help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2

In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.

Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.

The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.

Given

[tex](1/4)^{x-2} = 16[/tex]

[tex](1/4^{x-2}) = 16[/tex]

1 = 16 × [tex]4^{x-2}[/tex]

1 = 16 × [tex](2^2)^{x-2}[/tex]

[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]

[tex]$1 = 2^{2x}[/tex]

1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0

1 = 1

x = 0

Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

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Answer: c

Step-by-step explanation:

The quotient of the expression,

9(7y - 15) /  (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

We have an expression,

9(7y - 15) /  (110 - 6y ÷ 4)

Simplifying,

9(7y - 15) /  (110 - 6y ÷ 4),

= 9(7y - 15) x 4 / (110 - 6y)

= 36(7y - 15) / (110 - 6y)

= 18(7y - 15) / (55 - y)

Therefore, the quotient is 18(7y - 15) / (55 - y).

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Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.

Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.

5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.

Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

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Yes, substitution can be used to solve a linear system of equations.

Linear System of Equations:

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.

The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.

Yes, a linear system of equations can be solved via substitution.

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All normal density curves are symmetric and have a peak at the mean. 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

All normal density curves are symmetric. This means that the curve looks the same to the right and left of the mean (μ). The curve reaches its peak at the mean, which is the highest point on the curve. The area under the curve is equal to 1. The area under the curve that is within one standard deviation (σ) of the mean is equal to 0.68. This means that 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

The formula for calculating the area under the curve within one standard deviation of the mean is:

Area = 0.68 * 1

The formula for calculating the area under the curve within two standard deviations of the mean is:

Area = 0.95 * 1

These formulas can be used to calculate the area under the curve for any normal density curve.

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4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

An expression is combination of variables, numbers and operators.

Let m be the number of marbles.

The number of marbles April has be m.

Given that Carter has 10 fewer marbles than April.

If Carter has 10 less than m, that's m - 10.

Nicholas has 3 times as many marbles as April.

3m

marbles Carter and Nicholas have altogether

m-10+3m

4m-10

Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

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The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.

The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.

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The solution to the algebraic expression 3y - (2y - 3) ÷ 4 is; (10y + 3)/4

The algebraic expression is given as;

3y - (2y - 3) ÷ 4

With the aid of order of operations named PEMDAS which is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction. Thus, we can rewrite the expression as;

3y - (2y - 3)/4

The common denominator is 4 and when we distribute we will have;

(4(3y) - 2y + 3)/4

= (12y - 2y + 3)/4

= (10y + 3)/4

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Answer: AAS and both triangles are congruent

Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate.  The way you tell the difference between the two is by how the congruent angles and the congruent side is shown.  In ASA, the congruent side would be the included side between both congruent angles.  Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS.  This means that the triangles are congruent.  

Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles.  If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.

I hope this helps you!

The rocket was at a height of 19.75 meters after 0.5 seconds

The rocket hit the ground after 8.02 seconds

The maximum height is 81 m.

An equation is an expression that shows the relationship between numbers and variables.

The height (h) of the rocket t seconds after launch is modeled by:

h(t) = -5t² + 40t + 1

a) After 0.5 seconds:

h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters

b) The rocket hit the ground when h(t) = 0, hence:

-5t² + 40t + 1 = 0

t = 8.02 s

c) The maximum height is at h'(t) = 0

h'(t) = -10t + 40

-10t + 40 = 0

10t = 40

t = 4 s

h(4) = -5(4)² + 40(4) + 1 = 81 meter

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Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.

The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.

So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12

So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.

Step-by-step explanation:

Answer:

H = 20

Step-by-step explanation:

Looks like you got everything correct. Nice!

For your last one, let's get H by itself. Since 1/2 is division, let's multiple it by 2 to turn it into one. Because you multiply by 2 on the left side, you have to on the right side also...

(1/2)(2) = 1

(1)(h) = h

On the other side, 10(2) = 20.

