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Answer: C) 2/3

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Explanation:

Let's cross multiply and then get everything to one side

x/(2x-1) = (2x+1)/(x+2)

x(x+2) = (2x-1)(2x+1)

x^2+2x = 4x^2-1

0 = 4x^2-1-x^2-2x

0 = 3x^2-2x-1

3x^2-2x-1 = 0 .... see note below

x^2-(2/3)x-1/3 = 0

In that last step, I divided everything by the leading coefficient 3. That way, the leading coefficient becomes 1.

It turns out that anything in the form x^2-px+q has roots m and n such that

p = m+n

q = m*n

In short, the roots add to the negative of the middle coefficient, and they also multiply to the constant term. Again this only applies to quadratics where the leading coefficient is 1.

Comparing x^2-(2/3)x-1/3 with the form x^2-px+q, we see that

p = 2/3

q = -1/3

Therefore, p = m+n = 2/3

If you're curious why this works, it's because (x+a)(x+b) expands out to x^2+(a+b)x+ab, and note how the roots here are x = -a and x = -b.

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Note: Another route would be to solve 3x^2-2x-1 = 0 for x using any method you prefer (I recommend the quadratic formula). You would get the two solutions x = -1/3 and x = 1. They add to (-1/3)+1 = (-1/3) + (3/3) = (-1+3)/3 = 2/3.

Answer:

9

Step-by-step explanation:

Use PEMDAS

Parentheses (Bracketts go after parentheses but are not included in PEMDAS)

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

3

Step-by-step explanation: 15-(10+(3-2)2)+6

3-2=1x2=2+10=12 15-12=3

Answer:

The answer is A. (3x^4-5x^3+5x+2) =(x-2)

Step-by-step explanation:

we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

The remainder theorem states that when a polynomial p(x) is divided by

(x - a), then the remainder = f(a).

We have,

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2) ____(1)

We can directly find the remainder as:

x - 2 = 0

x = 2

Putting x = 2 in (1) we get,

= 3 x 16 - 5 x 8 + 5 x 2 + 2

= 48 - 40 + 10 + 2

= 20

The remainder is 20.

(3x³ + 7x² + 5x + 2) ÷ (x - 2) ) _______(2)

x - 2 = 0

x = 2

Putting x = 2 in (2) we get,

= 3 x 8 + 7 x 4 + 5 x 2 + 2

= 24 + 28 + 10 + 2

= 64

The remainder is 64.

(x³ + 5x² - 4x + 6) ÷ (x + 5) ______(3)

x + 5 = 0

x = -5

Putting x = -5 in (3) we get,

= - 125 + 5 x 25 - 4 x (-5) + 6

= -125 + 125 + 20 + 6

= 20 + 6

= 26

The remainder is 26.

([tex]x^{4}[/tex] - 8x² + 16) ÷ (x + 4) _______(4)

x + 4 = 0

x = -4

Putting x = -4 in (4) we get,

= 256 - 8 x 16 + 16

= 256 - 128 + 16

= 144

The remainder is 144.

Thus we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

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Answer:

coordinate of M (8,13)

Step-by-step explanation:

LM has L(-2,-9), P(3,2) mid point of LM

coordinate of mid point= x=x1+x1/2 and y=y1+y2/2

x1=-2 , x2 is the x of point M

xof P= (-2+x2)/2

3(2)=-2+x2

6=-2+x2 ⇒ x2=6+2=8

y of P= y1+y2/2

2=-9+y2/2

y2=2(2)+9⇒ y2=13

coordinate of M (8,13)

Answer:

it denotes distributive property of multiplication over addition

distributive property of multiplication over addition. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

Answer:

3

Step-by-step explanation:

The Greatest Common Factor between 42 and 45 is 3.

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Given two numbers are 42 and 45,

42 = 7*2*3

45 = 5*3*3

GCF = 3

Hence, The Greatest Common Factor between 42 and 45 is 3.

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Answer:

C

Step-by-step explanation:

A and c are parallel

B and d are parallel

A and c are intersecting

Answer:

Hey there!

If the midpoint is (-5, 18) and the endpoint is (3, 13) the other endpoint is (-13, 23)

Let me know if this helps :)

Answer:

2/5

Step-by-step explanation:

3/5 + ____ = 5/5

2/5

Answer:

θ  = [tex]30^{0}[/tex]

Step-by-step explanation:

Since the vertical height of the mountain is 800 feet, and the distance from the top to its base is 1600 feet. Let the angle of elevation be represented by θ, applying the required trigonometric function;

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin θ = [tex]\frac{800}{1600}[/tex]

        = 0.5

θ = [tex]Sin^{-1}[/tex] 0.5

θ  = [tex]30^{0}[/tex]

Thus, the angle of elevation from the base to the top of the mountain is [tex]30^{0}[/tex].

[tex]2^{-3}[/tex] is the same as [tex]\frac{1}{2^3}[/tex] because of the rule [tex]x^{-k} = \frac{1}{x^k}[/tex]

The negative exponent says to take the reciprocal of the base to make the exponent positive. The original base is 2, of which the reciprocal is 1/2.

Answer:

5/8

Step-by-step explanation:

slope: (y₂ - y₁) / (x₂ - x₁)

(3 - 8) / (1 - 9) = -5/-8 = 5/8

Answer:

m= 5/8

Step-by-step explanation:

The slope of a line can be found using the following formula:

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

where (x₁, y₁) and (x₂, y₂) are the points the line passes through.

The points given are: (1,3) and (9,8). Therefore,

[tex]x_{1}=1 \\y_{1}=3 \\x_{2}=9 \\y_{2}=8[/tex]

Substitute the values into the formula.

[tex]m=\frac{8-3}{9-1}[/tex]

Perform the operation in the numerator. Subtract 3 from 8.

[tex]m=\frac{5}{9-1}[/tex]

Perform the operation in the denominator. Subtract 1 from 9.

[tex]m= \frac{5}{8}[/tex]

The slope of the line is 5/8

Answer:

1,116

Step-by-step explanation:

2568 + ( - 1452)

= 2568 - 1452 ( because + × - makes -)

= 2568 - 1452

= 1,116

Answer:

the answer is 1116 I hope it's right

Answer:

DBH is an obtuse angle.

Step-by-step explanation:

D is around the 15 degree mark. h is around the 144 degree mark. Subtract 15 by 15 and 144 by 15 degrees, so that way angle D would be on the 0. You would get 129 degrees, which still makes it obtuse because is greater than 90 degrees

I hope this helps

Answer:

60 inches

Step-by-step explanation:

12 feet=144 inches

28in x 3 = 84

144-84= 60

Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.

The conversion of units is the process of converting a quantity between multiple units of measurement, usually using multiplicative conversion factors.

The conversion factor between inch and foot are:

1 foot = 12 inches,

or, 1 inch = 1/12 feet.

We are informed that Sarah has a wooden board that is 12 feet long.

We are asked that if she cuts three 28-inch pieces from the board, how many inches of the board will she have left.

To solve the problem, we convert the length of the wooden board from feet to inches.

The board is 12 feet long. We know 1 foot = 12 inches.

∴ 12 feet = 12*12 inches = 144 inches.

∴ Length of the board = 144 inches.

Size of the piece cut by Sarah = 28 inches.

She cuts 3 such pieces,

∴ Total piece of board cut = 3*28 inches = 84 inches.

∴ Length of the board Sarah is left with = Total length of the board - Total piece cut from the board = 144 - 84 inches = 60 inches.

∴ Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.

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Answer:

64 miles

Step-by-step explanation:

If he used 20% of the gas, he can go 20% of the miles

20% of 320 miles

.20 * 320

64 miles

Answer:

[tex]\huge\boxed{\sf 64\ miles}[/tex]

Step-by-step explanation:

A total tank travels to 320 miles

Let the miles be x

He used 20% of the full tank

=> 20% of the full tank = x

=> [tex]\frac{20}{100} * 320 = x[/tex]

=> 2 * 32 = x

=> x = 64 miles

So, He traveled 64 miles in 20% of the tank.

Answer:

10

Step-by-step explanation:

(10y+6) + (8y-6) =180

18y=180

y=10

JKM=10y+6=10(10)+6=106

MKL=8y-6=8(10)-6=74

Answer:

Step-by-step explanation:

10y+6+8y-6=180

then,y=10

therefore,

angle(JKM)=106

angle(MKL)=74

Answer:

  RS = 16

Step-by-step explanation:

The segment addition theorem tells you ...

  QR +RS = QS

  4 + (5x-9) = 4x

  x = 5 . . . . . . . . . . . add 5-4x

Then the length of RS is ...

  RS = 5(5) -9

  RS = 16

Answer:

675 calories

Step-by-step explanation:

I don't know about you but for me it's easier to multiply with decimals. I turned 2 1/4 to 2.25 and because n is right next to 300 we multiply (2.25 x 300) to get 675.

Hope that helps, and have a great day!

Answer:

Answer is 10^11 is the smallest power that would exceed 999,999,999,991

Answer:

10 to the power of 13 or 10^13

Answer:

it is 17.2 + 16.4

Step-by-step explanation:

because 8.6x2= 17.2

then 5.2x2=10.4

then 3+3=6

lastly 10.4+6= 16.4

so that makes it 17.2+16.4

Answer:

Video Games = $5.25

Movies = $1.25

Step-by-step explanation:

(3x + 5y = 30)2

6x + 2y = 18

                                           Video Games (y) = 5.25

  6x + 10y = 60

-  6x + 2y = 18  

      (8y)/8 = (42)/8

6x + 2(5.25) = 18

6x + 10.5 = 18

6x = 7.5

x = 1.25

Double Check by plugging in the numbers

Answer:

g-1(4)=-5

Step-by-step explanation:

because inverse mean that you will switch every x and y on the original graph

for example; point( 4,-2) inverse will be (-2,4)

so to find x=4 on the inverse than just find y=4 on the origin graph

Answer:

Perpendicular line through a point off a line

Step-by-step explanation:

Based on the markings in the diagram, we have;

Marking points E and F along AB extended forms two points equidistant from the point C on the line AB

Construction of the line HI by using equal arc lengths from E and F creates two points equidistant from E and F on either side of the line AB such that HI passes through C forming a perpendicular bisector from C to AB.

Therefore, a perpendicular line has been constructed from the point C off the line AB to the line AB

Hence the correct option is the construction of a perpendicular line through a point off a line.

Answer:

C. Perpendicular line through a point off a line (its off not on)  Took the test and got it right

Step-by-step explanation:

Answer:

$18.15

Step-by-step explanation:

Answer:

n+8

Step-by-step explanation:

8n=8(n)

n-8=n-8 (Since there is no commutative property in subtraction)

n=8 means 8=n

n+8=8+n

Because of commutative property in addition.

Hope this helps ;) ❤❤❤

Answer:

D

Step-by-step explanation:

The remaining material can be calculated as

volume of larger cube - volume of smaller cube

= a³ - b³ ← difference of cubes which factors in general as

= (a - b)(a² + ab + b²) → D

You need 3 numbers, divide the total by 3:

84/3 = 28

This is the middle value.

Now you use the one lower and the one higher:

27 + 28 + 29 = 84

The numbers are 27, 28, 29

Answer: 26, 28, 30

Step-by-step explanation:

26, 28, and 30 follow each other in consecutive order without haps of more than two and are arranged smallest to largest.