3. For the number line shown, which
statement is NOT true?

The value of x, so f(x)=7 is 5.

According to the graph, we have a linear function and linear functions have the same slope for all value of x, we can determine the value of  f(x) for x=7 by the means of the equation for the line:

[tex]\frac{y_{b}-y_{a} }{x_{b}-x_{a} }[/tex] = [tex]\frac{y_{c}-y_{a} }{x_{c}-x_{a} }[/tex]  ....................(1)

Where:

 [tex](x_{a},y_{a} )[/tex] = (2,0) and [tex](x_{b},y_{b} )[/tex] = (5,7) are the Known points.

[tex](x_{c},y_{c} )[/tex] is the Expected point.

The value of [tex]y_{c}[/tex] = 7

Then the value of  [tex]x_{c}[/tex] is,

[tex]x_{c}=x_{a} +\frac{ y_{c}-y_{a} }{y_{b}-y_{a} } *(x_{b} - x_{a} )[/tex]

= 2+ [(7-0) / (7-0)] * (5-2)

= 2 + (5-2)

= 2+3

= 5

Therefore, the value of x, so f(x)=7  is 5.

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The x and y coordinates of the line are utilized to compute the steepness of the line using the slope formula.We are aware that one of a line's most crucial qualities is its slope because it aids in determining the pace of change.

What is the point-slope form of the equation of the line?

A line's steepness can be determined by looking at its slope.Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Using the formula

m=y2y1/2x1,

which is the change of y over the change of x, determine the slope of the line between (3,5) and (9,1).

Slope is equal to the change in y over the change in x

, or rise over run.

m=change in y /change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates (also called rise).

m=y2−y1/x2−x1

To determine the slope, enter the values of x and y into the equation.

m=1−(5)/9−(−3)

m=-4/12

m=12/4

m=3

To replace x1 and y1 in the point-slope form yy1=m(xx1), which is derived from the slope equation

m=y2y1/x2x1,

use the slope 3 and the specified point (3,5).

y−(5)=3(x+3)

Keep the equation in point-slope form and make it simpler.

y−5=3(x+3)

Do the y math.

To continue, tap...

y=x+8

List the equation in all its variations.

Form of a slope-intercept:

y=x+8

Forming a point-slope: y=5=1(x+3)

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If the amount of money is even, then the item that costs an odd number of money has to be bought an even number of times. Some possible combinations could be 2 lb potato salad and 7 lb Mac salad, or 4 lb potato salad and and 4 lb mac salad, or 6 lb potato salad and 1 lb mac salad.

1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Total fencing Peter has = 480 yards

Now,

We can say that the total fencing he has in terms of length L and width W of the rectangle will be;

⇒ L + L + W + W = 480

⇒ 2(L+W) =480

Divide both sides by 2 to get

⇒ L+W = 240

Subtract W from both sides so we get L in terms of W;

⇒ L= 240 - W

Since, The area of a rectangle is Length times width.

So, Area = (L × W)

⇒ Area  = (240-W) W

⇒ Area  = 240W - W²

Now, By comparing the equation with an quadratic equation

ax² + bx + c , we get;

⇒ a = -1 and b = 240

Since, Area is maximum when;

W = -b/2a

W = - 240/-2

W = 120

So, for W = 120 yards area is maximum.

Hence, Length of yards = 240 - 120 = 120 yards.

(b) Maximum area of the rectangle can be found by substitute this

W = 120 in the Area equation;

So, the maximum area ,

A = 240 (120) - 120²

A = 28800 - 14400

A = 14400

Hence, Maximum area = 14,400 square yards.

Thus,

1. Length of rectangular area = 120 yards

Width of rectangular area = 120 yards

2. Maximum area = 14,400 square yards.

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The function g in terms of f so that the statement is true is g(x) = 4f(x)

The point (x, y) on the graph of f (x) is changed to the point (x, ky) on the graph of g (x), where k 1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same; otherwise, it shrinks vertically.