Combining the 2, H = 20

The possible sets of five tiles that she could have pulled out are (2,3),(3,2)

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

Given;

Number of tiles asha pulled out=5

Bag contains only positive and negative x and x² tiles

So, the equation will be

-x^2+x=5

x^2-x+5=0

Now,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2

x=2,3

x=3,2

Therefore, the quadratic equation solution will be (2,3),(3,2)

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Answer:

Slope intercept form =  y=mx+b

So

y-1=x

Add 1 to both sides

y=x+1

Answer:

area of sector = 49π/6 cm² ≈ 25.7 cm²

Step-by-step explanation:

area of sector = (n/360°)πr²

where n = central angle of sector, and r = radius of circle

Here, we have:

n = 60°

r = d/2 = 14 cm / 2 = 7 cm

area of sector = (60°/360°)π(7 cm)²

area of sector = (1/6)π(49 cm²)

area of sector = 49π/6 cm² ≈ 25.7 cm²

Answer:

7.5

Step-by-step explanation:

Since the segments are parallel, the side segment lengths are proportional.

8/10 = 6/x

4/5 = 6/x

4x = 30

x = 7.5

Answer:

In economics, the LOD or Law of Demand states that as the price increases on a good or service, there are less people that are willing and able to purchase that good or service.

Here is an example

On the image attached there is a Price Quantity Demanded Graph. The Line on the graph represents demand.  The furthur right the line of the graph goes, the larger the quantity of demand for a good is, vice versa. The Law Of Demand is demonstrated on the graph and the table, when price (Px) is at 5, then only Quantity Demanded (Dx) equals 100. When Px = 1 then Dx = 500. As price decreases, demand increases.

Hope this helped :)

Answer:

So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.

Step-by-step explanation:

We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.

The probability that it is a caramel truffle is 6/13.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A box contains only orange truffles, strawberry truffles, and caramel truffles and the ratio of orange truffles to strawberry truffles is 3 : 4.

Also given, The probability that it is an orange truffle P(O) is 3/13,

Hence  The probability that it is a strawberry truffle P(S) = 4/13.

Therefore, The probability that it is a caramel truffle P(C) is = 1 - 3/13 + 4/13.

= 1 - 7/13.

= 6/16.

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The probability of 5 heads in 10 flips.

A coin is flipped 10 times and we want to find the probability of getting exactly 5 heads.

This situation is a binomial distribution because it involves a fixed number of trials (10) and each trial has a fixed probability of success (1/2). . The probability of obtaining exactly 6 successes in 10 trials is given by the formula P(x) = nCx * px * (1-p)n-x. In this situation, the probability is P(x) = 10C6 * 0.26 * 0.84 = 0.17496. The probability of getting exactly 5 heads can be calculated using the formula P(X=5) = 10C5 * 0.5^5 * 0.5^5 = 0.246. This is the probability of 5 heads in 10 flips.

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Complete question:What is the probability of getting 5 heads when you toss a fair coin 10 times?

Answer:c

Step-by-step explanation:

The slope forms a uniform solution in each square box as shown in the drawing

here, s is the value or answer.

SOLUTION -

[tex] \frac{1}{2} = \frac{3}{6} \\ 1 \\ \frac{1}{2} = \frac{1}{2} \\ = \frac{1}{m } = \frac{1}{2} \\ m = 2[/tex]

Pareto chart is a type of bar graph which often displays the data in descending order of frequency.

It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.

For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.

Toga: 6

Hayride: 6 + 4 = 10

Beer Bash: 10 + 8 = 18

Masquerade: 18 + 2 = 20

The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.

Toga: 6 (30%)

Hayride: 10 (50%)

Beer Bash: 18 (90%)

Masquerade: 20 (100%)

Hence, the Pareto chart for the given data is as follows:

Toga: 30%

Hayride: 20%

Beer Bash: 40%

Masquerade: 10%

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Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:

A = {1, 2, 3, 4, 5 }

Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:

N: Set of all natural numbers

Z: Set of all integers

Q: Set of all rational numbers

R: Set of all real numbers

Z+: Set of all positive integers

A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.

Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members

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The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2

The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T

The  vertices are;

A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)

Thus;

Length of sides AB and CD

length = √(x₂ - x₁)² + (y₂ - y₁)²

AB =√(2 - 0)² + (5 - 3)²

AB = 2√2

length = √(x₂ - x₁)² + (y₂ - y₁)²

CD = √(2 - 6)² + (0 - 4)²

CD = 4√2

Formula to use for the mid segment is;

Mid segment = (AB + CD)/2

                      = (2√2 + 4√2) / 2

                      = 3√2

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