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.

Answers

Answer 1

Answer:

Perimeter of rectangle2 =  k × perimeter of rectangle 1

area of rectangle 2  =   × area of rectangle 1

Step-by-step explanation:

rectangle 1 :

Length x

Width y

perimeter1  =  2×(x + y)

area1  = x × y

……………………

•• rectangle 2 :

Length kx

Width ky

Perimeter2  =  2×(Kx + ky)

area2  = kx × ky

……………………………………………

therefore,

Perimeter of rectangle 2

= 2×(Kx + ky)

= 2×k×(x + y)

= k×2×(x + y)

= k × perimeter of rectangle 1

On the other hand,

area of rectangle 2

= Kx × ky

= k×k×(x × y)

= k²×(x × y)

= k² × area of rectangle 1


Related Questions

Which expression is equivalent to...​

Answers

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]

Answer: A) g^15 / 8h^6

Step-by-Step Solution:

= (2g^5)^3 / (4h^2)^3
= 8g^15 / 64h^6
=> g^15 / 8h^6

rewrite the equation y-8=2 into slope form

Answers

Answer:

y=2x+16 is the slope intercept form

Step-by-step explanation:

sorry if its wrong tried!!!

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene 97degree

Answers

Answer:

Obtuse and the rest of the question is incomplete.

Step-by-step explanation:

Below what price level would the firm go out of business in the long run?

Answers

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

When should a firm go out of business in the long run?

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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Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296

Answers

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:

What does the ratio 6 to 8 represent in the situation?

Answers

Answer:

its 80

Step-by-step explanation:

the ratio is 80 hope this helps!

I have a quick geometry question! Thank you!

Answers

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

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. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?

Answers

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

What is double-declining-balance?

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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Which one is it I need to finish this page fast

Answers

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.

Solve for x:

5(1 – x) = 20

x = __

Answers

[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.

--

Express the radical using the imaginary unit, i sqrt{-27}

Answers

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]

3 Three children share this chocolate equally.
What fraction does each child get?
Each child gets
CHALLENGE?

Answers

Answer: Each child gets 1/3

Step-by-step explanation: x/3

What is the solution to the equation below? Round your answer to two decimal places. 3e2x + 12 = 42

Answers

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:

Find the volume of a cylinder that has a diameter of 7 and a height of 8.
28 Pi
392 Pi
448 Pi
98 Pi

Answers

Required solution :Diameter (d) = 7 Height = 8

Therefore,

Radius (r) = d / 2Radius (r) = 7/2

We know that :

V = πr^2h

Substituting the values :

>> V = π × (7 / 2)^2 × 8

>> V = π × (49 / 4) × 8

>> V = π × 49 × 2

>> V = 98π

Henceforth,

98 pi is the answer.

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

Diameter - 7Height - 8radius = 7/2

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

Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.

Answers

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

How to find the area?

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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A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6, 0). The y-intercept
of the first parabola is (0, -12). The y-intercept of the second parabola is (0, -24). What is the positive difference
between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to
the nearest tenth.

Answers

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

look at the picture

thank you ​

Answers

The correct answer to this question is the first option

Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. If you connect a 2 megohm resistor (2× 10^6 ohms) across a 2.4 kilovolt voltage source (2.4×10^3 volts),what would be the current in amps?

Answers

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.

What is Ohm's Law?

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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ξ = {x:x is an integer, 2 ≤ x ≤ 14}
� = {x:x is a prime number}
� = {x:x is a multiple of 3}
Given that C ⊂ A, n(C)=3 and B ∩ C = ∅, list the members of a possible set C

Answers

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

Set theory

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



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

The expected number of hot dogs sold when the temperature is 50° would be
hot dogs.

If the vendor sold 35 hot dogs, the temperature is expected to be
degrees.

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

Answers

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.

What is the line of best fit?

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.

The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.If the vendor sold 35 hot dogs, the temperature is expected to be ___degrees.Based on the line of best fit, for every 10-degree increase in temperature, she should sell____more hot dogs.

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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Greg has a piece of string that is 3 1/3 yards long. If he cuts off 3/4 yard, how many yards of the string
will be left?

Answers

2(7/12) yards will be left

3(1/3) =10/3
10/3 - 3/4. = 40/12- 9/12
= 31/12
=. 2(7/12)

Simplify the following expression.

(4x + 7)2

Answers

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]

Multiply 2 x 4 = 8Multiply 2 x 7 = 14

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

Pisces04

On a coordinate plane, an absolute value graph has a vertex at (10, 6).
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing?

(–∞, 6)
(–∞, 10)
(6, ∞)
(10, ∞)

Answers

Answer: (10, ∞)

Step-by-step explanation:

See the graph in the attached image.

On May 6, Jim Ryan borrowed $14,000 from Lane Bank at 712% interest. Jim plans to repay the loan on March 11. Assume the loan is on ordinary interest. How much will Jim repay on March 11?

Answers

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.

What is ordinary interest?

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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If Yang solves the inequality -4y> -40, then which of the following answers would be true for this claim?

Answers

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.

__

reverse inequality

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, ...}

__

make coefficients positive

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, ...}

Another day, another math problem 3

Answers

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

Please answer! I will give you the brainliest :)

Answers

Answer:

K

Step-by-step explanation:

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

Answer is k (5.500) + (10.1500)

Prove that C(50,3) + C(50,4) = C(51,4)

Answers

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.

if cp=rs 400, loss=10% find sp

Answers

Answer:

cp = rs 400

loss = 10%

Then SP = 400 - 10% of 400

= 400 - 40

= 360

Therefore SP = Rs. 360

Sam wants to measure the height of a tree. She walks 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 33°. How tall is the tree? Round your answer to the nearest hundredth.

Answers

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

What is angle of elevation?

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:

tan∅ = H/B.............Equation 1

Where:

∅ = Angle of elevation from the ground to the top of the treeH = Height of the treeB = Distance of the base of the tree to the point where Sam looks up

From the question,

Given:

∅ = 33°B = 100 feet

Substitute these values into equation 1 and solve for H

tan33° = H/100H = tan33°×100H = 64.94 feet

Hence, the height of the tree is 64.94 feet.

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Which information would best be presented as prose in an informational text? A. The population change in Canada over time B. A detailed explanation of the history of Canada C. The percentage of Canadians who live in each province D. A list of the cities and provinces of Canada Why is it necessary for meiosis to produce cells with fewer chromosomes> Particles q1, 92, and q3 are in a straight line.Particles q1 = -5.00 x 10-6 C,q2 = -5.00 x 10-6 C,and q3 = -5.00 x 10-6 C. Particles q and q2 areseparated by 0.500 m. Particles q2 and q3 areseparated by 0.500 m. What is net force on 93?Remember: Negative forces (-F) will point LeftPositive forces (+F) will point Right-5.00 x 10-6 C910.500 m--5.00 x 10-6 C92-5.00 x 10-6 C930.500 m- Joshua has a job that pays $2,265 biweekly. How much is withheld annually for Medicare? A.$853.91 B.$32.84 C.$16.42 d.$35.58 E.$71.16 Which composition of similarity transformations maps LMN to L'M'N'?Option A: a dilation with a scale factor less than 1 and then a reflectionOption B: a dilation with a scale factor less than 1 and then a translationOption C: a dilation with a scale factor greater than 1 and then a reflectionOption D: a dilation with a scale factor greater than 1 and then a translation Write a one page paper on the education and training for Clinicians. What was the military significance of the creation of guns? pinnacle Corp. budgeted $262,220 of overhead cost for the current year. Actual overhead costs for the year were $257,640. Pinnacle's plantwide allocation base, machine hours, was budgeted at 45,150 hours. Actual machine hours were 53,260. A total of 97,480 units was budgeted to be produced and 98,000 units were actually produced. Pinnacle's plantwide factory overhead rate for the current year is: a.$2.69 per machine hour b.$5.71 per machine hour c.$5.81 per machine hour d.$2.64 per machine hour i need to Match each equation that represents each situation. Which of the following is a solution to this inequality?y which situation would be more likely to occur in the modern era then in earlier periods of human history Who is Lestrade in "The Adventure of the Six Napoleons"?a low-level criminal whom Holmes questions during the storythe manufacturer of the six busts of Napoleon in the storyone of the men who has his bust of Napoleon stolena police inspector investigating the case with Sherlock Holmes An _______ is a person who hosts the news show. Which set of side lengths forms a right triangle?O2, 3, 13O4, 6, 10O 9, 12, 18O 15, 36, 39 Which statement is true about the graphs of the two lines y=-8x-5/4and y=1/8x+4/5? The table of values represents a linear function g(x) where c is the number of days that have passed and g(x) is the balance in the bank account What happens to the ecosystems resilienceto disturbance 17. What is the value of x in the rhombusbelow?AC(x+ 40)B3xD18 A 1dm3 solution was made by mixing 0.0040 mol of HCl(aq) and 0.0025 mol of NaOH(aq). What was the pH of the resulting solution? Which equation can be used to solve for xxx in the following diagram?Choose 1 answer:Choose 1 answer:(Choice A)A2x = 4x2x=4x2, x, equals, 4, x(Choice B)B2x + 4x = 1802x+4x=1802, x, plus, 4, x, equals, 180(Choice C)C2x + 4x = 902x+4x=902, x, plus, 4, x, equals, 90(Choice D)D2x + 4x = 1502x+4x=1502, x, plus, 4, x, equals, 150