Factor: x^2 - 100y^2 plz​

Answer:

f(x) = (2x + 1)(2x − 1)

Explanation:

As we can see from the above function f(x) = 4[tex]x^{2}[/tex] − 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.

So let us Equate the function with zero

4[tex]x^{2}[/tex] - 1 = 0 => 4[tex]x^{2}[/tex] = 1 => [tex]x^{2}[/tex] = 1/4 => x = [tex]\sqrt{1/4}[/tex]

Hence we get 2 values of x, i.e., +1/2, and -1/2.

So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.

Option A - f(x) = (4x + 1)(4x − 1) = 3, -3

Option B - f(x) = (2x + 1)(2x − 1)  = 0

Option C - f(x) = 4(x2 + 1)  = 5

Option D - f(x) = 2(x2 − 1) = -3/2

Hence answer is Option B

Answer:

A. 1.0797

Step-by-step explanation:

Given the equation,

3e^2x+2=28

To solve for x, first we move 2 to the other side of the equation.

3e^2x = 28-2

3e^2x = 26

Dividing both sides by 3

e^2x = 26/3

e^2x = 8.67

Taking the natural logarithm if both sides

ln(e^2x) = ln8.67

2x = ln8.667

2x = 2.1595

x = 2.1595/2

x = 1.0797

Answer:

The denominator of the fraction is 2x and the answer is a= -[tex]\frac{b}{2x}[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation of the form:

ax²+bx+c

The axis of symmetry of the parabola is given by:

[tex]x= \frac{-b}{2a}[/tex]

From here, we must clear the value of a.

For this, we follow the following steps:

1) Pass 2a multiplying to the other side of the equation:

2ax=-b

2) Clear the value of a by passing 2x to divide:

[tex]a= \frac{-b}{2x}[/tex]

Answer:

B.

a= -b/2x

Step-by-step explanation:

Each computer costs $225 and each printer costs $150

Step-by-step explanation:

Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers

We need to find how much each computer and printer costs

Assume that the cost of each computer is $x and the cost of each printer is $y

∵ The cost of each computer is $x

∵ The cost of each printer is $y

∵ The cost of 3 computers and one printer is $825

- Multiply x by 3 and add the product to y, equate the sum by 825

∴ 3x + y = 825 ⇒ (1)

∵ The cost of 4 computers and 2 printers is $1200

- Add the product of 4, x and the product of 2 , y and equate the

  sum by 1200

∴ 4x + 2y = 1200 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 to eliminate y

∵ -6x - 2y = -1650 ⇒ (3)

- Add equations (2) and (3)

∴ -2x = -450

- Divide both sides by -2

∴ x = 225

Substitute the value of x in equation (1) to find y

∵ 3(225) + y = 825

∴ 675 + y = 825

- Subtract 675 from both sides

∴ y = 150

Each computer costs $225 and each printer costs $150

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By setting up a system of equations from the scenarios provided, we can determine that each computer costs $225 and each printer costs $150.

To determine the cost of each computer and printer, we can set up a system of equations based on the information provided. Let C represent the cost of one computer and P represent the cost of one printer. Using the first scenario where three computers and one printer cost $825, we can write the first equation as:

3C + P = $825 ... (1)

For the second scenario where four computers and two printers cost $1200, we can write the second equation as:

4C + 2P = $1200 ... (2)

Next, we'll solve this system of equations using either substitution or elimination method. To use elimination, we can multiply equation (1) by 2 to eliminate the printers:

6C + 2P = $1650 ... (3)

Now, we subtract equation (2) from equation (3) to find C:

6C + 2P - (4C + 2P) = $1650 - $1200

2C = $450

C = $225

We now know each computer costs $225. To find the cost of a printer, we can replace C in either equation (1) or (2). Let's use equation (1):

3(225) + P = $825

675 + P = $825

P = $825 - 675

P = $150

Thus, each computer costs $225 and each printer costs $150.

Answer:

Step-by-step explanation:

Intercept c = 21 and slope m = -5

y = mx + c

y = -5x + 21

Answer:

The markup percentage is 61.2

Step-by-step explanation:

Given as :

The cost price of each ornaments = $23

The sell price of each ornament = $37.08

Let The markup percentage = x

Now, According to question

Markup percentage = [tex]\dfrac{s.p - c.p}{c.p}[/tex] × 100

Or, x% = [tex]\dfrac{37.08 - 23}{23}[/tex]

Or, x% = [tex]\dfrac{14.08}{23}[/tex]

Or, x% = 0.612

∴ x = 0.612 × 100

I.e x = 61.2

So, The The markup percentage = x = 61.2

Hence, The markup percentage is 61.2 Answer

To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).

The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.

Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:

[(x + 7) / 2, (y + -9) / 2] = (3, -2)

Simplifying the equation, we get:

(x + 7) / 2 = 3

(y - 9) / 2 = -2

Multiplying both sides by 2, we have:

x + 7 = 6

y - 9 = -4

Subtracting 7 from both sides, we get:

x = -1

Subtracting -9 from both sides, we get:

y = 5

Therefore, the coordinates of the other endpoint are B(-1, 5).

