Mike wants to put 150 square feet of artificial turf in his front yard. This is the maximum area
of artificial turf allowed by his homeowners association. He wants to have a rectangular area
of turf with length one foot less than 3 times the width. Find the length and width. Round to
the nearest tenth of a foot.

Answer:

1/3 or 0.3

Step-by-step explanation:

5/8 x 4/5 x 2/3 =

1/3 or 0.3

Answer:

1/3 in^3

Step-by-step explanation:

In order to find the volume, you must multiply the length, by the width, by the height. This would mean you need to do 2/3x5/8x4/5=40/120

40/120 simplified will give you 1/3

Answer:

12

Step-by-step explanation:  18x 12= 216     and 54x4 = 216

In other words, everything but choice B

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Explanation:

You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division

There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

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Here's a fairly short proof:

Consider a polynomial q(x) such that

p(x) = (x-k)q(x)

which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.

If we plug x = k into the p(x) function, we get

p(x) = (x-k)q(x)

p(k) = (k-k)q(k)

p(k) = 0*q(k)

p(k) = 0

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How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.

So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.

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Plug x = 3 into the first function

A(x) = x^3 - 2x^2 - 4x + 3

A(3) = 3^3 - 2(3)^2 - 4(3) + 3

A(3) = 0

This shows (x-3) is a factor of the function A(x)

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Repeat for the second function

B(x) = x^3 + 3x^2 - 2x - 6

B(3) = 3^3 + 3(3)^2 - 2(3) - 6

B(3) = 42

We don't get an output of 0, so (x-3) cannot be a factor of B(x)

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Now onto the third function

C(x) = x^4 - 2x^3 - 27

C(3) = 3^4 - 2(3)^3 - 27

C(3) = 0

So (x-3) is a factor of C(x)

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Finally the last function

D(x) = x^4 - 20x - 21

D(3) = 3^4 - 20(3) - 21

D(3) = 0

Therefore (x-3) is a factor of D(x) as well.

The remainder theorem will be used to identify the polynomial that has a remainder of zero when divided by (x - 3)

The polynomials that have 0 as a factor are;

Reason:

According to the remainder theorem, we have;

The remainder following the division of a polynomial, by (x - a) is P(a)

Therefore, (x - 3) is a factor of the polynomial P(x) where P(3) = 0

For option (A), we have; A(x) = x³ - 2·x² - 4·x + 3

The remainder when (x³ - 2·x² - 4·x + 3) is divided by (x - 3) is therefore;

A(3) = 3³ - 2 × 2² - 4 × 2 + 3 = 14

Therefore, (x - 3) is not a factor of A(x) = x³ - 2·x² - 4·x + 3

For option (B), we have;

B(x) = x³ + 3·x² - 2·x - 6

The remainder when B(x) is divided by (x - 3) is therefore;

B(3) = 3³ + 3×3² - 2×3 - 6 42

Therefore, (x - 3) is not a factor of B(x) = x³ + 3·x² - 2·x - 6

For option (C), we have;

C(x) = x⁴ - 2·x³ - 27

The remainder when C(x) is divided by (x - 3) is therefore;

C(3) = 3⁴ - 2×3³ - 27 = 0

Therefore;

For option (D), we have;

D(x) = x⁴ - 20·x - 21

The remainder when D(x) is divided by (x - 3) is given as follows;

D(3) = 3⁴ - 20×3 - 21 = 0

Therefore;

Learn more here:

https://brainly.com/question/11456067

Answer:

42

Step-by-step explanation:

You add 21 twice because 3 is half of 6

Answer:

A - 42

Step-by-step explanation:

21 x 2 = 42

3 x 2 = 6

Answer:

Step-by-step explanation:

In order to find the values to factorize the equation, we need to find the factors the factors of 3 that sum to 4

The factors of 3 are [tex]\pm: 1, 3[/tex]

We can make 4 with 1 + 3

Since all the values are positive, both of the factors will have addition

[tex]x^2+4x+3\\(x+3)(x+1)\\\\x^2 + x + 3x + 3\\x^ + 4x + 3[/tex]

Answer:

That is correct

Answer:

yes its correct

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

y=x+4

Step-by-step explanation:

2y - 2x = 8

2y=2x+8

y=x+4

Answer:

3

Step-by-step explanation:

Answer:

No its about how many you get PER DAY

Step-by-step explanation:

Answer:

6 I think.

Step-by-step explanation:

6 I think. think

Answer:

270

Step-by-step explanation:

Answer:

x intercept: none

y intercept=: (0,-12)

Answer:

I suppose that each number is repeated 3 times, the actual question is:

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

Now, remember the relation:

Distance = Speed*Time

Let's define:

D1 = distance between Courtney's house and the beach.

D2 = distance between the beach and the park.

T1 = time that it took the first walk.

T2 = time that it took the second walk.

We know that the total distance Courtney walked is 8km, then:

D1 + D2 = 8km.

And we also know that the entire walk took 2 hours, then:

T1 + T2 = 2h.

We also have the equations:

D1 = 4km/h*T1

D2 = 5km/h*T2.

Then we have a system of equations:

D1 + D2 = 8km

T1 + T2 = 2h

D1 = 4km/h*T1

D2 = 5km/h*T2.

To solve this, first let's replace equations 3 and 4 in the first equation:

4km/h*T1 + 5km/h*T2 = 8km

Now we have only two equations left:

4km/h*T1 + 5km/h*T2 = 8km

T1 + T2 = 2h

Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:

T1 = 2h - T2.

Replacing this in the first equation gives:

4km/h*(2h - T2) + 5km/h*T2 = 8km

Now let's solve this for T2.

8km - 4km/h*T2 + 5km/h*T2 =  8km

8km + 1km/h*T2 = 8km

1km/h*T2 = 0

from this, we have T2 = 0

This would mean that T1 = 2h.

Then:

D1 = 4km/h*2h = 8km.

T2 = 0

D2 = 5km/h*0 = 0.

This happens because the numbers in the problem were not well thought.

You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.

Answer: 81.49% of bottle of mixed fruit juice is NOT apple juice.

Step-by-step explanation:

Quantity of mixed fruit juice  = 6.65 ounces

Quantity of apple juice in it = 1.231 ounce

Quantity of mixed fruit juice is NOT apple juice = (6.65-1.231) ounces

= 5.419 ounces

Fraction of bottle is not apple juice = [tex]\dfrac{5.419}{6.65}\approx0.8149=81.49\%[/tex]

Hence, 81.49% of bottle of mixed fruit juice is NOT apple juice.

Answer:

Step-by-step explanation:

-5400/-450

12 minutes

Answer:

12 minutes

Step-by-step explanation:

If the rate of the plane is -450 meters per minute, then you have to use the "division" operation in order to know how much time it takes for the plane to reach an altitude of -5,400 meters.

-5,400 meters ÷ -450 meters/minute = 12 minutes

It will take 12 minutes for the plane to reach an altitude of -5,400 meters.

Let's check:

-450 meters x 12 minutes = -5,400 meters

Answer:

14

Step-by-step explanation:

14

Answer:

You would need 13.5 2/3 cups.

Step-by-step explanation:

[tex]\frac{2}{3}[/tex]×[tex]\frac{13.5}{1}[/tex]=[tex]\frac{27}{3}[/tex]

27÷3=9

Answer:

[tex]y = 75 + 10x[/tex]

Step-by-step explanation:

Given

New Video Games

[tex]Cost = \$25[/tex]

[tex]Number = 3[/tex]

Used Video Games

[tex]Cost = \$10[/tex]

[tex]Number = x[/tex]

Required

Determine the amount spent (y)

First, we need to determine the total spent on new games

1 new game = $25

3 new games will be: 3 * $25

Next, we determine the total spent on old games

1 used game = $10

x used games will be: x * $10

So, total amount y, is:

[tex]y = 3 * 25 + x * 10[/tex]

[tex]y = 75 + 10x[/tex]

Answer:

The diagonal is 30 inches

Step-by-step explanation:

Assuming a rectangular suitcase (with right angles), we can use the Pythagorean theorem to solve this

a² + b² = c²

so we plug our two values to find the diagonal (hypotenuse)

24² + 18² = c²

576 + 324 = c²

900 = c²

c = √900

c = 30

The diagonal is 30 inches

Answer:

the diagonal is 30 inches

Step-by-step explanation:

you assume a suitcase is a rectangular shape, and the diagonal length makes 2 right triangles; therefore you can use Pythagorean theorem

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] ; where a = 24, b = 18 and c is the diagonal

[tex]24^{2}[/tex] + [tex]18^{2}[/tex] = [tex]c^{2}[/tex]

[tex]c^{2}[/tex] = 576 + 324

[tex]c^{2}[/tex] = 900

c = 30 inches

Answer:

x = 18

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

120/75=1.6

12 times 1.6=19.2

Answer: $6828

Step-by-step explanation:

James annual income = $85350

Income tax = 8%

The amount of income tax in dollars and cents that James has to pay will be calculated by multiplying the income tax by his annual income. This will be:

= 8% × $85350

= 8/100 × $85350

= 0.08 × $85350

= $6828

Answer: linear pair

Step-by-step explanation:

Because ce is shown to be bisected by line n, then the two expressions are added and will equal 180°. This is what is called a linear pair.

Answer:

6

Step-by-step explanation:

21/3=42/x

x=42*3/21

x=6

Answer: 105 degrees

Step-by-step explanation:

Both angles equal 180 so if we subtract 75 from 180 we get 105.

Answer:

105º

Step-by-step explanation:

<ONC and <BNJ are a linear pair, the angles are supplementary (eqauls 180º).

Answer:

Step-by-step explanation:

The explicit formula for a GP is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is the common ratio

a) If a3 = 36 and r = 6

a3 = ar^3-1

a3 = ar^2 = 36

ar^2 = 36

a(6)^2 = 36

36a = 36

a = 1

Get the nth term

Tn = 1(6)^{n-1}

Tn = 6^{n-1}

b)  If a6 = 64 and r = 2

a6 = ar^6-1

a6 = ar^5 = 64

ar^5 = 64

a(2)^2 = 64

4a = 64

a = 16

Get the nth term

Tn = 16(2)^{n-1}

Tn = 16*(2^n/2)

Tn = 8(2^n)