5. How can you use the Distributive Property to
factor the expression 6x + 15?

Answer:

B. 6k^11

Step-by-step explanation:

2k^8 • 3k^3

The • sign means

multiplication

So 2k^8 x 3k^3

6k^8+3

6k^11

Answer:  Rock particles clump together in aggregate

Step-by-step explanation:

Soil minerals form the basis of soil. They are produced from rocks (parent material) through the processes of weathering and natural erosion. Water, wind, temperature change, gravity, chemical interaction, living organisms and pressure differences all help break down parent material.

Answer:

D

Step-by-step explanation:

Answer:

After 2 hrs canoe rentals and kayak rentals cost would be same.

Step-by-step explanation:

Let the number of hours be 'x'.

Given:

Set up fee for Kayak rental = $5

Hourly rate for Kayaks rental = $8

Solution:

First we will find the total cost of Kayak rentals.

total cost of Kayak rentals can be calculated by sum of Set up fee for Kayak rental and Hourly rate for Kayaks rental multiplied by number of hours.

framing in equation form we get;

total cost of Kayak rentals = [tex]5+8x[/tex]

Now Given:

Set up fee for Canoe rental = $9

Hourly rate for Canoe rental = $6

Now we will find the total cost of Canoe rentals.

total cost of Canoe rentals can be calculated by sum of Set up fee for Canoe rental and Hourly rate for Canoe rental multiplied by number of hours.

framing in equation form we get;

total cost of Canoe rentals = [tex]9+6x[/tex]

Now to find the number of hours when both rentals would cost same we will make both the equation equal we get;

[tex]5+8x=9+6x[/tex]

Combining like terms we get;

[tex]8x-6x=9-5\\\\2x=4[/tex]

Now Dividing both side by 2 we get;

[tex]\frac{2x}{2}=\frac{4}2\\\\x=2\ hrs[/tex]

Hence After 2 hrs canoe rentals and kayak rentals cost would be same.

Final answer:

To find when the cost of renting a canoe equals the cost of renting a kayak, we set up an equation for each rental's cost, equalize them, and solve for the number of hours. It takes 2 hours for both to cost the same.

Explanation:

To determine the number of hours it takes for canoe rentals and kayak rentals to cost the same amount, we can set up an equation based on the cost structures provided:

If we let h be the number of hours, the costs for both rentals can be expressed as $5 + 8h (kayak) and $9 + 6h (canoe). To find when they cost the same, we can set these expressions equal to each other:

5 + 8h = 9 + 6h

Now, let's solve for h:

Subtract 6h from both sides to get the terms involving h by themselves:

5 + 8h - 6h = 9 + 6h - 6h

5 + 2h = 9

Next, subtract 5 from both sides to solve for h:

2h = 9 - 5

2h = 4

Finally, divide both sides by 2:

h = 4 / 2

h = 2

The number of hours it takes for the cost of renting a canoe and a kayak to be the same is 2 hours.

x = –6

Solution:

Given expression is [tex]\sqrt[3]{x-2}+5=3[/tex].

Step 1: Isolate the radical by subtracting 5 from both sides of the equation.

[tex]\Rightarrow\sqrt[3]{x-2}+5-5=3-5[/tex]

[tex]\Rightarrow\sqrt[3]{x-2}=-2[/tex]

Step 2: Cube both sides of the equation to remove the cube root.

[tex]\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3[/tex]

Cube and cube root get canceled in left side of the equation.

[tex]\Rightarrow\ x-2=-8[/tex]

Step 3: To solve for x.

Add 2 on both sides of the equation.

[tex]\Rightarrow\ x-2+2=-8+2[/tex]

[tex]\Rightarrow\ x=-6[/tex]

Hence the solution is x = –6.

Answer:

Segment addition postulate justify the statement if D is between A and B then Ad plus DB equals Ab

Step-by-step explanation:

This postulate states that if two points A and B are given and third point D lies on line segment AB only if distance between the points satisfy the equations AD+DB=AB.

