1) Determine the GCF and
2) write the expression in factored form.
(6x2 + 4x) + (4x2 – 8x)

How much do you owe?

Since each roommate will pay 20% of the $6,000 bill, you will owe 1 * 0.2 * 6000 = $1200.

What is 10% of the total repair bill?

10% of the total repair bill is 0.1 * 6000 = $600.

What will each roommate's 20% share be?

Each roommate's 20% share will be 0.2 * 6000 = $1200.

I hope this helps! Let me know if you have any other questions.

Answer:

5

Step-by-step explanation:

30 years => 20

60 years => 10

90 years => 5

We will be left with 5 g of Cesium-137 after 90 years, given its half-life of 30 years and the initial quantity we have as 40 g.

Many elements tend to decompose over some time. The period over which an element reduces to half of itself in quantity is called the half-life of that substance.

The formula for the quantity of the element at a certain time t can be given as:

[tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

Where,

[tex]N_{t}[/tex] is the quantity of the element at time t,

[tex]N_{0}[/tex] is the initial quantity of the element,

[tex]{t_{1/2}[/tex] is the half-life of the element.

In the question, we are given that an element, Cesium-137 has a half-life of approximately 30 years.

We are asked to find the quantity of this element left after 90 years when we had an initial sample of 40 g.

To solve for the quantity left, we can use the formula for the quantity of the element at a certain time t can be given as:

[tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

Where,

[tex]N_{t}[/tex] is the quantity of the element at time t,

[tex]N_{0}[/tex] is the initial quantity of the element,

[tex]{t_{1/2}[/tex] is the half-life of the element,

by taking t = 90 years, [tex]N_{0}[/tex] = 40 g, [tex]{t_{1/2}[/tex] = 30 years, and [tex]N_{t}[/tex] = ?.

∴ [tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{2} \right )^{\frac{90}{30}}} g[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{2} \right )^{3}} g[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{8} \right ) g[/tex]

or, [tex]N_{t} = 5 g[/tex] .

∴ We will be left with 5 g of Cesium-137 after 90 years, given its half-life of 30 years and the initial quantity we have as 40 g.

Learn more about the half-life of a substance at

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Step-by-step explanation:

BC is tangent to the circle with center A at point C and AC is radius.

[tex] \therefore AC \perp BC\\

\therefore \angle ACB =90°\\[/tex]

Now by Pythagorean theorem:

[tex] AB^2 = AC^2 + BC^2 \\

\therefore AC^2 = AB^2-BC^2\\

\therefore x^2 = 17^2-14^2\\

\therefore x^2 =289-196\\

\therefore x^2 =93\\

\therefore x =\sqrt{93}\\

\therefore x =9.64365076\\

\huge \purple {\boxed {\therefore x = 9.64\: units}} [/tex]

message me! i have made an edited file of it finished <3

Answer:

8, 9

Step-by-step explanation:

Since x > 7

This means that x cannot equal 7 but must be greater values than 7.

Thus 8 and 9 are solutions

Answer:

Quadrant 2

Step-by-step explanation:

Here's how you distinguish which points are in which quadrants.

Quadrant 1: (+x, +y)

Quadrant 2: (-x, +y)

Quadrant 3: (-x, -y)

Quadrant 4: (+x, -y)

(-3,6) has a negative x and a positive y. All the points in Quadrant 2 have a negative x and positive y.

Answer:

3.75

Step-by-step explanation:

3.75 you couldve used calculator :/

Answer:

3.75.

Step-by-step explanation:

15/4 = 3 with a remainder of 3. (3 3/4)

Then you make that into a decimal...

--> 3/4 is equal to 75 percent.

So 3.75..

Answer:

4 days

Step-by-step explanation:

268-112= 156    

156 divided by 39 = 4

Answer:

i think it is 4

Step-by-step explanation:

bc you do 268-112=156 then you take 156 and divide it by 39 and you end up getting 4.

Answer:

- the angles in the smaller prism measure 90 degrees

- the perimeter of the rectangular bases changes by a factor of 2

-the area of the rectangular bases changes by a factor of 4

Step-by-step explanation:

I just got it right

Answer:

the angles in the smaller prism measure 90 degrees

the perimeter of the rectangular bases changes by a factor of 2

the area of the rectangular bases changes by a factor of 4

Step-by-step explanation:

Answer:

The answer is x-5 or "B" on edge

Step-by-step explanation:

Given : If the hypotenuse of a 30-60-90 triangle has length 15 then the shorter leg has length  5.5 , 6.5 , 7.5.

To find : What is the length of the other leg and hypotenuse ?

Solution :

For a  30-60-90 triangle, sides are in the ratio  [tex]1:\sqrt{3}:2[/tex]

where, 1 is the shorter side,  

[tex]\sqrt{3}[/tex] the other side

and 2 the hypotenuse.

Short leg = 5.5

Other leg = [tex]5.5\times \sqrt3=5.5\sqrt3[/tex]

Hypotenuse = [tex]5.5\times 2=11[/tex]

Short leg = 6.5

Other leg = [tex]6.5\times \sqrt3=6.5\sqrt3[/tex]

Hypotenuse = [tex]6.5\times 2=13[/tex]

Short leg = 7.5

Other leg = [tex]7.5\times \sqrt3=7.5\sqrt3[/tex]

Hypotenuse = [tex]7.5\times 2=15[/tex]

Final answer:

In a 30-60-90 triangle with a hypotenuse of 15, the shorter leg has a length of 7.5, based on the ratio 1:√3:2.

Explanation:

If the hypotenuse of a 30-60-90 triangle has length 15, then to find the length of the shorter leg, we can use the properties of this special right triangle. In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. In other words, if the shorter leg is 'x', the longer leg is 'x√3', and the hypotenuse is '2x'.

Since the hypotenuse is 15, we set '2x' equal to 15 and solve for 'x':

2x = 15

x = 15 / 2

x = 7.5

The shorter leg of the triangle has a length of 7.5.

Answer:

4.73

Step-by-step explanation:

4 8/11=4+8/11

=4/1+811

=(4/1×11/11)+8/11

=44/11+8/11=52/11

We know that

52/11

is the same as

52÷11

Then using

Long Division for 52 divided by 11

and rounding to a Max of 2 Decimal Places gives us

=4.73

Final answer:

The equivalent decimal to the mixed number 4 8/11 is 4.7273, achieved by dividing 8 by 11 to get 0.7273 and adding it to the whole number 4.

Explanation:

To write the mixed number 4 8/11 as a decimal, we need to convert the fractional part to decimal form and then add it to the whole number. To convert the fraction 8/11 to a decimal, we divide the numerator by the denominator using a calculator or long division.

Dividing 8 by 11 gives us approximately 0.7273. Now we add this decimal to the whole number 4 to get the decimal equivalent of the mixed number. The final result is 4.7273.

Remember that when rounding to four decimal places, if necessary, you look at the fifth decimal place to determine whether to round up or leave the fourth place as is. Since we do not have a fifth decimal place in this conversion, our four-decimal-place number is accurate as is.

Answer:

Part A

Months, Pounds

3,5

4,9

5,13

6,17

7,21

8,25

9,29

Part B

1 year = 12 months

If we continue the chart it would look like this:

10,33

11,37

12,41

Lucky will weigh 41 pounds by 1 year.

Hope this helps!

Final answer:

Lucky will weigh 41 pounds by the time he is one year old.

Explanation:

To complete the table representing Lucky’s current weight as a function of his age, we'll calculate Lucky's expected weight at each month by using the growth rate of four pounds per month. Starting with Lucky's current weight at three months old, which is five pounds:

Age 4 months: 5 pounds + (1 month * 4 pounds/month) = 9 pounds

Age 5 months: 5 pounds + (2 months * 4 pounds/month) = 13 pounds

Age 6 months: 5 pounds + (3 months * 4 pounds/month) = 17 pounds

Age 7 months: 5 pounds + (4 months * 4 pounds/month) = 21 pounds

Age 8 months: 5 pounds + (5 months * 4 pounds/month) = 25 pounds

Age 9 months: 5 pounds + (6 months * 4 pounds/month) = 29 pounds

Continuing with the growth rate of four pounds per month, by the time Lucky is one year old, which is 12 months, the calculation would be:

Lucky's weight at one year old = initial weight + (growth over months)

12 months old: 5 pounds + (9 months * 4 pounds/month) = 41 pounds.

Answer:

Yes

Can I get brainliest

Answer:

Yes, I believe so.

Step-by-step explanation:

Answer:4/5

The required probability that the randomly picked counter is green is 4/5

According to the problem,

So, 16 green counters are the favorable cases.

∴ Required probability = 16/20 = 4/5

Find more about "Probability" here : https://brainly.com/question/25870256

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Answer:

3/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, convert 3/5 into 10ths.

