URGENT: FIFTEEN POINTS
What is 3452380952/100000000000 fully reduced?

Answer:

16y² - x² shows a correct difference of squares.

Step-by-step explanation:

Following are the given options from which we have to chose which represents the difference of squares.

A) 10y² - 4x²

B) 16y² - x²

C) 8x² - 40x+25

D) 64x² - 48x+9

Difference of square is given by:

a² - b² = (a + b) (a - b)

If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.

As in option A) 10y² - 4x²

10y²  is not a complete square of any number. Hence, option A) is incorrect.

As in option C) 8x² - 40x+25

Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.

As in option D) 64x² - 48x+9

The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.

Lets take the expression 16y² - x²  of option B) and solve it.

First simplify the terms separately to associate them as perfect squares as shown below:

       ⇒  16y² = (4y)²        Equation (1)

       ⇒   x² = (1x)²           Equation (2)

Now, take the difference of Equation (1) and Equation (2).

        ⇒  16y² - x²

          ⇒ (4y)² - (1x)²       Equation (3)

So,

Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).

Which is  

               (4y - x) (4y + x) = 16y² - x²

                                         = (4y)² - (1x)²

So, option B) i.e. 16y² - x² shows a correct difference of squares.

Keywords: difference of square

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Answer:

the correct answer would be

16y² - x²

Answer:

x=1, y=2. (1, 2).

Step-by-step explanation:

3x+y=5

5x-4y=-3

---------------

4(3x+y)=4(5)

5x-4y=-3

----------------------

12x+4y=20

5x-4y=-3

---------------

17x=17

x=17/17

x=1

3(1)+y=5

y=5-3

y=2

Answer:

-7/3

Step-by-step explanation:

-7 2/3=-23/3

5 1/3=16/3

-----------------

16/3+(-23/3)

16/3-23/3

-7/3

Final answer:

To express 5 1/3 plus (-7 2/3), separate and add the integers to get -2, then add the fractions to find -1/3, resulting in the final expression -2 1/3.

Explanation:

To express the sum of 5 1/3 and (-7 2/3) as the sum of its integer and fractional parts, we need to perform the following steps:

Our intuition about addition and subtraction of fractions can be helpful in visualizing the mixing of different pie pieces to form a whole, and understanding how changing the sign affects the direction of the operation.

Answer:

16 hours acts of television we must watch in eighth weeks to meet your goal.

Step-by-step explanation:

This problem requires us to determine the total hours we spend on watching television in eight week if we spend two hours watching television each week. This problem can easily be solved by multiplying 2 hours with number of week that is 8 week.

= 8 * 2 = 16

The solutions for x are -2, 0, 2

Solution:

Given that,

[tex]\text { Let } a = x^2 + 4[/tex]

Given equation is:

[tex](x^2 + 4)^2 + 32 = 12x^2 + 48[/tex]

[tex](x^2 + 4)^2 + 32 = 12(x^2 + 4)[/tex]

[tex]\text { Subtsitute } a = x^2 + 4 \text{ in above equation }[/tex]

[tex]a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0[/tex]

[tex]\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }[/tex]

[tex]a^2 -4a - 8a + 32 = 0[/tex]

Taking "a" as common term from first two terms and taking "-8" as common from last two terms

[tex]a(a-4)-8(a - 4) = 0[/tex]

[tex]\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0[/tex]

[tex]\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8[/tex]

[tex]\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4[/tex]

[tex]\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2[/tex]

[tex]\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0[/tex]

[tex]\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2[/tex]

Answer:

.2 or 1/5

Step-by-step explanation:

sorry for bad picture

Answer:The answer can be calculated by doing the following steps;

Step-by-step explanation:

Answer:

the Answer should be 2 2/9

Step-by-step explanation:

I can assure you i i worked this problem out and i'm 100% sure :) Hope i helped some of ya'll! :>

Answer:

Step-by-step explanation:

25 total people

5 drank coffee and tea

tea drinkers only : 10 - 5 = 5

coffee drinkers only : 12 - 5 = 7

total people who drank anything : 7 + 5 + 5 = 17

number of people who drank neither : 25 - 17 = 8 <=====

Answer:

x=-7

Step-by-step explanation:

Subtract 33 from -30 (because subtraction is the opposite of addition.

that's leaves 9x=-63

you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)

x=-7

Answer:

No

Step-by-step explanation:

Direct variation: two variables, one variable is a constant multiple of another variable

y = k x  .... k constant

-x+4y=-2

4y = x - 2

y = 1/4 x -1/2  ..... y = k x + b    y is not a simple multiple of x

The formula to calculate the height (h) of a cone, given its volume (V) and radius (r), is [tex]\(h = \frac{3V}{\pi r^2}\)[/tex]. This formula isolates the height by multiplying both sides of the volume formula by [tex]\(3/\pi r^2\).[/tex]

To isolate the height (h) in the volume formula of a cone ([tex]\(V = \frac{1}{3}\pi r^2 h\)[/tex]), we can rearrange the formula to solve for h.

