Solve using long division (6x^3-8x+5) ÷ (2x-4)

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{8}~,~\stackrel{y_1}{14})\qquad P(\stackrel{x_2}{-21}~,~\stackrel{y_2}{-39})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NP=\sqrt{(~~-21 - 8~~)^2 + (~~-39 - 14~~)^2} \implies NP=\sqrt{( -29 )^2 + ( -53 )^2} \\\\\\ NP=\sqrt{ 841 + 2809 } \implies NP=\sqrt{ 3650 }\implies NP\approx 60.42[/tex]

The value of x for a given logarithm is 49.9.

Log10(x²+4)=2+Log10x-Log10 20​=

x = 49.9

2 = log10( 100)

so we have

log10( x [tex]\times[/tex]2 4) = log10( 100) log10( x)- log10( 20).

factor out log10 from RHS.

also log10( [tex]x[/tex] x  2 4) = log10( 100x/ 20).

log10 cancel log10.so, break the quadratic equation after simplification to have x = 49.9 or0.080

That is, the logarithm of a given integer x is the exponent to which another set number, the base b, must be increased in order to produce x. In the most the logarithm counts the number of times the same factor appears in repeated addition; for illustration, since 1000 = 10 10 10 = 103, the" logarithm base 10" of 1000 is 3, or log10( 1000) = 3. When no mistake is conceivable, or when the base does not important, the logarithm of x to base b is expressed as logb( x), without logb x, or indeed without the base, logx.

To learn further about Logarithm from the given link

https//brainly.com/question/28346542

#SPJ9

For the given data-set, we have that:

1. The mean is of 1199.3, the median is of 1198 and the distribution is bimodal, with 1197 and 1198 as modes.

2. The Pearson coefficient is of 0.24, and since it is positive, the data is positively skewed.

3. The range is of 82.

4. The standard deviation is of 16.47.

Using a calculator, which just applies the concepts explained above, as the data-set is too large, the measures are given as follows:

The Pearson Skewness Coefficient is given by:

P = 3(Mean - Mode)/Standard Deviation

The meaning of the coefficient is:

For this problem, the coefficient is given by:

P = 3(1199.3 - 1198)/16.48 = 0.24.

The Pearson coefficient is of 0.24, and since it is positive, the data is positively skewed.

More can be learned about the statistical measures of a data-set at https://brainly.com/question/24732674

#SPJ1

The given quadrilateral is not a parallelogram.

According to the statement

We have to find that the whether the quadrilateral is a parallelogram or not.

So, For this purpose, we know that the

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

From the given information:

The coordinates of the vertices of quadrilateral ABCD are A(-6,-1), B(-5,2), C(-1.-5), and D(0.-2).

Then

To show that the diagonals are bisect each other, we have to find the midpoint of both diagonals and if the midpoint is same then they bisect each other.

So,

Midpoint of AC = Midpoint of BD

Midpoint of A(-6,-1),C(-1.-5)  = Midpoint of B(-5,2),D(0.-2)

( -6-1/2 , -1-5/2) = (-5+0/2 , 2-2/0)

( -7/2 , -6/2) = (-5/2 , 0/2)

And these midpoints are not same then they do not bisect each other and then it is not a parallelogram.

So, The given quadrilateral is not a parallelogram.

Learn more about parallelogram here

https://brainly.com/question/1509864

#SPJ1

The four sides of the quadrilateral are 9 m,10 m, 11 m and 12 m.

What is a quadrilateral?

A quadrilateral is a four-sided polygon with four angles and four vertices. The term "quadrilateral" comes from the Latin words "quadri," which means "four," and "latus," which means "side."

Let the four sides of the quadrilateral be (x-2), (x-1), x, (x+1).

Then, perimeter = (x-2) + (x-1) + x + (x+1)

i.e., x - 2 + x - 1 + x + x + 1 = 42

i.e., 4x - 2 = 42

i.e., 4x = 42 + 2

i.e., 4x = 44

i.e., x = 11

Hence, the four sides of the quadrilateral are 9 meters, 10 meters, 11 meters and 12 meters.

To know more about quadrilaterals, click on the link

https://brainly.com/question/12672291

#SPJ1

Answer:3

Step-by-step explanation:bc

a. S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

a. S, R, and Q are on a straight line. Therefore:

S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

Learn more about collinear points on:

https://brainly.com/question/13127256

#SPJ1

Answer:

[-10, 2]

Step-by-step explanation:

The domain is the set of x values.

Answer:

675,745.92

Step-by-step explanation:

(9.6 × 103) × (6.7 × 102)

(988.8) × (683.4)

= 675,745.92

I hope this helps!

The result function of  (fog)(x) in the given functions is 3x² - 1.

Given the functions in the questions;

Set up the composite result function and simplify.

(fog)(x) = f(g(x) = f(x²)

Evaluate f(x²) by substituting in the value of g into f

fx(x) = 3x - 1

f(x²) = 3(x²) - 1

Now, simplify

f(x²) = 3(x²) - 1

f(x²) = 3x² - 1

Therefore the result function of  (fog)(x) in the given functions is 3x² - 1.

Learn more about composite function here: https://brainly.com/question/20379727

#SPJ1

Answer:

x= 8

Step-by-step explanation:

Vertical lines have undefined slopes, with an equation of x= ____. This is because when using the slope formula, the denominator would be a zero. The coordinates of points that lie on a vertical line have the same y-coordinate, but different x-coordinate value.

Given that the line passes through (8, 6), the line has an equation of x= 8.

To learn more about the equations of vertical and horizontal lines, check out: https://brainly.com/question/28305863

Based on the area of Marcellus's lawn, the number of pounds of fertilizer needed for Marcellus's lawn is 4 ¹/₅ pounds

In order to fertilize an area of 2 acres, the number of pounds of fertilizer needed is 10 ¹/₂ pounds.

The area of Marcellus's lawn is only 4/5 of an acre however so to find the pounds of fertilizer needed, use direct proportion:

2 acres : 10 ¹/₂ pounds

4/5 acres : x

2x = 8.4

x = 8.4 / 2

x = 4.2 pounds

= 4 ¹/₅ pounds

Find out more on acres and fertilizer at https://brainly.com/question/25278761

#SPJ1

Answer:

3-x

Step-by-step explanation:

Step-by-step explanation:

464

first u will multiply 16 with 29

after u get that number that will be your answer

Answer:

  29

× 16

54

120

90

+ 200

= 464

(C) The perimeter of the ΔABC is 9 + √41 units.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

The vertices of the triangle on the girds are A( - 1, 5 ), B( 4, 5 ), and C( - 1, 1 ).

The distance formula for the length of a line segment is given as:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore,

[tex]AB=\sqrt{(4-(-1))^2+(5-5)^2}=\sqrt{(4+1)^2+0}=5[/tex]

[tex]BC=\sqrt{(-1-4)^2+(1-5)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25+16}\\BC=\sqrt{41}[/tex]

[tex]AC=\sqrt{(-1-(-1))^2+(1-5)^2}=\sqrt{(-1+1)^2+(-4)^2}\\AC=\sqrt{0+16}=4[/tex]

Hence, the length of the sides of the triangle are [tex]5,\sqrt{41},4[/tex] units.

Now, the perimeter of a triangle is the sum of all three sides of the triangle.

Therefore, the perimeter of the triangle ABC is:

P = AB + BC + AC

P = 5 + √41 + 4

P = 9 + √41 units

Therefore, the perimeter of ABC is 9 + √41 units.

Learn more about perimeter here:

https://brainly.com/question/27255543

#SPJ1

The complete question is mentioned below:

Triangle ABC is shown on the grid.

What is the perimeter of triangle ABC?

(A) 9 + √21 units

(B) 9 + √29 units

(C) 9 + √41 units

(D) 9 + √61 units

By definitions of collinearity and line segment, the length of the line segment KL is equal to 25 units.

In this problem we find four points that are collinear, that is, that lie in the same line. Therefore, there are three consecutive line segments: IJ, JK and KL, whose ratios are known. From the statement, we derive the following formula for KL:

KL = (5 / 12) · IL

KL = (5 / 12) · 60

KL = 25

The length of the line segment KL is equal to 25 units.

To learn more on collinear lines: https://brainly.com/question/2108998

#SPJ1

Answer:

Approximately 3 bottles

Step-by-step explanation:

28*4 = 112 tablets in a month

122/55 = 2.218 bottles

Basically, you will need to buy 3 bottles.

Answer:

  24

Step-by-step explanation:

You want the value of the product ...

  (√14 + √10i)(√14 - √10i)

The factoring of the difference of squares is ...

  a² -b² = (a +b)(a -b)

Here, we have a=√14 and b=√10i. The product of the sum and difference of these values is ...

  (√14 + √10i)(√14 - √10i) = (√14)² -(√10i)²

  = 14 -(10(-1)) = 24

The product is 24.

There are 2322432 coupons generated .

According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as

                         code = D L L L L   where D and L represent the digits and letters.

Now total digits we have is  = 7

       total number of letters we have = 24

So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.

Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways =   24⁴

Therefore the number of coupons that can be generated from the combination are :

                                7*24⁴ = 7*331776

                                          = 2322432

Hence the number of coupons generated are 2322432.

learn more about permutation here : https://brainly.com/question/12468032

#SPJ9

The labeled graph showing ABCDE, A'B'C'D'E', and the line of reflection x = -2 is shown. Also, m∠ A = m∠ A'.

In the question, we are given that the polygon ABCDE is reflected across the line x = - 2.

We are asked to graph and label the image A'B'C'D'E'. Also, we are asked if m∠ A = m∠ A'.

When the polygon ABCDE is reflected across the line x = - 2, all the coordinates on it are reflected across the line x = -2.

The reflection of any point with coordinates (x, y) on reflection across the line x = a, results in a point with coordinates (-x + 2a, y).

The coordinates of the vertices of the given polygon are:

A (-4, 4), B (-3, 3), C (-3, 2), D (-5, 1), and E (-5, 3).

Reflecting these points across the line x = - 2, we get:

A (-4, 4) → A' ( -(-4) + 2(-2), 4) = A' (0, 4).

B (-3, 3) → B' ( -(-3) + 2(-2), 3) = B' (-1, 3).

C (-3, 2) → C' ( -(-3) + 2(-2), 2) = C' (-1, 2).

D ( -5, 1) → D' ( -(-5) + 2(-2), 1) = D' (1, 1).

E (-5, 3) → E' ( -(-5) + 2(-2), 3) = E' (1, 3).

Plotting ABCDE, A'B'C'D'E', and the line x = -2 has been shown on the graph.

The angles m∠ A and m∠ A' are equal since ABCDE is reflected to make A'B'C'D'E' which makes the two figures congruent. And in congruent figures, the corresponding angles are equal.

Learn more about reflection at

https://brainly.com/question/2551977

#SPJ9

The bakery is short on half a bag of flour.This problem can be solved using fractions . So, first loaf of bread requires 2bags of flour and a quarter which can be written as  2[tex]\frac{1}{4}[/tex]second loaf of bread also requires the same amount which is 2[tex]\frac{1}{4}[/tex]

the third loaf of bread requires one bag and two third of another bag which can be written as 1[tex]\frac{2}{3}[/tex]

And the final loaf of bread requires half bag of flour which is [tex]\frac{1}{2}[/tex]

the total requirement of flour for making the four loaves of bread is

             = 2[tex]\frac{1}{4}[/tex] + 2[tex]\frac{1}{4}[/tex]+ 1[tex]\frac{2}{3}[/tex]+[tex]\frac{1}{2}[/tex]

              =[tex]\frac{9}{4}[/tex]  +[tex]\frac{9}{4}[/tex] + [tex]\frac{5}{3}[/tex] +       [tex]\frac{1}{2}[/tex]

              = [tex]\frac{27}{12}[/tex]+      [tex]\frac{27}{12}[/tex] +[tex]\frac{20}{12}[/tex] +[tex]\frac{6}{12}[/tex]

            = [tex]\frac{80}{12}[/tex]

To work out how much flour the bakery will have left after making these loaves we need to reduce the total requirement with total flour we have = 6 -[tex]\frac{80}{12}[/tex]

                                       =[tex]\frac{72}{12}[/tex] -  [tex]\frac{80}{12}[/tex]

                                     =- [tex]\frac{6}{12}[/tex] or- [tex]\frac{1}{2}[/tex]

therefore the bakery is short on half a bag of flour

To know more about fractions - https://brainly.com/question/10354322

#SPJ9

The vertices of the rectangle are:

P'(4,12)

Q'(12,12)

R'(12,8)

S'(4,8)

Given,the vertices of the rectangle are:

P(5,15), Q(15,15), R(15,10) and S(5,10)

also k= 4/5 to find the new vertices, that is:

P' = P×k

P' = P × 4/5

P' = (5×4/5 , 15×4/5)

P' = (4,12)

similarly:

Q' = Q×k

Q' = Q × 4/5

Q' = (15×4/5 , 15×4/5)

Q' = (12,12)

R' = R×k

R' = R × 4/5

R' = (15×4/5 , 10×4/5)

R' = (12,8)

S' = S×k

S' = S × 4/5

S' = (5×4/5 , 10×4/5)

S' = (4,8)

Hence we get the required points, for which we plot the graph.

Learn more about Transformations here:

brainly.com/question/2387958

#SPJ1

Answer:

8 students

c>=A+B

b=2a

24<=C

Answer:

Since the quantity started at 90 and then changed to 160, there was clearly an increase in its value.

Step-by-step explanation:

We get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.

We are given that the red line is perpendicular to the green line.

Also, we are given that the slope of the red line is - 5 / 2

m₁ = - 5 / 2

Now, we need to find the slope of green line.

Let the slope of the green line be m₂

We know that, when the lines are perpendicular, then the relationship between their slopes is given by:

m₁ ×  m₂ = - 1

Substituting the values, we get that:

- 5 / 2 × m₂ = - 1

m₂ = - 1 × - 2 / 5

m₂ = 2 / 5

Therefore, we get that the slope of the green line will be 2 / 5 when it is perpendicular to the red line.

Learn more about perpendicular here:

https://brainly.com/question/1202004

#SPJ9

Based on the statement given, the completion of the statement is 7 divided by 1/8 = 56.

The statement is asking for the number that would divide 7 such that the result of this division would be 56.

Assuming the number is x, the formula would be:
7/x = 56

Here, x would be the mystery number that would divide 7 to give 56.

Solving for x is:

7/x = 56

7 = 56x

x = 7/ 56

x = 1/8

In conclusion, when 7 is divided by 1/8, it gives 56.

Find out more on divisions at https://brainly.com/question/28031660

#SPJ1

Answer:

3

Step-by-step explanation:

-4|3| -1 = -13

-12 -1 = -13

-13 = -13

Answer:

3

Step-by-step explanation:

-4|3| -1 = -13

-12 -1 = -13

-13 = -13

The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches

The given parameters are

Average annual rainfall = 51 inches

Last year = 29 inches

The change in rainfall between the rainfall last year and the average (or mean) annual rainfall is calculated as

Change = |Annual rainfall - Last year|

This gives

Change = |51 - 29|

Evaluate

Change = 22

Hence, the change in rainfall between the rainfall last year and the average (or mean) annual rainfall is 22 inches

Read more about net change at:

https://brainly.com/question/1153322

#SPJ1

we need the table to answer the question