Help with graphing rational functions

Answer:

\(\huge\boxed{\sf 252\ in.\²}\)

Step-by-step explanation:

TOP and BOTTOM:

Surface Area = 2 ( Length * Breadth)

SA = 2 ( 6 * 12 )

SA = 2 (72)

SA = 144 in. ²

FRONT and BACK:

SA = 2 ( Length * Breadth)

SA = 2 ( 3*12 )

SA = 2 (36)

SA = 72 in.²

SIDES:

SA = 2 ( Length * Breadth )

SA = 2 ( 3 * 6 )

SA = 2 (18)

SA = 36 in.²

Adding all to get the SA of rectangular prism:

= 144 + 72 + 36

= 252 in.²

\(\rule[225]{225}{2}\)

Hope this helped!

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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Answer:

850,000

Step-by-step explanation:

Answer:

0.00085

Step-by-step explanation:

8.5 = Tenth

0.85 = Hundredth

0.085 = Thousandth

0.0085 = Ten Thousandth

0.00085 = Hundred Thousandth

Hope this helps!

Answer:

y = 0.4x

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 4 when x = 10 , then

4 = 10k ( divide both sides by 10 )

\(\frac{4}{10}\) = k , that is

k = 0.4

y = 0.4x ← equation of variation

The statements which are true about parallel lines are;

Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.

Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.

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Answer:

There are 256 pairs in all.

54 2/7% is the same as 54 2 divided 7/100

54 200/7

(378+200)/7

578/7

The fraction in the lowest term for 54 2/7% is 19/35

Given,

54 2/7%

We need to convert it into a fraction in the lowest terms.

The lowest term of a fraction means that there is no common factor between the numerator and the denominator.

Example:

2/4 is not the lowest term because we can write it as 1/2.

1/2 is the lowest term.

Convert 54 2/7% into a fraction.

= (7x54 + 2) / 7 %

= 380/7x100

= 380 / 700

= 38 / 70

Find the lowest fraction of 38/70.

We can have 2 as the common factor.

= 2 x 19 / 2 x 35

= 19/35

We don't have any common factor between 19 and 35.

Thus the lowest term fraction of 54 2/7% is 19/35.

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Answer:

Mercury-

57

million kilometers.

Scientific notation-

5.7

⋅

10

7

km

Venus-

108

million kilometers.

Scientific notation-

1.08

⋅

10

8

km

Earth-

150

million kilometers

Scientific notation-

1.5

⋅

10

8

km

Mars-

228

million kilometers

Scientific notation-

2.28

⋅

10

8

km

Jupiter-

779

million kilometers

Scientific notation-

7.79

⋅

10

8

km

Saturn-

1.43

billion kilometers

Scientific notation-

1.43

⋅

10

9

km

Uranus-

2.88

billion kilometers

Scientific notation-

2.388

⋅

10

9

km

Neptune-

4.5

billion kilometers

Scientific notation-

4.5

⋅

10

9

km

Answer:

7 x 3 1/4 = 91/4 or 22 3/4

Step-by-step explanation:

To calculate 7 x 3 1/4, we can first convert the mixed number 3 1/4 to an improper fraction:

3 1/4 = (3 x 4 + 1) / 4 = 13/4

Then, we can multiply 7 by 13/4 as follows:

7 x 13/4 = (7 x 13) / 4 = 91/4

Therefore, 7 x 3 1/4 = 91/4 or 22 3/4 (if we want to express the answer as a mixed number).

Answer:

22 3/4

Step-by-step explanation:

There are plenty of ways of solving this question. The improper fraction of 3 1/4 is 13/4.

7 · 3 1/4

\(\frac{7}{1}\) x \(\frac{13}{4}\) = \(\frac{91}{4}\)

\(\frac{91}{4}\) = 22.75 = 22 3/4

9514 1404 393

Answer:

  \(\displaystyle\sqrt{x+7}-\log{(x+2)}\)

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  \(\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}\)

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

1.  27y^3

2. 32c^5

3. 16m^4

4. 64g^3

5. 49j^2

6. -3125z^5

Step-by-step explanation:

Can you help answer my question too, please?

