Long division synthetic remainder theorem and factor theorem

[tex](4n^3 - 18n + 21 - 8n^2) ÷ (2n - 6)[/tex]
​

Answer:

x = 2

Step-by-step explanation:

x + 3 + 1/2 x + 3 +x + 1 = 12  Combine like terms

21/2 x + 7 = 12   Subtract 7 from both sides of the equation

2 1/2 x = 5

Another name for 2 1/2 is [tex]\frac{5}{2}[/tex]        ([tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex])

[tex]\frac{5}{2}[/tex] x = 5  Multiply both sides of the equation by [tex]\frac{2}{5}[/tex]

[tex](\frac{2}{5})[/tex][tex](\frac{5}{2})[/tex]x = [tex]\frac{2}{5}[/tex][tex](\frac{5}{1})[/tex]

x = 2

Answer:

3(2(4)(3)(2.8))

3(24(2.8))

3(67.2)

2016

The numerical length of GH = 20 units

FH is a line segment.

G is a point on the line segment.

Then G divides the line segment FH into two line segments FG and GH.

We are given the lengths of FH, FG and GH in terms of x.

That is,  FH=4x+8, FG=x and GH=5x

We need to find the numerical length of the line segment GH. We first need to find the x for this.

As G cuts the line segment FH into two parts, the length of the line segment FH is the sum of the lengths of the line segments FG and GH.

That is, FH = FG + GH

⇒ 4x+8 = x +5x

⇒ 4x+8 = 6x

⇒ 2x = 8

⇒ x = 4

So the numerical length of GH = 5x = 5 x 4 = 20 units

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Answer:

(x,y)=(10,11)

Step-by-step explanation:

Drew actually has almost finished the equation. So I'm starting with the left part

[tex]2.5x+ 6= 31[/tex]

Cancel out 6 from both sides and divide both sides 2.5 which leaves us with

[tex]x=\boxed{10}[/tex]

Plug in the value of x into the second equation and simplify

y=-2.10+ 31

[tex]y=\boxed{ 11}[/tex]

Answer:

Terms: x, 4y, 32

variables: x, y

constant: 32

coefficients: 4, 1

Step-by-step explanation:

Hope this helps!

California is the most populated state, New York is the least populated, and 26% of Americans live in California, New York, and Texas.

Convert all statistics to percentages:

CA: 3 25 = 0.12 or 12%, 0.12 100 to calculate percentages.

NY: 3 50 = 0.06, or 6%, and 0.06 100 to get the percentage.

TX: 2 25 = 0.08 = 8%, 0.08 100 = percent

(A) California has the largest population of the three states.

(B) New York has the smallest population of the three states.

(C) USA = 100%, CA + NY + TX = 26%, so 74% of Americans do not live in these three states.

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Answer:

x=22

Step-by-step explanation:

Since a straight line is equal to 180 degrees,

(3x+3)+(5x+1) = 180

(3x+3)+(5x+1)-180=0

8x+4-180=0

8x-176=0

8x=176

x=176/8

x=22

Which also means that the first angle is (3(22)+3)=69 degrees

the second angle is (5(22)+1) = 111 degrees

111 + 69 = 180  

Answer:

D

Step-by-step explanation:

the sum of the 3 angles in Δ DEF = 180° , that is

∠ D + 90° + 35° = 180°

∠ D + 125° = 180° ( subtract 125° from both sides )

∠ D = 55°

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

using the tangent and cosine ratios in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{12}[/tex] ( multiply both sides by 12 )

12 × tan35° = DE , then

DE ≈ 8.40 ( to 2 dec. places )

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

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{12}{DF}[/tex] ( multiply both sides by DF )

DF × cos35° = 12 ( divide both sides by cos35° )

DF = [tex]\frac{12}{cos35}[/tex] ≈ 14.65 ( to 2 dec. places )

[tex]8 + 3x = 1 + 7.9x \\ \\ \implies 3x - 7.9x = 1 - 8 \\ \\ \implies - 4.9x = - 7 \\ \\ \implies \: x = \frac { \cancel{- 7}}{ \cancel{ - 4.9} } \\ \\ \implies \: x = 1.43[/tex]

choti bachi hô kya itne simp question ka answer kon puchta hai xD

Answer:

a) the answer it 10 so no

b) the answer is −39 so nah

c) the answer is 48, nope

d) the answer is  34, did you mean to write 34 instead of 24?

Step-by-step explanation:

Answer:

16/5

Step-by-step explanation:

The direct variation equation (where k is the constant variation):

z = kw

First, we must solve for k:

k = w/z

Plug in -5 and 2:

k = 2/-5 = -2/5

Now plug k into the formula with 8 to solve for z:

z = -2/5 x 8 = 16/5

Answer:

y = mx + b

y = 1/4x + 2

Step-by-step explanation:

m(slope) = rise/run = 1/4

b(y intercept) = 2

Answer:

x= -1, -13

Step-by-step explanation:

Answer: x=-13   x=-1

Step-by-step explanation:

[tex]x^2+14x=-13\\x^2+2(x)(7)+7^2-7^2=-13\\(x^2+2(x)(7)+7^2)-49=-13\\(x+7)^2-49=-13\\(x+7)^2-49+49=-13+49\\(x+7)^2=36[/tex]

[tex](x+7)^2-36=36-36\\(x+7)^2-36=0\\(x+7)^2-6^2=0\\(x+7+6)(x+7-6)=0\\(x+13)(x+1)=0\\x+13=0\\x+13-13=0-13\\x=-13\\x+1=0\\x+1-1=0+(-1)\\x=-1[/tex]

Answer:

2; 6

Step-by-step explanation:

for the first shape there are 2 lines of symmetry

TWO

for the hexagon or the regular polygon there are 6 lines of symmetry

SIX

you can find lines of symmetry by drying a line down and seeing if when you fold them they will be exactly the same

Answer: y=-47/5

Step-by-step explanation:

Yw

     To prove this, we need to show that 2 is equal to x.

     Given:

2(x + 5) - 3x = 7x - 6

     Distribute:

2x + 10 - 3x = 7x - 6

     Combine like terms:

-1x + 10 = 7x - 6

     Add 1x to both sides of the equation:

10 = 8x - 6

     Add 6 to both sides of the equation:

16 = 8x

     Divide both sides of the equation by 8:

2 = x

     Reflexive property:

x = 2

       ✓

2(x + 5) - 3x = 7x - 6

x = 2

The total distance climbed by Kristen and her family is 16 meters.

It is given in the question that Kirsten and family climb down to 8 meters below ground level. Then they climb the opposite of 8 meters to return to ground level.

We have to find the total distance climbed by Kristen and her family.

We know that,

Total distance climbed by Kristen and her family = Distance climbed down the cave + distance climbed up the cave to reach ground level

Hence, we can write that,

Total distance climbed by Kristen and her family = 8+8 = 16 meters.

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Price of key ring = £1.6

Price of purse = £3.2

The unitary approach is a strategy for problem-solving that involves first identifying the value of a single unit, then multiplying that value to figure out the required value.

Given Data

Vicky makes 8 purses and 9 key rings to sell for charity.

Vicky wants to get a total of exactly £40

Suppose the price of key ring be v

and the price of purses be 2v

£40 = £8(2v) + £9(v)

40 = 16v + 9v

40 = 25v

v = [tex]\frac{40}{25}[/tex]

v = 1.6

Price of key ring = £1.6

Price of purse = £3.2

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The value of x is found as 3 using the method of substitution.

For the given expression, use substitution method to solve.

2x + y = 7  ........eq 1

y = 2x - 5  ........eq 2

Substitute the value of y from eq 2 in eq 1.

2x + 2x - 5 = 7

Solving;

4x = 7 + 5

4x = 12

x = 3

Thus, the value of x is found as 3.

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Answer:

36

Step-by-step explanation:

24 customers dividend into 4 tables

so 24/4 = 6

then 6 customers can sit in 1 table

in case of 6 tables 6×6 =36

36 customers would sit in 6 tables

She buy 48 inches of ribbon to have the exact amount that she needs.

Given,

Area of the ribbon = 144 sq. inches

and, We know the formula for side of square is =[tex]\sqrt{Area of a square }[/tex]

Plug the value of area of square in above formula

Side of a Square = [tex]\sqrt{144}[/tex] = 12 inches

Now, we get the side of a square i.e., 12 inches

According to the question:

Sonya wants to sew ribbon along each side of a square pillow.

So, we need to find the perimeter of the square pillow.

and, Perimeter of a square is = 4 x side

=> Perimeter = 4 x 12 = 48 inches.

Therefore, She buy 48 inches of ribbon to have the exact amount that she needs.

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Answer:

the answer you are looking for is D

Answer: Alternate exterior angles

Step-by-step explanation:

The value of of slope of is 1/4.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.

Any two distinct places along the line can be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the "vertical change" to the "horizontal change" in each case. The difference between the line's y and x coordinate changes is known as the slope of the line. Net changes in the y and x coordinates are as follows: y = y and x = x.

m = [tex]y_{2} - y_{1} /x_{2} x_{1}[/tex]

m = 1/4

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Answer:

1.34 units.

Step-by-step explanation:

The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.

Let this line be y = -1/2x + c.

Its passes through (4, 6) so:

6 = -1/2*4 + c

6 = -2 + c

c = 6 + 2 = 8

So, equation of this line is y = -1/2x + 8.

Now we find the point where the 2 lines intersect:

y = 2x - 5

y = -1/2x + 8

2x - 5 = -1/2x + 8

2x + 1/2 x = 5 + 8

(5/2)x = 13

x = 26/5

  = 5.2.

and y = 2(5.2) - 5

          = 5.4.

So, the point of intersection is (5.2, 5.4)

and the distance between the point (4,6) and the line y = 2x - 5

= √((6 - 5.4)^2 + (4-5.2)^2)

= √(0.36 + 1.44)

= √1.8

= 1.34

There is a formula you can use directly to solve this.

The linear equation in point-slope form of a line with a slope of 23 and point (3,-2) is y = 23x - 71.

The slope intercept formula is expressed as;

y = mx + b

Where m is the slope and b is the y-intercept.

Given the data in the question;

Point: (3,-2)

First, use the the formula for the equation of line to determine the y-intercept 'b'.

y = mx + b

Plug in slope m = 23 and point (3,-2)

-2 = (23)3 + b

-2 = 69 + b

b = -2 - 69

b = -71

Now that we have both the slope m ( 23 ) and y-intercept b ( -71 ), plug these values into y = mx + b to find the linear equation.

y = mx + b

y = 23x + (-71)

y = 23x - 71

Therefore, the equation of the line is y = 23x - 71.

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Answer:

‎

4 + (-125)‎

= 4 - 125‎

= -121‎

‎