Louis wants to carpet the rectangular basement. The basement has an area of 874 square feet. The width of the basement is 2/3 it’s length. What is the length?

Answer:

1a. 210 m^2  1b. 14 ft^2  1c. 199.5 in^2

2a. 270 cm^2  2b. 162 m^2  2c. 272 cm^2

3a. 348 ft^2  3b. 230 in^2  3c. 312.5

Step-by-step explanation:

The area of a triangle can be calculated with one equation...

A = 1/2bh

b stands for base, h stands for height

1a. A = 1/2(21)(20)

    One half divides 20 easily..

A = 21(10)

A = 210

1b. A = 1/2(7)(4)

    One half divides 4 easily..

A = 2(7)

A = 14

1c. A = 1/2(19)(21)

A = 1/2(399)

A = 199.5

2a. A = 1/2(36)(15)

    One half divides 36 easily..

A = 18(15)

A = 270

2b. A = 1/2(18)(18)

   One half divides 9 easily..

A = 9(18)

A = 162

2c. A = 1/2(32)(17)

  One half divides 32 easily..

A = 16(17)

A = 272

3a. A = 1/2(29)(24)

  One half divides 24 easily..

A = 12(29)

A = 348

3b. A = 1/2(23)(20)

  One half divides 20 easily..

A = 10(23)

A = 230

3c. A = 1/2(25)(25)

A = 1/2(625)

A = 312.5

Finding area of triangle --> [tex]\frac{1}{2}*b*h[/tex]

     Question 1:

         a.   [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*20*21 = 210 m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*4*7 = 14 ft^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h= \frac{1}{2} *21*19=199.5in^2[/tex]

     Question 2:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *36*15 = 270cm^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *18*18 = 162m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *17*32 = 272cm^2[/tex]

     Question 3:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *24*29 = 348ft^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *20*23 = 230in^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *25*25 = 312.5cm^2[/tex]

Finding Area of Parallelogram --> b * h

     Question 1

         a. [tex]Area = b * h = 24 * 26 = 624cm^2[/tex]

         b. [tex]Area = b * h = 15 * 30 = 450in^2[/tex]

         c. [tex]Area = b * h = 21 * 31 = 651 mm^2[/tex]

      Question 2

         a. [tex]Area = b * h = 18 * 17 = 306 in^2[/tex]

         b. [tex]Area = b * h = 10.5 * 15 = 157.5m^2[/tex]

         c. [tex]Area = b * h = 12.5*11=137.5cm^2[/tex]

      Question 3:

          a. [tex]Area = b * h = 5.7*11.5=65.55in^2[/tex]

          b. [tex]Area = b * h = 8 * 12.5 = 100ft^2[/tex]

          c. [tex]Area = b * h = 1.7 * 3.6 = 6.12m^2[/tex]

Hope that helps!

Answer:

I dont see any triangle but the sum of the interior angles of every triangle is 180

Step-by-step explanation:

<+<+<=180˚

Answer:

3(x-6)=3x-18

Step-by-step explanation:

Answer:

The answer is 37.

Step-by-step explanation:

First of all we use Pemdas. Add the parantheses first. So its 7-18(-5/3) then you multiple the -18 to 5/3 Because after Parantheses its Exponents multiplication. So it becomes 30. Then you add 7 to get 37. I hope this is helpful.

Answer:

-8.5

Step-by-step explanation:

this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.

Answer:

109.2 degrees

Step-by-step explanation:

Use the cos law to find angle F

3.1^2 = 2^2 + 1.8^2 - 2 (2)(1.8) cos F

shows cos f = -.329

arc cos( - .329) = angle F =109.2 degrees

Answer:

Step-by-step explanation:

The coefficients of x and y in the first equation will be the 2 x 2 matrix first row and the coefficients of x and y in the second equation will be the second row:

[tex]\left[\begin{array}{ccc}9&5\\2&-10\\\end{array}\right]\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}-16\\-48\\\end{array}\right][/tex]

When you take the inverse of that 2 x 2 matrix and multiply it with the right side matrix (-16 -48), you can find the solution for x and y.

Answer:

Step-by-step explanation:

Answer:

________________________________________________________

Multiply all numbers by the multiplier, the smaller number, and then use any extra digits you carry, bringing you to the ten thousands place.

________________________________________________________

Ask me in the comments box, I can help.

Answer:

No

Step-by-step explanation:

6 time 180 is only 108

108<120

There is not enough chalk.

