The population of a county is growing at a rate of 9% per year, compounded continuously. If the county currently has 14,934 people, how many will there be in this county in 10 years? Round to the nearest person.

Answer:

I'm pretty sure that this one is the correct factorization of the polynomial above: c) (3x+4)(9x^2-12x+16)

(3x−4)⋅(9x  

2

+12x+16)

See steps

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

 33x3 -  64

STEP

2

:

Trying to factor as a Difference of Cubes

2.1      Factoring:  27x3-64  

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  27  is the cube of  3  

Check :  64  is the cube of   4  

Check :  x3 is the cube of   x1

Factorization is :

            (3x - 4)  •  (9x2 + 12x + 16)  

Trying to factor by splitting the middle term

2.2     Factoring  9x2 + 12x + 16  

The first term is,  9x2  its coefficient is  9 .

The middle term is,  +12x  its coefficient is  12 .

The last term, "the constant", is  +16  

Step-1 : Multiply the coefficient of the first term by the constant   9 • 16 = 144  

Step-2 : Find two factors of  144  whose sum equals the coefficient of the middle term, which is   12 .

     -144    +    -1    =    -145  

     -72    +    -2    =    -74  

     -48    +    -3    =    -51  

     -36    +    -4    =    -40  

     -24    +    -6    =    -30  

     -18    +    -8    =    -26  

For tidiness, printing of 24 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 (3x - 4) • (9x2 + 12x + 16)

Answer:

C

Step-by-step explanation:

When factorising the sum of cubes, we use the formula

a^3+b^3=(a+b)(a^2−ab+b^2).

In this case of 27x3+64,

27x^3=a^3

64=b^3

Find a:

27x^3=a^3

3^√27x^3=3^√a^3

3x=a

Find b:

64=b^3

3^√64=3√b^3

4=b

Substitute a=3x and b=4 into

 (a+b)(a^2−ab+b^2)

(3x+4)((3x)^2−(3x×4)+4^2)

= (3x+4)(9x^2−12x+16)

(3x+4)(9x^2−12x+16) is the factorised form of 27x^3+64

Answer:

9 more weeks

Step-by-step explanation:

because if you do 740-500 you get 240

so then i divide 240 by the money per week (25) and

get 9.6 so it is 9 weeks

Answer:

D

Step-by-step explanation:

it is D because you always want x to be a lone fraction and that would be the first step im 99% sure unless someone can correct me :)

Answer:

d) subtract 15 from both sides

Step-by-step explanation:

Process of elimination:

a) 2.5 and x are being multiplied, not subtracted, so (a) is wrong right off the bat.

b) you may divide 2.5 by both sides, but you want to get "x" on one side first. So you would do (b) first either.

c) to get rid of 15, which we need to somehow, we need to do the opposite operation than the one in the equation. 15 is +15, not negative, and so you would need to subtract to get rid of 15. This is why (c) is also wrong.

That leaves us, with (d), because you need to subtract 15 to isolate "x".

Answer:5.4

Step-by-step explanation:

Answer:

The two pairs of alternate interior angles are CHG and HGB and DHG and HGA.

mCHG  =  mHGB  =  48.81°

mDHG  =  mHGA  =  131.19°

The two pairs of alternate exterior angles are EHC and BGF and EHD and AGF.

mEHC  =  mBGF  =  131.19°

mEHD  =  mAGF  =  48.81°

Step-by-step explanation:

STRAIHGT FROM PLATO BOOOOIIIIII

Answer:

it is makeing me do it

Step-by-step explanation:

Answer:

A. No solutions

Step-by-step explanation:

2x-2x=-9

0= -9

Since 0 does not equal -9, there are no solutions.

Answer: y=2x-1

Step-by-step explanation:

In slope intercept form y=Mx+b

Mx=slope and b=intercept

Y=2x-1

The equation of line with slope m = 2 and y-intercept is -1 is given by

y = 2x - 1

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the slope of the line m = 2

Let the y intercept of the line b = -1

Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

y = 2x - 1   be equation (1)

Therefore , the value of A is y = 2x - 1

Hence , the equation of line is y = 2x - 1

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Answer:

SEE BELOW

Step-by-step explanation:

INTERRIOR ANGLES

3.

∠A + ∠B + ∠C = 180

(180 - 103) + (3x - 14) + (3x + 9) = 180

6x = 180 - 77 + 14 - 9

x = 108 / 6

x = 18

m∠ACB = (3x - 14)

             = 3(18) - 14

             = 40

m∠ABC = (3x + 9)

              = 3(18) + 9

              = 63

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

INTERRIOR ANGLES

4.

∠A + ∠B + ∠C = 180

(180 - 97) + (2x + 2) + (14x - 1) = 180

16x = 180 - 83 - 2 + 1

x = 96 / 16

x = 6

m∠BCA = 2x + 2

             = 2(6) + 2

             = 14

m∠ABC = 14x - 1

             = 14(6) - 1

             = 83

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

EXTERIOR ANGLES

5.

∠B

180 - 15x + 20

15x = 180 + 20

   x = 200/15

   x = 13.33

∠C

180 - 9x + 10  

9x = 190

 x = 190/9

 x = 21.11

∠E

180 - 17x + 2

17x = 182

  x = 182/17

  x = 10.706

m∠BEF = 17x + 2

             = 17 (10.706) + 2

             = 184

m∠ABC = 15x + 20

             = 15(15.33) + 20

             = 220

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

EXTERIOR ANGLES

6.

first solve x by adding all the interior angles = 180

∠B + ∠E + ∠C = 180

2x + x + 93 = 180

3x = 180 - 93

x = 87/2

x = 43.5

m∠BEC = 360 - x

             = 360 - 43.5

             = 316.5

m∠ABC = 180 - 2x

             = 180 - 2(43.5)

             = 93

Answer:

7 hours

Step-by-step explanation:

$247.50 - $45.00 (how much he charges for the first hour) = $202.50

$202.50 ÷ $33.75 (how much he charges for the additional hours) = 6 hours

But he charges 45 dollars for the first hour so he 7 hours in total

Answer: It's 4

Step-by-step explanation: 12-8 is 4, 4-3 is 1

Answer:

amberjack 21 pounds

kingfish 42 pounds

marlin 84 pounds

tarpon 105 pounds

Step-by-step explanation:

The weight of the fish is given below,

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jon caught four fish that weighed a total of 276 pounds. The kingfish weighed twice as much as the amberjack and the white marlin weighed twice as much as the kingfish. The weight of the tarpon was 5 times the weight of the amberjack.

The equation can be written as,

KF+A+W+T=276

Other relations are,

KF = A / 2

W = A /4

T = 5A

Substitute all the values in the above equation and solve for A.

KF+A+W+T=276

A / 2 + A + A / 4 + 5A = 276

2A + 4A +A +20A = 276 x 4

27A = 1104

A = 40 pounds

kingfish = KF = A / 2 = 20 pounds

White marlin = W = A / 4 = 10 pounds

Tarpon = T = 5A = 200 pounds

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Answer: 8/15

Step-by-step explanation:

(-4/5) divided by (-3/2) becomes (-4/5) x (-2/3) because when dividing fractions, change it to multiplication and flip the divider (in this case -3/2)

Multiply numerators to get 8 and denominators to get 15 resulting in 8/15

Answer:

$40.2 dollars

Please make me brainliest!

Answer:

y= -x+7, b= sqrt(2P/a), c=3P^2-b

Step-by-step explanation:

First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will      get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.

Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).

Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.

Answer:

2.5

Step-by-step explanation:

you can use pythag theorem and divide c by two:

-3^2+4^2=c^2

9+16= 25

c=5

however, 5/2=2.5

Answer:

441

Step-by-step explanation:

Use a proportion.

