Simplify $\frac{3}{2 \sqrt 3 - 3}.$[tex]Simplify $\frac{3}{2 \sqrt 3 - 3}.$[/tex]

Hello! :)

Answer:

[tex]\huge\boxed{BC = 6.4 }[/tex]

Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:

[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]

Let BC = x:

[tex]\frac{8}{15} = \frac{x}{12}[/tex]

Cross multiply:

[tex]8 * 12 = 15 * x[/tex]

[tex]96 = 15x[/tex]

[tex]x = 6.4[/tex]

Therefore, BC = 6.4 units.

Hope this helped you!

Answer:

Step-by-step explanation:

Answer:

-1/20

Step-by-step explanation:

For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.

To find slope the formula is (y2-y1)/(x2-x1)

So in this case it is 2-4/40-0

-2/40

This reduces to -1/20

Answer:

the perimeter of ΔABC is 32in

Step-by-step explanation:

We know that intersection point of the angle bisectors refers to the incenter of the triangle,.

Given tmthe radius of 4inch for the centre of the incircle.

One of the properties of the incircle is that the distances (d) from vertex C to the nearest touchpoints are equal and have the value

In an incircle , the distances (d) along vertex C and touchpoints have equal value and can be expressed as

d = 1/2(a +b -c)

And a, b, c represent lengths of the sides

We were given the hypotenuse (c) as 12 in, with the radius of 4inch for the

distance from the right-angle vertex C to the incircle touchpoints .

We can determine the sum a+b as

4 = (1/2)(a+b -12) .

4/(1/2)= (a+b -12)

8= (a+b -12)

20=a+b

Which is the addition of length of the two legs of the triangle.

We can determine the perimeter which is the addition of the leg lengths as well as the hypotenuse length.

perimeter = 20 in + 12 in = 32 in

Therefore, the perimeter of ΔABC is 32in

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

Answer:

x = s/2

Step-by-step explanation:

● s states have joined the union in 1788

● half of s have joined in 1889

Let x be the number of states that have joined in 1889

● x = (1/2)× s

● x = s/2

Answer:

1/4 or 25%

Step-by-step explanation:

Each dice has six sides, meaning the numbers that are even are: 2,4, and 6, three even numbers per dice. Meaning the chance of rolling ONE dice is 50%. So if you were to get two even numbers on TWO dice, it would be 25% hope this helps.

The odds in favor of rolling two even numbers when rolling a pair of dice would be 25% or 1/4.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Each dice has six sides, means the numbers that are even are:

2,4, and 6, three even numbers per dice.

The total number of outcomes is 6 x 6 or 36.

Meaning the chance of rolling ONE dice is 50%.

The odds in favor of rolling two even numbers when rolling a pair of dice would be 25%.

Learn more about probability here;

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Answer:

Step-by-step explanation:

The variation p varies directly with T is written as

p = kT

where k is the constant of proportionality

To find p when T =500 we must first find the formula for the variation

That's

when p = 105 and T = 400

105 = 400k

Divide both sides by 400

So the formula for the variation is

when

T = 500

Substitute it into the above formula

That's

[tex]p = \frac{21}{80} \times 500[/tex]

Simplify

The final answer is

Hope this helps you

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30

Answer:

7 : 18

Step-by-step explanation:

1. Convert to the same units (cents)

70 cents = 70 cents

$1.80 = 180 cents

2. Simplify

70 : 180 (divide both by ten)

7 : 18

7 and 18 cannot be simplified any further.

Answer:

1.) ( -4, -2 ), ( -6, - 3 )

2.) ( 0, 2 ) , ( 0 , 4 )

Step-by-step explanation:

The inequality sign of >=, the greater than or equal to sign, the upper region will be shaded while for less than sign <, the lower region will be shaded.

Please find the attached file for the solution and the answer.

Answer:

u^18

Step-by-step explanation:

(u^3)^6

=

u^(3*6)

=

u^18

Hope this helps!

Answer:

Answer choices A, B and C identifies the relevant information in the problem

Step-by-step explanation:

Sarah left the house at 12:15 pm

She spent $42.20 on two books for her children

She spent $5.67 on a toy for her dog

Sarah arrived home at 1:00 pm

How much did Sarah spent on each book?

If she spent $42.20 on two books for her children,

Then, it means she has two children and the book cost $21.10 each

Answer choices A, B and C identifies the relevant information in the problem

Answer:

its A all the other one dont make sence sorry if im wrong but i got it right on my test

Step-by-step explanation:

Answer:

(D) [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]

Assuming that a is our x² term, b is our x term, and c is the constant, we can substitute inside the equation.

[tex]\begin{array}{*{20}c} {\frac{{ - (-5) \pm \sqrt {5^2 - 4\cdot1\cdot3} }}{{2\cdot1}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 12} }}{{2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]

So the answer is D, [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex].

Hope this helped!

Answer:

99

Step-by-step explanation:

x = 90 x 10/100 + 90

=> x = 900/100 + 90

=> x = 9 + 90

=> x = 99

Answer:

572 7s are needed to be added together

Step-by-step explanation:

Basically, what we are asked here is the multiple of 7 which is closest to but above 4,000

Then, from this multiple , the number of 7s which are added together to give it is our answer.

By multiplication; 7 * 572 = 4,004

This is the closest multiple of 7 to 4000 which is also above it.

So the fewest number of 7s which we can add together is 572

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

[tex]$x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2} $[/tex]

[tex]\text{Consider the discriminant as }\Delta[/tex]

[tex]\Delta=b^2-4ac[/tex]

Once we got a trinomial here, just put in factored form:

[tex]$\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{\Delta}}{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{b^2-4ac}}{2a} $[/tex]

Answer:

center=0,0 vertices=(0,5)(0,-5) foci=(0,4)(0,-4)  

Step-by-step explanation:

used calculator

Answer: The number of pounds depend on the total price.

Step-by-step explanation:

Answer: it’s c

Step-by-step explanation:

It just is also, it’s for plato

Answer:

Identity Property of Multiplication

Step-by-step explanation:

The Identity Property of Multiplication states that any number multiplied by 1 will equal the same number.

Since we have one item that costs $14.50, we know that the total cost will be $14.50 since we are multiplying $14.50 by 1.

Hope this helped!

Answer:

Identity property of multiplication.

Step-by-step explanation:

When we multiply any number by 1, we will get the same number.

5 *1 = 5

-8 * 1 = -8

Answer:

  a. almost 8 years

Step-by-step explanation:

Brenda's expected annual increase in salary is ...

  $63,292 -45,258 = $18,034

If we assume that Brenda's cost of education includes going without 2 years' salary as well as the cost of tuition, her degree's total cost will be ...

  2×$45,258 +15,000 = $105,516

__

Once Brenda starts earning again, she is recovering this cost at the rate of $18,034 per year, so it will take ...

  $105,516/($18,034 /yr) = 5.85 yr

to recover that cost.

Since Brenda spent 2 years in school, from the time she decides to start school until she has recovered her cost, it will be 2 + 5.85 = 7.85 years, almost 8 years.

_____

If Brenda can continue working while going to school, she can recover her tuition cost in about 10 months after graduation.

Answer:

C

Step-by-step explanation:

Answer:

$307.20

Step-by-step explanation:

8×24=192

Convert 192 square feet to square yards, which is 21.3333

Then multiple: 21.333×14.40=307.1999

Then round to the nearest hundredths

The final answer is $307.20

Incomplete Question:

The content of the pie chart is as follows:

Hamsters  = 9% ; Snakes  = 10% ; Cats  = 23%

Birds  = 21% ;  Dogs  = 26% ;  Fish  = 11%

Answer:

The number of citizens who chose cat or fish is 47,600

Step-by-step explanation:

Given

Number of citizens = 140,000

Required

Determine the number of those that chose fish or cats

First, we need to calculate the percentage of those whose pets are either cats or fish

[tex]Percentage = Cat + Fish[/tex]

Substitute 23% for cat and 11% for fish

[tex]Percentage = 23\% + 11\%[/tex]

[tex]Percentage = 34\%[/tex]

Next, is to multiply the calculated percentage by the number of citizens

[tex]Cat\ or\ Fish = Percentage * Number\ of\ Citizens[/tex]

[tex]Cat\ or\ Fish = 34\% * 140000[/tex]

[tex]Cat\ or\ fish = 47600[/tex]

Hence, the number of citizens who chose cat or fish is 47,600

the number of citizens who chose cat or fish is 47,600

= Number of citizens × total percentage

[tex]= 140,000 \times (23\% + 11\%)\\\\= 140,000 \times 34\%[/tex]

= 47,600

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Answer:

The probability it will land on green every time is [tex]\frac{1}{27}[/tex].

Step-by-step explanation:

We are given that a spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow.

The pointer is spun three times.

As we know that the probability of an event is described as;

  Probability of an event =  [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]

Here, the favorable outcome is that the spinner will land on green every time.

So, the number of green regions = 2

Total number of regions = 3(red) + 2(green) + 1(yellow) = 6 regions

Now, the probability it will land on green every time is given by;

        Probability =  [tex]\frac{2}{6}\times \frac{2}{6}\times \frac{2}{6}[/tex]

                           =  [tex]\frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}[/tex]

                           =  [tex]\frac{1}{27}[/tex]

Hence, the probability it will land on green every time is [tex]\frac{1}{27}[/tex].

Using the concept of probability, the probability of landing on green for all 3 spins is [tex] \frac{1}{27}[/tex]

Total number of portions = (3 + 2 + 1) = 6

Recall :

Probability of rolling green on a single spin :

Therefore, the probability of obtaining green on all spins :

Learn more : https://brainly.com/question/15929089

Answer:

Step-by-step explanation:

The shaded regions consist of a triangle and a semicircle

Area of shaded regions = Area of Triangle + Area of semicircle

Area of Triangle = (h x b) ÷ 2

Height, h = 10 cm

Base, b = 8 cm

Are of the triangle component = (10 x 8) ÷ 2

= 80 ÷ 2

= 40 cm^2

 Area of semicircle = πr^2 ÷ 2

Diameter, D = 8 cm

Radius, r = 8 cm ÷ 2 = 4 cm

Are of the semicircle component = [π(4^2) ÷ 2)

= 16π ÷ 2

= 16π cm^2

 Total area of shaded regions

= (40+16π) cm^2

= 8 (5 +2π) cm^2

Answer:

[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]

[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]

Step-by-step explanation:

Area of the figure:

Firstly: Area of semicircle:

[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]

Then Area of Triangle

[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]

Area of Figure = Area of Semicircle + 2(Area of triangle)

=> 8π + 2(20)

=> 8π + 40 cm²

Perimeter of Semicircle:

Firstly, we'll have to find the hypotenuse

[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]

Then, Perimeter of the semi-circle:

=> πr

Where r = 4 cm

=> 4π

Now, the perimeter of the whole figure:

=> 4π + 2(11)

=> 4π + 22 cm

Answer:

A pear is 3.4

Step-by-step explanation:

Answer: A pear cost $4.

Step-by-step explanation:

If the total price of four oranges and five pears is $32 then we could represent it by the equation  4x + 5y = 32   where x is cost of one orange and y is the cost of one pear.

The same way we could represent the second statement by the equation

3x + 2y = 17      

We know have the two systems of equations:

4x + 5y = 32

3x + 2y = 17         Solve using the elimination method

  Multiply the top equation by -3 and the down equation by 4 to eliminate x.

-3(4x + 5y) = -3(32) =  -12x - 15y = -96

 4(3x +2y) = 4(17)  =   12x + 8y = 68    

We now have the two new equations:

-12x -15y = -96      Add both equations

12x + 8y = 68            

      - 7y = -28

     y= 4    

Which means the cost of one pear is $4.

Answer:

9 dollars per hour

Step-by-step explanation:

36/4=9

Answer:

9

Step-by-step explanation:

4 hours : $36

1 hour : $ x

we need to find x so,

4 hours ÷ 4 = 1 hour

1 : $

since we have divided 4 by 4,

we need to do that to 36 aswell

36  ÷ 4 = 9

1 hour : $9

Step-by-step explanation:

For example:

Ex: 2:3 :: 6:9

In this question, the means are 3 and 6.

The extremes are 2 and 9.

We use this method to find whether the two ratios are equal or not.

We multiply the means and the extremes, and if there products are same, then these two ratios are proportional.

If these two ratios are proportional, their "means" = "extremes"

=> Means = Extremes

=> 3 x 6 = 2 x 9

=> 18 = 18

So, these two ratios are proportional.

Hope this helps you.

Answer:

y^6 - 9y^4 + 27y² - 27

Step-by-step explanation:

(y² - 3) (y^4 - 6y² + 9)

y^6 - 6y^4 + 9y² - 3y^4 + 18y² - 27

y^6 - 9y^4 + 27y² - 27

Answer:

hey hon! 2 liters is equal to 67.628 fluid ounces :) hope you have a nice day.