Which expression is equal to (2x − 2)(3x – 3)?
6x2 - 12x +6
5x2 - 6x-5
6x2 – 123 - 5
6x2 + 12x - 6​

The final factored expression using the GCF is: 14x+63=7(2x+9)

To factor the expression 14x + 63 using the Greatest Common Factor (GCF), let's first find the GCF of the numerical coefficients 14 and 63. The largest number that divides both 14 and 63 without a remainder is 7, making it the GCF.

Next, we divide each term by the GCF:

14x divided by 7 is 2x

63 divided by 7 is 9

Now that we have divided each term by the GCF, we can write the original expression as a product of the GCF and the simplified expression:

14x + 63 = 7(2x + 9)

This expression is fully factored as the product of the GCF (7) and the binomial (2x + 9).

Answer:

[tex]A_{5} = 1875[/tex]

Step-by-step explanation:

The geometric sequence is represented by

[tex]A_{n} = 5 \times A_{n - 1}[/tex] .......... (1) and [tex]A_{1} = 3[/tex]

So, [tex]A_{2} = 5 \times A_{2 - 1} = 5 \times A_{1} = 5 \times 3 = 15[/tex]

{Putting n = 2}

Again, putting n = 3 in equation (1), we get

[tex]A_{3} = 5 \times A_{2} = 5 \times 15 = 75[/tex]

Again, putting n = 4 in equation (1), we get

[tex]A_{4} = 5 \times A_{3} = 5 \times 75 = 375[/tex]

Again, putting n = 5 in equation (1), we get

[tex]A_{5} = 5 \times A_{4} = 5 \times 375 = 1875[/tex] (Answer)

Answer: 17

================================

How I got that answer:

(2,3) and (3,1) have '3' in common in that the y value of the first pairs with the x value of the second.

If you picture a chain, then you start with x = 2, move to y = 3, then move to x = 3 and then y = 1

2 ---> 3 ---> 3 ---> 1

So f(f(2)) = f(3) = 1

If g(x) = f(f(x)), then we know (2,1) is on the graph of g(x)

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

Repeat for (3,1) and (1,5)

3 ---> 1 ---> 1 ---> 5

f(3) = 1

g(x) = f(f(x)) = f(f(3)) = f(1) = 5

We know that (3,5) is on the graph of g(x)

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

The two points on g(x) are: (2,1) and (3,5)

Comparing that to (a,b) and (c,d) we can see

a = 2, b = 1, c = 3, d = 5

a*b + c*d = 2*1 + 3*5 = 2 + 15 = 17

Answer:

So if you're having difficulty visualizing the differences, you can rewrite them so they all have the same denominator

7/12 = 35/60

1/2 = 30/60

2/3 = 40/60

4/10 = 24/60

1/6 = 10/60

So now it's easier to see how they compare to each other.

10/60, 24/60, 30/60, 35/60, 40/60

And then simplify them or just refer to what they were before

1/6, 4/10, 1/2, 7/12, 2/3

I hope this helps!

Answer:

2.8

Step-by-step explanation:

.8*2=1.6  1.2

1.6+1.2=2.8

Answer:

2.8

Step-by-step explanation:

Simply Substitute for X:

[tex]0.8(2) + 1.2\\1.6+1.2\\2.8[/tex]

You would get 2.8 as the answer.

Answer:

[tex]3y^2[/tex]

Step-by-step explanation:

Given:

To find the GCF of [tex]3y^2\ and\ 24y^3[/tex] using prime factorization.

Writing each in prime factors:

3 = 1 [tex]\times[/tex] 3

24 = 1 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex]2 [tex]\times[/tex] 3

Now, GCF of 3 and 24 is 3

[tex]y^2=1\times y\times y[/tex]

[tex]y^3=1\times y\times y\times y[/tex]

GCF of [tex]y^2[/tex] and [tex]y^3[/tex] is [tex]y\times y=y^2[/tex].

Therefore, the overall GCF of the two terms is [tex]3y^2[/tex]

Answer:

x = 90°

Step-by-step explanation:

We are given a trigonometric function of x from which we have to a solution for x.