There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x.y/4) rather than f(x)=y.

g(x) = 4f as a result of transformation (x)

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The statement is true g(x) = 4 +f(x).

The point (x, y) on the graph of f (x) is changed to the point (x, k y) on the graph of g (x), where k=1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same otherwise, it shrinks vertically.

There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x. y/4) rather than f(x)=y.

g(x) = 4 +f(x) as a result of transformation of x.

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If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ .

The volume of  the cube with side length "a" can be calculated using the formula

Volume = a³ ,

For Example : if the side length of the cube is 2m , then the volume of the cube will be

Volume = 2³  = 8m³ .

In the question ,

it is given that ,

the  side length of the cube is x⁻² inches ,

So, substituting the value of side length in the Volume formula , we get

volume = (x⁻²)³

= x⁻⁶         ....(as (xᵃ)ᵇ = (x)ᵃˣᵇ = xᵃᵇ )

Therefore , If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ inches³ .

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Explanation

to find the area of the stove that does not include the area of the burnes ( yellow area), we can subtract the area of the 4 circles from the area of the full rectangle

so

Step 1

then, Let

for circle:

diameter= 6 in

for rectangle

length= 24 in

width= 22 in

Step 2

replace,

Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.

The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.

[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.

2² × 2³ = (2×3)² = 6², using the power of a product.

[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.

The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.

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Answer:

the least common denometer for 5/12, 7/16 would be 48.

Step-by-step explanation:

Answer:

  13

Step-by-step explanation:

You want the sum of f^-1(-7) and f(-7) given the function definition in the table.

The inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...

  (x, f^-1(x)) ≡ (f(x), x)

Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:

  f^-1(-7) = 6 . . . . . from the 4th column of the table

We can read the function value directly from the table:

  f(-7) = 7 . . . . . . the first column of the table

Then the sum of interest is ...

  f^(-1)(-7) +f(-7) = (6) +(7)

  f^(-1)(-7) +f(-7) = 13

__

Additional comment

The inverse function ordered pairs are ...

  (x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}

As per the long division, the value of 19 divided by 6,927 is 0.002742

Long division:

Long division is the mathematical method for dividing large numbers into multiple smaller groups or parts. The number which we divide into small groups is called the dividend, the number by which we divide is called the divisor.

Given,

Here  we have to divide the number 19 by 6927.

When we divide the number, we have to following the following steps,

1) Set up the problem with long division bracket. Put dividend inside bracket and divisor on outside left.

2) 6927 goes into 19000 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 19000 to get remainder (19000-13854=5146).

3) Now, bring down 0 from the dividend, to make 51460

4) 6927 goes into 51460 (7-times). Put a 7 in the next place of quotient and multiply 6927 by 7 to get 48489. Subtract 48489 from 51460 to get remainder (51460-48489=2971).

5) Now, bring down 0 from the dividend, to make 29710

6) 6927 goes into 29710 (4-times). Put a 4 in the next place of quotient and multiply 6927 by 4 to get 27708. Subtract 27708 from 29710 to get remainder (29710-27708=2002).

7) Now, bring down 0 from the dividend, to make 20020

8) 6927 goes into 20020 (2-times). Put a 2 in the next place of quotient and multiply 6927 by 2 to get 13854. Subtract 13854 from 20020 to get remainder (20020-13854=6166).

This process is continued so we have to take only up to these one.

Then this can be displayed in the following figure.

Question: Divide the number 19 by 6,927 using the long division method.

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As The triangles are congruent the value of y = 1 and x = 4

The basic polygonal shape of a triangle has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol. It has three connected vertices. Triangles can be divided into a variety of categories according on their sides and angles.

AS the triangles are congruent

15x-8y = 52.....(i)

6x +14y +142=180

6x +14y = 38

3x +7y =19 ....(ii)

x=[tex]\frac{19-17y}{3}[/tex]

15([tex]\frac{19-17y}{3}[/tex])-8y = 52

5(19-17y)-8y=52

95-85y-8y =52

93y =93

y = 1

x =4

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Answer:

-868

Step-by-step explanation:

-Absolute change is simply defined as the number by which a change has occurred.

