Mathematics High School

What are the solutions to the equation x2 = 64?

A.
8 only

B.
32 and –32

C.
8 and –8

D.
32 only

Answers

Answer 1
[tex]x^2=64[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{64}[/tex]
[tex]x=\pm8[/tex]

[tex](\pm32)^2[/tex] is 1,024.
Also, all square root functions have a positive and a negative result.

Related Questions

Solve the following formula for R: C=2πR
Choose ALL equivalent variations of your answer.

Answers

Based on the given value above, in order to solve for the given formula for R, here is how we got the equivalent variations of the answer.
First is I divided both sides by 2π and got r=c/2π. Given variation, this is also equivalent to r=1/2πC. Therefore, the correct answer for this would be the last option. Hope this answer helps. 

To solve for R in the equation [tex]C=2\pi R[/tex] divide both sides by 2π to get [tex]R = C / (2\pi )[/tex].

To solve the equation [tex]C=2\pi R[/tex] for R, we need to isolate R on one side of the equation. Here are the steps to do this:

Start with the original equation: [tex]C=2\pi R[/tex]

Divide both sides of the equation by 2π to isolate [tex]R: R = C / (2\pi ).[/tex]

Given variation, this is also equivalent to [tex]r=1/2\pi C[/tex].

Now, R is the subject of the equation, and you can use this formula to find the radius (R) if you know the circumference (C) of a circle.

name the property of real numbers illustrated by the equation step by step

-10+4=4+(-10)

Answers

That illustrates the commutative property of addition. This property is technically 
a + b = b + a. 
In this case, you are using -10 for a, and 4 for b. 

The Commutative Property of Addition. 
The Commutative property of addition i think

How many kilograms are in 500 grams? ...?

Answers

Hi , the answers is 0.5 kilograms.

Explain why a point in the polar plane cannot be named by a unique ordered

pair (r, theta).

Answers

 you can describe any point but you can describe the same point in potentially infinite ways. 
example; the rectangular coordinate of (1,1) 

in polar you can describe this point as (pi/4,1) or (5pi/4, -1) and so on

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Final answer:

A point in the polar plane can have multiple representations due to the periodic nature of angles and the possibility of using negative radii to represent a point in the opposite direction from the pole.

Explanation:

The question asks to explain why a point in the polar plane cannot be named by a unique ordered pair (r, θ). In the polar coordinate system, each point is determined by a radius (r) and an angle (θ).

However, a point can have multiple representations due to the periodic nature of angles. If you add or subtract multiples of 2π radians (or 360 degrees) from θ, you will land on the same point in the polar plane.

Additionally, if the radius (r) is negative, the direction is reversed, which also leads to the same point being represented by (-r, θ + π), where θ is the initial angle.

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the slope of the line below is 0.8 write the equation of the line in point slope form using the coordinates of the coordinates of the labeled point do not use parenthesis on the y side

Answers

Final answer:

The equation of the line in point-slope form is y - y1 = 0.8(x - x1), where the point on the line and the slope are given.

Explanation:

To write the equation of a line in point-slope form, we need the slope of the line and the coordinates of a point on the line. In this case, the slope is given as 0.8. Let's assume the labeled point has coordinates (x, y). The equation in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the labeled point. Substituting the given slope and the coordinates of the point, the equation becomes:

y - y1 = 0.8(x - x1)

Remember to not use any parentheses on the y side of the equation.

Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at a speed of 4 ft/s. His distance d from you after t seconds is given by d = |120 − 4t|. After how many seconds is your neighbor 30 ft from you?

Answers

Final answer:

To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.

Explanation:

To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.

Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.

For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.

For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.

So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.

why are both accuracy and precision important in making a measurement?

Answers

Accuracy helps us make sure that the reading obtained is the actual value; however, without the ability to repeat that reading, precision, the reading becomes invalid.
I am pretty sure that the reason why both accuracy and precision are important in making a measurement is that the measurement needs to be close to the true value and the same if done several times

a number , x,rounded to 1 decimal place is 3.7 what is the error interval for x

Answers

The error interval will be [3.65,3.75).

What is an error interval?

The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.

Given here the decimal number is 3.7 which is after rounded to 1 decimal place.

As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05

Then the lower limit of the error interval will be 3.7-0.05= 3.65

the higher limit of the error interval will be 3.7+0.05= 3.75

the error interval will be 3.65≤x<3.75

As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.

