A rectangle has sides of length 8a cm and 7a cm respectively. The perimeter of the rectangle is 42 cm more than the perimeter of a square with side 4a cm. Find the length of the side of the square.

Answer:

[tex]ax^5+ by^5=241[/tex]

Step-by-step explanation:

Given:

We can re-write the left sides of the given equations as follows:

[tex]ax^2+ by^2=(ax+by)(x+y)-xy(a+b)[/tex]

[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]

[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]

Therefore, following this pattern:

[tex]ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]

Use the given values and the expanded expressions to create 2 equations to help find the values of (x+y) and xy:

Equation 1

[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]

[tex]\implies 25=11(x+y)-xy(1)[/tex]

[tex]\implies 25=11(x+y)-xy[/tex]

Equation 2

[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]

[tex]\implies 83=25(x+y)-xy(11)[/tex]

[tex]\implies 83=25(x+y)-11xy[/tex]

Multiply Equation 1 by 11:

[tex]\implies 275=121(x+y)-11xy[/tex]

Then subtract Equation 2 from this to eliminate 11xy and find the value of (x+y):

[tex]\implies 192=96(x+y)[/tex]

[tex]\implies (x+y)=2[/tex]

Multiply Equation 1 by 25:

[tex]\implies 625=275(x+y)-25xy[/tex]

Multiply Equation 2 by 11:

[tex]\implies 913=275(x+y)-121xy[/tex]

Subtract the 2nd from the 1st to eliminate 275(x+y) and find the value of xy:

[tex]\implies 288=-96xy[/tex]

[tex]\implies xy=-3[/tex]

Therefore, we now have:

Substitute these into the equation for ax⁵ + by⁵ and solve:

[tex]\implies ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]

[tex]\implies ax^5+ by^5=(83)(2)-(-3)(25)[/tex]

[tex]\implies ax^5+ by^5=166+75[/tex]

[tex]\implies ax^5+ by^5=241[/tex]

Answer:

D

Step-by-step explanation:

A function input can only have ONE output value

so the number 5 can't output two different numbers

Answer:

27.5%

Step-by-step explanation:

Given:

Review:

Concepts:

Formula:

Now we must convert 275 milliliters to liters.

1. Divide the volume by 1,000.

275 ÷ 1000 = 0.275

2. Add the Unit Symbol for Liter.

0.275 ⇒ 0.275 L

Now we have to find how much of 1 liter- 0.275 liters as a percentage is.

To convert 0.275 to percent multiply 0.275 by 100. The result is 27.5 percent, or, using the percent sign, 27.5 %.

The correct answer is option c. Which is the function is increasing when x is greater than zero.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

In the graph, we can see that at the origin the graph becomes zero. When the graph proceeds rightwards the value of the function is increasing as the value of x is increasing.

Therefore the correct answer is option c. Which is the function is increasing when x is greater than zero.

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Answer:

g(x) = (x + 2)² + 1

Explanation:

Given parent function: f(x) = x²

If the function translates two units right

If the function translates one units up

Answer:

It would take him 4 hrs.

Step-by-step explanation:

Hope this helps!

Time taken by mike alone to finish the Task is 12 hours.

steve can complete a task in 6 hours.
he and mike can complete the same task in 4 hours.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
Rate of steve finishing task per hour = 1/6
Rate at which both finishes the task per hour = 1/4
Rate at which mike finishes the task per hour = M
now

M = 1/4-1/6
M = 3-2/12
M = 1/12
here, mike finishes his task at 12 hours

Thus, Time taken by mike alone to finish the Task is 12 hours.

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Area of a Parallelogram = base x height

base = 3.3

height = 8.4

Area = 3.3 x 8.4 = 27.72

Answer: 27.72 cm^2

Hope this helps!

Answer:

see explanation

Step-by-step explanation:

the set of x- values ( the input ) are called the domain

Answer:

domain

Step-by-step explanation:

as the y values is the range

Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C.

Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C. It is a two-dimensional variant of Stokes' theorem.

The path of the particle is positively oriented so we can use Green's theorem to find the work done in moving particle along C.

The work done is given by [tex]\oint_{c}\vec F \cdot \vec{dr}[/tex]

Here, [tex]\vec F[/tex](x,y)=<x+y, y²-x>

Then [tex]\oint_{c}\vec F \cdot \vec{dr} = \oint_{c}(x+y)dx+(y^2-x)dy[/tex]

In comparison with [tex]\oint_{c}Pdx+Qdy[/tex] what we have,

P= x+y and Q=y²-x

Then [tex]\dfrac{\partial P}{\partial y} = 1[/tex] and [tex]\dfrac{\partial Q}{\partial x} =-1[/tex]

Using the Green's Theorem,

[tex]\oint_{c}Pdx+Qdy = \iint_{D} \left ( \dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}\right )dA[/tex]

Here D in polar Co-ordinates is given by,

D={(r,θ) : 0 ≤ r ≤ 7, 0 ≤ θ ≤ π}

Then

[tex]\oint_{c}(x+y)dx+(y^2-x)dy\\\\=-\iint_D 2dA\\\\=-\int_{\pi}^{0}\int_{0}^7 2r drd\theta\\\\=-49\pi[/tex]

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Answer:

Radius = 20+5 = 25

We can find CE with the pythagorean theorem

20^2 + CE^2 = 25^2

CE = 15

The what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units

A square is a shape with 4 sides

Let the side of the square be x units. If the length of the diagonal is 5√2, the value of x can be expressed using the pythagoras theorem as shown;

x² + x² = (5√2)²

2x²  = 25(2)

x² = 25

x = 5 units

Determine the volume

V = x³

V = 5³

V = 125 cubic units

Hence the what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units

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Answer:

Yes, it is rational because it is a fraction. All rational numbers are either decimals or fractions. Since a fraction can also be represented as division, creating a decimal when divided, it counts as a rational number.

Step-by-step explanation:

p = 2r + pi×r

p = r(2 + pi)

r = p/(2 + pi)

Answer:

r = [tex]\frac{p}{2+\pi }[/tex]

Step-by-step explanation:

p = 2r + πr ← factor out r from each term

p = r(2 + π) ← divide both sides by (2 + π )

[tex]\frac{p}{2+\pi }[/tex] = r

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

The given expression is :

[tex]\qquad \sf  \dashrightarrow \:4x + 8[/tex]

plug the value of x as 3

[tex]\qquad \sf  \dashrightarrow \:4(3) + 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:12 + 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:20[/tex]

Therefore, the required value is 20

Explanation:

Jamie has 7 choices for the first slot, then 6 choices for the next, and 5 choices for the final slot. Order matters. He has 7*6*5 = 210 permutations.

Alternatively you can use the nPr permutation formula with n = 7 and r = 3.

That formula is

[tex]nPr = \frac{n!}{(n-r)!}[/tex]

The exclamation marks indicate factorials. For instance, 4! = 4*3*2*1 = 24.

Answer:

B. 210 is correct!

Step-by-step explanation:

I got it correct on the quiz.

Answer:

15

Step-by-step explanation:

First lets simplify the left side :

5/12 + 5/12 + 5/12 = 15/12

15/12

To make the right side into 15/12 we must multiply it by 15:

15 × 1/12 = 15/12

So the blank is 15

Hope this helped and brainliest please.

Answer:

15/1

Step-by-step explanation:

you simply add the 5's only not the 12. when u multiply 1 and 12 u get 12 and when you multiply 15 and 1 you get 15

The area of the shaded region = area of semicircle - area of triangle ACB = 11.32 cm².

Area of a triangle = 1/2(base)(height).

Area of a semi-circle = 1/2(πr²).

m∠ACB is a right triangle based on the central angle theorem. Therefore, ΔACB is a right triangle.

Radius of circle = OC = 4 cm

CB = 4 cm

Diameter AB = 2(4) = 8 cm

Using the Pythagorean theorem, find AC in ΔACB:

AC = √(AB² - CB²)

AC = √(8² - 4²)

AC ≈ 6.9 cm

Area of ΔACB = 1/2(CB)(AC)

Area of ΔACB = 1/2(4)(6.9)

Area of ΔACB ≈ 13.8 cm²

Area of semicircle = 1/2(πr²) = 1/2(π)(4²)

Area of semicircle ≈ 25.12 cm²

Area of the shaded region = area of semicircle - area of triangle ACB = 25.12 - 13.8

Area of the shaded region = 11.32 cm²

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Answer:

hope this will help you

[tex]let \: the \: angle \: be \: \alpha \\ \cos( \alpha ) = \frac{b}{h} \\ \cos(60) = \frac{x}{9} \\ \frac{1}{2} = \frac{x}{9} \\ x = \frac{9}{2} \\ x = 4.5[/tex]

Answer:

113.04m^2

Step-by-step explanation:

Surface area for Base and top

[tex]2*\pi d=2*3.14*4=25.12[/tex]

Surface area for the other part

[tex]\pi d*h = 12.56*7 = 87.92[/tex]

you will get

113.04m^2

The value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We can solve this problem by exponential function:

The word  depreciate means the price is decreasing.

We can find the value be when the car is 10 years old:

p = 38800(1 - 0.06)¹⁰

p = 38800(0.94)¹⁰

p = 20898.266 ≈ $20898.27

Thus, the value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.

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this is the answer hope it helps please if am wrong ask another person

thank you

Answer:

the answer is 14

Step-by-step explanation:

precalculus honors

The test statistic is -0.46 and the p-value is gotten as 0.3340

The question is not complete because the data from the sample is 105, 107, 117, 106, 110.

Mean of sample is;

Mean = (105 + 107 + 117 + 106 + 110)/5

Mean; x' = 109

From online standard deviation calculator, the standard deviation of the sample is; S = 4.848

Now, the claim is that your team scored an average significantly less than 110 points. Thus, let's define the hypothesis as;

Null Hypothesis; μ = 110

Alternative Hypothesis; μ < 110

standard error of the mean; S_m = S/√n

S_m = 4.848/5

S_m = 2.17

Thus, the t-statistic is;

t = (x' - μ)/S_m

t = (109 - 110)/2.17

t = -0.46

Degree of freedom for this sample size is;

D.F = N - 1 =5 - 1 = 4

From online p-value from t-score calculator, we have;

p-value = 0.3340

The p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that your team scored an average significantly less than 110 points.

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Answer:

C 17.25

Step-by-step explanation:

i think aanswer its c

To find the length of the diagonal, we need to calculate the length of the base first and then use the value to calculate the diagonal since we are given the value of height of the triangle.

This theorem is used to find the missing side of a right angle triangle given that we have the length of two sides.

To calculate the base of the triangle, let's use Pythagorean theorem here

[tex]x^2 = y^2 + z^2\\x^2 = 2^2 + 3^2\\x^2 = 4 + 9 \\x^2 = 13\\x = \sqrt{13} \\x = 3.61[/tex]

Having the length of the base, let's consider the height of the triangle which is 6 and substitute the values.

[tex]d^2 = 6^2 + 3.61^2\\d^2 = 36 + 13.0321\\d^2 = 49.0321\\d = \sqrt{49.0321} \\d = 7.00[/tex]

From the calculations above, the values of the triangle are

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Answer:

  0.8

Step-by-step explanation:

The change of base formula for logarithms can be used to find this value exactly. (Your calculator can also tell you.)

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]

__

Using this relation with the given numbers, we have ...

  [tex]\dfrac{\log(256)}{\log(1024)}=\dfrac{\log(2^8)}{\log(2^{10})}=\dfrac{8\cdot\log(2)}{10\cdot\log(2)}=\dfrac{8}{10}\\\\\boxed{\dfrac{\log(256)}{\log(1024)}=0.8}[/tex]

Answer:

$87.5

Step-by-step explanation:

Original price also means COST PRICE

C.P=$50

S.P=75% of $50-$50

To find the sale price it will be 75% of C.P -C.P

75% × $50 + $50= 0.75 × $50-$50

=$37.5-$50.

= $12.5

therefore the sale price is $12.5

THANK YOU

The price of the sweatshirt at the sale is $12.5 which is 75% off of the original price.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The original price of a sweatshirt is $50.

Also given that the sale price is 75% off the original price So, the cost of the sweatshirt is (100 - 75)% = 25% of the original price which is,

= (25/100)×50.

= $12.5.

So, The sale price of the sweatshirt is $12.5.

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Answer:

3/20

Step-by-step explanation:

0.15 = 15/100

This is not simplified though :

15/100 ÷ 5/5 = 3/20

This is simplified

Hope this helped and brainliest please.

Answer:

[tex]x = -3~\text{and}~ x = -\dfrac 35[/tex]

Step-by-step explanation:

[tex]~~~~~~5x^2 +18x +9=0\\\\\implies 5x^2 +15x +3x +9 = 0\\\\\implies 5x(x+3) +3(x+3) = 0\\\\\implies (x+3)(5x+3) = 0\\\\\implies x = -3,~ x = -\dfrac 35[/tex]

Answer:

x = -3

OR

x = -(3/5)

Step by step explanation:

Given:

To Find:

Soln:

Use quadratic formulae:

[tex] \rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}[/tex]

According to the question,on the formula,

So substitute them on the formula:

THEN solve for x.

[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{18 {}^{2} - 4(5 \times 9) }}{2 \times 5} [/tex]

[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 20 \times 9) }}{10} [/tex]

[tex]\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10} [/tex]

[tex] \rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10} [/tex]

[tex] \rm \implies \: x = \cfrac{ - 18 \pm12}{10}[/tex]

[tex] \rm \implies \: x = \cfrac{9 \pm 6}{5} [/tex]

Final solution will after adding first(9+6),then secondly subtracting both 9-6

[tex] \rm \implies \boxed{x = - \cfrac{3 }{5} }[/tex]

[tex] \implies \boxed{\rm x = - 3}[/tex]

So there'll be two possible answers.