Answer:

9

Step-by-step explanation:

700,000

90,000

6,000

100

40

2

Answer:

9

Step-by-step explanation:

796,142

100000  10000    1000  100  10   1

Step-by-step explanation:

SinP = sin30° = 1/2

sinQ = sin60° = root3/2

cosR = cos90° = 0

cosQ = cos60° = 1/2

sinR = sin90° = 1

We are given with a sequence, which is a GP (Geometric Progression), as the ratio [tex]{\bf{a_{n+1}:a_{n}}}[/tex] is 1/3 for every [tex]{\bf{n\in \mathbb{N}}}[/tex], so 1/3 is the comman ratio r, and we needa find sum till 6 terms, so n = 6, and first term is 6, so putting all the values we will be having ;

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg\{1-{\bigg(\dfrac13\bigg)}^{6}\bigg\}}{1-\dfrac13}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg(1-\dfrac{1}{3^{6}}\bigg)}{\dfrac{3-1}{3}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\div \dfrac23}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\times \dfrac32}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^{6}-1}{3^{4}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^6}{3^4}-\dfrac{1}{3^4}}[/tex]

[tex]{:\implies \quad \sf S_{6}=3^{2}-\dfrac{1}{81}}[/tex]

[tex]{:\implies \quad \sf S_{6}\approx 9-0.012\approx 8.988\approx \boxed{\bf{8.99}}}[/tex]

Although Alex and Lauren will both step into position 4,6, they will not do it at the same time, so they will not meet.

Lauren:

Alex:

Both will step in the position 4,6, However, Lauren will be in this positon in the second 4, while Alek will do it on the second 3.

Learn more about parametric equations in: https://brainly.com/question/12718642

#SPJ1

Answer:

3780/90

what number close to 37 is divisible by 9 ? 36 !!

3600/90=40 or 3690/90=41

3780/90=42

this an underestimate because the compatible numbers 3600 and 3690 are less than 3780

yall be safe

Our estimate is 38. This estimate is an overestimate because we rounded up both numbers, so we expect the actual quotient to be slightly smaller than our estimate.

Compatible numbers are numbers that are simple to mentally work with and can be used to estimate or simplify a more complex calculation.

When performing addition, subtraction, multiplication, or division, for example, it is often helpful to choose numbers that are easy to manipulate in your head or by hand, such as multiples of 10, 100, or 1000.

To estimate the quotient of 3,780 divided by 90 using compatible numbers, we can round 3,780 to 3,800 (which is divisible by 100) and round 90 to 100. Then, we have:

3,800 ÷ 100 = 38

Thus, the estimate is 38. This estimate is an overestimation because we rounded both numbers, so we anticipate that the actual quotient will be slightly lower than our estimate.

For more details regarding Compatible numbers, visit:

https://brainly.com/question/926291

#SPJ2

Answer:

As Per Provided Information

We have been asked to find the length , perimeter and area of square .

First let's calculate the side of square .

Using Formulae

[tex] \boxed{\bf \:Diagonal_{(Square)} \: = side \sqrt{2}}[/tex]

On substituting the value in above formula we obtain

[tex] \qquad\longrightarrow\sf \:4 \sqrt{2} = side \sqrt{2} \\ \\ \\ \qquad\longrightarrow\sf \:4 \cancel{\sqrt{2}} = side \cancel{ \sqrt{2}} \\ \\ \\ \qquad\longrightarrow\sf \:side \: = 4 \: cm[/tex]

Therefore,

Finding the perimeter of square.

[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]

Substituting the value we obtain

[tex]\qquad\longrightarrow\sf \:Perimeter_{(Square)} \: = 4 \times 4 \\ \\ \\ \qquad\longrightarrow\sf \:Perimeter_{(Square)} = 16 \: cm[/tex]

Therefore,

Finding the area of square .

[tex] \boxed{\bf \: Area_{(Square)} = {side}^{2}}[/tex]

Substituting the value we get

[tex]\qquad\longrightarrow\sf \:Area_{(Square)} \: = {4}^{2} \\ \\ \\ \qquad\longrightarrow\sf \:Area_{(Square)} = 16 \: {cm}^{2} [/tex]

Therefore,

Answer:

Step-by-step explanation:

In order to determine the correct answer, we need to confirm it first by making the solution below:Costs: $89.95 = New Lamp $239.99 = Comforter 6 3/5% = Sales Tax (convert this to decimal and we get 6.6%)  $351.72 = Total amount the Chang's paidLet's get the total costs first which is $329.946.6% of 329.94 is $21.78The total cost with the tax would be $351.72.Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.

Answer:

49/3 or 16.33...

