HINT: the table IS PROPORTIONAL, so that means we can compare any y/x value from the table to get r. r = y/x

r = ?

Given

(1,7) and (4,1)

y=-2x+9

Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]

Answer:

f(x) = (2x + 3)(2x + 1)

Explanation:

The form that best reveals the zeros of the function is:

f(x) = (x - a)(x - b)

Where a and b are the zeros of the function.

So, we need to apply the distributive property as:

Then, we can factorize the quadratic function as:

So, now we can identify the zeros of the function if we solve the following equation:

Therefore, the form that best reveals the zeros in the function is:

f(x) = (2x + 3)(2x + 1)

In the given isosceles triangle, the value of x is 10 units.

So, the value of 'x' will be:

Given triangle is an isosceles triangle. Then,

Therefore, in the given isosceles triangle, the value of x is 10 units.

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Answer:

Step-by-step explanation: if the width is x then the length is 2x+3

The perimeter is 2x+2(2x+3)=42

then 6x+6=42

6x=36

x=6

Then the length is 2*6+3=15

Using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.

So, the pounds of pork the girl bought:

Calculate pork as:

Therefore, using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.

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The expression that equals 3C+3D in standard form is:

x²+7x+1

Given:

C = -x+2

and D = x²+8x-1

we are asked to find out an expression which equals 3C+3D in standard form.

based on the conditions, formulate:

3C+3D

substitute C and D values.

⇒ 3(-x+2) + 3(x²+8x-1)

Apply multiplicative distribution law:

⇒ open the parenthesis.

⇒ -3x+6+3x²+24x-3

calculate the product or quotient

⇒ arrange the like terms.

⇒ 3x²+21x+3

⇒ Reduce the terms.

⇒ x²+7x+1

Hence we get the equation in standard form.

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[tex]\frac{325}{520}[/tex] fraction of the workforce kept their jobs

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

What is Percentage change?

The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.

where growth in number equals new number minus initial number.

Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.

decreasing number where original number - new number

In other words, there is a percentage decline if the response is negative.

Here, It is given:

In January 520 workers were employed;

In the end, 195 employees were redundant;

So, The fraction of the workforce who kept their job:-

The fraction of the workforce who kept their job=[tex]\frac{520-195}{520}[/tex]

The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]

Hence,

The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]

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Answer:

-20x9= -180.    2 to the power of three =8  if you want the quotient it would be -22.5

Step-by-step explanation:

Answer: 20

Step-by-step explanation: They are both equal to each other, so 3x+50=6x-10. Then just solve for x by canceling out both sides.

The rules of BODMAS are useful in calulating mathematical expressions involving many operators. The given expression can be simplified as a simple fraction 28 / 27.

The rules of BODMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given expression can be written as,

4 / 5 ÷ 9 / 5 × 7 / 3

In the given expression there are three fractions separated by the sign of multiplication and division.

As per the rule of BODMAS, the division operator has the priority over multiplication operator.

Apply the rule mentioned above in the given expression to get,

4 / 5 ÷ 9 / 5 × 7 / 3

= 4 / 5 × 5 / 9 × 7 / 3

= 4 / 9 × 7 / 3

= 28 / 27.

Hence, the given expression is simplified to get the result as 28 / 27.

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On solving the equation 2x+y=-4 and 43x-12y=-4 for y we get the value of y=-164/67 as the definition of solution of equation says "A solution to an equation is a number that can be plugged in for the variable to make a true number statement".

A group of equations involving one or more variables is known as a system of equations. The variable mappings that cause all component equations to be satisfied or intersected are the solutions to systems of equations.

Here,

2x+y=-4

43x-12y=-4

43(2x+y=-4)

2(43x-12y=-4)

86x+43y=-172

86x-24y=-8

subtracting equation,

67y=-164

y=-164/67

As stated in the definition of equation solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," we arrive at the value of y=-164/67 after solving the equations 2x+y=-4 and 43x-12y=-4 for y.

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We can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.

So, the difference in the graph of the given functions:

Plot on the graph as follows:

(Refer to the graph attached below)

Therefore, we can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.

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To earn at least $122.50 per day, Wing Ko must replace 5 watch bands

Here, we want to find the number of bands that Wing Ko must replace to earn at least $122.50 per day

Let the number of watch bands be x

Using mathematical relatio to represent this inequality, we have;

To calculate the unit race price per copy, we can divide $6.00 by 200 copies:

Each copy cost $0.03, to determine how much will cost 150 copies, we have to multiply the unit rate price by 150:

150 copies will cost $4.5

we can do a triangle to solve the apothem

the upper angle is equal to 360 divided by 8 since 360 ​​is a complete turn and an octagon is composed of 8 equal triangles, so is 45

now we take a triangle from the triangle to apply trigonometric ratios and solve a

the upper angle of the new triangle is the half of the original so is 45/2

now i will use the trigonometric ratio of tangent

where alpha is the angle, O the opposite side drom the angle and a the adjacent side from the angle

so replacing

and solve for a

the aphotem is 8.4

and the formula of the area of the octagon is

where a is the aphotem and l the measure f each side so 7

replacing

the area is 235.2 square units

Answer:

12. 0 = 11

No Solution

21. 0 = -132

No Solution

Step-by-step explanation:

12.

5 - 8x = 16 - 8x

-8x + 5 = -8x + 16

      - 5 =        -  5

-8x = -8x + 11

-8x = -8x

0 = 11

No Solution

21.

12x + 32 = 12x - 100

      - 32           -  32

12x = 12x - 132

-12x   -12x

0 = -132

No Solution

Answer:

2,6x +5 = y

Step-by-step explanation:

Don’t know if you wanted the equation, but this is how it’s written

The surface area of the prism is 1440 mm²

Given,

Triangular prism

Height of the prism = 32 mm

Base  of the prism = 24 mm

Length of the prism = 7 mm

We have to find the surface area of the prism;

Surface area, SA = bh + (b₁ + b₂ + b₃) l

Here,

Base, b = 24 mm

Height, h = 32 mm

Length, l = 7 mm

b₁ = 24 mm

b₂ = 32 mm

b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm

Then,

Surface Area = bh + (b₁ + b₂ + b₃) l

SA = 24 x 32 + (24 + 32 + 40) 7

SA = 768 + 96 x 7

SA = 768 + 672

SA = 1440 mm²

That is,

The surface area of the prism is 1440 mm²

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The equation of the line 4 · x - y + 15 = 0 is parallel to the line y = 4 · x + 1.

In this problem we must determine the equation of a line that is parallel to the line y = 4 · x + 1 and that passes through the point (x, y) = (- 2, 7). Lines are represented by algebraic equations of the form:

y = m · x + b

Where:

Two lines are parallel if both share the same slope.

First, find the slope of the first line:

m = 4

Second, determine the intercept of the parallel line:

b = y - m · x

b = 7 - 4 · (- 2)

b = 7 + 8

b = 15

Third, write the resulting expression and find its standard form:

y = 4 · x + 15

4 · x - y + 15 = 0

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STEP 1: Identify and Set Up

We are required to get the angle subtended by the arc DE.

We first acknowledge that it is part of the angles in a quadrant as this will help us find it.

STEP 2: Execute

First find angle DAE

When a polynomial is dived by x - a, to find the remainder, we can plug is x = a into the equation and find the remainder.

When it is divided by x + a, the remainder is found by plugging in x = -a.

Now, the polynomial here is:

It is divided by x + 5, so we need to plug in x = -5 to get the remainder, which is:

The remainder is - 41, 1st answer choice.

Answer:25

Step-by-step explanation:

1. you place the numbers in order from least to greatest so 1,1,3,8,12

2. then you add those all up

3.then you divide how many numbers there are together

1+1+3+8+12=25

then you divide by 5 because that's how many numbers are shown for the daily snow fall

HOPE THIS HELPS

Answer:

1) B, 2) C

===========

As per definition, functions have only one y-value per x-value.

Let's test it with given sets and tables.

A)

x y

0 1

0 2

1 3

2 3

B)

x y

1 0

2 0

3 1

3 2

C)

x y

​​−1 −1

0 −1

2 0

3 2

D)

x y

−1 −1

−1 0

0 2

2 3

1) The set of ordered pairs that represents y as a function of x is;

B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}

2) The table that represents y as a function of x is; Table 3

An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.

1) The first function given as  {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.

The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.

The third function {(0, 0), (1, 1), (2, 2), (3, 3)};  This is a function because each input has unique output values.

The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ;  This cannot be regraded as a function because the input x = 2 is repeated with different output values.

2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.

Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.

Table 3 is a Function because each input has unique output values.

Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.

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We need to find the center and the radius of

The general circle equation is the following

where

(h,k) is the center and

r is the radius

1. rearrange the equation

2. Add 25 on both sides

3. Factor

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5

The model is a linear function that shows $3.25 money that  Ilya has all together

The phrase linear function relates to two distinct but related concepts in mathematics:

Some authors use the term "linear function" only for linear mappings that accept values in the scalar field; these are more frequently known as linear forms.

Calculus' "linear functions" qualify as "linear mappings" when (and only when) f(0,..., 0) = 0, or, equivalently, when the aforementioned constant b equals zero.

A linear function in calculus and related fields is one whose graph is a straight line, that is, a polynomial function of degree zero or one. The word affine function is commonly used to distinguish such a linear function from the other idea.

A linear function is also known as a linear map in linear algebra, mathematical analysis, and functional analysis.

Given,

Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet.

Total money=$1.40+$1.85

=$3.25

The model is a linear function that shows $3.25 money that  Ilya has all together.

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The mean number of miles that the employees in a department live from work is 24.

What is a z-score?

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The z-score is given as

x = 29

s = 3.6

z = -1.5

Then the mean will be

[tex]-1.5 = \frac{29-u}{3.6}[/tex]

μ = 29 - 5.4

μ = 23.6 ≅ 24

Hence the answer is the mean number of miles that the employees in a department live from work is 24.

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Answer:

[tex]2 {d}^{2} + 5d - 7 [/tex]

[tex](2d + 7)(d - 1)[/tex]