Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0.


Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1.

The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

To calculate the height of the tree , we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the height of the tree is 64.94 feet.

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The correct answer to this question is the first option

Answer:

y=2x+16 is the slope intercept form

Step-by-step explanation:

sorry if its wrong tried!!!

Therefore,

We know that :

Substituting the values :

>> V = π × (7 / 2)^2 × 8

>> V = π × (49 / 4) × 8

>> V = π × 49 × 2

>> V = 98π

Henceforth,

We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.

Therefore, putting the values, we get,

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]

[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]

Hence , the volume of cylinder is 98 pi

The expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

The question is incomplete.

The complete question is:

A hot dog vendor at the zoo recorded the average temperature in degrees, x, and the average number of hot dogs she sold, y.

The equation for the line of best fit for this situation is shown below.

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Based on the line of best fit, complete the given statements.

We have a line of best fits:

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Plug x = 50 in the line of best fit.

y = (3/10)50 + 8

y = 15+8

y = 23

Plug y = 35

35 = (3/10)x + 8

27 = (3/10)x

x = 90 degree

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

Thus, the expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees, and based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

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Answer:

[tex]2\sqrt{x+1}-3\\domain:[-1, \infty)[/tex]

Step-by-step explanation:

[tex]g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\[/tex]

the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1

Answer:

=8x+14 or

=16x²+56x+49

[tex]\bf{(4x+7)2 }[/tex]

[tex]\bf{=2(4x+7)}[/tex]

[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]

[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]

[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]

[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]

Hii!

__________________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]

The value of x is -3! ^^

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]

[tex]\bullet[/tex] First multiply 5 times 1 and -x

[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]

[tex]\twoheadrightarrow\sf 5-5x=20[/tex]

[tex]\bullet[/tex] Now subtract 5 from both sides

[tex]\twoheadrightarrow\sf -5x=15[/tex]

[tex]\bullet[/tex] Now divide both sides by -5

[tex]\twoheadrightarrow\sf x=-3[/tex]

--

Hope that this helped! Best wishes.

--

Answer:

E; 10% off %20 sweater with $6 shipping

Step-by-step explanation:

Similar to what I said last time,

this time is with percentages,

How to calculate percent off?

Divide the number by 100 (move the decimal place two places to the left).

Multiply this new number by the percentage you want to take off.

Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
  0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
    which the total would be $26.75

B. 20% off $35 is
   0.2x35=7 and 35-7 = 28 so your total is $28

C. 30% off $30 with $6 for shipping is

   0.3x30=9 and 30-9 is $21 plus the shipping fee
   $27

D.  $20 sweater with $5 shipping is $25 no discount involved :D

E. 10% off %20 sweater with $6 shipping is

    0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.

By definition of the binomial coefficient,

[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]

so we have

[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]

as required.

Answer:

  (a)  9, 8, 7, 6, 5, ...

Step-by-step explanation:

The solution to the inequality can be done a couple of ways. The solution is similar to that for a one-step linear equation.

__

We know that multiplying numbers by a negative value reverses their order. For example, 1 < 2, but -1 > -2. That is, multiplying by -1 requires a change in the comparison operator if it is to remain true.

For our inequality, we want to solve it by multiplying both sides by -1/4:

  -4y > -40

  (-1/4)(-4y) < (-1/4)(-40) . . . . . multiply both sides by -1/4 (reverses order)

  y < 10 . . . . . . . . . . . simplify

The first few decreasing integer values that are part of this solution are ...

  {9, 8, 7, 6, 5, ...}

__

We can add 4y+40 to both sides of the inequality. The result will be an inequality with positive coefficients. This can be solved in one step.

  -4y > -40 . . . . . given

  (-4y) +(4y +40) > (-40) +(4y +40) . . . . . . add 4y+40 to both sides

  40 > 4y . . . . . . . . . . . . . . . simplify

  10 > y . . . . . . . . . . . . divide by 10 (order is unchanged)

  y < 10 . . . . . . . . . rearrange to put y on the left

Integer solutions to this inequality are ...

  {9, 8, 7, 6, 5, ...}

Answer:

[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])

Step-by-step explanation:

When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.

Answer:

(3x – 6)4

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]

The members of a possible set C are {6, 9, 12}

The universal set is the set that contains all other sets. Given the following sets

ξ = {x:x is an integer, 2 ≤ x ≤ 14}

B = {x:x is a prime number}

A = {x:x is a multiple of 3}

The sets B and A are:

B = {2, 3, 5, 7, 11}

A = {3, 6, 9, 12}

If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.

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Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.

Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.

The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)

                                  = 1.2 × 10⁻³ amp

Hence, the current in the amp is 1.2 × 10⁻³.

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Answer:

K

Step-by-step explanation:

(1*500 * 5) + (10 * 3*500)

Answer:

1/2

Step-by-step explanation:

First parabola  f(x1)   =  a ( x+4)(x-6)    use point 0,-12 to find a = 1/2

                                = 1/2 (x+4)(x-6)

Second parabola    a ( x+4) (x-6)       using point  0, -24    shows a = 1

                       f(x2)       = (1)(x+4)(x-6)

Difference between the 'a' values =  1 - 1/2 = 1/2

A firm should go out of business in the long run when its price level is less than the average total cost.

The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.

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Answer: Each child gets 1/3

Step-by-step explanation: x/3

Answer:

X= 5.52

Step-by-step explanation:

1. Solve the equation:

e×2x + 12= 42

x=15/e

2. Round x=15/e to the required place

x=5.52

Answer:

X=1.15

Step-by-step explanation:

The asset’s fourth full year of depreciation expense will be $6,666.67.

An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.

An asset has a cost of $50,000, with a residual value of $10,000.

It has a life of 5 years and was purchased on January 1.

Then the asset’s fourth full year of depreciation expense will be

Annual depreciation = (cost – salvage value)/ useful life

Annual depreciation = (50000 – 10000) / 5 = $8,000

Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.

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Answer:

Obtuse and the rest of the question is incomplete.

Step-by-step explanation:

Answer:

its 80

Step-by-step explanation:

the ratio is 80 hope this helps!

Answer:

cp = rs 400

loss = 10%

Then SP = 400 - 10% of 400

= 400 - 40

= 360

Therefore SP = Rs. 360

The amount to be repaid by Jim Ryan is $14,891.78.

Given that, Principal (P) =$14,000, the rate of interest (R) =7[tex]\frac{1}{2}[/tex]% and T=310 days.

Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year.

Now, the interest=14,000×7.5 %×[tex]\frac{310}{365}[/tex].

=$891.78

The amount to be repaid=14,000+891.78=$14,891.78

Therefore, the amount to be repaid by Jim Ryan is $14,891.78.

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Answer: (10, ∞)

Step-by-step explanation:

See the graph in the attached image.

Answer:

27i

Step-by-step explanation:

Since we define i as [tex]\sqrt{-1}[/tex], [tex]\sqrt{-27} = 27i[/tex]

Answer:

Step-by-step explanation:

i [tex]i \sqrt{-27} =i\sqrt{-1 \times 27} =i\sqrt{27i^2} =i \times i\sqrt{27} =i^2\sqrt{9 \times 3} \\=-1\times 3\sqrt{3} \\=-3\sqrt{3}[/tex]

The area of the region bounded by the line y =3x -6 and line y=-2x+8 is  12/5 units

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

2x = 8

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

e4fodor8rsidididi2f2

Answer:

9

Step-by-step explanation:

3:4

AB:12

cross multiply giving

3×12:4AB

36: 4AB

divide both sides by 4,thus

AB=9