find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]

The first factor with the value of the product is compared as below.

Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.

For example, 10 = 2 × 5

So we can say that 2 and 5 are factors of 10.

Here there are 3 products.

(a) [tex]\frac{1}{3}[/tex] × 1

Here the first factor is [tex]\frac{1}{3}[/tex].

And the product of the two factors is [tex]\frac{3}{9}[/tex].

[tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{3}[/tex]

Numerator and denominator when take three times gives the product.

(b) First factor is [tex]\frac{2}{3}[/tex] and the product is [tex]\frac{14}{21}[/tex].

[tex]\frac{14}{21}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{7}{7}[/tex]

Numerator and denominator when multiplied by 7 times gives the [tex]\frac{14}{21}[/tex].

(c) First factor is [tex]\frac{5}{2}[/tex] and the product is [tex]\frac{25}{10}[/tex].

[tex]\frac{25}{10}[/tex] = [tex]\frac{5}{2}[/tex] × [tex]\frac{5}{5}[/tex]

Numerator and denominator when multiplied by 5 gives [tex]\frac{25}{10}[/tex].

Hence the first factor and products are compared.

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Answer:

s=3

Step-by-step explanation:

Answer:

it's c

Step-by-step explanation:

because for .087  you move the decimal 3 times

                  so the decimal is going to end up 08.7

                                                                                here

We can write 0.87 as 87 / 100.

Option D is the correct answer

Given,

0.087

We have to see the other form it can be written.

The numbers which have a decimal point.

Example: 23.4

It can be written in fractions aswell.

23.4 = 234/10

We have,

0.87

Since there are two numbers after the decimal point we can write it as:

= 0.87
= 087 / 100

= 87 / 100

Thus we can write 0.87 as 87 / 100.

Option D is the correct answer.

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Final answer:

Ana's conjecture that Raul lost 2/5 of his teeth is correct, as it simplifies from Raul's stated 4/10 after losing 8 out of the total 20 baby teeth.

Explanation:

Raul has said he lost 4/10 of his baby teeth, while Ana said Raul lost 2/5 of his teeth. To figure out which conjecture is true, we must consider Raul's claim first. Since a human usually has 20 baby teeth and Raul has lost 8 of those, we calculate the fraction of teeth he has lost by dividing the number of lost teeth by the total number of baby teeth: 8 ÷ 20 = 2/5. This simplifies to the fraction 2/5, which means Ana's conjecture is indeed the correct one. Both fractions actually represent the same value, because when you simplify 4/10 by dividing the numerator and the denominator by 2, you get 2/5.

Answer: The graph is represented by the inequality y>3x+2

Step-by-step explanation:

Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).

In the given question we have the linear inequality represented by graph

We can see the line in the graph passing through the point (-3,-7)

Let's check which option satisfy the point

1) y<3x+2 for this the line should be y=3x+2

⇒ -7=3(-3)+2

⇒-7= -9+2⇒-7=-7,which is true.

2) y>3x+2 which similar as first.

3) y<x+2 for this the line should be y=x+2

⇒ -7= -3+2

⇒-7=-1 which is not true.

4) y > x + 2 is similar to third.

Option 3) and 4) cannot be the required linear inequality.

Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]

Therefore, 2)  y > 3x + 2 is the required linear inequality which is represented by the graph.

The linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex] .

Further explanation:

It is given that a line passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex]  as shown below in Figure 1.

The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex]is calculated as follows:

[tex]m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}[/tex]                    ........(1)

Here, the slope of a line is denoted as [tex]m[/tex] and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] , [tex]2[/tex]  for [tex]{y_1}[/tex] , [tex]-3[/tex]  for [tex]{x_2}[/tex]  and [tex]-7[/tex]  for [tex]{y_2}[/tex]  in equation (1) to obtain the slope of a line that passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] .

[tex]\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}[/tex]

Therefore, the slope is [tex]3[/tex] .

The point-slope form of the equation of a line with slope [tex]m[/tex]  passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:

[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex]                                 .......(2)

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] ,  [tex]2[/tex] for [tex]{y_1}[/tex]  and [tex]3[/tex]  for [tex]m[/tex]  in equation (2) to obtain the equation of line.

[tex]\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex]  is [tex]3x+2[/tex] .

Since the shaded part in Figure 1 is above the equation of line [tex]y=3x+2[/tex], therefore, greater than sign is used instead of is equal to.

Thus, the linear inequality is [tex]y>3x+2[/tex]  as shown below in Figure 2.

Now, the four options are given below.

[tex]\begin{aligned}{\text{OPTION A}}\to &y<3x+2\hfill\\{\text{OPTION B}}\to &y>3x+2\hfill\\{\text{OPTION C}}\to &y<x+2\hfill\\{\text{OPTION D}}\to &y>x+2\hfill\\\end{aligned}[/tex]

Since OPTION B matches the obtained equation that is [tex]y>3x+2[/tex] .

Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex]  and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex].

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality

Final answer:

Catrina used 25 tiles to create a square, which means she made 5 rows with 5 tiles in each row, as the square root of 25 is 5.

Explanation:

Catrina used 25 square green tiles to form a square in the middle of her floor.

To find out how many rows she made and how many tiles she put in each row, we need to think about the properties of a square.

A square has equal sides, so the number of tiles in each row must be the same as the number of rows. Since the total number of tiles is a perfect square (25), we find the square root of 25 to determine the size of each side of the square.

The square root of 25 is 5, so Catrina created 5 rows with 5 tiles in each row. This forms a perfectly square area on her floor with green tiles.

the answer is 68

if you like at the other persons answer, they explain

but all i know is that its 68

thxs: to the person that answered this question first

Answer: y =  9, z = 8

Step-by-step explanation:

Here, the given equations are,

150x + 80y + 12z = 2,466 ---------(1)

380x + 95y + 48z = 5,419 ---------(2)

210x + 130y + 60z = 3,960 --------(3)

4 × equation (1) - Equation (2),

220x + 225y = 4,445  ------------(4)

5 × equation (1) - equation (3),

540x + 270y = 8,370

⇒ 270 y = 8370 - 540 x

⇒ y = 31 - 2 x

Substituting the value in equation (4),

220 x + 225 ( 31 - 2 x ) = 4445

220 x + 6975 - 450 x = 4445

- 230 x = - 2530

x = 11

By putting this value in equation (5),

we get, y = 31 - 22

y = 9

By putting the value of x and y in equation (1),

1650 + 720 + 12 z = 2466

2370 + 12 z = 2466

12 z = 96

z = 8

Answer:

Y=9

Z=8

For the next one, the solution can be expressed as 11,9, and 8

Step-by-step explanation:

Just did it on edg!

Answer: THE 3RDDDDDDDDDDDDDDDDDDDDD

To calculate the sales tax on the second item, we determined the sales tax rate from the first item and applied it to the second item's cost, resulting in $7.99 sales tax on the second item.

To find the sales tax on the second item, we use the information provided about the first item to determine the rate of sales tax and then apply this rate to the second item. If the first item costs $147 with a sales tax of $14, we can find the sales tax rate by dividing the sales tax by the cost of the item before tax:

Sales tax rate = Sales tax / Price before tax

= $14 / $147

= 0.0952 or 9.52%

Once we have the sales tax rate, we can calculate the sales tax on the second item, which costs $84 before tax:

Amount of sales tax = Price × Rate of sales tax

= $84 × 0.0952

= $7.99 (rounded to the nearest cent)

Therefore, the sales tax on the second item is $7.99.

20 is 25% of 80. so the number is 80.

percentage, a relative value indicating hundredth parts of any quantity.

We need to find 20 is 25% of what number

Let x be the number which we have to find.

Convert 25% to decimal number.

25/100=0.25

Now multiply 0.25 with x which results 20

0.25x=20

Divide both sides by 0.25

x=20/0.25

x=80

Hence, 20 is 25% of 80. So 80 is the required number.

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Answer:

.56 (C)

Step-by-step explanation:

Answer: For the second part it is B on edgu

Step-by-step explanation:

The solution is P ( 4 , 3 )

The vertex of the function is given by the coordinates P ( 4 , 3 )

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation be represented as A

Now , the parabola is

f ( x ) = | x − 4 | + 3   be equation (1)

Now ,

The vertex of f ( x ) = | x | is located at the origin, (0,0)

So , in the form f ( x ) = a | x - h | + k, the h-value translates the graph left/right and the k-value translates the graph up/down

And ,

In the function, f(x) = | x - 4 ) | + 3 , the h-value is 4, and the k-value is 3

So , the vertex of the function moves from the origin, (0,0) and translates 4 units right and 3 units up.

Therefore , the vertex is located at P ( 4,3 )

Hence , the vertex of equation is at P ( 4 , 3 )

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Answer:

Please see the attachment for graph.

Step-by-step explanation:

We are a given a equation and need to graph it.

It is square root function. We make table of x and y and then plot the points on graph and join the points.

We will take some random values of x and then find the value of y corresponding to the value of x.

For x=1, Put x=1 into equation

[tex]y=-4\sqrt{1}=-4[/tex]

For x=4, Put x=4 into equation

[tex]y=-4\sqrt{4}=-8[/tex]

For x=9, Put x=9 into equation

[tex]y=-4\sqrt{9}=-12[/tex]

Table of x and y

     x          y

     1         -4

    4         -8

    9         -12

Now we plot the points on graph and join the points.

Please see the attachment for graph.

If 30 cents out of every 1 dollar go to taxes, the remaining 70 cents is the net income. Therefore, the ratio of taxes to net income is 3:7.

The question asks for the ratio of taxes to net income if 30 cents out of every 1 dollar go to taxes. This question is asking for a mathematical comparison between the amount of money that goes to taxes and the remaining amount of money, which is the net income.

If 30 cents go to taxes out of 1 dollar, that means 70 cents (or $0.70) is the net income because 1 dollar minus 30 cents equals 70 cents. To arrive at the ratio, we compare the amount that goes into taxes to the net income. This would be 0.30 (taxes) to 0.70 (net income).

When we express this as a ratio in simplest form, we do not usually use decimals. Instead, we can convert the decimal into a whole number. Think of the 0.30 and the 0.70 as 30 and 70. The greatest common divisor of 30 and 70 is 10. If we divide both numbers by 10, we get 3 and 7. So, the ratio of taxes to net income is 3:7. Thus, the correct option is C. 3 : 7.

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