Starting with the given formula:

[tex]\[ V = \frac{1}{3}\pi r^2 h \][/tex]

To find h, we can multiply both sides of the equation by [tex]\(3/\pi r^2\)[/tex] to isolate h:

[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]

Therefore, the formula to calculate the height (h) of a cone, given its volume (V), radius (r), is:

[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]

This formula allows you to determine the height of a cone when you know its volume and radius.

Let...

length=x+6

width=x

x+x+x+6+x+6=72

4x+12=72

4x=60

x=15

x+6=21

answer: length=21 and width=15

To solve for the length and width of the rectangle, we first need to understand the formulas and relationships involved:
- The perimeter (P) of a rectangle is the total distance around its boundary, which is calculated by adding together twice the length (L) and twice the width (W): `P = 2L + 2W`.
- We have two pieces of information to work with:
 1. The length is 6 yards longer than the width, which we can express as `L = W + 6`.
 2. The perimeter is 72 yards, so `P = 72`.
With these equations, we can set up our system to solve for the length and width:
1. Substitute the expression for L from the first piece of information into the perimeter formula:
  `P = 2(W + 6) + 2W`
2. Plug in the value for the perimeter:
  `72 = 2(W + 6) + 2W`
3. Distribute the 2 through the parentheses:
  `72 = 2W + 12 + 2W`
4. Combine the W terms:
  `72 = 4W + 12`
5. Isolate the W term by subtracting 12 from each side:
  `72 - 12 = 4W`
  `60 = 4W`
6. Divide by 4 to solve for W:
  `W = 60 / 4`  
  `W = 15`
Now that we have the width, we can use the first equation to solve for the length:
`L = W + 6`
`L = 15 + 6`
`L = 21`
So, the width (W) is 15 yards and the length (L) is 21 yards.

Answer:

the anwer of youre question is B.5 .

Answer:

12.8oz.

Step-by-step explanation: 128 oz in a gallon/5/2

The correct answer is:

The equation simplifies to [tex]\(x = 0\)[/tex] after combining like terms and isolating [tex](x\), resulting in \(x\)[/tex] being zero.

the equation [tex]\(18x - 2x = 4x\)[/tex] step by step:

1. Original equation:

[tex]\[ 18x - 2x = 4x \][/tex]

2. Combine like terms on the left side:

[tex]\[ 16x = 4x \][/tex]

  Explanation: We add or subtract coefficients of like terms. Here,[tex]\(18x - 2x\) simplifies to \(16x\).[/tex]

3. Subtract [tex]\(4x\)[/tex] from both sides:

 [tex]\[ 16x - 4x = 0 \][/tex]

  Explanation: We want to isolate [tex]\(x\)[/tex] on one side. Subtracting [tex]\(4x\)[/tex] from both sides ensures the equation remains balanced.

4. Simplify:

[tex]\[ 12x = 0 \][/tex]

  Explanation: After subtracting, we simplify the expression [tex]\(16x - 4x\) to \(12x\).[/tex]

5. Divide both sides by [tex]\(12\)[/tex]:

[tex]\[ \frac{12x}{12} = \frac{0}{12} \] \[ x = 0 \][/tex]

  Explanation: To solve for [tex]\(x\), we divide both sides by the coefficient of \(x\), which is \(12\).[/tex]

Therefore, the solution to the equation [tex]\(18x - 2x = 4x\) is \(x = 0\)[/tex]. This means [tex]\(x\)[/tex] is zero, satisfying the equation.

Final answer:

20% does not directly convert into a whole number; it represents a fractional part of a whole. If you look at the percent as a part of some quantity, you calculate 20% of that quantity to find the represented part. However, 20% by itself is 0.20 in decimal form, not a whole number.

Explanation:

What is 20% as a whole number?

When talking about percentages, it's important to understand that a percent is a way of expressing a fractional amount as part of a whole divided into 100 parts. For example, 5% means 5 out of 100.

In the case of 20%, you are looking at 20 out of 100. As a whole number, however, percentages less than 100% do not directly convert since they represent a part of a whole, not the whole itself. 20% can be represented as 0.20 in decimal form, which still does not constitute a whole number. The closest concept related to whole numbers would be if you had some quantity that you wish to find 20% of; you would then calculate 20% of that number to find the part it represents. But the 20% by itself remains a fraction, not a whole number.

Answer: -4x+2

Step-by-step explanation: Simplify the expression.

Hope this helps you out! ☺

Answer:

0.4714

Step-by-step explanation:

The diagram shows:

Then the total number of registered voters is

[tex]3,371,556+3,006,202=6,377,758[/tex]

Thus, the probability that a registered voter voted in the election is

[tex]\dfrac{3,006,202}{6,377,758}\approx 0.4714[/tex]

The probability that a registered voter participated in the election can vary significantly. In the U.S. 2020 Presidential Election, 77 percent of registered voters voted. However, it's vital to consider the full context, including the total and voting-age populations, and understand that turnout rates can vary by factors like age.

The probability that a registered voter voted in the election depends on various factors such as the year, voters' ages and other socioeconomic factors. In the U.S., for instance, in the 2020 Presidential Election, 77 percent of registered voters cast their vote. However, it's vital to keep in mind that while this data is significant, it doesn't give full context without considering factors such as the eligible voting-age population or the total population.

Furthermore, it's useful to understand the concept of a 90 percent confidence level when interpreting statistics related to voter turnout. In this context, the statement 'We estimate with 90 percent confidence that between 56.4 percent and 63.6 percent of all students are registered voters.' suggests that there's a 90 percent probability that the actual percentage of registered voters among all students falls between the specified range.

On a related note, the age group also influences voter turnout. For instance, in 2016, 51 percent of eligible voters between the ages of eighteen and twenty-four registered, but only 39 percent of them voted. Conversely, 75 percent of eligible voters aged from sixty-five to seventy-four registered, and of these, 68 percent voted. Hence, the probability of a registered voter voting in the election can vary quite a bit based on age, among other factors.

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$ 82.03  in 25 yrs

$ 74.30 in 20 yrs

Step-by-step explanation:

Every year, the cost of the jeans increases by 2% which is equivalent to 0.02 in decimal points. The get the cost of the jean for every year we are multiplying the principle cost by;

100 % + 2% = 102% OR 1.02 in decimal

This increase occurs 25 time for 25 years. Therefore;

1.02 ^ 25 * 50

= 1.641 * 50

= $ 82.03

To get the price in 20 years;

1.02 ^ 20 * 50

= 1.486 * 50

= $ 74.30

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Answer:

I believe the answer is 55.

Step-by-step explanation:

Because if Malachy gets 44 and the ratio is 4:5 it would only make sense if Paul got 55.

   Statement                            Reason

-------------------------------------------------------------------------------------

1. CD=DC                        Reflexive Property

2. D-midpoint of AB                Given

3. AD=BD                         Definition of Midpoint

4. CD⊥AB                                  Given

5. m<CDA=m<CDB         Definition of Perpendicular Lines

6. ΔACD≅ΔBCD                           SAS

Answer:

10 000

Step-by-step explanation:

For each choice of the first two digits you have 10 choices for the third digit. Thus you have 10x10x10 = 1000 choices for the first three digits. Finally you have 10 choices for the fourth digit and thus there are 10x10x10x10 = 10 000 possible 4 digit combinations from 0-9.

Answer:

Karen has 6 quarters and 2 dimes

Step-by-step explanation:

Let

x ----> the number of quarter coins Karen has

y ----> the number of dimes coins Karen has

Remember that

[tex]1\ quarter=\$0.25\\1\ dime=\$0.10[/tex]

we know that

Equation that represent the amount of coins Karen has

[tex]x+y=8[/tex]

isolate the variable y

[tex]y=8-x[/tex] ----> equation A

Equation that represent the value of coins Karen has

[tex]0.25x+0.10y=1.70[/tex] ----> equation B

Solve the system of equations by substitution

substitute equation A in equation B

[tex]0.25x+0.10(8-x)=1.70[/tex]

solve for x

[tex]0.25x+0.80-0.10x=1.70[/tex]

[tex]0.25x-0.10x=1.70-0.80[/tex]

[tex]0.15x=0.90[/tex]

[tex]x=6[/tex]

Find the value of y

[tex]y=8-x[/tex] ----> [tex]y=8-6=2[/tex]

therefore

Karen has 6 quarters and 2 dimes

Michelle's annual salary, including benefits, is $43,330.

To calculate Michelle's annual salary, we need to add up her base salary and the value of her benefits. Based on the information given, her base salary is $32,000 per year. In addition, her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation, as well as saving $2,500 on clothing costs. Let's calculate the value of these benefits:

Now let's add up the base salary and the value of the benefits:

Base salary: $32,000

Health insurance: $5,000

Paid holidays: $1,000

Retirement contributions: $1,600

2-week paid vacation: $1,230

Savings on clothing costs: $2,500

Total annual salary, including benefits: $43,330

Answer:

123,000

Step-by-step explanation: 40×15=600

For 1 worker

600×250=123,000

For all 250 workers

Answer:

(x, y ) → (- y, - x )

Step-by-step explanation:

Consider the coordinates of corresponding vertices of the 2 triangles, that is

A(1, 7 ) → D(- 7, - 1 )

Note the coordinates of D are the negative reversals of A

Thus (x, y ) → (- y, - x )

Answer:

360,000.

Step-by-step explanation:

9! - 4! (5!)

= 9*8*7*6*5*4*3*2*1 - 4*3*2*1 * 5*4*3*2*1

= 5*4*3*2*1 ( 9*8*7*6 - 4*3*2*1)

=  120( 3024 - 24)

= 120 * 3000

= 360,000

Answer:

11 cars

Step-by-step explanation:

There are 20 cars in my building's parking lot, 15 cars are 4-door, then

[tex]20-15=5[/tex] cars are 2-door.

5 cars are 2-door, 4 of them are 2-door and white, then

[tex]5-4=1[/tex] car is 2-door and red.

12 cars are red, 1 car is 2-door and red, then

[tex]12-1=11[/tex] cars are 4-door and red.

(1/3) are red  =  30 *1/3  = 10 are red

So...20  are white

50% are 4 door   = 15  are 4 door

So....15 are 2 door

8 are 2 door  and white.....so 12 are 4 door and white  since we have 20 white total

And since 15 are 4 door  and 12 of these are white...then 3 must be 4 door and red

Make a two-way table as follows:

                                           RED                            WHITE

2-DOOR                               7                                        8

4-DOOR                               3                                      12

TOTALS                               10                                     20

 So, it looks like you have 3 cars that are red and have 4 doors.

Answer:

(A) [tex]r[/tex]  is < than equal to 17

Step-by-step explanation:

Total amount Jim had for the carnival =$25.00

Amount spent on food = $3.75

Amount left with him = [tex]\$25.00-\$3.75=\$21.25[/tex]

Jim plans to sped rest on tickets for rides.

Cost of each ride ticket = $1.25

Given: [tex]r[/tex] represents the number of ride tickets bought.

Using unitary method

If 1 ride ticket cost = $1.25

Cost of [tex]r[/tex] ride tickets in dollars will be = [tex]1.25r[/tex]

Amount spent on rides must be less than or equal to the total amount left with Jim which is =$21.25.

So, we have:

⇒ [tex]1.25r\leq 21.25[/tex]

Dividing both sides by 1.25.

⇒ [tex]\frac{1.25r}{1.25}\leq \frac{21.25}{1.25}[/tex]

∴ [tex]r\leq 17[/tex]

Thus, the inequality representing te number of tickets Jim can purchase is given by:

[tex]r\leq 17[/tex]

Answer:

The length of A'C' will also be 5 units.

Step-by-step explanation:

If a reflection takes triangle CAT to C'A'T', what is A'C'?

Starting with ΔCAT triangle as shown in figure (a).

Reflections are said to be Isometries as it does preserve the distances.

If the shape or triangle ΔCAT reflected it will remain the same size. As a result, the reflected image would be 'congruent' to the original object.

Lets suppose, ΔCAT is reflected across  y axis.  

The rule for reflection of the point (x,y) across the y-axis is actually the point (-x,y).

Reflect a point across the y-axis, the y-coordinate will remain the same, but the x-coordinate will be transformed into its opposite (the sign of x-coordinate will be changed).

C(0, 0)   →  C'(0, 0)

A(-2, 1)  →  A'(2, 1)

T(-1, 4)  →  T(1, 4)

length of Side AT = 3 units

length of Side TC = 4 units

length of Side AC = 5 units

As reflections are said to be Isometries as it does preserve the distances.

So, if ΔCAT reflected is reflected across  y axis. ΔC'A'T' preserves the distances. The length of each segment of the preimage would be equal to its corresponding side in the image as shown in figure (a).

So, the length of A'C' will also be 5 units.

Keywords: reflection, transformation, triangle

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Answer:

The length of A'C' will also be 5 units.

Step-by-step explanation: