Write an algebraic expression for the sum of six times a number and 25

Answer: C) 2/3

========================================================

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.

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

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:

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

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:

C

Step-by-step explanation:

A and c are parallel

B and d are parallel

A and c are intersecting

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

[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:

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:

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:

  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:

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

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.

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:

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:

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].

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:

2/5

Step-by-step explanation:

3/5 + ____ = 5/5

2/5

Answer:

1.   The star's mass is 1.3 x 10^32 kg.

2.  The star's mass is 1.3 x 10^32 kg.

Step-by-step explanation:

1.

Divide numbers written in scientific notation by dividing the coefficients and then subtracting the exponents.

let The sun's mass is 2.0×10^30 kg.

and the coefficient = 1.5x10^-2

divide the coefficients

2.0 ÷ 1.5 =  1.3  

Then subtract the exponents.

= 10^30 - 10^-2

= 30 - (-2)

= 32

Combine the results of the two operations

= 1.3 and x 10^32

= 1.3 x 10^32

therefore,

The star's mass is 1.3 x 10^32 kg

===============================

2.

given:

The sun's mass is 2.0×10^30 kg.

mass of a star = sun's mass divided by 1.5×10^-2 kg

find:

Express the answer in Scientific notation.

mass of a star = 2.0×10^30 kg

                           1.5×10^-2 kg

mass of a star = 1.3 X 10^32 kg

therefore,

The star's mass is 1.3 x 10^32 kg

===============================

Answer:

1.   The star's mass is 1.3 x 10^32 kg.

2.  The star's mass is 1.3 x 10^32 kg.

Step-by-step explanation:

i got them right on my quiz

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:

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:

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:

C. Point P

Step-by-step explanation:

sqrt(92) = 9.59

The point closest to 9.59 is point P.

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:

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:

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:

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:

25 mph

Step-by-step explanation:

Because you know mi/h means the miles PER hours, and we know that when we see the word "per" we're dealing with a rate. What we have to do here, is multiply 10(mph) is like the average, or limit. So if I'm running 2.5 miles I multiply 10 x 2.5 to get 25.

Or just move the decimal point one space because of the zero in 10.

Hope this helps, and have a great day!

If i run at an average speed of 10 mi/h, the time needed for me  to run 2.5 miles is, 0.25 hour

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance =  Time × Speed

Given that,

An average speed  = 10 mi/h,

If distance travelled = 2.5 miles

Time needed = ?

Time needed =  Distance/Speed

                       =  2.5 / 10

                       =  0.25

Hence, The time needed is 0.25 hour

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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