Answer:

Segment Addition Postulate

Step-by-step explanation:

The whole line segment would be AB. The midpoint of the line segment would be D. If we add AD (the first portion of the line segment), and DB (the second portion of the line segment), then we get AB (A-D-B)

Representation:

              (AD)                    (DB)

|--------------------------|---------------------------|

A                            D                             B

|------------------------------------------------------|

                   (line segment AB)

Answer:

awnser b

Step-by-step explanation:

Volume of the hexagonal prism = 1732.7772 ft³

Solution:

Height of the prism (H) = 15.4 ft

Side of the hexagon base (b) = 6.58 ft

Height from center to the side length (h) = 5.7 ft.

Let us first find the area of the base.

Area of the base (B) =  [tex]6\times\frac{1}{2}\ bh[/tex]

                                 [tex]$=6\times\frac{1}{2}\times 6.58 \times 5.7[/tex]

Area of the base (B) = 112.518 ft²

To find the volume of the hexagonal prism:

Volume of the hexagonal prism = Area of the base × Height

                                                     = 112.518 × 15.4

                                                     = 1732.7772 ft³

The volume of the hexagonal prism is about 1732.7772 ft³.

Answer:

18m by 12m

Step-by-step explanation:

Check attachment

I hope this was helpful, Please mark as brainliest

Answer:length is 18m and breadth is 12m

Step-by-step explanation:see attachment for detailed explanation

Answer:

I believe 4.5, 2 and 1/2

Answer:

4.5 , 2 , 1/2

Step-by-step explanation:

Because if you multiply 5 by 0.9, which is less than 1, you will get 4.5

If you multiply 5 by 0.4, which is less than 1, you will get 2

And finally if you multiply 5 by 0.1, which is less than 1, you will get 1/2

The equation of line is [tex]y+3=2(x+2)[/tex]

Option A is correct.

Step-by-step explanation:

We need to find the equation of the line.

Looking at the graph the two points are: (2,5) and (-2,-3)

We will first find the slope of these points using formula:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here x₁ = -2, y₁=-3, x₂=2 and y₂=5

Putting values and finding slope

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{5-(-3)}{2-(-2)}\\Slope=\frac{8}{4}\\Slope=2[/tex]

So, slope of the line is 2.

Considering that both lines are parallel (as not given in question). both lines will have same slope.

Now using Point slope form to find the equation.

[tex]y-y_1=m(x-x_1)[/tex]

Using point (-2,-3) and slope m= 2

[tex]y-y_1=m(x-x_1)\\y-(-3)=2(x-(-2))\\y+3=2(x+2)[/tex]

So, the equation of line is [tex]y+3=2(x+2)[/tex]

Option A is correct.

Answer: [tex]diameter=38\ in[/tex]

Step-by-step explanation:

Based on the picture I assume that the exercise asks for the diameter of the sphere.

So, it is necessary to remember the following:

1.  the volume of a sphere can be calculated with the following formula:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

2. The radius is twice the diameter.

So, knowing that the volume of the sphere is:

[tex]V=9,145.33\pi\ in^3[/tex]

You can substitute them into the equation and then solve for "r" in order to find its value:

[tex]9,145.33\pi\ in^3=\frac{4}{3}\pi r^3\\\\\frac{(3)(9,145.33\pi\ in^3)}{4\pi}=r^3\\\\\sqrt[3]{\frac{(3)(9,145.33\pi\ in^3)}{4\pi}}=r\\\\r=19\ in\\\\[/tex]

Then, the diameter is:

[tex]d=2r\\\\d=2(19\ in)\\\\d=38\ in[/tex]

Replace a and b with the given values:

3.14(3^2 + 3x4)

Simplify:

3.14(9 +12)

3.14(21)

Multiply:

3.14 x 21 =65.94

the car trave after 12 minute in mile

the car travels 8 miles after 12 minutes.

To find out how far the car travels after 12 minutes, we first need to determine the time interval that includes 12 minutes. From the table, we see that the time intervals are spaced by 10 minutes each.

