What is the slope of the line that passes through these two points (8, 4) and (5, 3)?

The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))

We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.

             4x² + 3x - 8

          -------------------------

3x - 1  | 12x³ + 5x² - 27x + 13

         -  12x³ - 4x²        

          -----------------------------

                     9x² - 27x  

                 -   9x² - 3x

          -----------------------------

                            -24x + 13

                        -    -2x + 8

          -----------------------------

                                      5

          -----------------------------

Expressing the solution of the polynomial division in the given quotient and remainder form gives us;   4x² + 3x - 8 + (5/(3x - 1))

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Answer:

The range is the allowed values of y.

Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}

Interval notation: [-9,0]

Hope that helps

Answer:

C

Step-by-step explanation:

f(x) =0

when the curve intersects the x axis

goodluck :)

For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

As given in the question,

For the saving account,

Amount deposited is directly proportional to the number of weeks

Let y be the amount deposited and x be the number of weeks

y ∝ x

y = kx

'k' is the constant of proportionality

As per data unit rate is measured in dollars per week

For y = $14 then x = 2 weeks

14 = 2k

⇒ k = $7

For y = $35 then x = 5weeks

35 =5k

⇒ k = $7

Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

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The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The water remaining is illustrated as y.

The time taken is t.

The appropriate equation will be:

y = 28 - (2 × t)

y = 28 - 2t

This illustrates the water remaining in the tank.

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Answer: x = -33

Explanation:

Given the following question:

x - 11 = -44

Step 1: collect the like terms

x = -44 + 11

x = -33

Therefore, x = -33

17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.

Expression is a combination of variables, operators and numbers.

The given phrase is

"Seven more than the product of 17 and Julie's savings"

and j is variable to represent Julie's savings.

In the phrase we have Seven more than, it means we are adding 7 to something.

According to problem we are adding 7 to "product of 17 and Julie's savings"

Product means multiplying a number with another factor. Here the factor is julies saving j.

17j+7 is the translated algebraic expression.

Hence 17j+7 is the translation of  Seven more than the product of 17 and Julie's savings.

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This is because

distance = rate*time

Rate is another term for speed.

Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.

An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."

A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.

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Answer:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Step-by-step explanation:

Point slope form is shown below:

[tex](y-y_1)=m(x-x_1)[/tex]

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

[tex](y--2)=\frac{2}{3} (x-5)[/tex]

Simplify:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Answer:

DF = 13

Step-by-step explanation:

Congruent triangles:

        In ΔABC & ΔDEF,

                     ∠A = ∠D

                     ∠C = ∠F

                      CB = FE

            ΔABC ≅ ΔDEF   {Angle Angle Side congruency}

              DF = AC = 13

Hello!

Let's take this problem step by-step:

What is the formula for the circumference of a circle:

 [tex]\text{Circumference} = 2\pi *\text{radius}[/tex]

Since the circumference is 25 cm

  [tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]

Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]

Hope that helps!

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Answer:

price for one ribbon =19 cents

she got $20

20- 16.77 the rest from the money = 3.23

so she spends 3.23 from buying the ribbon

how much ribbon does she buy

3.23 ÷ 0.19= 17 ribbons

We can multiply each side by 14ft yo find the value on feet and late calculate the area

tha area formula is

where b=84ft and h=112ft

the area is 4,704ft2

We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

So, let 'D' be the diameter and 'C' be the circumference.

Calculate C as:

(A) D = 5 m and C = 22 m

So, C = 15.7 m does not approximate 22 m.

(B) D = 19 in and C = 60 in

So, C = 59.66 approximates 60 in.

(C) D = 33 cm and D = 80 cm

So, C = 103.62cm does not approximate 80cm.

Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.

The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13  .

In the question ,

the equation is given as

(x+yi)+(4+9i)=9-4i

to find the value of x and y , we solve LHS and RHS of the equation separately

So LHS =

(x+yi)+(4+9i)

x+yi+4+9i

Adding the real and imaginary terms , we get

(x+4)+(y+9)i which is equal to RHS that is 9-4i

So , on comparing , we get

x+4 = 9    and      y+9 = -4

x= 9-4      and      y = -4-9

x = 5       and       y = -13

Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .

The given question is incomplete , the complete question is

What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i  ?

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The solution of the given linear equation is x = -9.53

Here we have the linear equation:

-0.24*x - 16.4 = 1.48*x

To solve this, first we need to move all the terms with x to the left and the terms without x to the right.

-0.24*x - 1.48*x = 16.4

(-0.24 - 1.48)*x = 16.4

-1.72*x = 16.4

Now we can divide both sides by -1.72 to get:

x = 16.4/-1.72 = -9.53

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Answer: c) (is it c?)

Step-by-step explanation: c) x= - 74.5

0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4

0.24x= -17.88    (divide)

x= −74.5

there

i hope this helps!!

Answer:

its 12

Step-by-step explanation:

Answer:

113.85

Step-by-step explanation:

230*55% because 100%-45%=55% is 126.5

Then 126.5*90% because 100%-10%=90% which is 113.85

The number of homes in 2011 is 44,313

Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:

2003: 43,800 + 57

2004: 43,800 + 57 + 57

2005: 43,800 + 57 + 57 + 57

This goes on until 43,800 + 57n

where n is the number of years after 2002.

2011 is 9 years after 2002, so the number of homes will be:

43,800 + 57(9)

= 43,800 + 513

= 44,313

Answer:

-130

Step-by-step explanation:

g(18)= -8(18)+14

=-144+14

=-130

Answer:

x²[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

given

5[tex]\sqrt{20x^4}[/tex] - 3[tex]\sqrt{45x^4}[/tex]

simplify the 20 and 45 inside the radicals

[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]

[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]

Then

= 5(2[tex]\sqrt{5}[/tex] x² ) - 3(3[tex]\sqrt{5}[/tex] x² )

= 10[tex]\sqrt{5}[/tex] x² - 9[tex]\sqrt{5}[/tex] x²

= x²[tex]\sqrt{5}[/tex]

The number of pounds of pork he bought in decimal is 12.21 lb

Decimal:

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example 12.34 is a decimal.

Given,

At a butcher​ shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.

Here we need to find the number of pounds of pork he bought using a decimal.

First, we have to convert the given fractions into decimal then we get,

Amount of beef = 2 7/20

Which is equal to,

=> 2 + 7/20

=> 2 + 0.35 = 2.35 lb

Similarly,  total amount of meat = 14 14/25

=> 14 + 14/25

=> 14 + 0.56 = 14.56

Therefore, the amount of pork is,

=> total amount of meat - the amount of beef

=> 14.56 - 2.35

=> 12.21.

Therefore, the the number pounds of pork in decimal is 12.21 lb.

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The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."

Here the values are

-0.5,-2.8,1.9,0.9 and -1.7

The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7

The positive numbers are 1.9 and 0.9

The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions

Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."

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Answer:

Undefined slope

Step-by-step explanation:

Slope , m is equal to rise/run    Or   ( y1-y2) / ( x1 -x2)

              This line is a vertical line at x = -8    And thus has undefined slope

              (Because you cannot divide by zero)

Answer:

Undefined

Step-by-step explanation:

Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.

We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:

[tex]y=mx+b[/tex]

When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:

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

Now, all we have to do is plug in the values as such and solve:

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

[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]

From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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The coordinates of the endpoint G is (0, 7).

The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -

Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)

Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].

(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)

Relating the x and y values -

x value :

3 = [tex] x_{1}[/tex] + 6/2

[tex] x_{1}[/tex] + 6 = 3×2

[tex] x_{1}[/tex] + 6 = 6

[tex] x_{1}[/tex] = 6 - 6

[tex] x_{1}[/tex] = 0

y value :

6 = [tex] y_{1}[/tex] + 5/2

[tex] y_{1}[/tex] + 5 = 6×2

[tex] y_{1}[/tex] + 5 = 12

[tex] y_{1}[/tex] = 12 - 5

[tex] y_{1}[/tex] = 7

Thus, the coordinates of point G from the line GH is (0, 7).

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The Simplification of square root of three times square root of twenty one is; C: three square root of seven

The Laws of Exponents are;

We have the expression;

√3 * √21

= √3 * √3 * √7

= (√3 * √3) * √7

= 3√7

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Answer:

c) f = 28

Step-by-step explanation:

Given problem,

→ f³ = 21952

Now the value of f will be,

→ f³ = 21952

→ f = ³√21952

→ [ f = 28 ]

Let's check the following,

→ 28³

→ (28 × 28) × 28

→ 784 × 28 = 21952

Hence, option (c) is correct.