-We therefore determine the difference between the two years by subtracting the new value from the old or reference value

Answer:

C. 1/36

Explanation:

The probability of rolling a 2 in a six-sided die is 1/6 because there are 6 possible outcomes and 1 of them is 2. In the same way, the probability of rolling a 6 is also 1/6 because there are 6 possible outcomes and 1 of them is 6.

Then, the probability of rolling a 2 and then a 6 can be calculated as:

Because they are independent events and each one has a probability of 1/6.

Therefore, the answer is:

C. 1/36

Answer:

1:2

Step-by-step explanation:

For every triangle there are two squares.

The coordinates of the point that at 7/8 from a to b are (5, -5/8)

On the segment, we have the following endpoints

A = (-2, 2)

B = (6, -1)

Also, we have the line ratio to be

Ratio, m : n = 7/8

Express the ratio as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point at the given distance is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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The outcome of the quotient between the two fractions 3/4 and 2/3 is 9/8

So let's define two fractions as:

a/b and c/d.

The quotient between the fractions a/b and c/d can be written as:

(a/b)÷(c/d).

Now, the quotient is equal to the product with the inverse, so we can rewrite this as:

(a/b)÷(c/d) = (a/b)*(d/c)

Now, in this case, we want to find 3/4 divided by 2/3, this will be:

(3/4)÷(2/3) = (3/4)*(3/2) = 9/8

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Based on given diagram we can conclude that d || e.

As per the diagram given there are some lines and angles which are defined and some of them are to be find so that we can conclude answer from the given options.

The attached image shows the Angles which are solved for the solution of the question as follows;

For line 'a' makes an angle of 110° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'a' with line 'd' will be 180° - 110° = 70° a shown in the attached figure.

For line 'c' makes an angle of 115° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'c' with line 'd' will be 180° - 115° = 65° a shown in the attached figure.

For line 'b' makes an angle of 60° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'b' with line 'd' will be 180° - 60° = 120° a shown in the attached figure.

By Comparing All the angles we can conclude that line a ∦ b, a ∦ c, b ∦ c.

∴ Line 'd' is parallel to line 'e'.  => d || e.  

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ANSWER

637.5π mm³

EXPLANATION

The volume of a cylinder is the product of its base area and its height. In this problem, the radius of the base of the cylinder is 5 mm, and its height is 25.5 mm. The volume is,

Hence, the volume is 637.5π mm³.

Answer:

A. 366-249=125

B. 13386-9608=4788

To know if a graph represents a function, we have to use the vertical line test, which consists in drawing a vertical across the curve.

If the vertical line intercepts twice the curve, then it's not a function.

Then, the graph has no function symmetry because the graph is not that of a function.

a. The length is (3b) meters

b. length of hall is 36m.

We have given,

a. Breadth of the rectangle = b meters,

Since, length of a rectangular hall is 3 times the breadth of the hall,

⇒ Length = 3 × Breadth

⇒ Length = 3b

Hence, the length of the rectangle is (3 b) meters.

b. if the breadth is 12 m

Then, the length of the hall = [tex]3\times 12[/tex]

                                           = 36m.

Length is a measure of distance. In the International System of Quantities, length is a quantity that has a measured distance. In most  measurement systems, a base unit of length is chosen from which all other units are derived. In the International System of Units, the basic unit of length is the meter.  Length generally refers to  the widest dimension of a fixed object. However, this does not always happen and may depend on the location of the object.

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Let:

We can find the slope m, using the following formula:

Answer:

0

In the picture there is a parallel line with the intersection line. ∠5=91° and ∠2=(8x+1)°and x value is 11.

Given that,

In the picture there is a parallel line with the intersection line.

We have to find the x value.

Given ∠5=91° and ∠2=(8x+1)°

We know that if there are 2 parallel line and 1 line is intersecting to the parallel line then the corresponding angles are equal.

∠1=∠5

So, ∠1=91°

Now,

We can write as ∠1+∠2=180° because the ∠1 and ∠2 are on 1 line.

91+8x+1=180

8x+92=180

8x=180-92

8x=88

x=88/8

x=11

Therefore, x value is 11.

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The set of irrational numbers is the union of the set of rational numbers Q in the real numbers R. Therefore, the correct answer option is C. union.

An irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.

A rational number simply refers to a type of number which comprises fractions, integers, terminating or repeating decimals such as 4.

In Mathematics, the union of the set of all irrational numbers (Q') and the set of all rational numbers (Q) are generally referred to as a set of real numbers (R).

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Complete Question:

The set of irrational numbers is the ______ of the set of rational numbers Q in the real numbers R

Select one:

A. complement

B. ratio

C. union

D. Intersection

∠1 and ∠8 are alternate exterior angle.

∠2 and ∠4 are corresponding angle.

∠3 and ∠6 are alternate interior angle.

∠6 and ∠7 are consecutive interior angle.

When a transversal intersects two or more lines, alternate exterior angles are produced. These angles are created on the various transversal sides' outer sides.Any two parallel lines that cross a transversal produce a few pairs of angles with the transversal. In the area inside the parallel lines, interior angles are generated, whilst alternate external angles are created in the area outside the parallel lines.

Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). Angle p and angle w, for instance, are the matching angles in the illustration below.

The pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. All of these angles are equal. There is another way to look at this. The alternative interior angles can establish the parallelism or non-parallelism of the given lines. The supplied lines that are crossed by a transversal are said to be parallel if these angles are equal.

The pair of interior angles that are not contiguous to one another and are on the same side of the transversal are referred to as consecutive interior angles. Things that follow one another are referred described as being "consecutive." On a transversal's internal side, adjacent interior angles are found next to one another.

∠1 and ∠8 are alternate exterior angle.

∠2 and ∠4 are corresponding angle.

∠3 and ∠6 are alternate interior angle.

∠6 and ∠7 are consecutive interior angle.

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The ending balance Statement of Changes in Owner's Equity for this data is given by: $222,000.

The ending balance is given by the difference between all the amounts that were on the account, and were added, by all amounts that were removed from the account.

The amounts that were added to the balance are given as follows:

The amounts that were removed from the balance are given as follows:

Hence the ending balance is calculated as follows:

6,000 + 200,000 + 15,000 + 10,000 + 56,000 - 5,000 - 60,000 = $222,000.

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Two or more expressions with an Equal sign is called as Equation.π=  C/d for equation C = πd

Two or more expressions with an Equal sign is called as Equation.

The given equation is  C = πd

c equal to pi times of d

We need to solve it for  π

To solve for  π we have to separate  π from d. To make this We have to divide both sides by d.

So C/d= π

Hence π=  C/d for equation C = πd

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The radius of the hole to the nearest hundredth of a foot will be 0.20 feet.

The problem we are dealing with here is related to volume, which is referred to as may be a degree of involved three-dimensional space. It is regularly measured numerically utilizing SI-inferred units (such as the cubic meter and liter) or by different majestic units (such as the quart, gallon, and cubic inch) and the volume formula we are referring to is of the cylinder which is,

Volume = πr²h

Where r is the radius of the cylinder, π is the constant which is equal to  3.14 and h is the height of the cylinder.

From the information given to us, the volume of the hole ( cylindrical in  this case ) is  3500 cubic feet and the height is   4.8 miles

So First we Converting  the 4.8 miles to feet,

Since we know 1 mile = 5280 feet

therefore, 4.8 miles = 4.7 × 5280 = 25344 feet

Now putting the desired in the formula,

=>3500 = 3.14 × r² × 25344

=> 79580.16r² = 3500

=>r² = 3500/79580.16

=>r²= 0.04398

=>r = √0.04398

     = 0.2097 feet

    = 0.20 feet

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