3/5 = 6/10

Now, we know what 3/5 is equal to, we subtract.

9/10 - 6/10 = x

When we subtract, we get 3/10.

So that means, x =3/10

Hope this helps, have a great day, and stay safe.

Answer:

625 miles

Step-by-step explanation:

This is because, since each 25 miles takes one gallon 25 gallons would mean you would go 25 times 25 miles which is 625 miles in all.

Answer:

A-168

B-81

C-117

Step-by-step explanation:

you multiply all of the numbers together.

Answer:

8 in

Step-by-step explanation:

The ratio of sides and perimeter in similar figures are equal.

let x be the perimeter of the smaller figure, then by proportion

[tex]\frac{7}{28}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )

7x = 56 ( divide both sides by 7 )

x = 8

The perimeter of the smaller pentagon is 8 in

Answer:

3

Step-by-step explanation:

The average rate of change of g(x) in the closed interval [ a, b ] is

[tex]\frac{g(b)-g(a)}{b-a}[/tex]

Here [ a, b ] = [ - 3, 2 ], thus

g(b) = g(2) = - 2² + 2(2) + 8 = - 4 + 4 + 8 = 8

g(a) = g(- 3) = - (- 3)² + 2(- 3) + 8 = - 9 - 6 + 8 = - 7

average rate of change = [tex]\frac{8-(-7)}{2-(-3)}[/tex] = [tex]\frac{15}{5}[/tex] = 3

Answer:

31000 cm2

Step-by-step explanation:

Answer:

x > (c - a)/b

Step-by-step explanation:

a > -bx + c

We need to make x the subject of the inequality so, first remove c from the right hand side of the inequality by adding -c to both sides. So,

a - c > -bx

Now, we need to remove -b from the right hand side. So, we will divide both sides of the inequality with -b. Multiplying the inequality with a negative number will also change the sign of the inequality. So,

-(a-c)/b < x

x > (c - a)/b

Answer:

C on edge

Step-by-step explanation:

Answer:

The stereo is now being sold for $227.80.

Step-by-step explanation:

To calculate percentage discounts, multiply the original price (268) by the discount percentage (.85). Make sure to put move the percentage value two places to the right before multiplying, as percentages are percentages of a whole.

268 * .85 = 227.8

Answer:

135 grams

Step-by-step explanation:

Since there are 15 grams of powder in a 22oz serving, if you divide 198 by 22 you will get 9 total servings. If you multiply 15 by 9 you will get 135 total grams.

Answer:

Take the coefficient of ''n'', divide it by 2, and raise it to the second power;

[tex]n^2+n+(\frac{1}{2})^2[/tex]

[tex]n^2+n+\frac{1}{4}=0[/tex]

[tex]=(n+\frac{1}{2} )^2[/tex]

Answer:

it is repeating decimal.

Answer: repeating

Step-by-step explanation:

Answer:

adding salt makes the water freeze slower and evaporate slower too.

Step-by-step explanation:

While pure water freezes at 0°C (32°F), salt water needs to be colder before it freezes and so it usually takes longer to freeze. The more salt in the water, the lower the freezing point.

Answer:

1) [tex]\frac{8\pi }{3}[/tex] or 8.38

2) [tex]\frac{9\pi }{8}[/tex] or 3.53

3) 4[tex]\pi[/tex] or 12.57

Step-by-step explanation:

The formula for arc length is [tex]2\pi r(\frac{angle}{360})[/tex]

1) 2[tex]\pi[/tex](4)× [tex]\frac{120}{360}[/tex]

2)[tex]2\pi (1.5)[/tex]×[tex]\frac{135}{360}[/tex]

3) [tex]2\pi(3)[/tex]×[tex]\frac{240}{360}[/tex]

To find the surface area of a 10-quarter stack, calculate the surface area of each quarter and then multiply by the number of quarters.

To find the surface area of a 10-quarter stack, we need to calculate the surface area of each quarter and then multiply it by the number of quarters in the stack. The surface area of a quarter can be calculated using the formula for the surface area of a cylinder: SA = 2πr^2 + 2πrh.

Since the diameter of a quarter is 2.2 cm, the radius (r) is half of that, which is 1.1 cm. The approximate height (h) of a quarter is 0.17 cm.

Substituting these values into the formula, we get: SA = 2π(1.1 cm)^2 + 2π(1.1 cm)(0.17 cm). Calculating this gives us the surface area of a single quarter. Then, multiplying it by 10 gives us the surface area of a 10-quarter stack.