Step-by-step explanation:

15 + 4/3.

15/1 + 4/3

45/3 + 4/3.

ANSWER: 49/3

For questions 4 – 6, name all of the radii of the circle shown in the figure.

For questions 7 – 10, find the measure of the radius of the circle. 7. 8.

Answer:

center(-2,5) r=6

Answer:

1, 5

Step-by-step explanation:

I may be a little wrong but;

Multiply it by 3 and 4-

-12x+9y=-51

12x-16y=44

-7y=-7

y=1

x=5

Answer:

x = 5

x = -15

Explanation:

Let the number be "x"

===================

Answer:

x= 5 or -15

Step-by-step explanation:

let the number be x

(x+5)^2=100

x^2+10x+25=100

x^2+10x-75=9

look for factors of 75 that when you gives you 10 and when you multiply gives you -75

those factors are 15 and -5

replace 10x with 15x and -5x

x^2+15x-5x-75=0

then group them, and factorize

x(x+15)-5(x+15)=0

x-5=0 or x+15=0

x= 5 or x= -15

Answer:

Jason can afford 5 more additional lines, making 9 lines total because

175-120=55

55/10=5.5 so He can not afford more than 5 more additional lines.

Step-by-step explanation:

Answer:

0.55

Step-by-step explanation:

In this question we need to find the Z score says that the area under the standard normal curve to the right is 0.29. So here in this question I have drawn here the normal distribution curve. So at this point we need to calculate the z value And with the probability of 29%. So to find the value of Z says that probability of zero great Small, that is equal to 0.29. So I can write this left hand side as one minus probability of less than small. It's called a 0.29 probability of zero, less than or equal to zero will do 0.29 one minus .29 which is equal to 0.71. So here we know the value of probability And we need to find the value of zero and there are various methods to calculate that one is the using the normal distribution tables and then there is the um MS Excel should. So from the table you can find the area closest to 0.71. So here the flow chart for finding me value. Using normal distribution table is given. So the first thing is from this table of the standard normal distribution, look at the probability value. So as you can see from this this is the snapshot of the table we need to find the probability value. So We have got the value of 0.71. So this is the nearest value to that you need to, next second is move left until the first column is reached. So move left until the first column is rich. This is the first column. Move upward until the top row is rich. Note that value. So here as you can see it is 0.5 and here it is 0.05. The intersection of the Roman columns gives the area of the two day loves. So which is 0.5 Plus 0.05 is equal to zero 55. This is the value of Z. Or as you can use the um xxl shoot to calculate the value of Z. Here, I have given the flow chart for that. Also you can use this to calculate the value of Z. So probability of mhm Less than or equal to 0.55 Is equal to 0.71. This is the answer. 0.55 is the answer for the solution.

I bet the sum you're referring to is supposed to be

[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]

or equivalently,

[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Recall the binomial series,

[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]

which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)

Differentiating both sides with respect to x gives

[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]

Multiply both sides by some arbitrary x in |x| < 1 :

[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]

Repeat:

[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]

[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]

Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to

[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]

In order to solve this equation, we need to take the square root of both sides (in order to get rid of the square and isolate x, because we are asked to determine the value(s) of x)

x²=36

√x²=√36

x=6

Is this the only solution?

A negative times a negative is a positive...

-6 is another solution of this equation! :)

Hence, the answers are:-

[tex]\boxed{\boxed{\bold{x=6; ~x=-6}}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Hello! My name's Cupcake, And I will be helping you today! :D

In order to solve this equation, we need to take the square root of both sides.

Why? Because we need to isolate x. Our goal is:- To find the value of x.

So in order to get rid of the square and find the value of x, we take the square root of both sides:-

x^2=36

x=6, x=-6 (solutions)

Hope it helps!

Any queries - comment !

Answer:

At this point, you have walked 17/24 miles in all.

Hope this helps

Answer:

x = -12

Step-by-step explanation:

⇒ -5x = 60

Isolate the variable "x" by dividing by -5 on each side.

⇒ -5x/-5 = 60/-5

⇒ x = -12

The solution is x = -12

[tex]\boxed{ \sf \bold{x = -12}}[/tex]

Explanation:

[tex]\dashrightarrow \ \ \sf -5x = 60[/tex]

divide both sides by -5

[tex]\dashrightarrow \ \ \sf \dfrac{-5x}{-5} = \dfrac{60}{-5}[/tex]

simplify

[tex]\dashrightarrow \ \ \sf x = -12[/tex]

Δ perimeter of swimming area:

Δ area of roped off section: