What is the sum of the infinite geometric series?

Answer: B. on e2020

Step-by-step explanation:

The transformation of parent function to h(x) = - ∛x + 3 is such that it is reflected over the horizontal axis, and then translated up 3 units.

The correct option is B.

Transformations are changes done in the shapes on a coordinate plane by rotation or reflection or translation.

Given function,

h(x) = - ∛x + 3

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis

Parent Function: f(x) = ∛x

Horizontal Shift: None

Vertical Shift: Up 3 Units

Reflection about the x-axis:

f(x) → -f(x)

∛x → - ∛x  

Reflection of the function is over x - axis.

Hence, the transformation from the parent equation to given function can be found  by reflecting over X- axis and translate up 3 units.

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Answer:

A. 90.5 cubic meters pet second.

B. 3.77 square meters per second.

C.  [tex]\frac{dV}{dS} = \frac{r}{2}[/tex]

Step-by-step explanation:

The radius of a sphere is increasing at a constant rate of 0.05 meters per second.

Therefore, [tex]\frac{dr}{dt} = 0.05[/tex] ......... (1)

A. Now, volume of the sphere is given by  

[tex]V = \frac{4}{3}\pi  r^{3}[/tex]

Now, differentiating both sides with respect to t we get,

[tex]\frac{dV}{dt} = \frac{4}{3}\pi (3r^{2}) \frac{dr}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]

Then at r = 12 meters, the rate of increase in volume will be

[tex]\frac{dV}{dt} = 4 \times (\frac{22}{7}) \times 12^{2} \times 0.05 = 90.5[/tex] cubic meters pet second. {From equation (1)}

B. When the volume of the sphere is 36π cubic meters, then  

[tex]\frac{4}{3}\pi r^{3} = 36\pi[/tex]

⇒ [tex]r^{3} = 27[/tex]

⇒ r = 3 meters.

Now, surface area of a sphere is given by  

S = 4πr² .......... (2)

Differentiating both sides with respect to time (t) we get,

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt} = 8 \times (\frac{22}{7}) \times 3 \times 0.05 = 3.77[/tex] square meters per second. {From equation (1)}

C. Now, [tex]V = \frac{4}{3}\pi  r^{3}[/tex] and S = 4πr²

⇒ [tex]V = \frac{1}{3} (4\pi r^{2})r = \frac{Sr}{3}[/tex]

Now, differentiating with respect to S both sides we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{S}{3} \frac{dr}{dS}[/tex] ......... (3)

Now, we have, S = 4πr²

Differentiating with respect to S both sides, we get

[tex]1 = 8\pi r\frac{dr}{dS}[/tex]

⇒ [tex]\frac{dr}{dS} = \frac{1}{8\pi r }[/tex] ......... (4)

Now, from equations (2), (3) and (4) we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{4\pi r^{2} }{3} \times \frac{1}{8\pi r }[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{3} + \frac{r}{6}[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{2}[/tex] (Answer)

Question:

C. Express the rate at which the volume of the sphere changes with respect to the surface are of the sphere (as a function of r)

Step-by-step explanation:

Here's how you solve part C of this question.

Start with what you know:

dV/dt = 4pir^2 x (dr/dt)

(dr/dt) = 0.05

S(r) = (Surface Area) = 4pir^2

So, since S(r) is equal to 4pir^2, we replace 4pir^2 with S(r). We also know that (dr/dt) = 0.05, so we replace (dr/dt) with 0.05.

Now the equation should look like this:

dV/dt = 0.05 x S(r) <----- (your answer).

Hope this helped!! :)

The statements which are true are:

(6, 6) is the midpoint of CD

(4, 3) is the intersection point of diagonals of parallelogram

Solution:

The mid point (x,y) = [tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

A(-2, -1) and B(6, 1)

[tex]\text{ midpoint of AB } = (\frac{-2+6}{2} , \frac{-1+1}{2})\\\\\text{ midpoint of AB } = (2, 0)[/tex]

Thus statement 1 is wrong

B(6, 1) and C(10, 7)

[tex]\text{ midpoint of BC } = (\frac{6+10}{2} , \frac{1+7}{2})\\\\\text{ midpoint of BC } = (8, 4)[/tex]

Thus statement 2 is wrong

Here ,

[tex]x_1[/tex] = 10

[tex]x_2[/tex]= 2

[tex]y_1[/tex]= 7

[tex]y_2[/tex]=5

now substituting these values,

mid point of CD  = [tex](\frac{10+2}{2},\frac{7+5}{2})[/tex]

mid point of CD  = [tex](\frac{12}{2},\frac{12}{2})[/tex]  

mid point of CD  = [tex](6, 6)[/tex]

Therefore (6, 6) is the midpoint of CD

Statement 3 is correct

A = (-2, -1) and D = (2, 5)

[tex]\text{ mid point of AD } = (\frac{-2+2}{2} , \frac{-1+5}{2})\\\\\text{ mid point of AD } = (0, 2)[/tex]

Thus statement 4 is wrong

Let AC and BD be the diagonals of parallelogram

The diagonals of a parallelogram bisect each other, therefore, the point of intersection is the midpoint of either.

Midpoint of AC:

A = (-2, -1) and C(10, 7)

[tex]\text{ Midpoint of AC } = (\frac{-2+10}{2} , \frac{-1+7}{2})\\\\\text{ Midpoint of AC } = (4,3)[/tex]

Thus statement 5 is correct

√12x^3÷√6x

Factor 6 out of both the numerator and denominator:

√2x^3÷√x

Cancel out common factors to get:

√2x^2

Pull the terms out from under the radical to get:

D. x√2

Answer:

$1.40

Step-by-step explanation:

40 times 30% = 28 because 30% of 40 is 12 so 40-12 =28

28 times .05= 1.40 which  is the tax of  the final total

Answer:140

Step-by-step explanation:

Answer:

189

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

(x+4)/3=6

Multiply by 3 on both sides

x+4=18

Subtract 4 from both sides

x=14

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Answer:

3x ≥ 2 + 2x

Step-by-step explanation:

Given:

[tex]x\geq 2[/tex]

Solution:

Now, we have to write an inequality with x on both sides whose solution is x is greater than or equal to 2.

[tex]x\geq 2[/tex]

Now we add 2x on both side.

[tex]x + 2x\geq 2 + 2x[/tex]

[tex]3x\geq 2 + 2x[/tex]

Therefore, the inequality which has a solution x ≥ 2 is:

3x ≥ 2 + 2x

Answer:

The scale factor is 2.

Step-by-step explanation:

Take the vertical sides of the 2 triangles.

Their length is 3 and 6 so the scale factor is 6/3 = 2.

Also we see than the horizontal lines are in the same ratio 4 : 2  = 2:1.

Answer: 301

Step-by-step explanation:

the least amount one of the wrestlers could weigh is 301.

The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given that,

Mean μ = 265,

Standard deviation σ = 28 lbs.

Let the least amount one of the wrestlers could weigh is x.

To find x such that P(X≥x) = 0.10

1 - P(X<x) = 0.10

P(X<x) = 1 - 0.10

P(X<x) = 0.90

z for area = 0.90 in equal to 1.28 in statistical table,

z = 1.28

Use  formula, to find the value of x,

x = μ + z × σ

x = 265 + 1.28 × 28

x = 265 + 35.84

x = 300.84

x = 301(Rounded to the nearest integer)

The required value of x is 301.

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Answer:

There are 7 chairs in each row.

Step-by-step explanation:

Hue is arranging some number of chairs. If she arranges them in 6 rows of equal lengths then there will be 3 chairs leftover, or she arranges them in 8 rows of that same length then she requires 11 more chairs.

Let us assume that there are P numbers of chairs and there are x chairs in each row.

