Solve the following quadratic function by utilizing the square root method. y = x2 - 64​

Solve The Following Quadratic Function By Utilizing The Square Root Method. Y = X2 - 64

Answers

Answer 1

Answer:

[tex]x=\pm\sqrt{y+64}[/tex]

Step-by-step explanation:

All you need to do is isolate the x.

First, add 64 to both sides:

[tex]y=x^2-64\\x^2-64+64=y+64\\x^2=y+64[/tex]

Then, take the square root of both sides:

[tex]\sqrt{x^2}=\sqrt{y+64}\\x=\sqrt{y+64[/tex]

Actually, that is:

[tex]x=\pm\sqrt{y+64}[/tex]

Here's the reason for that. An example would be:

[tex]x^2=4[/tex]

Here, you'd take the square root of both sides to solve for x.

[tex]\sqrt{x^2}=\sqrt{4}\\x=2[/tex]

Right? But X could also be a -2, because a negative times a negative is a positive.

[tex](-2)^2=4\\-2\times-2=4\\4=4[/tex]

Therefore, [tex]x=2, -2[/tex] or [tex]x=\pm2[/tex]

[tex]x^2=2\times2=4\\x^2=-2\times-2=4[/tex]


Related Questions


Select the correct answer.

The difference of half a number and its reciprocal is represented by this expression.

Which expression also represents the difference?

Answers

Answer:

b

Step-by-step explanation:

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The expression which shows the difference is (n² - 2)/2n, the correct option is B.

What is an Expression?

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

The difference of half a number and its reciprocal is represented by this expression.

(n/2) - (1/n)

On solving

(n² - 2)/2n

To know more about Expression

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What is the result when this equation is solved for y?
4x²+10x-2y=6​

Answers

Answer:

B. y = 2x² + 5x - 3

Step-by-step explanation:

[tex]4x^2+10x-2y=6\\\\4x^2+10x-2y-4x^2-10x=6-4x^2-10x\\\\-2y=-4x^2-10x+6\\\\\frac{-2y}{-2}=\frac{-4x^2-10x+6}{-2}\\\\y=2x^2+5x-3[/tex]

The result when the equation is solved for y is y = 2x² + 5x - 3.

To solve the equation 4x² + 10x - 2y = 6 for y, follow these steps:

Step 1: Move all terms containing y to one side of the equation:

4x² + 10x - 6 = 2y

Step 2: Divide both sides of the equation by 2 to isolate y:

(4x² + 10x - 6) / 2 = y

Step 3: Simplify the right side of the equation:

y = 2x² + 5x - 3

So, the result when the equation is solved for y is y = 2x² + 5x - 3.

To know more about equation:

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Given numbers 2 ,5,11, 4.5, 1/10, V3 then
a. Write two prime numbers from the above.
b- An integer root 121
c- A number 25 % of 18
d- An irrational number

Answers

Answer:

a. pick two between 2,5 or 11, they are all primes.

b. it's 11 since

[tex]11 {}^{2} = 121[/tex]

c. that's

[tex]18 \times \frac{25}{100} = 4.5[/tex]

(or think about it as half the half of 18, so half of 9)

d.

[tex] \sqrt{3} [/tex]

Rest can be written as a fraction

7. Paul has 49 cups of water. Is this enough water to make 25 batches of green slime for a class​ project? Explain.

Answers

It depends but short answer yes

If it takes 1 cup of water to make one batch of slime then yes! Because 25 is less than 49.

But if it takes 2 cups to make a batch then NO! because 25x2= 50 and 50 is more than 49

Hi! I'm 12 years old trying to move up in maths, does anyone have any tips about any one of these topics?

- Bearings
- Number scales
-Ratios
-Proportionally calculating quantities to recipes (??)
-Averages
-Times tables in general

Thank you so much if you decide to answer this!! Im trying to become a barrister when im older:)

Answers

Answer:

For number remember that the negative number are smaller, but if it question like this which one is bigger -5 or -6 will -5 will be the answer because it is not smaller than -6. For ratios just remember divide or number of something like there are 3 to 8 child in the classroom then thee ratios would be 3:8. Lastly for the times tables learn all of your times tables like your favorite game, so things will be easier on you.

A=rt + q solve for t

Answers

Answer: t= [tex]\frac{A-q}{r}[/tex]

Step-by-step explanation: subtract q from both sides, to get A-q=rt, then divide r by both sides to get the answer above

HELPMEPLZZ.

Figure ABCD is transformed to obtain figure A'B'CD Part A Write the sequence of transformations that changes figure ABCD to figure A'B'C'D' Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points) Part B: Are the two figures congruent? Explain your answer (4 points)​

Answers

Answer: yes because they both go to the 0 and has the same shape.

Step-by-step explanation: yes

1 gal = ____ pt

A) 8.085 pt
B) 8.85 pt
C) 88.5 pt
D) 0.8085 pt

eh? ​

Answers

Answer:

1 gal = ____ pt

A) 8.085 pt

lelz XD

i need help on this last question

Answers

Mag aral ka Magdasal kamatulog ka ng maaga wag mong pagka alagaanbsari mo Kasi responsibilidad ko yun

Find the inverse (pre-calc)

Answers

Answer:

f^(-1)(x) = e^(x/3)

Step-by-step explanation:

1.  Replace 'f(x)' by 'y:'  y = 3ln x

2. Interchange x and y:  x = 3ln y => x/3 = ln y

3. Solve for y:  

   e^(x/3) = y

4.  Replace this 'y' with 'f^(-1)(x)'

    Then f^(-1)(x) = e^(x/3)

solve pls brainliest

Answers

Answer:

20yd²

Step-by-step explanation:

6 × 6 = 36

4 × 4 = 16

36

-16

20

The area of the garden is gonna be 20 yards squared (20yd^2)

What is the value of the 9 in the number 567.09?

Answers

Answer:

After the decimal point (left to right) are the tenths, hundredths, thousandths, ten-thousandths, and so on. The value of the 9 would be 9 hundredths.

:)

The value of 9 is 9 hundredths

m = – 3; (2, 2) help pls

Answers

Answer:

try  maltpling 3 *2*2

Step-by-step explanation:

Geometry problem, Name the angle pair relationship and then determine which lines must be parallel based on the angles given If they do not prove lines parallel, write none.

Answers

Answer:

see below

Step-by-step explanation:

a) 1 = 4 they are corresponding angles when j and k are parallel

b) 3 + 4 = 180 these just lies on same straight line and they add up to 180 so none

c) 5 + 7 = 180 are consecutive interior angles when k and l are parallel

d) 6 = 7 they are alternate interior angles when k and l are parallel

and refer this link for theory on this topic

https://www.ixl.com/math/lessons/transversals-of-parallel-lines

How to do multiplication with decimals.

Answers

Answer: just line up the decimals.

Step-by-step explanation:

is there a specific question I can help you with?

order the values from least to greatest​

Answers

Answer:

-7.2, -6.3, [5], [-6.3], 8

Johan has recorded 32 show usings his cable television service. Each week, he records 6 new shows.

Write an expression to show the total number of shows Johan has recorded after w week.

Answers

Answer:

32+6w=x

Step-by-step explanation:

Johan already has the 32

he is adding 6 every week which gives you the total-x

if it was two weeks, 32+6(2)= 32+12=44

Need help with this pls asap

Answers

Need help asap beds helpbasap plzzzzzz need help asp

please help asap…………

Answers

Answer: linear

Step-by-step explanation:

Someone please answer this, I’ll give you brainliest and 50 points!

Answers

Answer:

3

Step-by-step explanation:

Answer:

Answer 2

Step-by-step explanation:

Anything number raised to the zero power is

Answers

Answer:

It is equal to 1 when raised to the zero power.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Any number raised to the zero power equals 1. This is by definition to make the rules of exponents work.

Look at this example:

Any number (except zero) divided by itself equals 1.