There are the numbers below which on rounding give 3.7

3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74

Therefore the error interval will be [3.65,3.75).

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Final answer:

The error interval for a number x, which when rounded to one decimal place is 3.7, is [3.65, 3.75).

Explanation:

When a number, x, rounded to one decimal place is 3.7, the error interval for x represents the range of actual values x could be to give that rounded figure. So, if x is rounded to 3.7, it means that the value must be at least 3.65 and less than 3.75 when considering rounding to one decimal place. Essentially, the number must be in the half-open interval [3.65, 3.75).

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Why is the absolute value of a number always positive?

Answers

Because the number is positive

It's not. The absolute value of any number is the positive version of that number except for the absolute value of 0. This is the only situation where the absolute value of a number is not positive. The absolute value of 0 is just 0.

A ball is thrown horizontally at a speed of 24 meters per second from the top of the building. If the ball hits the ground 4.0 seconds later approximately how high is the building? ...?

Answers

Final answer:

The height of the building is approximately 78.4 meters.

Explanation:

To find the height of the building, we can use the formula d = v0t + 1/2gt2, where d is the height, v0 is the initial horizontal speed, t is the time, and g is the acceleration due to gravity. In this case, since the ball is thrown horizontally, the initial vertical speed is 0 and there is no initial vertical acceleration. So, d = 0(4.0) + 1/2(9.8)(4.0)2. Solving this equation gives us a height of approximately 78.4 meters.

Why do new cars costing $20,000 rent for $40 a day, while tuxedos costing only $500 rent for around $90?

Answers

You use cars for much longer than you use a tuxedo. A tuxedo is once-off, whereas cars you use for days and days and days... After a while, the $20 you pay per day is going to add up!

Whats the product of 86 and the depth of the river?

Answers

Here is how you are going to get the answer:

Let the depth of the river = d

So in order to find the product, you simply multiply

so the product of 86 and the depth of the river would be 86 * d

or 86d.

Hope this answers your question. Have a great day!

Which of the statements about the following quadratic equation is true?
6x2 - 8 = 4x2 + 7x

The discriminant is greater than zero, so there are two real roots.

The discriminant is greater than zero, so there are two complex roots.

The discriminant is less than zero, so there are two real roots.

The discriminant is less than zero, so there are two complex roots.

Answers

After manipulating above equation we get, 2x^2 - 7x - 8= 0. Discriminant= b^2 - 4ac = (-7)^2 - 4(2)(-8) = 113>0. So there are 2 real roots :)

If the discriminant of a quadratic equation is positive then, there are two real roots. Here, the discriminant obtained is 113 which is greater than zero. Hence, option a is correct.

What is quadratic equation ?

A quadratic equation are polynomial equation with one variable having the degree of 2. This general form a quadratic equation is written as follows:

ax² - b x + c = 0

The discriminant for a quadratic equation is the term b² - 4ac.

Given the quadratic equation is 6x² - 8 =  4x²  + 7 x

it can be rearranged as: 2x² - 7x - 8 =0

If the discriminant of the equation is greater than zero, then there will be two real roots.

solving the discriminant here:

b² - 4ac = (-7)² - 4× 2×(-8) = 113

Here, the  discriminant is greater than zero. Therefore,  there are two real roots.

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1. alicia and jamal completed the following "
given : 3x+7=x-5
prove: x=-6
Alicia's workt.
3x+7=x-5 : given
2x+7=-5: subtraction property of equality
2x=-12: subtraction property of quality
x=-6: division property of equality

jamal's work

3x+7=x-5 : given
7=-2x-5 : subtraction property of equality
12=-2x: addition property of equality
-6=x : division property of equality
who completed the proof correctly?
a) alicia only
b) jamal only
c) both alicia and jamal
d) neither alicia nor jamal

Answers

Answer:

both alicia and jamal

Step-by-step explanation:

From the given steps we can see that both Alicia and Jamal completed the proof correctly.

Option C

Given :

3x+7=x-5

prove: x=-6

Alicia's workout

3x+7=x-5 : given

2x+7=-5: subtraction property of equality

2x=-12: subtraction property of quality

x=-6: division property of equality

Alicia's steps are correct. She proved x=-6

jamal's work

3x+7=x-5 : given

7=-2x-5 : subtraction property of equality

12=-2x: addition property of equality

-6=x proved

Jamal's steps are also correct. Jamal started by subtracting 3x from both sides. That approach is also correct. He proved x=-6

so, both Alicia and Jamal are correct

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Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled for the flowers to last the longest. Her cylinder vase has a radius of 4 inches and a height of 10 inches. How much water should Mary pour into the vase?

Answers

Yes i did area i meant to do volume in that case just plug in the numbers for the formula of the volume of a cylinder which is 10 and 4 and you should get 502.65

In that case if you are filling it up with 100% water you can fit 502.65 of water in the vase sorry for the mess up but i fixed it. (give or take a few due to the flowers taking up space)

Pi*r^2*h = Volume of the cylinder Pi*4^2*10 = your answer. Use your calculator

What is the principle for f)? The math is Simple Interest

Answers

see the attachment °_° I hope it helps :-)

Answer:

E

Step-by-step explanation:

The pair of points (3,8) and (x, 6) are on the graph of am inverse variation. What is the missing value?

Answers

1) 
y varies inversely with x 
y=k/x , where k is any constant 
y=-16 when x=-64 

-16 = k/ (-64) 
-16 = k/-64 
k=(-16)(-64) = 1024 

2) 
y =k/x , where k is any constant 

y=8 when x=3 
8 = k/3 
k=24 

y=24/x 
when y=6 
6 = 24/x 
6x=24 
x=4 

Missing value is 4 

3) 
xy/4=-3 
xy=-12 
y=-12/x 
y=kx 
k=-12 

4)

the french club is sponsoring a bake sale. if their goal is to raise at least $135, how many pastries must they sell at $3.00 each in order to meet that goal? write and solve an inequality.

Answers

They would have to sell 45 pastries.

Answer:

45 or more

Step-by-step explanation:

If x is the amount of pastries they sell, we need to multiply it by $3.00 to know how much they raise. Total earnings: $3.00x

They need to raise at least $135, that is $135 or more.

So, $3.00x has to be greater than $135 or equal.

Written as an inequality is:

$3.00x [tex]\geq[/tex] $135

We divide both sides by $3.00 and we have:

x [tex]\geq[/tex] $135/$3.00 = 45

Therefore, they need to sell 45 or more pastries to meet the goal.

Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.
A. π/3+nπ/2
B. π/12+nπ
C. π/6+nπ/2
D. 5π/12+nπ ...?

Answers

the solution is B. π/12+nπ

proof 
sinx cosx = 1/4 is equivalent to  2 sinx cosx = 1/2 or sin2x =1/2
so 2x = arcsin(1/2) = π/6 + 2nπ,  so x = π/12+nπ

Answer:

Its B and D.

Step-by-step explanation:

y = (1/4)x^2 - (1/2)lnx..over the interval (1, 7e) ...what is the arc length ?

Answers

So, f[x] = 1/4x^2 - 1/2Ln(x) 
thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x 
thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) 
thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 
thus Sqrt[...] = (x/2 + 1/2x) 

What is 481 divided by 8?Is it 60 with a remainder of 1 ?

Answers

Yes. 60 remain 1 or 60.125 . 

The hypotenuse of a 30- 60- 90 triangle has length 13. What is the length of the side opposite the 60 angle? If necessary, round your answer to two decimal places.

Answers

The side opposite the 60 degree angle - [sqrt(3/2]17 = 14.72

Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
$42
$36.60
$34
$33.60

Answers

Answer:

$33.60 is the correct answer.

Step-by-step explanation:

Price of the shirt = $40.00

discount rate = 20% or 20/100

so price of the shirt = 40 × 0.20 = 8

Shirt's price after 20% discount = 40 - 8 = $32.00

Now she paid 5% tax on the price after discount.

5% tax of 32.00

0.05 × 32 = $1.60

This amount will be added to his discounted price of a shirt.

= 32.00 + 1.60 = $33.60

Lydia pay $33.60 for the shirt.

How is each function related to y=x? Graph the function by translating the parent function

1) y=x+2 2) y=x-1.2

I need help with this. I don't know what to do. I was sick and stayed home but I had homework and I wasn't taught how to do it could. Someone help me with this by explaining it step by step? Thank you.

Answers

The parent function is:  y = x.
1 )  y = x + 2
It is translated vertically 2 units up.
2 ) y = x - 1.2
It is translated vertically 1.2 units down.
The graph is in the attachment.

Solve this problem
-2=c+2

Answers

c= -2 -2 = -4
answer it -4
c=-4
 i need 20 characters sorry  weoiwnfoaeirnf

Which of these numbers has the least value?
a. 7.2 x 10
b. 8.1 x 10
c. 9,100,000
d. 9.5 x 10

Answers

the answer is a.......

As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.

What is rounding a number to some specific place?

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

The digit 5 acts as a limit.

After solving we get.

a. 7.2 x 10 will gives 72.

b. 8.1 x 10 will gives 81.

c. 9,100,000

d. 9.5 x 10 will gives 95.

As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.

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a system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. is this statement true?
Always
Sometimes
Never

I think the answer is Sometimes . X=Y and X^2-Y^2=0 Has infinitely Solutions

Answers

Your answer would be No, never. Hope this helps!

Answer:

The statement that says that a system constructed by a linear and a quadratic equation, has infinitely solutions is never true.

Step-by-step explanation:

This situations can be explained more easy by the graphic solution of the system of equations. As we know, a cuadratic equation represents a parabola and the linear equation a line, so the solution of the system can be understood as the interseption od the parabola and the line.

In the attached figure above we expouse the three different cases could hapend. In the first case, we have two interceptions, so 2 solutions. For the second case, we have 1 interseption, which represents one solution. In the third case the line doesnt touch the parabola in any point thus we get no solution.  

Therefore in none of the cases explained we found infinite solutions, this situacion can never happens.

In the example the second equation doesnot represents a quadratic equation. A quadratic equation has the form of:

Y = aX^2 + BX +  C

Thus the given system cannot be understood as a the example of the kind.

Given the vector "v" and its inital point, find the terminal point:
"v"=<-1,3>;Initial Point:(4,2) ...?

Answers


The final point can be done by simple vector addition. Just add the corresponding components.

Final point: (4 + -1, 2 + 3) = (3, 5).

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

A car is traveling at a speed of 90 kilometers per hour. What's the car's speed in meters per second? How many meters will the car travel in 10 seconds? Do not round your answers.

Answers

It's 25 meters per second, and it travels 250 meters in ten seconds.

To convert kilometers per hour to meters per second, you start with turning that into a fraction, 90km/1hr. To convert to meters, you have to multiply that fraction by another fraction with km as a label on the denominator, and m(meters) as a label for the numerator. That fraction would be 1,000m/1km, because there are 1,000 meters in 1 kilometer. You would also add another fraction to the multiplication sentence to convert hours to seconds. There are 3,600 seconds in 1 hour, so that fraction would be 1hr/3,600sec, and then cross out all km and hr labels. After that, you could cross reduce two of the zeros in 3,600 and 1,000 because they are diagonal to each other, and this also makes simplifying way easier. You are left with this: 90/1 times 10m/1 times 1/36sec. Multiply straight across and you would get 900 meters/36 seconds. Divide both sides by 36, and you are left with 25 meters/1 second. The car travels 25 meters per second. Now we have to find how many meters the car travels in 10 seconds. This step is very simple: just multiply 25 meters by 10 and 1 second by 10 to get the number of meters. 25 times 10 = 250, so the car travels 1 meter per second and 250 meters in 10 seconds.

Solve for x: 3 − (2x − 5) < −4(x + 2)

x < −8

x > −8

x < −3

x > −3

I just need help because i don't know how i would do it with x on both sides

Answers

The answer is x < −8

3 − (2x − 5) < −4(x + 2)
3 - 2x + 5 < -4x - 8
8 - 2x < -4x - 8
4x - 2x < -8 - 8
2x < -16
x < -8

Answer: [tex]x<-8[/tex]

Step-by-step explanation:

The given inequality : [tex]3-(2x-5)<-4(x+2)[/tex]

To solve the inequality for x , first we open the parenthesis , we get

 [tex]3-2x+5<-4x+(-4)2[/tex]

 [tex]\Rightarrow\ 3-2x+5<-4x-8[/tex]   [Note : (-)(+)=(-)]

[tex]\Rightarrow\ 3+5-2x<-4x-8[/tex]

[tex]\Rightarrow\ 8-2x<-4x-8[/tex]

Add 4x on both sides , we get

[tex]8-2x+4x<-4x-8+4x[/tex]

[tex]8+2x<-8[/tex]

Subtract 8 from both sides , we get

[tex]2x<-16[/tex]

Divide both sides by 2 , we get

[tex]x<-8[/tex]

Hence, the correct answer is : [tex]x<-8[/tex]

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