Answer:

The area of each slice of cake is [tex]\frac{25}{12}\pi\ in^2[/tex]

Step-by-step explanation:

step 1

Find the area of the complete cake

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (5)^{2}[/tex]

[tex]A=25\pi\ in^2[/tex]

step 2

Find the area of each slice of cake

Remember that the area of complete circle subtends a central angle of 360 degrees

If you cut the cake into 12 equal slices

then

the central angle of each slice is equal to [tex]\frac{360^o}{12}=30^o[/tex]

so

Using proportion

Find out the area of each slice for a central angle of 30 degrees

[tex]\frac{25\pi}{360^o}=\frac{x}{30^o} \\\\x= \frac{25\pi}{360^o}(30^o)\\\\x=\frac{25}{12}\pi\ in^2[/tex]

Note This problem could be solved by directly dividing the area of the circle by 12, however, proportions and concepts of central angle were applied for didactic purposes

Each slice of the 10-inch diameter cake, cut into 12 equal slices, has an area of approximately 6.54 square inches.

To find the area of each slice of the cake, we need to calculate the area of the entire cake first and then divide it by 12 since the cake is divided into 12 equal slices.

The formula for the area of a circle is: Area = πr².

Given the diameter of the cake is 10 inches, we first need to find the radius: radius = diameter / 2 = 10 / 2 = 5 inches.

Now, calculate the area of the entire cake:

Area of the full cake = π × (5 inches)² = 25π square inches.

Since the cake is cut into 12 equal slices, the area of each slice is:

Area of each slice = (25π) / 12 = 25π / 12 ≈ 6.54 square inches.

Therefore, each slice of cake has an area of approximately 6.54 square inches.

Answer:

[tex]\large\boxed{x=\dfrac{50y-585}{156}}[/tex]

Step-by-step explanation:

[tex]y=0.39(8x+30)\qquad\text{use the distributive propety}\\\\y=(0.39)(8x)+(0.39)(30)\\\\y=3.12x+11.7\qquad\text{multiply both sides by 100}\\\\100y=312x+1170\qquad\text{subtract 1170 from both sides}\\\\100y-1170=312x\qquad\text{divide both sides by 312}\\\\\dfrac{100y-1170}{312}=x\\\\x=\dfrac{100y:2-1170:2}{312:2}\\\\x=\dfrac{50y-585}{156}[/tex]

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Given a System of linear equations, the solution of the system is the point [tex](x,y)[/tex] in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.

Having the following System of equations:

[tex]\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.[/tex]

You can use the Elimination method to find the value of "x":

-Multiply the second equation by 3.

- Add the equations.

- Solve for "x".

Then, you get:

[tex]\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2[/tex]

Answer :The value of x when log(x) = -5 is 0.00001.

Step-by-step explanation:

burned: 756 calories

hours: 3

same number of calories each hour

-> to find this, we must split the number of calories evenly among the hours

steps

756/3

= 252 calories per hour

Answer:

252

Step-by-step explanation: 756/3

Answer:

Step-by-step explanation:

30 lbs in 3 hrs....

30/3 = 10 lbs per hr <==

Answer:

10 pounds

Step-by-step explanation:

if you divide 30 by 3 you will get 10 and becuase there are three hours you will have the answer as 10

30÷3=10

10×3=30

Answer:

yes

Step-by-step explanation:

it is possible that a body can be moving and at rest at the Same time. this is relative motion. an object that seem to be in motion for one subject can be stationary for another.

For example, A passenger in a bus. he/she is moving for a person walking on the pathway. but for the passenger next to him/her, they are at rest.

Answer:

Yes

Step-by-step explanation:

It is possible if you take into account different points of reference.

If you are in a car, sitting on a seat, while the car is moving, you are not moving with respect with the car. Since the car is moving with respect to the ground, you are moving with respect to the ground.

If you think bigger, you are always in motion. You may be standing in a position not moving at all with respect to the ground, but since the Earth is moving around the sun, you are moving with respect to the sun.

Answer:

Mean= 59.8 and median = 59.5

Step-by-step explanation:

Mean  = Summation of values/ No. of Values

Mean of Girls' height= 61+58+63+57+58+59+62+64+60+56/10

Mean=  598/10= 59.8

Arranged Data = { 56, 57,58,58,59, 60, 61,62,63,64}

As the number of observations is even so the 5th and 6th value will be added and divided by 2

59+60/2= 59.5

Median = 59.5

Matched pairs before and after design?

The design of this experiment is a Within-Subjects Design, where each participant is exposed to both types of signs and their reaction times are compared.

The design of this experiment most closely resembles a Within-Subjects Design. In this design, each participant is exposed to both conditions, in this case, the No Left Turn and the Left Turn Only signs. The participants' reaction times to each sign are measured and compared within the same group of participants, allowing for a direct comparison between the two types of signs.