The function is [tex]\cos^{2} x + 2\sin x - 2 = 0[/tex]

⇒ [tex]1 - \sin^{2} x + 2\sin x - 2 = 0[/tex]  

{Since we know the identity [tex]\sin^{2} \alpha + \cos^{2} \alpha = 1[/tex]}

⇒ [tex]\sin^{2} x - 2 \sin x + 1 = 0[/tex]

⇒ [tex](\sin x - 1)^{2} = 0[/tex]

{Since we know the formula (a - b)² = a² - 2ab + b²}

⇒ [tex](\sin x  - 1) = 0[/tex]

⇒ [tex]\sin x = 1 = \sin 90[/tex]

⇒ x = 90° (Answer)

To solve cos^2 x + 2sin x - 2 = 0, we convert cos^2 x to 1 - sin^2 x and solve the quadratic equation sin^2 x - 2sin x + 1 = 0, finding that sin x equals 1. Thus, the numerical value of the trigonometric function is sin x = 1.

To find a numerical value of one trigonometric function of x for the equation cos2x + 2sin x - 2 = 0, let's start by expressing everything in terms of sin x:

Using the Pythagorean identity, we know that cos2x = 1 - sin2x. So, we can write:

(1 - sin2x) + 2sin x - 2 = 0

Simplifying, we get:

1 - sin2x + 2sin x - 2 = 0

-sin2x + 2sin x - 1 = 0

This is a quadratic equation in terms of sin x. Let's solve it:

sin2x - 2sin x + 1 = 0

We recognize this as a perfect square trinomial:

(sin x - 1)2 = 0

So, we have:

sin x - 1 = 0

Therefore:

sin x = 1

So, the numerical value of one trigonometric function of x from the given equation is sin x = 1.

Answer:

The answer is undetermined

Step-by-step explanation:

i'm not joking the when the line is parallel to the y axis it has no slope because it runs vertically but if the line was horizontal the slope would be 0

Answer:

44 quarts of paint

Step-by-step explanation:

Given,

75-foot fence needs = 4 quarts.

We have to use the unitary method to determine how many quarts will be needed for the fencing system. Hence,

75-foot fence needs         = 4 quarts of paint

1-feet fence needs            = (4/75) quarts of paint

825-foot fence needs      = (4 x 825)/75 quarts of paint

                                          = 3,300/75 quarts of paint

                                          = 44 quarts of paint

Therefore, we need 44 quarts of paint for 825-foot fence.

To determine how many quarts of paint are needed for an 825-foot fence, we can set up a proportion and solve for the unknown quantity.

To determine how many quarts of paint are needed for an 825-foot fence, we can use the concept of ratios. Since we know that 4 quarts of paint are needed for a 75-foot fence, we can set up a proportion:

To solve for the unknown quantity, we can cross-multiply and solve for the missing value:

Dividing both sides of the equation by 75, we get:

By performing the calculation, we find that quarts of paint is approximately 44 quarts. Therefore, 44 quarts of paint are needed for an 825-foot fence.

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Answer:

Step-by-step explanation:

10/25=20/50=40/100

6/8=3/4=12/16

3/5=6/10=60/100

1/10=10/100

Answer:

it's D

Step-by-step explanation:

y= .05x+20

x=50

y=.05(50)+20

2.5+20

y=22.5

y=.25x+10

x=50

y=.25(50)+10

12.5+10

y=22.5

Total cost of tickets for one movie showing is calculated by multiplying the total number of seats (n rows times m seats per row) by the cost per ticket, which is $5.60.

To calculate the total cost of all tickets for one movie showing in a theater with n rows and m seats per row, you'll need to use multiplication to find the total number of seats and then multiply it by the cost per ticket. Here is a step-by-step guide:

For example, if a theater has 10 rows with 20 seats in each row, the total number of seats is 10 × 20 = 200. The total cost for all tickets would then be 200 × $5.60 = $1120.

Answer:

[tex]l(AB)=5\ units[/tex]

is the distance between the point A and point B.

Step-by-step explanation:

Let

A ≡ (x₁, y₁) ≡ (-9 , -8 )

B ≡ (x₂, y₂) ≡ (-6 , -4 )

Now by Pythagoras  Distance formula we have

a² + b² = c²

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}\\\\l(AB) = \sqrt{((-6--9)^{2}+(-4--8)^{2} )}\\\\l(AB)=\sqrt{(3)^{2}+(4)^{2}  }\\\\l(AB) =\sqrt{25} \\\\l(AB) = 5\ units[/tex]

Answer

c= √(a² + b²)

c=√( -6  –  -9 )² + ( -4 –  -8 )²

Step-by-step explanation:

Answer:

$1.40

Step-by-step explanation:

1.75-(1.75×.2)

1.75-.35

1.4

Answer:

$1.40

Step-by-step explanation:

100% - 20% = 80%

Therefore, Multiply $1.75 by 80% to get this week's price of orange

$1.75 x 80% = $1.40 per pound

Answer:

Ratio = [tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

The perfect squares from 1-30 are:

1, 4, 9, 16, 25

Total no. of perfect squares = five =5

Total no. of non perfect squares = 30-5 = 25

Ratio =[tex]\frac{Perfect.squares}{non.Perfect.squares}[/tex] = 5 / 25 = [tex]\frac{1}{5}[/tex]

The ratio of perfect squares to non-perfect squares for the numbers 1 to 30 is 1:5.

A perfect square is a number that is the square of an integer. For the numbers 1 to 30, the perfect squares are 1, 4, 9, 16, 25, as these numbers are squares of integers 1, 2, 3, 4, 5 respectively. The number of perfect squares is 5.

The total number of tiles is 30. So the number of non-perfect squares is 30 - 5 = 25.

The ratio of perfect squares to non-perfect squares in simplest form, then, is 5 : 25. Simplified, this ratio is 1 : 5.

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Answer:

B is the answer at least i think also are you in gaca? if so webmail me my name is Angela Petersen

it is d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

First find how many bottles Ginger will need.

15 mL x 365 day = 5475 mL for 1 yr

5475 mL / 350mL = 16 bottles

Then find the price for the 16 bottles.

16 bottles x $4.85 = $77.60

Answer:

The missing part is given below.

500=(2xL)+(__2__x_90___)

500=2L+__180_____

_320__=2L

_320____ divided by 2=L

_160____=L

Step-by-step explanation:

Given:

Perimeter of Rectangle = 500 feet

Width = 90 feet

Length = L

Solution:

[tex]\textrm{Perimeter of Rectangle} = 2(Length + Width)\\\\\textrm{On substituting the given values in it we get}\\500 = 2\times L + 2\times 90\\\\500 - 180 =2\times L\\320 =2\times L\\\\\frac{320}{2}=L\ ....................... (\textrm{320 divided by 2}) \\160 = L[/tex]

Final answer:

To find the length of the garden, the formula for the perimeter of a rectangle is used (P = 2L + 2W), where the perimeter is 500 feet and the width is 90 feet. By substituting these values and solving for L, we find that the length of the garden is 160 feet.

Explanation:

Finding the Length of a Garden

To find the length of a rectangular garden when you know the perimeter and the width, you can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P stands for the perimeter, L is the length, and W is the width. The student has provided that the width (W) of the garden is 90 feet and the perimeter (P) is 500 feet.

Substituting the values we know into the formula, we get:

500 = 2L + 2(90)

Now, we solve for the length (L) by following these steps:

First, do the multiplication: 500 = 2L + 180

Next, subtract 180 from both sides to isolate the term with L: 320 = 2L

Finally, divide both sides by 2 to solve for L: 160 = L

Therefore, the length of the garden is 160 feet.

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

in this problem

For x=-14, y=-7

Find the value of the constant of proportionality k

[tex]k=y/x[/tex]

substitute

[tex]k=-7/-14=0.5[/tex]

so

The linear equation is

[tex]y=0.5x[/tex]

Find x when the value of y=10

substitute the value of y in the equation

[tex]10=0.5x[/tex]

solve for x

Multiply by 2 both sides

[tex]x=20[/tex]

Final answer:

In direct variation relationship 'y = kx', using the given y = -7 when x = -14, the constant of variation 'k' is found to be 0.5. To find x when y = 10, we use 'y = kx' to get x = 20.

Explanation:

The student's question revolves around the concept of a direct variation, which is a fundamental topic in algebra. The direct variation relationship between two variables 'x' and 'y' can be expressed as 'y = kx', where 'k' is the constant of variation. To determine the constant 'k', we can use the given condition, which states that when x = -14, y = -7. This equation simplifies to 'k = y/x', so 'k = (-7)/(-14)' which equals 0.5.

Now, we need to find 'x' when y is 10. Using the direct variation equation 'y = kx' and our calculated 'k' value of 0.5, we can set up the equation '10 = 0.5x'. Solving for 'x', we get 'x = 10/0.5' which simplifies to 'x = 20'. Thus, when y equals 10, the corresponding value of x is 20.

The questions pertain to the analysis of linear relationships between variables using scatter plots, lines of best fit through linear regression, and understanding correlation coefficients to identify the strength and direction of relationships in data.