Since 12 minutes falls between 10 and 20 minutes, we need to find the corresponding distance for this time interval.

Given that the car travels at a constant speed, we can see that the distance traveled in each time interval is constant.

From the table:

- From 0 to 10 minutes, the car travels 8 miles.

- From 10 to 20 minutes, the car also travels 8 miles.

Therefore, if the car travels 8 miles in the first 10 minutes, it would also travel 8 miles in the next 2 minutes (from 10 to 12 minutes).

So, the car travels 8 miles after 12 minutes.

The complete Question is given below:

A car travels at a constant speed. The table shows the distance y (in miles) that the car travels after x minutes. How far does the car travel after 12 minutes?

Time(minutes),  x  0 | 10 | 20 | 30

Distance(miles), y 0 | 8   | 16  | 24

Step-by-step explanation:

Let the width be x feet.

Therefore, length = 2x - 10

Perimeter of rectangle = 52

[tex]2(2x - 10 + x) = 52 \\ 2(3x - 10) = 52 \\ \therefore \: 3x - 10 = \frac{52}{2} \\ \therefore \: 3x - 10 = 26\\ \therefore \: 3x = 26 + 10\\ \therefore \: 3x = 36 \\ \therefore \: x = \frac{36}{3} \\ \therefore \: x = 12 \\ \purple{ \boxed{\therefore \: width \: of \: rectangle = 12 \: feet }}[/tex]

The system of equations to represent each student comment is:

2x - y = 5

x - y = -9

Solution:

Let "x" be the score point of Elena

Let "y" be the score point of Koran

Elena says, “You earned so many more points than I did

If you earned 5 more points, your score would me twice mine

Which means,

Koran score + 5 = twice of Elena

y + 5 = 2x

Rearranging it we get,

2x - y = 5 ------- eqn 1

Kiran says, “Oh, I don’t think I did that much better

I only scored 9 points higher than you did

Elena score + 9 = Koran score

x + 9 = y

Rearranging it we get,

x - y = -9 --------- eqn 2

Thus eqn 1 and eqn 2 represents eacch student comment

The system of equations which represents the scenario described based on the statements made by kiran and Elena are :

Representing their scores using variables :

Using Elena's statement :

Kiran's score + 5 = Elena's score × 2

y + 5 = 2x

2x - y = 5 - - - - - - (1)

Using Kiran's statement :

y = x + 9

x - y = - 9 - - - - - (2)

Hence, the system of equation is (1) and (2)

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Margo will pay $1.5 in interest after borrowing $100 at an annual interest rate of 6% for 6 months, using the simple interest formula I = PRT.

To calculate the interest Margo will pay after 6 months on a $100 loan with an annual interest rate of 6%, we have to first convert the annual rate to a semiannual rate because interest is being calculated for half a year. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount ($100), R is the rate of interest per period, and T is the time the money is borrowed for, in years.

In this case, R would be 6% per year, or 0.06 (when converted to a decimal). However, since only half a year (which is 6/12 or 0.5 years) has passed, we will need to adjust this interest rate by half, resulting in R = 0.03 for 6 months. We then calculate the interest I using the formula:

I = PRT = $100 * 0.03 * 0.5 = $1.5

Therefore, Margo will pay $1.5 in interest after 6 months.

f(x) = 3x + 3

Solution:

Let us take f(x) = y.

The points indicated in the graph are (0, 3) and (–2, –3).

Slope(m) of the line passing through two points formula:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points in the above formula,  

[tex]$m=\frac{-3-3}{-2-0}[/tex]

    [tex]$=\frac{-6}{-2}[/tex]

m = 3

constant is the y-intercept which implies c = 3.

The equation of a line standard form is y = mx + c.

y = 3x + 3

The equation of a line is

f(x) = 3x + 3

Answer:

The correct option is 7.5

Therefore the length of BE is 7.5 units

Step-by-step explanation:

Given:

AB || CD

AE = 5

DE = 2

EC = 3

DC = 1.5

To Find:

BE = ?

