Write each sum as the product of two factors 2r+r+s+2s

Answer: this is very easy

Step-by-step explanation:

The solution to the polynomial division is;  -3x² - x - ³/₂  + (- ³/₂)/(2x - 3)

We want to use polynomial long division to divide -6x³ + 7x² + 3 by 2x - 3.

A long division polynomial is defined as an algorithm that is used to divide a polynomial by another polynomial of the same or a lower degree.

Thus, we have;

         -3x² - x - ³/₂        

2x - 3| -6x³ + 7x² + 3

        -  -6x³ + 9x²

                   -2x² + 3

               -   -2x² + 3x

                           -3x + 3

                          -3x + ⁹/₂

                              - ³/₂  

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By comparing the given equations we get the values a= 1 b = -5 and

c = 6

What is Quadratic equation ?

Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where c is constant.

a is the coefficient of x^2

b is the coefficient of x .

Given ,

Quadratic equation is x^2  - 5x + 6

So, the quadratic equation is always be in the form of ax^2+bx+c

and from above we can see that it is in the given form .

So,

By comparing both equations x^2 - 5x + 6 and ax^2+bx+c

So,

we get,

a = 1

b = -(5)

b = -5

c = 6

So, By comparing the given equations we get the values a= 1 b = -5 and

c = 6

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The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.

Two straight lines or rays intersect at a common endpoint to form an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner." Two rays (half-lines) combined into an angle have a single endpoint. The latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms. Two lines converge at a common point to form an angle.

given

The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .

The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.

The equality's subtraction property states that if 3x = 9 then x = 3.

The premise of angle congruence is Since x = 7 if 7 = x

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The amount of tax paid is found applying the proportions, and the correct proportion is obtained from the table in the problem.

Her taxable income is given as follows:

$125,000.

Hence the tax proportions are given as follows:

Meaning that the taxes paid are given as follows:

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The value of the inverse function [tex]f^{-1}(7)[/tex] is 2.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Let the given function is  [tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

This means, inverse of 'f' is undo operator, that takes back the effect of 'f'

We are given that f(x) = 3x+1 and [tex]f^{-1} = x-\frac{1}{3}[/tex]

Then We can find it by plugging 7 in for x in the [tex]f^{-1}(x)[/tex].

So, [tex]f^{-1}(7)[/tex] =  7-1/3

[tex]f^{-1}(7)[/tex] = 6/3

[tex]f^{-1}(7)[/tex] = 2

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Proportionately, the dollar amount of the Gentrys' annual transportation and taxes combined is $11,004.70.

Proportion refers to the relative value of a number compared to another amount.

Proportions are ratios equated to one another.

Multiplying the proportional percentage of the combined transportation and taxes to the total budget of the Gentrys gives the dollar amount.

Yearly income for the Gentrys = $29,742.42

Percentage of income that is taxes = 28%

Percentage of income that is transportation = 9%

Combined percentage of taxes and transportation = 37% (28 + 9)

Combined transportation and taxes in dollars = $11,004.70 ($29,742.42 x 37%)

Thus, based on their proportional percentages, the Gentrys' combined annual transportation and taxes are $11,004.70.

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A student's grade is a weighted calculation. Sam's grade is 83.07%

Suppose we have variables v1, v2, v3, ..., and their weights are: w1, w2, w3, ..., then the weighted average is computed by:

weighted average = v1 x w1 + v2 x w2 + v3 x w3 + ...

The following table shows the weighs and the score

Component             weigh              Score

Homework                25%                 84%

Midterm exam          30%                  84.7%

Discussion                15%                   81%

Final exam                30%                  81,7%

Sam's grade = 25% x 84% + 30% x 84.7% + 15% x 81% + 30% x 81.7%

                        = 83.07%

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The price of car in October with respect to August is given as 112%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Suppose the price in August be c.

Then, in September it is given as,

⇒ c - 20% × c = 4/5c

And, in October it is given as,

⇒ 4/5c + 40% × 4/5c = 28/25c

The price in October with respect to August can be obtained in percent value as follows,

Price in October ÷ Price in August × 100

⇒ 28/25c ÷ c × 100 = 112%

Hence, the price in October is 112% of the price in August.

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Increasing the value of a variable change the value of the expressions

An expression is combination of variables, numbers and operators.

A variable in expression is a characteristic that can be measured and that can assume different values.

When the variable value is increased then the value of expression will be also increases because with the variable the value of expression is interlinked.

2x+4 is an expression

Let x=1

then 2(1)+4=6

Value of expression is 6.

If x=2 then the value of expression is 8

Now the other expression is 5x+3

For x=1, 8 is the value of expression.

For x=2, 13 is the value of expression.

as values of x increases then value of expression will be increased.

Hence,  increasing the value of a variable change the value of the expressions

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the second largest year-on-year increase for female is from year 4 to 5, which is 72.

A bar graph is a graph that shows complete data with rectangular bars and the heights of bars are proportional to the values that they represent. The bars in the graph can be shown vertically or horizontally. Bar graphs are also known as bar charts and it is a pictorial representation of grouped data.

Given that, the average cost (£GBP) of car insurance for Males and Females over a 5-year period.

From the graph

The average cost (£GBP) of car insurance for Males

year 1: 789

Year 2: 872

Year 3: 854

Year 4: 878

Year 5: 890

The average cost (£GBP) of car insurance for Females

Year 1: 638

Year 2: 635

Year 3: 742

Year 4: 801

Year 5: 873

Increase in cost insurance from year 2 to 3 is 742-635 =107

Increase in cost insurance from year 3 to 4 is 801-742 =59

Increase in cost insurance from year 4 to 5 is 873-801 =72

Therefore, the second largest year-on-year increase for female is from year 4 to 5, which is 72.

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The running average is calculated by dividing the sum of all the input numbers by the number of inputs. Here is the Pseudocode:

The pseudocode above outlines the steps for calculating a running average of numbers input by the user. The running average is calculated by dividing the sum of all the input numbers by the number of inputs. The loop continues until the user stops inputting numbers, at which point the final average is emitted by dividing the sum by the count. This allows the user to input any number of numbers and continuously see the running average as they go.

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The end behavior of the graph is given as

as x → - ∞, f(x) → -∞ and as x → ∞, f(x) → -∞

The term end behavior is used to describe the effects a function or graph has as the extremes.

The end behavior of function typically says the characteristics of the function at the ends

The end behavior of the graph of the given graph is deduced to be

as x tends to negative infinity (∞), f(x) tends to negative infinity -∞

as x tends to positive infinity ∞, f(x) tends to negative infinity  -∞

x ⇒ -∞ f(x) ⇒ -∞

x ⇒ ∞ f(x) ⇒ -∞

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Answer: 16

Step-by-step explanation:

So 0.9 + 0.8 + 0.2 is approximately 2.

Then, Add the two together  ( 14 + 2 = 16
So then the answer would obviously be 16

Hope this helped ^^

Option c) The factor in the expression is (y³ + 7).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.

An integer m that can be multiplied by another integer to create the number n is referred to as a divisor of an integer n, also known as a factor of n. One may also state that n is a multiple of m in this situation.

A factor is a number that is multiplied by another number to get the desired result. The answer to a multiplication puzzle is a product. Imagine multiplying the components in a multiplication problem to get the answer. For instance, the factors 2 and 4 add up to 8: Just two things or a great many factors can affect a number.

The function is

−3+8 (y³ + 7)

The factor that is in the option is (y³ + 7) . (option c)

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Answer:

  (1, -2)

Step-by-step explanation:

You want the coordinates of the vertex of the parabola defined by ...

We can add and subtract the square of half the x-coefficient to put the equation in vertex form:

  y = x² -2x -1

  y = x² -2x +(-2/2)² -1 -(-2/2)²

  y = (x² -2x +1) -1 -1

  y = (x -1)² -2

Comparing this to the vertex form equation ...

  y = (x -h)² +k . . . . . . parabola with vertex (h, k)

we see that the vertex is ...

  (h, k) = (1, -2)

The coordinates of the vertex are (1, -2).

<95141404393>

The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic.

The mean of the sampling distribution is np and the standard deviation is  [tex]$\sqrt{np(1-p)}$[/tex].

Round the standard deviation to three decimal places, it is [tex]$\sqrt{np(1-p)}$ = $\sqrt{n \cdot p \cdot (1-p)} \approx \sqrt{n \cdot p \cdot 0.99}$[/tex].

The sampling distribution of is a binomial distribution with parameters n and p, where n is the sample size and p is the population proportion of the specified characteristic. The mean of the sampling distribution is np and the standard deviation is [tex]$\sqrt{np(1-p)}$[/tex]. This means that for a given sample size n and population proportion p, the standard deviation of the sampling distribution can be calculated by taking the square root of the product of n, p, and (1-p).

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From the given figure the angles in the form as Same side interior angles, vertically opposite angles and etc.

What are parallel lines ?

Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.

Given in the figure,

parallel lines and we have to find the how the angles are related to each other.

In the given figure 1 ,

The angles are Same side Interior Angles .

In the given figure 2 ,

The angles are Vertically opposite  Angles .

In the given figure 3 ,

The angles are Alternate Exterior Angles .

In the given figure 4 ,

The angles are Alternate Interior  Angles .

In the given figure 5 ,

The angles are Alternate Exterior  Angles .

In the given figure 6 ,

The angles are Corresponding Angles .

In the given figure 8 ,

The angles are Vertically opposite Angles .

In the given figure 9,

The angles are Alternate Interior Angles .

Hence, From the given figure the angles in the form as Above.

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Answer:

y = 3x

Step-by-step explanation:
Slope = change in y / change in x

x, y
Given points: (2,6) and (1,3)

2 - 1 = 1
6 - 3 = 3
3/1 = 3
y = mx
y = 3x

The variable values and measures of the side lengths of the isosceles triangle and type of triangles are;

3) x = 23, WX = WY = 95, XY = 108

4) (a) Triangle ΔDEF is a scalene triangle

(b) Triangle ΔDEF is an isosceles right triangle

An isosceles triangle is a triangle that has a two sides of the triangle which are congruent.

The specified parameters are;

[tex]\overline{WX} \cong \overline{WY}[/tex]

WX = 3 + 4·x

XY = 5·x - 7

WY = 7·x - 66

[tex]\overline{WX} = \overline{WY}[/tex], definition of congruency

3 + 4·x = 7·x - 66, by the substitution property

7·x - 4·x = 66 + 3 = 69

3·x = 69

x = 69 ÷ 3 = 23

x = 23

The length of each side are;

WX = 3 + 4 × 23 = 95

WX = 95

WY = WX = 95

XY = 5 ×23 - 7 = 108

4) The lengths of the sides of the triangle are;

(a) DE = √((-1 - 8)² + (-3 - (-6))²) = √(90) = 3·√(10)

EF = √((-2 - (-1))² + (5 - (-3))²) = √(65)

DF = √((-2 - 8)² + (5 - (-6))²) = √(221)

The length of the sides of the triangle ΔDEF are all different, indicating the triangle is a scalene triangle. ΔDEF

(b) (a) DE = √((5 - (-2))² + (5 - 3)²) = √(53)

EF = √((5 - (-4))² + (5 - 10)²) = √(106)

DF = √((-4 - (-2))² + (10 - 3)²) = √(53)

The length of DE is congruent to DF

[tex]\overline{DE}[/tex]² = 53

[tex]\overline{DF}[/tex]² = 53

[tex]\overline{EF}[/tex]² = 106

53 + 53 = 106

Therefore;

[tex]\overline{DE}[/tex]² + [tex]\overline{DF}[/tex]² = [tex]\overline{EF}[/tex]²

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The line from the hospital meets the line from the stadium, is where the University is located.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A sketch of the described bearings and locations of the stadium, university and the hospital is presented in the attached image to this question.

On The map, draw a four-cardinal points' cross at the stadium draw a line from the bearing 050° from the stadium's four cardinal points' cross. Leave the line as it is.

Then, draw another four cardinal points' cross at the hospital and draw a line from the bearing 300° from the hospital's four cardinal points' cross.

Wherever the line from the hospital meets the line from the stadium, is where the University is located.

Hence,  the line from the hospital meets the line from the stadium, is where the University is located.

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Answer:

$110

Step-by-step explanation:

$20 + ($15/hr)(6 hr) = $110

Answer:

is 42 3 fraction

Step-by-step explanation:

Evaluate 4/2 for w = 3​

Answer:

Step-by-step explanation:

its a bit blured

Considering the expression of a line, the y-intercept of the line given by the equation y=5x +16 is 16.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know that the line is y=5x + 16

where:

Finally, the y-intercept is 16.

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Using Pythagoras theorem, the height of the building is 161.6m and the length of the ramp is 319.2m

According to Pythagoras' Theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the two legs. It can be mathematically stated as a²+b² =c², where a and b represent the lengths of the triangle's two legs and c represents the length of the hypotenuse.

7)

Using Pythagoras's theorem, we can find the height of the ramp.

185² = 90² + b²

b² = 185² - 90²

b² = 26125

b = √26125

b = 161.6m

8)

Using Pythagoras's theorem,

x² = y² + z²

320² = 10² + z²

z² = 320² - 10²

z² = 102300

z = 319.8m

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considering the graph of exponential function given , the statement that correctly compare the function is

X - intercept and Y - intercept are the two main intercepts.

The x-intercept of a point where the line crosses the x-axis, while the y-intercept is where the line or graph crosses the y-axis.

At x - intercepts the value of y is zero h=following the given values the x intercept for function f is 3 units and 4 units for the y intercept

For function g, following the table, the x intercept is (2, 0) and the y intercept is (0, 4)

the end behavior for function f is x → ∞, y → -∞

the end behavior for function g is x → ∞, y → -∞

hence they have different x and y intercept but same end behavior

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The side length of the equilateral triangle is 29 inches.

What is perimeter?

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides. Area is the portion of the plane that a closed form occupies, whereas perimeter is the space surrounding the closed figure.

Here in equilateral triangle all side of the triangle is equal . Then

Perimeter of triangle = 3× side. = 3s

Now perimeter of square = 4×side = 4a

Here perimeter of an equilateral triangle is 9 inches more than the perimeter of a square

=> Perimeter of square = perimeter of triangle + 9

=> 4a = 3s+9 ---------> 1

Now side of the triangle is 5 inches longer than the side of the square.

=> s = a+5-------> 2

=> a = s-5 --------> 3

Now put 3 into 1 then,

=> 4(s-5) = 3s+9

=> 4s-20 = 3s +9

=> 4s-3s = 20+9

=> s = 29 inches.

Hence side length of the equilateral triangle is 29 inches.

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The surface area of the cylinder is 87.92 mm²

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We need to find the surface area of cylinder.

The cylinder has radius of 2mm

Height of the cylinder is 5 mm

The surface area of cylinder=2πrh+2πr²

=2πr(r+h)

=2×3.14×2(2+5)

=12.56(7)

=87.92 mm²

Hence,  the surface area of the cylinder is 87.92 mm²

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Answer:

m = -6/5

Step-by-step explanation:

(-2, 4) and (3, -2)

m = -2-4/3+2

m = -6/5

Final Answer:

In-depth explanation:

Hi! The question is asking us to find the slope of the line.

We're given two points that the line passes through:

(-2,4) and (3,-2)

We can use the slope formula to find the slope:

[tex]\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

Plug in the data:

[tex]\bf{m=\dfrac{-2-4}{3-(-2)}}[/tex]

[tex]\bf{m=\dfrac{-6}{3+2}}[/tex]

[tex]\bf{m=\dfrac{-6}{5}}[/tex]

[tex]\bf{m=-\dfrac{6}{5}}[/tex]

Therefore, the slope of this line is -6/5.