The questions provided are centered around the concepts of linear equations, scatter plots, correlation, and regression analysis in the realm of mathematics. Scatter plots are graphical representations showing the relationship between two variables. In these types of questions, the independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis. To analyze the relationship, one can use linear regression to find the line of best fit, which is a straight line that best represents the data on a scatter plot. The correlation coefficient, often denoted as r, indicates the strength and direction of the linear relationship between two variables.

The line of best fit can be found by calculating the least-squares line, which minimizes the sum of the squares of the vertical distances of the points from the line. The equation of this line is typically in the form y = a + bx, where 'a' is the y-intercept and 'b' is the slope. The slope indicates how much the dependent variable changes for a one-unit change in the independent variable. The y-intercept is the value of the dependent variable when the independent variable is zero. A correlation coefficient of zero implies no linear relationship between the variables.

When looking at data such as stock market trends or health-related measurements like BMI and cholesterol, understanding the strength and type of correlation is essential for making predictions. For example, a positive correlation indicates that as one variable increases, the other variable tends to increase, while a negative correlation indicates the opposite. It's important to note that correlation does not imply causation; just because two variables are correlated does not mean that one causes the other.

Answer:

[tex]\large\boxed{\dfrac{1}{8}\%=\dfrac{1}{800}}[/tex]

Step-by-step explanation:

[tex]p\%=\dfrac{p}{100}\\\\\dfrac{1}{8}\%=\dfrac{\frac{1}{8}}{100}=\dfrac{1}{8}\cdot\dfrac{1}{100}=\dfrac{1}{800}\\\\\text{other method}\\\\\text{Convert the fraction to the decimal:}\\\\\dfrac{1}{8}=0.125\to\dfrac{1}{8}\%=0.125\%\\\\0.125\%=\dfrac{0.125}{100}=\dfrac{0.125\cdot1000}{100\cdot1000}=\dfrac{125}{100000}=\dfrac{125:125}{100000:125}=\dfrac{1}{800}[/tex]

Answer:20652.00

Step-by-step explanation:

The formula would be p*r*t

p is the principal which is amount of money before interest

r is the interest rate

t is time period

so it would be 57,366.66*9 2/5%*4

9 2/5 as a decimal would be 9.4 or 0.09

57,366.66*9.4=539246.604*4=2156986.416

The correct amount would be $20652.00 in 4 years

Use 0.09  when u multiply instead of 9.4 because it is much easier

Answer:

Step-by-step explanation:

It’s 35 because 9*5 is 45 and 80-45 is 35

Answer:

Yes (6,3) is a solution

Step-by-step explanation:

It because both of the lines that are shaded intercepted so it works for both

Answer:

The price of a senior ticket is $12.

Step-by-step explanation:

Given:

Mr. Smith purchased 8 senior tickets and 5 child tickets for $136. Mr. Jackson purchased 4 senior tickets and 6 child tickets for $96.

Now, to get what is the price of a senior ticket.

Let the senior ticket be [tex]x[/tex] and the child ticket be [tex]y[/tex]:

So, according to question

[tex]8x+5y=136[/tex].........(1)

[tex]4x+6y=96[/tex]...........(2)

Now, we have system of equations:

Multiplying the equation (2) by -2 we get:

[tex]-8x-12y=-192[/tex].......(3)

Now, adding the equation (3) and (1) the variables and the numbers:

[tex]-8x-12y+8x+5y=-192+136[/tex]

[tex]-7y=-56[/tex]

Dividing both sides by -7 we get:

[tex]y=8[/tex]

Putting the value of y in equation (2) we get:

[tex]4x+6(8)=96[/tex]

[tex]4x+48=96[/tex]

On solving the equation we get:

[tex]x=12[/tex].

Therefore, the price of a senior ticket is $12.

The series will be:

[tex]4+16+64+.......+2^{50}[/tex]

Hence, Option A is the right answer

Step-by-step explanation:

The series can be fount out by putting the values of i in the expression written with the summation

The expression is:

[tex]2^{2i}[/tex]

while i = 1 to 25

Putting i = 1

[tex]2^{2(1)}\\= 2^2\\= 4[/tex]

Putting i = 2

[tex]2^{2(2)}\\= 2^4\\= 16[/tex]

Putting i = 3

[tex]2^{2(3)}\\= 2^6\\= 64[/tex]

....

Putting i = 25

[tex]2^{2(25)}\\= 2^{50}[/tex]

The series will be:

[tex]4+16+64+.......+2^{50}[/tex]

Hence, Option A is the right answer

Keywords: Summation, Series

Learn more about summation at:

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Answer:

multiply all together

Step-by-step explanation

Answer:

6

Step-by-step explanation:

8-2=6