Solution:

In Δ ABE and Δ DCE

∠ABE ≅ ∠DCE …………..{ Alternate angles are equal since AB || CD }  

∠AEB ≅ ∠DEC ……….....{Vertical opposite angles are equal}  

Δ ABE ~ Δ DCE….{Angle-Angle Similarity test}  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}=\dfrac{AB}{DC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{BE}{CE} =\dfrac{AE}{DE}[/tex]

[tex]\dfrac{BE}{3}=\dfrac{5}{2}\\\\BE=\dfrac{15}{2}=7.5[/tex]

Therefore the length of BE is 7.5 units

The least number of tabke that will seat all the bus members is 17.

To find the least number of tables needed to seat all 130 people, you can divide the total number of people by the number of people each table can seat (8).

Number of tables = Total number of people / Number of people per table

Number of tables = 130 / 8

Number of tables = 16 tables with 2 people left over

To seat all 130 people, you would need at least 17 tables.

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To find the least number of tables needed to seat all 130 people, you divide 130 by 8, and then round up to the nearest whole number. This gives you a total of 17 tables.

The subject of this question is a Mathematics problem, specifically a division problem involving the concept of rounding up. You are asked to determine the least number of tables needed to seat all 130 people, given that each table can seat 8 people.

In order to solve this problem, you need to divide the total number of people by the number of people that can be seated at each table (130 ÷ 8 = 16.25). Because you can't have a fraction of a table, you round this value up to the nearest whole number. Thus, you will need 17 tables to seat all 130 people.

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Answer:

[tex]They\ will\ meet\ after\ 5.43\ hours\ or\ 5\ hours\ 25.8\ minutes.[/tex]

Step-by-step explanation:

[tex]Let\ they\ meet\ after\ x\ hours.[/tex]

Distance covered by Karissa:

[tex]Speed=12\ mph\\\\Time=x\ hours\\\\Distance=speed\times time\\\\Distance=12\times x\\\\Distance=12x[/tex]

Distance covered by Erin:

[tex]Speed=9\ mph\\\\Time=x\ hours\\\\Distance=speed\times time\\\\Distance=9\times x\\\\Distance=9x[/tex]

Total distance:

[tex]Total\ distance=114\ miles\\\\Total\ distance=Distance\ covered\ by\ Karissa+Distance\ covered\ by\ Erin\\\\Total\ distance=12x+9x\\\\12x+9x=114\\\\21x=114\\\\x=\frac{114}{21}\\\\x=5.43\ hours[/tex]

Answer: No.

Step-by-step explanation:

If you divide 54183 by each number, it would be in decimal form.

Answer:

No

Step-by-step explanation:

Final answer:

The librarian receives a total of 214 books, with the first box containing 136 books and the second box containing 78 books (58 fewer than the first).

Explanation:

To find the total number of books the librarian receives, we first need to determine how many books are in the second box. We are told that the second box has 58 fewer books than the first box, which contains 136 books. Therefore, we can calculate the number of books in the second box by subtracting 58 from 136.

The calculation for the second box will be: 136 books - 58 books = 78 books.

To find the total number of books, we then add the number of books in the first box to the number of books in the second box:

Total books = 136 books + 78 books = 214 books.

Thus, the librarian receives a total of 214 books.

Final answer:

Subtract 58 from 136 to find the number of books in the second box (78 books), then add the number of books from both the first and the second box to get the total (214 books).

Explanation:

The student has asked how to calculate the total number of books a librarian receives if the first box contains 136 books and the second box contains 58 fewer books than the first. To find the number of books in the second box, we subtract 58 from 136, which gives us 78 books. To find the total number of books received, we then add the number of books in both boxes together: 136 books from the first box plus 78 books from the second box equals 214 books in total.

Answer:

975,462.00000

Step-by-step explanation:

975,462 rounded to hundred thousand

The number 975,462 rounded to the nearest hundred thousand is 1,000,000 because the ten thousand digit (7) is more than 5.