Answer:

L = 25

Step-by-step explanation:

Let's call the Length x and width x - 15 since the width is 15 less than length

Eric needs 70 of fencing in total, the perimeter of a rectangle is calculated by adding all sides

x + x + (x - 15) + (x - 15) = 70 add like terms

4x - 30 = 70 add 30 to both sides

4x = 100 divide both sides by 4

x = 25

Answer :

Given :

To find :

Solution :

We know that for fencing we need to find the perimeter ,

Let us assume the value of length be x yards

Solving the question we get ,

Length = 25 yards

Breadth = 25 - 4

Answer:

Step-by-step explanation:

Answer:

(6 ± 3i)/5

Step-by-step explanation:

12x = 9 + 5x²

5x² - 12x + 9 = 0

Method 1

Factors that add to = b (-12) and multiply to = ac (45):  3 and -15

5x² + 3x - 15x + 9 = 0

5x(x - 3) + 3(x + 3) = 0

(x-3) and (x+3) do not match !!!!

Method 2 - Quadratic Formula

-b ± √(b² - 4ac)/2a

12 ± √((-12)² - 4(5)(9))/2(5)

12 ± √((-12)² - 4(5)(9))/2(5)

12 ± √(144 - 180)/10

12 ± √-36/10

(12 ± 6i)/10

(6 ± 3i)/5

I hope this helps!

Answer:

The answer is 1 year Tommy will take 1 year to his investment

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Median - The middle number in a set a data

First, you need to list the numbers least, on the left, to greatest, on the right.

3, 3, 4, 5, 5, 5, 6, 8, 8

Once you have done this, you can follow these steps.

Cross off the lowest number. Cross off the highest number. Repeat until there is one or two numbers left.

3, 4, 5, 5, 5, 6, 8

4, 5, 5, 5, 6

5, 5, 5

5

Since there is one number left, that is the median. In case of there being two numbers left, you add them together. Then divide by 2 and that would be your median

Answer:

\(\Large \boxed{\sf 5}\)

Step-by-step explanation:

Data set is 3, 3, 4, 5, 5, 5, 6, 8, 8

Median is the middle value in a data set

You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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Answer:

16

Step-by-step explanation:

8 goes into 24 3 times total so 2/3 of 24 would be 16

hope this helps!

Answer:

1+(6*.01)

Step-by-step explanation:

\(\large{\sf{Question:}} \\ \\\)

How to write 1.06 in expanded form

Solution :

1.06

\( \implies\) 1 + 0.0 + 0.06

840 different numbers can be created selecting 4 of the digits from the number

From the question, we have the following parameters that can be used in our computation:

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Answer:

4 2/3

Step-by-step explanation:

When dividing fractions you multiply the recipricol of the second term by the first.

1/3 x 5/1 = 5/3.

2 x 1 = 3

5/3 = 1 2/3

3 + 1 2/3 = 4 2/3.

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The simplest form of the resultant fraction when 2 1/3 divided 1 1/5

is 1 17/18.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given are two fractions 2 1/3 divided by 1 1/5.

We know,

2 1/3.

= (2×3 + 1)/3.

= 7/3 and similarly 1 1/5 is 6/6.

So, 7/3 divided by 6/5.

= (7/3)/(6/5).

= (7/3)×(5/6).

= 35/18.

= 1 17/18.

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Answer:

It SHOULD be 527.79(m2) If I'm not mistaken.

Step-by-step explanation:

Answer:

7000

Step-by-step explanation:

7×1000=7000

5×5=25÷5=5-5=0

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

-5, 3

Step-by-step explanation:

Answer:

500 divided by 3 maybe...

Step-by-step explanation:

the 362 I think is the number of the table and its $3 each and you have to spend $500 I think, the wording isn't as great but that's what I think.