Therefore, we can write that  

6x + 3 = P ....... (1) and  

8x = P + 11  

⇒ 8x - 11 = P ........ (2)

Now, from equations (1) and (2) we get,

6x + 3 = 8x - 11

⇒ 2x = 14

⇒ x = 7

Therefore, there are 7 chairs in each row. (Answer)

Answer:

Circumcenter describes the point equidistant to the refrigerator, stove and the sink

Step-by-step explanation:

The basic construction of the circumcenter is to identify the midpoints of the original triangle. This circumcenter is the point where all the perpendicular bisector of the sides of the triangle intersects. For an triangle that is  acute-angled, its circumcenter will lie inside the triangle. For an obtuse-angled triangle, the circumcenter lies outside of the triangle

, In a right-angled triangle, Circumcenter lies at the midpoint of the hypotenuse side of triangle.

To Find the circumcenter of the triangle

Answer:

Circumcenter

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=2and y=−1

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Answer:

x=2, y = -1

Step-by-step explanation:

Given the system of equation;

5x + y = 9 ... (1)

3x + 2y = 4 ...(2)

We will solve it simultaneously to get variables x and y.

Using substitution method,

From equation 1, y = 9-5x ...(3)

Substituting equation 3 into 2 we will have;

3x + 2(9-5x) = 4

3x + (18-10x) = 4

3x + 18 -10x = 4

3x-10x+18 = 4

-7x+18 = 4

-7x = 4-18

-7x =-14

Dividing both sides by -7, we will have;

-7x/-7 = -14/-7

x = 2

Substituting x = 2 into equation 1 to get y we will have;

5x+y= 9

5(2) + y = 9

10+y = 9

y = 9-10

y = -1

Therefore x = 2 and y = -1 is the solution to the simultaneous equation.

The coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

Next, we need to reflect ∆CDE across the line x = 0. This me The vertices of ∆CDE are C(–5, 3), D(–6, 1), and E(–1.5, 2). Which figure shows the image of ∆CDE for a glide reflection where the translation is (x, y) → (x, y – 3) and the line of reflection is x = 0?

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

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Step-by-step explanation:

equation -

(X+7) (x-1) =0

equation = x2 -x -7x -7 = x2 -8x -7

standard form = x2 -8x -7

factor form = (x+7) (x-1)

Answer:2³*3²

Step-by-step explanation:

Answer:

r=-2

Step-by-step explanation:

difference in y/difference in x =slope

-r-8/1-2=-9

-r-8=-9*-1

-r=10+8

r=-2

The shoot would last eight hours, and the cost would be $699 whether the photographer hires Craig or Kaya.

This question can be solved using algebra, particularly the concept of system of equations, where we set two linear cost equations equal to each other to find out when they cost the same. Given: Craig's cost is $195 + $63p, and Kaya's cost is $171 + $66p, we form an equation $195 + $63p = $171 + $66p. Subtracting $171 and $63p from both sides leaves us with $24 = $3p. So, dividing both sides by $3, we get p = 8.

This means the photo shoot would last 8 hours, and the cost would be either Craig's or Kaya's cost for 8 hours, which is $195 + $63*8 = $699 or  $171 + $66*8 = $699.

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The cost for the photo shoot would be $699, and the duration of the shoot would be 8 hours.

Let's denote:

- [tex]\( C_C \)[/tex]: Total cost if the photographer hires Craig.

- [tex]\( C_K \)[/tex]: Total cost if the photographer hires Kaya.

- [tex]\( h \)[/tex]: Number of hours of the photo shoot.

Given the charges:

- Craig charges $195 for showing up, plus $63 per hour.

- Kaya charges $171 for showing up, plus $66 per hour.

The equations for the total cost [tex]\( C_C \)[/tex] and [tex]\( C_K \)[/tex] are:

[tex]\[ C_C = 195 + 63h \][/tex]

[tex]\[ C_K = 171 + 66h \][/tex]

The photographer realizes that the costs are the same, so:

[tex]\[ C_C = C_K \][/tex]

Substitute the expressions:

[tex]\[ 195 + 63h = 171 + 66h \][/tex]

Now, solve for [tex]\( h \)[/tex]:

[tex]\[ 195 - 171 = 66h - 63h \][/tex]

[tex]\[ 24 = 3h \][/tex]

[tex]\[ h = \frac{24}{3} \][/tex]

[tex]\[ h = 8 \][/tex]

So, the duration of the photo shoot is 8 hours.