To round the number 975,462 to the nearest hundred thousand, you have to look at the ten thousand digit. In this case, that's 7. If this digit is 5 or more, you round up the hundred thousand digits. If it is less than 5, you leave the hundred thousand digits as it is. In our number, the ten thousand digit is 7, so we round up the hundred thousand digit which is 9 to 10. Since there is no '10' in the digit system, it overflows to the next digit, making it 1,000,000. So, 975,462 rounded to the nearest hundred thousand is 1,000,000.

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Answer:

The information you'll include is the amount of spaces moved from ABC to form A'B'C' which will be based on the opposite side.

To describe a translation of triangle ABC, you need to identify the direction and distance of the translation. The triangle's shape, size, and orientation remain the same after translation.

In describing a translation of triangle ABC, you would include the direction and distance of the translation. The direction could be up, down, left, or right. The distance would determine how far the triangle moves from its original position.

For instance, you may describe a translation as moving the triangle ABC 3 units to the right and 2 units down. It's important to note that under a translation, the shape of the triangle does not change. The size, shape, and orientation of triangle ABC remain consistent in the translated image.

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Answer:

im not sure but I think it's 1.5

Answer:

7:15

Step-by-step explanation:

21:45

21/3 = 7 and 45/3 = 15

Thus, 21:45 ratio simplified is 7:15

Answer: They are 37 feet apart each other

Step-by-step explanation:

We are told that two divers are at a certain distance between them. The first diver is at a depth of 122 ft and the second diver is at a depth of 159 feet.

Note we are talking about depth, since both divers are below sea level.

Now, if we want to know the distance that separates them, we only have to take the difference between both depths:

[tex]159 ft-122 ft=37 ft[/tex] This is the distance beweent both divers.

This means they have to reduce their distance by 2 feet in order to accomplish the safety rules.

Answer:

C) 19

Step-by-step explanation:

9+10 = 19

Answer:

B) 21

Step-by-step explanation:

Because 3×3=9 and 2×5=10

If you switch it, 3×2 and 3×5, that is equal to 6 and 15.

6+15=21

Answer:

C)  [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given:

Number of freshmen = 3

Number of sophomores =3

Number of juniors =3

Number of seniors = 3

The team's captain is randomly selected from any grade level.

To find the the probability that a freshman will not be selected as captain.

Solution:

Total number of members in the team = [tex]3+3+3+3[/tex] = 12

Probability that a freshman will be selected as captain will be:

⇒   [tex]\frac{Number\ of\ freshmen}{Total\ members}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Reducing to simple fraction by dividing numerator and denominator by 3.

⇒ [tex]\frac{3\div3}{12\div 3}[/tex]

⇒ [tex]\frac{1}{4}[/tex]

Thus, probability that a freshman will not be selected as captain will be given as:

⇒ [tex]1-\frac{1}{4}[/tex]

Taking LCD.

⇒ [tex]\frac{4}{4}-\frac{1}{4}[/tex]

Subtracting the numerators.

⇒ [tex]\frac{3}{4}[/tex]     (Answer)

Answer:

c

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

4 elephants = 1 blue whale

4 blue whales = 1 tree = 16 elephants

2 trees = 1 monument = 32 elephants

The Washington Monument is 32 elephants tall.

To determine how many elephants tall the Washington Monument is, we need to set up a proportion using the given comparisons between elephants, blue whales, Redwood trees, and the Washington Monument.

First, let's establish the individual proportions:

1 blue whale = 4 elephants in length.

1 Redwood tree = 4 blue whales in height.

1 Washington Monument = 2 Redwood trees in height.

Now we can combine these proportions to find out how many elephants equal the height of one Washington Monument:

1 Washington Monument = 2 (Redwood trees) = 2 * 4 (blue whales) = 2 * 4 * 4 (elephants) = 8 * 4 elephants = 32 elephants.

Thus, the Washington Monument is 32 elephants tall.

Answer:

202 times with a remainder of 5 but if you need an exact number that i would go with 203 because if you round it up

Step-by-step explanation: