Rationalize the denominator Square root 12+Square root 6/Square root 3+1
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[tex]\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\[/tex]

Multiply both parts of the equation by 7:

[tex]\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}[/tex]

The properties of the function are:

The absolute value equation of the function is given as

y = |x|

On the incomplete table of values, we do not have any x values

So, we can make use of any x value

To do this, we make use of the following x values

x = -3, -1, 0, 1 and 3

Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x|

So, we have:

y = |-3| = 3

y = |-1| = 1

y = |0| = 0

y = |1| = 1

y = |3| = 3

When represented on a table of values, we  have

x | y

-3 | 3

-1 | 1

0 | 0

1 | 1

3 | 3

Next, we plot the graph of the absolute value equation

See attachment for the graph of the absolute value equation

From the graph of the absolute value equation, we have the following properties:

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In the picture, there is a square and a shaded region inside the square. The shaded portion has a 13.76 square meter area.

Given that,

In the picture, there is a square and a shaded region inside the square.

We have to find the shaded portion area.

The side of the square is 8cm.

Now,

First we see the unshaded region on the square is there are 4 unshaded regions.

In the figure u can see there is a unshaded region we named that has tile 1, tile2, tile 3, and tile 4.

If we restock them we can see that we got a circle with that 4 tiles.

Now, the side is 8 cm then the 1 tile will be of 4 cm.

So, the radius of the circle is 4 cm.

In the other picture we can see that the area of the shaded region is equal to area of square- area of circle.

Area of the shaded region =s²-πr²

Area of the shaded region =8²-π(4)²

Area of the shaded region =64-π(16)

Area of the shaded region =64-16π

Area of the shaded region =64-16(3.14)

Area of the shaded region =64-50.24

Area of the shaded region =13.76

Therefore, The shaded portion has a 13.76 square metre area.

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Answer:

3x + 4

.................

The factor 3x + 4 have common in both the given expressions.

A whole number that is a factor of two or more numbers is referred to as a common factor. The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).

The given expressions are,

[tex]9x^2 + 24x + 16, 9x^2 - 16[/tex]

The expression [tex]9x^2 + 24x + 16[/tex] is of the form [tex](a + b)^2[/tex]

where [tex]a = 3x , b = 4[/tex]

Therefore,   [tex]9x^2 + 24x + 16 = (3x + 4)^2.[/tex]

The expression [tex]9x^2 - 16[/tex]   is of the form [tex]a^2 - b^2[/tex].

It can be written as, [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

Here, [tex]a = 3x , b = 4[/tex]

Therefore,

[tex]9x^2 - 16 = (3x - 4)(3x + 4)[/tex]

So, in both the expressions the factor (3x + 4) is common.

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Answer:

139

Step-by-step explanation:

Add 132 to both sides, so it will cancel out on the left side and you are left with only p.

[tex]p - 132 + 132 = 7 +132\\p = 139[/tex]

Answer:

This sequence is geometric with common ratio -2.

The least common multiple of 32, 48, and 16 is 96

The first step is to get the prime factors of each number

The prime factors of 32 are 2, 2, 2, 2 and 2.

The prime factors of 48 are  2, 2, 2, 2 and 3

The prime factors of 16 are 2,2,2 and 2

The least common multiple of 32, 48 and 16 can be calculated as follows

2 × 2 × 2 × 2 × 2 × 3

= 32 × 3

= 96

Hence the least common multiple of 32, 48, and 16 is 96

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Answer:

y=8

Step-by-step explanation:

Because we can't divide by zero, the correct option is x = 0.

For which value of x the quotient is not a rational number?

Here we have the quotient:

12/x

We want to find a value of x such that it is not a rational number, where a rational number is any number that can be written as the quotient of two integers.

Here is a trick, remember that we can't divide by 0, so if we choose x = 0, technically we can't take the quotient, so in that case we wouldn't have a rational number.

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Answer: a = 6 and 1/4

Step-by-step explanation:

you subtract the 1/4 to the other side and theres your answer

A statement which best describes the meaning of function f(150) is that: A. This is the average number of days the house stayed on the market before being sold for $150,000.