For example, 25/25 = 1,

but 25 = 5²,

so 25/25 = 5²/5²

The rule of dividing two powers with the same base is to use the same base and subtract the powers.

5²/5² = 5^(2 - 2) = 5^0

By the rule of exponents, 5²/5² = 5^0,

but we saw above that 5²/5² = 25/25 = 1, so

5^0 must equal 1.

This led to the following definition of zero exponent.

Definition:

For any number a, a^0 = 1.

The data for the distance d, in miles, remaining for a train to travel to its destination t hours after it departs a station are
shown in the scatter plot. Which of the following functions best fits the data?

Answers

Using the slope - intercept format, the equation which models the data represented by the graph is d(t) = -50t + 300

According to the general form of a linear regression equation :

y = bx + c b = slope ; c = intercept

Slope, b = (Δy ÷ Δx)

Slope = (200 - 50) ÷ (2 - 5)

Slope = 150 ÷ -3 = -50

Intercept is the point where the regression line crosses the y - axis.

From the graph, the intercept = 300

Hence, the regression equation is y = -50t + 300

Learn more : https://brainly.com/question/19017188

Reduce 36 to simplest form?

Answers

Answer:

[tex]2^{2} *3^{2}[/tex]

Step-by-step explanation:

You would have to prime factorize the number.

36=4x9

4=2x2

9=3x3

36=2x2x3x3

Answer:

36 reduced into simplest form is 12.

Step-by-step explanation:

12 is the simplest form of 36 because it has the smallest numerator and denominator possible to represent that amount.

2/7 x (-7/9) xdx lel'jobrfjb13rgifj2noinf ehelp

Answers

When multiplying by fractions you multiply the numerator by the numerator and the denominator by the denominator. 2x-7=-14. 7x9=63 so the answer is -14/63. Hope that helped :D

a. Why does the provided equation support the fact that there is a horizontal asymptote of F(x) that is not
on the x-axis?
(ax-3)(x-2)divide2(x+3)(x-2)
Y=-2 is a horizontal asymptote

Answers

Applying limits, it is found that since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

The function is given by:

[tex]F(x) = \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}[/tex]

The horizontal asymptote is the limit of the function as x goes to infinity, hence:

[tex]y = \lim_{x \rigtharrow \infty} F(x) = \lim_{x \rigtharrow \infty} \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}[/tex]

Considering only the terms with the highest exponents:

[tex]y = \lim_{x \rigtharrow \infty} \frac{ax^2}{2x^2} = \frac{a}{2}[/tex]

Since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

For more on horizontal asymptotes and limits, you can check https://brainly.com/question/11598999

Do number 6. This is not a quiz

Answers

Answer:

C

Step-by-step explanation:

B .  -A .   -b .   -b .   +a .   +b .   +c

b + b -b -b +a -a +c

c

16+4(q+11)+10q
simpaly

Answers

Answer:

14q + 60

............................

Answer : 60 + 14q

Explanation: you have to distribute the 4 to the q and 11 which will then get u 16 + 4q + 44 + 10q then you would add 4q and 10q which would get you 14q and then add 16 + 44 and that would get you 60 so your answer would be 14q+60

In a factory, 53 workers receive a wage of 7,576 each per month. Find the total wages received by all the workers for one financial year. Also, find the annual wage of 1 worker.​

Answers

Step-by-step explanation:

as you know, there are 12 months per year.

also, the word "annual" means "per year" (of again 12 months).

each worker gets 7,576 per month.

that means each worker gets an annual salary of

7,576 × 12 = 90,912

the salaries/wages of all 53 workers together in a year are then

90,912 × 53 = 4,818,336

Definition: The points where a graph intersects the x-axis are called it’s __.

Answers

Answer:

zeroes or x-intercepts

Step-by-step explanation:

The value of a baseball card can be represented by the equation y=3x+39,where x represents the number of years that Robert has owned the card and y represents the total value,in dollars,of the card.What was the value of the card when Robert originally purchased it?

Answers

Answer:

Im pretty sure it's $39

Step-by-step explanation:

if x=0 it cancels out leaving y=39

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