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Answer:

61%

Step-by-step explanation:

15.25/25

=0.61

Multiply it by 100 and you will get the answer

Whole row form: 15.25/25*100

61 percentage was received.

Hope that helps! :)

Answer: He received 61%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To, find the percentage (p):

p = t/T x 100

Replacing with the values given:

p = (15.25/25)x100

p= 0.61 x 100=61%

He received 61%

Feel free to ask for more if needed or if you did not understand something.

Answer:

9000

Step-by-step explanation:

When you are rounding to the thousands, if the hundreds place is 500 or greater you have to round up in the thousands place.

That would mean 8923 rounded to the thousands place would equal 9000

Hope This Helps!

Answer:

9000  

Step-by-step explanation:

To  round a number to the nearest thousand, you look at the number in the hundreds place.

If the number in the hundreds place is

Here's how to round 8923 to the nearest thousand.

The rounded number is 9000.

Answer:

24%

Step-by-step explanation:

Formula:

   x                 new price - old price

---------    =     ---------------------------------

100%                      old price

Good evening ,

Answer:

x²-9x+12 = (x - (9/2))²- (33/4)

Step-by-step explanation:

Look at the photo below for the details.

:)

In order to find the variables p and q in the equation x^2 - 9x + 12 = (x-p)^2 - q, we first complete the square on the left-hand side which leads us to determine that p=4.5 and q=32.25.

The original equation given is x^2 - 9x + 12 = (x-p)^2 - q. To find the values of p and q, we need to rewrite the left-hand side of the equation in the format of (x-p)^2. This can be done through a process known as completing the square. Looking at the equation x^2 - 9x + 12, we have a perfect square x^2 - 9x + (9/2)^2 = (x-4.5)^2. However, remember, we added (9/2)^2 to both sides, so we have (x-4.5)^2 = x^2 - 9x + 12 + 20.25. Simplifying, (x-4.5)^2 = x^2 - 9x + 32.25, which is our original equation format. Thus, p=4.5 and q=32.25.

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Answer:

2x^2-16x+34

Step-by-step explanation:

Since Y is equal to -5

And  you substitute -5 in the equation.

You now have -5=2x^2-16x+29

Add 5 to both sides

5-5=2x^-16x+29+5

The solution of the system of equations will be given as x = 4 ± i.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = – 5                      ....1

y = 2x² – 16x + 29    ....2

From equation 1 and 2, we have

2x² – 16x + 29 = –5

2x² – 16x + 34 = 0

x² – 8x + 17 = 0

Then the value of x will be

[tex]\rm x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 * 1 * 17}}{2*1}\\\\x = \dfrac{8\pm \sqrt{-4}}{2}\\\\x = \dfrac{8 \pm 2\iota}{2}\\\\x = 4 \pm \iota[/tex]

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Answer:

x =  28/5

Step-by-step explanation:

Step 1: Cross-multiply

x  / 28 = 2/10

x*(10)=(2)*(28)

10x=56

Step 2: Divide both sides by 10.

10x  / 10 = 56/10

x = 28/5

The given ratios can be solved to obtain x as 5.6.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given expression is x/28 = 2/10.

In order to find the equality of two ratios, the cross products of their numerators and denominators are equal which is given as,

10x = 2 × 28

⇒ x = 56/10

⇒ x = 5.6

Hence, the value of x is given as 5.6.

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The taxable amount was $80.86

Step-by-step explanation:

Given,

Sales tax = .07

Total grossed = $1236.00

Let,

x be the price before sales tax, therefore,

Amount of sales tax = 0.07x

Price before sales tax + Sales tax = Total amount grossed

x+0.07x = 1236

1.07x=1236

Dividing both sides by 1.07

[tex]\frac{1.07x}{1.07}=\frac{1236}{1.07}\\x=1155.14[/tex]

Taxable amount = Total amount grossed - Price before tax

Taxable amount = 1236 - 1155.14 = $80.86

The taxable amount was $80.86

Keywords: subtraction, addition

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Answer:

$80.86 was taxed

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of bracelets sold = 5

The number of necklaces sold = 1

Cost of the necklace = $22.50

Cost of the bracelets = x

The amount left = $150

The total amount in the account after selling them = $235

Now,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

Thus,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

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Answer:

2.480 is test statistic

Step-by-step explanation:

Given that the claim is most adults would ease all of their personal information online if they could.

[tex]H_0: p = 0.50\\H_a: p >0.50[/tex]

(right tailed test)

p difference = 0.05

Std error=

[tex]\sqrt{pq/n} =\sqrt{0.5*0.5/609}[/tex]

0.0202

p difference / std error

Test statistic = p difference / std error

= [tex]\frac{0.05}{0.0202} \\=2.480[/tex]

Answer:

Okay, so the first one is" The point (0, 2.50) is on the graph" second one is "The graph has a y-intercept but no x-intercept" And the third one would be "The graph increases from left to right"