Chloe discovers that her rectangular shed is 6 feet longer than three times the width. If the perimeter of the shed is 100 feet, find the dimensions. (Recall: the perimeter of a rectangle is given by the formula P = 2 L + 2 W .)

Answer:

A,C,and D are parralelograms

The parallelogram are shapes with figures having opposite sides which are parallel

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The sum of angles of a parallelogram is 360°

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , from the figure 1

a)

The figure is having opposite sides are parallel

where AB = CD

And , BC = AD

So , it is a parallelogram

b)

The figure does not have any sides parallel

So , it is not a parallelogram

c)

The shape is having 2 sides as parallel

And , AB = CD

So , it is a parallelogram

d)

The shape is having 2 sides as parallel

And , AB = CD

So , it is a parallelogram

Hence , the parallelogram is solved

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Answer:

-7 and -4

Step-by-step explanation:

The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function,

f(x) = (x + 4)⁶ (x + 7)⁵

When the function cross the X axis, the value of the function will be 0.

Let f(x) = 0

(x + 4)⁶ (x + 7)⁵ = 0

This implies that, either x + 4 = 0 or x + 7 = 0

x + 4 = 0 ⇒ x = -4

x + 7 = 0 ⇒ x = -7

Hence the roots are -4 and -7 where the function crosses the X axis.

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Answer:

1) [tex]7 \frac{11}{16} [/tex]

2) [tex] \frac{7}{15} [/tex]

Step-by-step explanation:

1) Let's convert the mixed fraction into a improper fraction.

[tex]5\frac{1}{8} \\ = \frac{5(8) + 1}{8} \\ = \frac{41}{8} [/tex]

Let the number be x.

[tex] \frac{2}{3} x = \frac{41}{8} \\ x = \frac{41}{8} \div \frac{2}{3} \\ x = \frac{41}{8} \times \frac{3}{2} \\ x = \frac{123}{6} \\ x = 7 \frac{11}{16} [/tex]

2)[tex]4 \frac{3}{8} = \frac{35}{8} [/tex]

[tex]9 \frac{3}{8} = \frac{75}{8} [/tex]

[tex]4 \frac{3}{8} \div 9 \frac{3}{8} \\ = \frac{35}{8} \div \frac{75}{8} \\ = \frac{35}{8} \times \frac{8}{75} \\ = \frac{7}{15} [/tex]

Answer:

a = -50/51

Step-by-step explanation:

1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0

  1 +   3 +   5 + ...  + 99 +   2a +    4a + ... + 98a + 100a = 0     Eq. 1

99 + 97 + 95 + ... +    1  + 98a + 96a + ... +   4a  +    2a  = 0    Eq. 2

Add Eq. 1 and Eq. 2

100 + 100 + ... + 100 + 102a + 102a + ... 102a = 0

50(100)/2 + 50(102a)/2 = 0

2500 + 2550a = 0

2550a = -2500

a = -2500/2550

a = -250/255

a = -50/51

Answer:

16.59

Step-by-step explanation:

Given:

[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]

Expanding the left hand side, we have:

[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]

Therefore:

[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]

To find the minimum value, we take the derivative and solve for its critical point.

[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]

Recall that:

[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]

The minimum possible value of the coefficient of x is 16.59.

Answer:

173

Step-by-step explanation:

For sympliciy let the box equal y.

Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that  (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].

Answer:

If it is on the maximum, then the y-value of the point cannot be any higher and  still be on the graph of the function. If it is on the minimum, the the y-value of the point cannot be any lower and still be on the graph of the function. If it isn't either the maximum or the minimum, it is neither.

Answer:

Maximum =  756

Minimum =  600

Step-by-step explanation:

A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.

And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:

(1 + 3 + 5 + 8 + 10) ×  (2 + 4 + 6 + 7 + 9) = 756

At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:

(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600

Step-by-step explanation:

a, 3

b,

draw lines through the corresponding corners of each shape  These lines will cross at the centre of enlargement O

Answer:

Step-by-step explanation:

Part A:

We have two lines: y = 2 - x and y = 4x + 3 . Given two equations that are both required to be true. The answer is the points where the lines cross, this means we have to make the equations equal to each other. It will look like this:

                                                       2 - x = 4x + 3

Part B:

In order to solve the equation we need to put the like terms together. So we will add x on each side.

                                                       2 - x = 4x + 3

                                                           +x   +x

So now we get:

                                                           2 = 5x + 3

Now that x is on one side and is positive we will move 3 on the left side by subtracting it from each side.

                                                           2 = 5x + 3

                                                           -3         -3

So now we get:

                                                           -1 = 5x

Now that the like terms have been combined we need to find out what x alone is so we divide 5 on each side:

                                                           [tex]\frac{-1}{5}[/tex] = [tex]\frac{5x}{5}[/tex]

No we see that:

                                                           x = [tex]-\frac{1}{5}[/tex]

Answer:

22.467

Step-by-step explanation:

Hello,

You just have to do the computation in XL or using a calculator, and round each number to the nearest hundred

x sqrt(x)

1 1

2 1.414

3 1.732

4 2

5 2.236

6 2.449

7 2.646

8 2.828

9 3

10 3.162

and do the sum which is 22.467

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

300

Step-by-step explanation:

First let's square all the integers from 1 to 10 inclusive. We get:

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100.

Rounding to the nearest hundred, we get that 1, 4, 9, 16, 36, and 49 all round to 0 and 64, 81, and 100 round to 100.

Therefore, we obtain 

0+0+0+0+0+0+0+100+100+100,

or 300.

Answer:

Step-by-step explanation:-

-

-8239910.76

Answer:

Period: 2pi  vertical shift: 2 units up

Step-by-step explanation:

Answer:

D. period: 4pi; vertical shift: 2 units up

Step-by-step explanation:

Just did the test right now hope this helps some of yall :)

Answer:

y = 1

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex] (x₁ + x₂ ), [tex]\frac{1}{2}[/tex] (y₁ + y₂ ) ]

Here (x₁, y₁ ) = (4, - 3) and (x₂, y₂ ) = (- 8, 5), thus the y value of midpoint is

y = [tex]\frac{1}{2}[/tex] (- 3 + 5) = 0.5 × 2 = 1

Answer: 58

Step-by-step explanation:

The sum of the two digit number is 13. On reversing its digits the new number is 27 more than the original number find the number?

Let's set up a system with two variables: x = tens place of our answer, y = units place of our answer.

Digit sum of a two digit number is 6:

x+y=13

Reverse the digits and you get 27 more than the original value:

10y+x=10x+y+27

Now let's solve:

y=13-x

10(13-x)+x=10x+(13-x)+27

130-10x+x=130x-10x + 27

130-9x=9x+40

-90=18x

x=5

y=13-5

y=8

So our original number was 58. Sum of digits is 13. Swap the order of the digits to make 85, and you have a number 27 more than the original number.

The value of original number is, 58.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The sum of digits in two-digit number is 13.

And, If the place values of the digits are reversed, the new number is 27 more than the original number.

Now, Let the one's place digit is y and the ten's place is x of the original number.

Then, We get;

⇒ x + y = 13  .. (i)

And, If the place values of the digits are reversed, the new number is 27 more than the original number.

So, We get;

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y + x - 10x = 27

⇒ 9y - 9x = 27

⇒ y - x = 3

⇒ y = x + 3   ... (ii)

Substitute the value of y from (ii) in (i), we get;

⇒ x + y = 13

⇒ x + x + 3 = 13

⇒ 2x = 13 - 3

⇒ 2x= 10

⇒ x = 5

And, From (ii);

⇒ y = x + 3  

⇒ y = 5 + 3

⇒ y = 8

Thus, The original number is,

⇒ 10x + y = 10 × 5 + 8

               = 50 + 8

               = 58

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Answer:

1024 pi

Step-by-step explanation:

r = 32 units.

Area = pi * r^2

Area = 3.14 * 32^2

Area = 1024 * pi

Tt = pi??

Answer:

144 cm^2

Step-by-step explanation:

8x6+4x10+4x8+4x6

48+40+32+24

80+40+24

120+24

144

Answer:

507x223 is greater than 530 x 200

914x385 is less than 900 x 400

Answer:

y=11x+6

Step-by-step explanation:

Simplify: 22x-2y=-12

22x-2y=-12

-22x

-2y=-22x=-12

/-2

y=11x-6

For this question, the time given confuses me.  I know the rate of return is just total return divided by divided by investment, Assuming that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500, Now, if Matt's dividends were reinvested into the stock - and if you have a 401(k) or IRA, that's what usually happens - then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500. Note:  In the real world, in current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

hope this helped you ;)

Matt probably would have got about a 5% return on a good stock.

The rate of return is just the total return divided by investment.

Consider that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500.

Now, if Matt's dividends were reinvested into the stock then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500.

In the real, current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

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Step-by-step explanation:

AD ≅ BC, Given

∠BCD ≅ ∠ADC, Given

CD ≅ CD, Reflexive property

ΔBCD ≅ ΔADC, SAS congruence

∠BDC ≅ ∠ACD, CPCTC

ΔECD is an isosceles triangle, definition of isosceles

DE ≅ CE, properties of isosceles triangles

Answer:

A

Step-by-step explanation:

Descending order is where the monomials of a polynomial are arranged in decreasing exponent order so the answer is A.

Answer:

the answer is option a because all the expression in option a is written descending power form.

Answer:

see below

Step-by-step explanation:

Multiplication and division are also inverse operations

15 * 10 = 150

150 ÷10 = 15

Divide 150 by 10 and we get 15 back

The division undoes the multiplication

This also works in reverse

150 ÷ 10 = 15

15*10 =150

The multiplication undoes the division

Answer:

2 cm

10 cm

Step-by-step explanation:

14/7 = 2

This helps to find because area of rectangle = bh or base times height.

A = 1/2 bh

30 = 1/2 b 6

30 = 3b

b = 10

Answer:

b = 2 cm

b = 10 cm

Step-by-step explanation:

Area of a Rectangle: A = lw

Area of a Triangle: A = 1/2bh

We are given area and length, so simply plug it in:

14 = 7w

w = 2 cm

We are given area and height, so simply plug it in:

30 = 1/2(6)(b)

30 = 3b

b = 10 cm

Hey there! :)

Answer:

5m - 2.

Step-by-step explanation:

We can use long division to divide the two expressions:

             5m - 2

5m - 2 | 25m² - 20m + 4

            25m² - 10m

           -

            0m² - 10m + 4

                    -10m  + 4

                  -

                      0

The quotient of this operation is 5m - 2.

Answer:

needddd

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex]y=\frac{-9x-5}{-8}[/tex]

factoring out a negative[tex]y=\frac{9x+5}{8}[/tex]

Answer:

Option D is the correct option.

Step-by-step explanation:

Given that

9x - 8y = 0

finding y-intercept

put x = 0 , we get

9(0) - 8y + 5 = 0

Calculate the product

-8y + 5 = 0

Move the constant to L.H.S and change its sign

-8y = 0 - 5

Calculate the difference

-8y = -5

divide both sides of the equation by -8

-8y/-8 = -5/-8

Calculate

y = 5/8

Hope this helps...

Good luck on your assignment...

Answer: CPCTC

Step-by-step explanation:

because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.

By CPCT [Corresponding Part of congruent Triangle]

<h=<j

hope i helped

-lvr

Answer:

144

Step-by-step explanation:

x = ((n-2)π / n) radians = (((n-2)/n) x 180° ) degrees

Step-by-step explanation:

The exterior angle of a regular n-sided polygon is given by

Exterior angle = 360/n  

The interior angle is therefore the supplement of the exterior angle,

Interior angle = 180 - 360/n

for n=10, decagon,

Interior angle of a decagon = 180 - 360/10 = 180-36 = 144 degrees