The average rate of change can be defined as a type of function that is used for describing the average rate at which a quantity either decreases or increases with respect to another quantity.

A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this scenario, the function f(150) can be evaluated as follows:

Function f(150) = 150 × p

Function f(150) = 150 × $1,000.

Function f(150) = $150,000

Therefore, the function f(150) simply means the average number of days this house stayed on the market before it was then sold for $150,000.

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The total cost of painting per cm will be 45.2% i.e. option(d).

Total cost of painting = Rate × Surface area of sphere

We know the radius is increases by 10%.

Thus, the Surface area will change by 21%

using formula a + b + (a × b)/ 100

The total change in cost of painting will be

= 20+21 +(20x21)/100

= 45.2%.

What is surface area?

The total area of all faces (or surfaces) on a 3D form is the surface area. For example:

There are six rectangular faces of a cuboid.

Add the areas of each of the cuboid's six faces to determine its surface area.

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It is true given the above logical analysis to state that RS = 2UV. This is known as a conditional statement also known as an If-then-statement.

A conditional statement (also known as an If-Then Statement) is a statement that begins with a hypothesis and ends with a conclusion.

A conditional statement can also be defined as "If this happens, then that will happen." A conditional statement's hypothesis is the first, or "if" element. While the "Then" is the Conclusion.

Hence, the hypothesis from the above statement is:

IF RS = ST and ST = 2UV [Hypothesis]

Then RS = 2UV [Conclusion]


Put differently we can say

A → B and B→C; then
A → C.

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The Venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon

We have given that

The Distance of moon from the earth(in miles)= a=  [tex]2.4 * 10^5[/tex] miles

The Distance of venus from the earth(in miles)= b =   [tex]1.59 * 10^8[/tex] miles

The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects.

Now,

Let the distance from which venus is further away from the earth than the moon be x

So, x = b - a

x = [tex]1.59 * 10^8-2.4 * 10^5[/tex]

x = [tex]1590 * 10^5 - 2.4*10^5[/tex]

x = [tex](1590 - 2.4)*10^5[/tex]

x = [tex]1587.6*10^5[/tex]

x = [tex]1.5876 * 10^8[/tex]

Therefore, venus is at a distance of  [tex]1.5876 * 10^8[/tex] further away from the earth than the moon.

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In this question we have 3 lines, where 2 parallel lines intersect the other.

Now, because the 2 lines are parallel, their corresponding angles are congruent. Therfore, we can derive the equation:

[tex]2x-43 = x+9[/tex]

[tex]2x = x+9+43[/tex]

[tex]2x = x+52[/tex]

[tex]2x-x = 52[/tex]

[tex]x = 52[/tex]

Answer: 57920 per month

Step-by-step explanation: 905 x 64 = 57920

Answer: 8:16

24(games)-16(wins)=8. 8=the losses

Step-by-step explanation:

Using rotation rules, considering the 90º clockwise rotation, the coordinates of point A are given as follows:

(-2,0).

The origin has coordinates (0,0), hence the rule for a 90º clockwise rotation about the origin is:

(x,y) -> (y, -x).

Considering a point (xP, yP) as reference, the rule for the coordinates of the vertices after the rotation is given as follows:

(x,y) -> (y - yP, -x + xP).

For this problem, point B is the reference point, hence the reference coordinates are as follows:

xP = 2, yP = 1.

Then the rule is:

(x, y) -> (y - 1, -x + 2).

Point A is located at:

x = -2, y = -1.

After the rotation, the coordinates will be given as follows:

(x, y) -> (-1 - 1, -2 + 2) = (-2,0).

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The most appropriate choice for Linear Inequation and area will be given by-

value of h > 8.

What is Linear Inequation and area?

Linear Inequation involves comparision between two values with the help of <,   >,   [tex]\leq[/tex],  [tex]\geq[/tex].

Area of a 2D shape is the total space taken by that shape.

Here ,

Area of vegetable patch of Jake = [tex]h[/tex] [tex]m^{2}[/tex]

Area of vegetable patch of Aliya = ([tex]3h + 7[/tex]) [tex]m^{2}[/tex]

Area of vegetable patch of Lucy = [tex]5h[/tex] [tex]m^{2}[/tex]

Total area of vegetable patch of Jake, Aliya and Lucy

                                                                                       = [tex](h + 3h+7+5h)[/tex] [tex]m^{2}[/tex]

                                                                                       = [tex](9h+7)[/tex] [tex]m^{2}[/tex]

By the problem,

                          [tex]9h + 7 > 79\\9h > 79 - 7\\9h > 72\\h > \frac{72}{9}\\ h > 8[/tex]

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Answer:

answer is D prettyy sure

Using permutation, there are a total of 24 different orders possible.

If there are a total of 4 floats in a parade then the number of possible orders = 4!

If we further calculate it we will get,

               4 x 3 x 2 x 1 = 24

So there are a total of 24 possible orders in which the floats should appear.

The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.

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In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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Answer:

The domain for this function is all real numbers greater than -2.

It is to be noted that the square root of 7-2√10 is √5-√2. See the explanation below.

It is to be noted that square root, in mathematics, refers to a factor of a number which when multiplied by itself, results in the original number. For example, both 3 and –3 are square roots of 9.

Hence the solution to the above expression or problem is given as stated below:

7-2√10 = 5 + 2 - 2 2√10

= (√5)² + (√2)² - 2(√5)(√2)

Hence

7-2√10  = (√5 - √2)²

√(7-2√10) = √5 - √2

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The statement that explains why one source is the most reliable is D. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.

Reliable sources are necessary for reliable information. A trustworthy source will offer a "complete, well-reasoned hypothesis, argument, etc. based on substantial evidence," according to UGA Libraries.

Scholarly, peer-reviewed articles and books are examples of widely regarded sources. trade publications, professional books, etc.

It should be noted that a reliable source should be based in facts and should not be biased.

Therefore, the correct option is D.

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The ways that describes how they could gather the opinions include:

From the information, the local news station wants to find out opinions on the economy for their next broadcast.

It should be noted that in this case, a sample will be used and not the entire population. Therefore, they can ask randomly selected people's opinions on the economy as well as the members of the local news station about their opinions on the economy.

Therefore, the correct options are A and B.

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Pairs of values that could be the number of grams of protein and fiber in the protein bar are:

10 grams of protein and 20 grams of fiber. That is, (10, 20)

and

15 grams of protein and 10 grams of fiber. That is, (15, 10)

From the question, we are to determine the pair of values that could be the number of grams of protein and fiber in the protein bar

From the given information,

The protein has 80 calories from p grams of protein and f grams of fiber

and

The equation that represents the relationship is

4p + 2f = 80

To determine the pair of values, we can determine the values of f for certain values of p

When p = 10

4p + 2f = 80

4(10) + 2f = 80

40 + 2f = 80

2f = 80 - 40

2f = 40

f = 40/2

f = 20

A pair of values is 10 grams of protein and 20 grams of fiber.

When p = 15

4p + 2f = 80

4(15) + 2f = 80

60 + 2f = 80

2f = 80 - 60

2f = 20

f = 20/2

f = 10

Thus,

Another pair of values is 15 grams of protein and 10 grams of fiber.

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Answer:

Step-by-step explanation:

The formula for function g(x) that describes the transformations performed on the basic function f(x) = |x| is g(x) = - ( |x| + 4 )

As per the question statement, we are given a basic function f(x) = |x| and we are supposed to find the formula for function g(x) that describes the transformations performed on the basic function f(x) = |x|.

Solution is as follows:

Reflected about X - axis and translated 4 units down to X - axis.

Basic function y = |x| - 2

Transformed function g(x) = - ( |x| + 4 )

Reflected across y = -2

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Answer:

7.071068 ≈ 7.07

Step-by-step explanation:

The distance, d,  between 2 points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

The two points as determined from the graph are (1, 5) and (2, -2)

[tex]d = \sqrt {(2 - 1)^2 + (-2 - 5)^2}[/tex]

[tex]d = \sqrt {(1)^2 + (-7)^2}[/tex]

[tex]d = \sqrt {{1} + {49}}[/tex]

[tex]d = \sqrt {50}[/tex]

[tex]d = 7.071068[/tex]