Now, substitute [tex]\( h = 8 \)[/tex] back into either equation to find the cost:

Using [tex]\( C_C \)[/tex]:

[tex]\[ C_C = 195 + 63 \cdot 8 \][/tex]

[tex]\[ C_C = 195 + 504 \][/tex]

[tex]\[ C_C = 699 \][/tex]

Using [tex]\( C_K \)[/tex]:

[tex]\[ C_K = 171 + 66 \cdot 8 \][/tex]

[tex]\[ C_K = 171 + 528 \][/tex]

[tex]\[ C_K = 699 \][/tex]

Answer:

Let's find out!

Step-by-step explanation:

15 ounces / 2.49 dollars

≈ 6.024 ounces per dollar

20 ounces / 3.32 dollars

≈ 6.024 ounces per dollar

Your answer is:

C) The unit rates are equal

The amount of ounces per dollar is the same, so your answer MUST be C).

Answer:

C) The unit rates are equal.

Step-by-step explanation:

Answer:

P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

"What is p? 4 1/2 + p = -5 3/4" was the question you have asked

So basically, in this equation we are looking for what the variable, P, is.

We already know that P plus 4[tex]\frac{1}{2}[/tex] equals -5[tex]\frac{3}{4}[/tex].

Now here's how you solve it:

So when trying to find the value a variable has, you should use inverse operations. What are inverse operations? Well let's look at this example:

453-T=56

How you would solve this is that you would subtract 56 from 453, removing 56 on the other side by subtracting it from the other side. *When performing inverse operations you always do it on BOTH sides*

We subtracted because 56 is positive and when performing operations on both sides of an equation, you do the inverse operation in both which in this case is to subtract.

453-T=56

-56      -56

↓

397-T=0

Now you may wonder 'What now? The other side is just 0! That didn't solve for T.' This is true. We have not solved for T just yet. But after this we will

397-T=0

     +T  +T

        ↓

397 = T

Tada! T is solved! We added T to both sides as T was negative and the opposite of negative is positive.

There are a few other ways to solve this equation like for example you could of subtracted 453 from both sides instead and have made it look like this:

453-T=56

-453    -453

↓

-T = -397

(Multiply both sides by negative 1 to make the -T and the -397 positive)

-1 (-T) = (-397) -1

↓

T = 397

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

Now that we've explained the basics of how that works let's now *actually* solve the problem:

4 1/2 + p = -5 3/4  

-4 1/2          -4 1/2

↓

P = -41/4

(4 1/2 is positive so the inverse operation was to subtract)

(A negative number subtracted by a negative number is a negative number that is even more negative than before)

--

ITS DONE!

Anyways let's check the equation to make sure it is right!

This is not needed but it is helpful to know how to check when you doubt that the value you got for a variable is correct.

You check by simply just pluging in the number you got into the variable and solving the equation to see if makes sense.

Here is how you would check this:

4 1/2 + p = -5 3/4

becomes

4 1/2 -[tex]\frac{41}{4}[/tex] = -5 3/4

subtract 41 fourths from 4 1/2

[tex]\frac{18}{4}[/tex]-[tex]\frac{41}{4}[/tex]= -[tex]\frac{23}{4}[/tex]

↓

-[tex]\frac{23}{4}[/tex] = -[tex]\frac{23}{4}[/tex]

Because the sides are equal, it is correct!

So, P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

The value of p in the given algebraic equation 4 1/2 + p = -5 3/4 is -10.25. This is found by isolating p.

To resolve this algebraic equation, you need to subtract 4 1/2 (which is 4.5 in decimal form) from each side of the equation, in order to isolate p. Hence, the equation then becomes p = -5 3/4 - 4 1/2.

First, convert -5 3/4 and 4 1/2 to decimal form. -5 3/4 becomes -5.75 and 4 1/2 becomes 4.5.

Secondly, subtract 4.5 from -5.75. Therefore, p is equal to -5.75 - 4.5 = -10.25.

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Each friend should contribute $196.5 towards the party supplies.

To solve this problem, we need to follow these steps:

1. Calculate the total cost of all party supplies:

  - 100 balloons cost $720

  - 100 plates cost $475

  - 100 cups cost $5.45 each

  - 100 napkins cost $2.09 each

  - 10 invitations cost $1.60 each

  - We need to find the cost of the plastic punchbowl.

2. Find the cost of the plastic punchbowl:

  - To find the cost of the plastic punchbowl, we subtract the total cost of the known items from the total cost of all party supplies.

3. Calculate the total cost of all party supplies:

  - Calculate the cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Calculate the cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Sum up the costs of all known items.

4. Find the cost per friend:

  - Once we have the total cost of all party supplies, we divide this total by the number of friends (10) to find out how much each friend should contribute equally.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60\)[/tex]

  - Total cost of known items [tex]= \(720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - [tex]\(10 \times \$1.60 = \$16\[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16\)[/tex]

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

Let's compute these steps to find the solution.

Let's calculate step by step:

1. Calculate the total cost of all party supplies:

  - Cost of 100 balloons: $720

  - Cost of 100 plates: $475

  - Cost of 100 cups: [tex]\(100 \times \$5.45 = \$545\)[/tex]

  - Cost of 100 napkins: [tex]\(100 \times \$2.09 = \$209\)[/tex]

  - Cost of 10 invitations: [tex]\(10 \times \$1.60 = \$16\)[/tex]

  - Total cost of known items = [tex]\(720 + 475 + 545 + 209 + 16 = \$1965\)[/tex]

2. Find the cost of the plastic punchbowl:

  - Total cost of all party supplies - Total cost of known items = Cost of plastic punchbowl

  - Total cost of all party supplies  - $1965 = Cost of plastic punchbowl

3. Calculate the total cost of all party supplies:

  - Total cost of all party supplies = [tex]720 + 475 + (100 \times 5.45) + (100 \times 2.09) + (10 \times 1.60)[/tex] = 720 + 475 + 545 + 209 + 16 = $1965

4. Find the cost per friend:

  - Total cost of all party supplies / Number of friends = Cost per friend

  - [tex]\( \frac{\$1965}{10} = \$196.5 \)[/tex]

So, each friend should contribute $196.5 towards the party supplies.

the complete Question is given below:

For a party, 10 friends are buying 100 cups, 100 plates, a punchbowl, and 200 balloons. If the friends share the cost equally, how much should each friend contribute? Party Supplies 100 balloons $720 100 plates $475 100 cups $5.45 100 napkins $2.09 What steps do you need 10 invitations $1.60 to solve to find the plastic punchbowl

There are triangles ΔABC, ΔFDE, and ΔGIH must be congruent. The correct answer is option A.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

In the given information, we can see that AB is congruent to both DF and GI, and BC is congruent to HI. Also, we know that ∠B is congruent to both ∠D and ∠G.

Using these properties, we can conclude that triangles ABC and FDE are congruent by the Side-Angle-Side (SAS) congruence theorem, since AB is congruent to DF, BC is congruent to DE, and ∠B is congruent to ∠D.

Similarly, we can conclude that triangles ABC and GIH are congruent by the Side-Side-Side (SSS) congruence theorem since AB is congruent to GI, BC is congruent to HI, and AC is congruent to GH.

Therefore,  ΔABC, ΔFDE, and ΔGIH must be congruent.

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Answer:

altitude

Step-by-step explanation:

Answer: The nearest whole number to 6.58 would be 7.

Step-by-step explanation: The whole number 7 is closer to 6.58 than any other whole number. Hence, 6.58 rounded to the nearest whole number would be 7.

Answer:

Total price of the glass is = $904.78

Step-by-step explanation:

Let's start by finding what is the surface area (in square meters) of the circular piece of glass. The information we have is that the radius of it is 8.0 meters. So we recall the formula for the area of the circle in terms of its radius (the product of the number [tex]\pi[/tex] times the square of the circle's radius):

Area of circle = [tex]\pi \,r^2[/tex]

Therefore, since the circle we need to investigate has radius 8 meters, the formula now becomes:

Area of circle = [tex]\pi \,r^2=\pi\,\,(8\,m)^2=201.062\,m^2[/tex]

Now, since they charge the glass per square meter ($4.50 per square meter), we just multiply the number of square meters we found for the glass' surface times the price per square meters, and get:

Total price = $4.50 * 201.062 = $904.78

Final answer:

The given equation has no solution because it leads to a contradiction.

Explanation:

To determine whether the given equation has one solution, no solution, or infinitely many solutions, we need to simplify the equation and see if it leads to a contradiction or identity. Simplifying the equation:

2/3x = 9 - 2(-1/3x + 3)

We can start by distributing the -2 to (-1/3x + 3):

2/3x = 9 + 2/3x - 6

Combining like terms:

2/3x - 2/3x = 9 - 6

0 = 3

Since we have a contradiction (0 cannot equal 3), there is no solution to the equation. Therefore, the correct answer is no solution.

Each student worked on 115 math problems.

Step-by-step explanation:

Given,

Problems solved in 4 hours = 8970

Number of students in competition = 78

As each student solved same number of problems, we will divide the total problems solved by number of students to find the amount of problems solved by one student.

Problems solved by one student = [tex]\frac{8970}{78}[/tex]

Problems solved by one student = 115

Each student worked on 115 math problems.

Keywords: division

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Each student works 115 problems.

Explanation:

I'm going to copy and paste the question here, and bold important info.

"Rayville Elementary sponsors a math competition for 78 students. During the competition, the students work a total of 8,970 math problems in 4 hours. Each student works the same number of problems. How many problems does each student work?"

Now everything not bolded? Forget about it. All you need to know is that there are 78 students. They all do 8,970 # of problems. And all the students do the same amount. Now you just have to divide the # of probs. by the amount of students in the competition, and you have your answer.

8970÷78=115

Hope that helped!

Answer:

[tex]\large \boxed{\math{8\frac{1}{4}}\text{ km}}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{lcll}2\frac{1}{5} \times 3\frac{3}{4} & = & \dfrac{11}{5} \times \dfrac{15}{4} & \text{Converted the mixed numbers to improper fractions}\\\\& = & 11 \times\dfrac{3}{4}& \text{Cancelled the 5s}\\\\& = & \dfrac{33}{4}& \text{Multiplied numerators and denominators}\\\\& = &\mathbf{8\frac{1}{4}} & \text{Converted the mixed number to a fraction}\\\end{array}\\\text{The length of the road is }\large \boxed{\mathbf{8\frac{1}{4}}\textbf{ km}}}[/tex]

Answer:

You may or may not need to include the units.

A = 18x - 18

P = 6x + 6

Graph is attached below. (2, 18)

Step-by-step explanation:

Substitute the information we need, "l" and "w", into the formulas.

l is for length, 6cm.

w is for width, (3x - 3)cm.

Use the formula for area of a rectangle.

A = lw

A = (6)(3x-3)cm²

A = (18x - 18)cm²  or 18x - 18

Use the formula for perimeter of a rectangle.

P = 2(l + w)

P = 2(6 + (3x - 3))cm

P = 2(3x + 3)cm

P = (6x + 6)cm  or 6x + 6

Linear equations are written in the form y = mx + b, so we do not need to factor or further simplify the formulas.

To graph, first turn the "m" value into a fraction form.

8 -> 8/1

6 -> 6/1

You need two points to graph each line.

For each equation, the first point is on the y-axis at the "b" value. Then use the "m" in the equation to count the number of units up (numerator) and to the right (denominator).

The solution is (2,18)

Max needs to run 15 laps around the track.

Step-by-step explanation:

Given,

Distance Max wants to run = 512 miles

Length around the track = 34 mile

34 miles = 1 lap

1 mile = [tex]\frac{1}{34}\ laps[/tex]

512 miles = [tex]\frac{1}{34}*512[/tex]

512 miles = 15.06 laps

Rounding off to nearest whole number;

512 miles = 15 laps

Max needs to run 15 laps around the track.

Keywords: unit rate, division

Learn more about division at:

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