The formula for future value is given by

$FV=PMT\frac{(1+i)^{n}-1}{i}$

where

FV = future value

PMT = amount deposited each period and is given as 200

i = rate per period = r/m where r is the interest rate and m the frequency of compounding. Here it is mentioned that r = 2.25% and interest is compounded annually ie once per year so m = 1

i = 2.25%/1 = 2.25% = 2.25/100 = 0.0225

The number of payments n = 48 since we make quarterly payments (4 per year) and we are asked to compute for 12 years

Plugging these values into the formula gives

$FV=200\frac{(1+0.0225)^{48}-1}{0.0225}$

which evaluates to

$16,974.57 which can be rounded up to $16975

depending on the accuracy you desire

6 0

5 months ago