756 miles is to 12 hours as x miles is to 7 hours

756/12 = x/7

12x = 7 * 756

12x = 5292

x = 441

Answer: 441 miles

Answer:

441

Step-by-step explanation:

756 divided by 12 = 63

Jim drives 63 miles in 1 hour

Multiply 63 by 7

63 ⋅ 7 = 441

Jim will drive 441 miles in 7 hours

Hope I helped :)

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Answer:

it looks like it is Addition Property Of Equality

Step-by-step explanation:

Answer:

YES IT IS A PERFECT SQUARE

Step-by-step explanation:

equate the equation to zero

x^2+8x+16=0

c is the product while the coefficient of b is the sum

P=16

S=8

find a pair of numbers that the product is 16 and the sum is 8

the numbers are (4,4)

(x^2+4x) (4X+16)

ignore 8x and arrange as shown above

then bracket the equation

x(x+4)+4(x+4)

you simplify and remain with (x+4) (x+4)

having similar roots making it a perfect square

The solution x > -3 represents all values of x that are greater than -3. On the other hand, the solution x = -3 represents a single value of x that is equal to -3.

Given that,

An equation is,

- 4(2x - 3) = 36

Here, Jake's solution to the equation - 4(2x - 3) = 36 is,

-4(2x - 3) = 36

Apply distributive property,

-8x + 12 - 36

- 8x + 12 - 12 = 36 - 12

Subtract 12 on both sides,

-8x = 24

x = - 24/8

x = - 3

So, the solution x = -3 represents a single value of x that is equal to -3.

Therefore, x > -3 represents a range of values greater than -3, while x = -3 represents a single value that is equal to -3.

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Answer:

7/3 or 2.333333333

Step-by-step explanation:

Answer:

Answer is 2 1/3

Step-by-step explanation:

7/9 divided by 1/3 you can't divide fractions so you multiply so it would look more like:

7/9 * 1/3 = 7/3

you then divide 7 by 3 and get 2 1/3

So your answer is 2 1/3

Answer:  

At what type of boundary do strike-strip basins form? transform

At what type of boundary do wedge basins form? convergent

At what type of boundary do rift basins form? divergent

At what type of boundary do arc basins form? convergent

Step-by-step explanation:

Hope this helps!

Answer:

Answer the questions using the drop-down menus.

✔ transform

At what type of boundary do wedge basins form?

✔ convergent

At what type of boundary do rift basins form?

✔ divergent

At what type of boundary do arc basins form?

✔ convergent

Step-by-step explanation:

Answer:

y= 50x + 150

charge for each hour is 50

one time fee is 150

Step-by-step explanation:

Answer:

n ≥ -4

Step-by-step explanation:

-3/4n ≤ 3

-4/3(-3/4n) ≤ 3(-4/3)

n ≥ -12/3

n ≥ -4

CHECK:

correct

-3/4(-4) ≤ 3

12/4 ≤ 3

3 = 3

correct

-3/4(5) ≤ 3

-15/4 ≤ 3

-3.75 < 3

incorrect

-3/4(1) ≤ 3

-3/4 is not ≤ 3

Answer:

x= 0.5

Step-by-step explanation:

It makes sense

The value of x is 1/2.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

–3x + 1 + 10x = x + 4

Now, solving for x

-3x+ 10x - x = 4 - 1

7x - x = 3

6x = 3

x= 3/6

x= 1/2

Hence, the value of x is 1/2.

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Answer:

A::True

Step-by-step explanation:

For the quadratic function the domain is all real numbers since the horizontal extent of the graph is the whole real number line. Because the graph does not include any negative values for the range, the range is only non-negative real numbers.

Answer:

not equivalent

Step-by-step explanation:

2a+11

5+9/2a

Answer:

3/4(2x+1)=2

3/2x+3/4=2

3/2x=2 -3/4

3/2x=-10/4

3/2x(2)=-10/4(2)

3x= -5/2

3x/3 = -5/2 * 1/3

x= -5/6

Answer:

3 benches needed

Step-by-step explanation:

Answer:

3 benches

Step-by-step explanation:

4 people to one bench

12 people divided by 4 = 3 benches