Simplify 3 square root of 2 - 3 square root of 18

Answer:

(a)  12.96 ft²

(b)  21.5 in²

Step-by-step explanation:

(a) For the first diagram

Area of the shaded region (A) = Area of Tripezium- area of circle

A = [1/2(a+b)h]-[πr²]............... Equation 1

Where a and b are the parallel side of the tripezium respectively, h = height of the tripezium, r = radius of the circle.

From the diagram,

Given: a = 15 ft, b = 6 ft, h = 12 ft, r = h/2 = 12/2 = 6 ft.

Constant: π = 3.14

Substitute these values into equation 1

A = [12(15+6)/2]-(3.14×6²)

A = 126-113.04

A = 12.96 ft²

(b) For the second diagram,

Area of the shaded region (A') = Area of square- area of circle

A' = (L²)-(πr²)............. Equation 2

Where L = lenght of one side of the square, r = radius of the circle

From the diagram,

Given: L = 2r = (2×5) = 10 in, r = 5 in

Substitute these values into equation 2

A' = (10²)-(3.14×5²)

A' = 100-78.5

A = 21.5 in²

Given:

The equation is:

[tex]x^2+5x=2[/tex]

To find:

The solution of the given equation by completing the square.

Solution:

We have,

[tex]x^2+5x=2[/tex]

We need to add the square of half of the coefficient of x on both sides.

Adding [tex]\left(\dfrac{5}{2}\right)^2[/tex] on both sides, we get

[tex]x^2+5x+\left(\dfrac{5}{2}\right)^2=2+\left(\dfrac{5}{2}\right)^2[/tex]

[tex]\left(x+\dfrac{5}{2}\right)^2=2+\dfrac{25}{4}[/tex]

[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{8+25}{4}[/tex]

[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{33}{4}[/tex]

Taking square root on both sides, we get

[tex]x+\dfrac{5}{2}=\pm \sqrt{\dfrac{33}{4}}[/tex]

[tex]x=\pm \dfrac{\sqrt{33}}{2}-\dfrac{5}{2}[/tex]

[tex]x=\dfrac{\pm \sqrt{33}-5}{2}[/tex]

[tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex]

Therefore, the solutions of the given equation are [tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex].

Answer: d and e

Step-by-step explanation:

edge 2021 :)

Answer:

87

Step-by-step explanation:

first find x

all triangles = 180°

180=32+2x+x+15

combine like terms

180=47+3x

180-47=133

133=3x

133/3=44.334 or 44 1/3

2(44.334)= 88.66 ooor 87 if you round it

Answer:

sorry not sure

Step-by-step explanation:

Answer:

[tex]3174cm^{2}[/tex]

Step-by-step explanation:

Each square has an area of [tex]529cm^{2}[/tex]

So we multiply that by the number of squares which is 6.

Answer:

Triangle!!

Step-by-step explanation:

If you cut the pyramid in half, it will leave triangles. Hope this helps!

Answer:

the correct answer is C

4x=52

52 divided in 4 parts is 13, so each ticket is 13 dollars

Answer:

b

Step-by-step explanation:

6 of the numbers are even from a total of 13

6/13 is roughly 46%

Answer:

The probability of choosing a number is ≈46%.

Step-by-step explanation:

What is probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

The number set is:

{1,2,3,4,5,6,7,8,9,10,11,12,13}

The even numbers is:

{2,4,6,8,10,12}

Total outcomes = 13

Number of possible outcomes = 6

The probability of the outcome is:

[tex]P(E)=\frac{6}{13} *100\\ =46.153%[/tex]

≈46%

Hence, the answer is option B.

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Answer:

About 2288 miles

Step-by-step explanation:

43.6 rounded is 44.  There are 52 weeks in a year.  Therefore, 44x52 equals about 2288

Answer:

Infinitely many solutions

Step-by-step explanation:

Both sides are same, it means regardless the value of x the equation is correct. The equation has infinitely many solutions

Answer:

4C2 * 6C2 * 5C2

Step-by-step explanation:

White balls = 4

Yellow balls = 6

Red balls = 5

In other to select a total of 6 balls, of which there must be 2 balls each of color white, yellow and red :

That means :

2 red balls from 5 red balls = 5C2

2 balls for 6 yellow balls = 6C2

2 balls from 4 white balls = 4C2

To obtain the number of possible combinations, take the product of the three combinations :

4C2 * 6C2 * 5C2

If bag contains 4 white balls, 6 yellow balls, and 5 red balls then  6 balls can be chosen if there must be 2 balls of each color in 900 ways

permutation is way of selecting and arranging things while combination is way of selecting things .

Given that  bag contains 4 white balls, 6 yellow balls, and 5 red balls

we have to select 6 balls

it's given that there must be 2 balls of each color

So here's how we can select them

2 white balls ,2 yellow balls and 2 red balls

So we have to select 2 white balls out of 4  white balls ,2 yellow balls out of 6 yellow balls and 2 red balls out of 5 red balls

so number of ways of selecting

[tex]{4 \choose 2} \times {6 \choose 2}\times {5 \choose 2}[/tex]

[tex]=6\times15\times10\\\\=900[/tex]

If bag contains 4 white balls, 6 yellow balls, and 5 red balls then  6 balls can be chosen if there must be 2 balls of each color in 900 ways

To learn more about  combination visit :  https://brainly.com/question/25821700

Answer:

3) never

Step-by-step explanation:

Because if both lines are the same then they will have infinite solutions in common.

Answer:

3- Never

Step-by-step explanation:

Answer:

$39.36

Step-by-step explanation:

Since its 20% off that means we still have a remaining 80% so first multiply 0.8 to the 82

82x0.8= 65.6

Since there is a additional 40% off multiply by 0.4 to get the discount amount

65.6x0.4= 26.24

Subtract the discount from the price

65.6-26.24= 39.36

This looks super complicated, but it can actually be solved with the application of a couple of area equations.

Let's establish one fact before we start this question that may have been the reason why this was so confusing for you. No matter what kind of triangle, the area will always be [tex]\frac{1}{2}[/tex] times the length of the base times height.

Alright, with that established, let's start trying to solve for the area.

In this question, we seem to have a triangle with a circle shape taken out of it. We are told to find the area of the shaded area.

The overall equation would be:

[tex]Area_{triangle}[/tex] - [tex]Area_{circle}[/tex]

This makes sense, right? If we find the area of the triangle and subtract the area of the circle within it, it should give us the total shaded area.

Now, let's begin solving for said shaded area:

[tex]Area_{triangle}[/tex] - [tex]Area_{circle}[/tex]

([tex]\frac{1}{2}[/tex] * base * height) - (π*[tex]r^{2}[/tex])

The given base of the triangle is 40 km, the height 27 km, and the circle's diameter is 12. Therefore:

([tex]\frac{1}{2}[/tex] * 40 * 27) - (π * [tex](\frac{12}{2})^{2}[/tex])

(540) - (π * [tex]6^{2}[/tex])

540 - 36π

Use 3.14 as the value for pi:

540 - 36(3.14)

426.96

Round to the nearest tenth:

427.0

Shaded area = 427 ([tex]km^{2}[/tex])

If you have any questions on how I got to the answer, don't be afraid to ask!

- breezyツ

Answer:

-22

Step-by-step explanation:

Use inverse operations.

So, if Sushil last divided, we would need to multiply.

-5*3 =-15

After multiplying, we should subtract the positive seven from negative fifteen.

-15-7 =-22

Answer:

You are more likely to grab a red marble. You are less likely to grab a green marble.

Step-by-step explanation:

6/16 is greater than 5/16. The bigger the number, the higher the probability.

Have a great day!

Answer:

Rico Spent $6.50 on each car.

Step-by-step explanation:If you divided 52 by 8 you get 6.5 in money it would be $6.50.

My answer is reasonable because my estimate ÷ 10 = $6.50

Answer:

The answers are: 6.5$ , divided by, and 5$

Step-by-step explanation:

In order to figure out the price of each toy car, we must divide 52/8 (the total price of the toy cars divided by the number of the cars) which equals to 6.5, meaning that each toy car costs 6.5$, since they all have the same price. We know that this is a reasonable price because say we were to estimate, meaning we'd take a guess without doing any calculations. Let's say we paid 50$ in total, which is easily divided by 10, if we were to round up both numbers, we'd get 5$ each. That's close to the true answer, making it reasonable to take such a guess.

Answer:

0.50

Step-by-step explanation:

5/10=1/2

100/2=50

50*1=50

50 equals to 0.50 as a decimal

Answer:

b) 3 1/2 units^3

Step-by-step explanation:

Answer: d. Date

Step-by-step explanation:

Some of the information printed on the bottom of a check include the check number which is typically a security measure that is used in the identification of payment so as to prevent fraud.

The routing number also informs the bank where the funds for the check can be found.

The account number informs the person that collects the check about the account that the money is coming from.

We should note that the date is at the top of the check and one has to fill it himself or herself before giving the check to the recipient.

Answer:

first give options it is very hard to do

Answer:

50 students from each grade

Step-by-step explanation:

If we get the similar amount of people from each and every grade so this would represent the percentage occur from each grade this determine the number of people who vote per grade and represent that how much would the vote for student comes

Also 50 is easily divisible by 750

Therefore the above represent the answer

Answer:

I dont know the W and the L but to find the area of the shaded part. multiply the width of the shaded part and the length of the shaded part and you will get the area

Answer:

The angle measure is 43 degrees

Step-by-step explanation:

The right angle adds up to 90 degrees in whole, you already have 47 degrees so you want to subtract 47 from 90, then you will get your answer.

Answer:

c

Step-by-step explanation:

Answer:

(-12, -18)

Step-by-step explanation:

https://www.omnicalculator.com/math/endpoint

Answer:

I = $337.50

Step-by-step explanation:

I = prt

I = 4500(.025)(3)

I = 337.50

The interest earned is $337.50.

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.

Simple Interest = Principal x Interest Rate x Time/ 100

Given:

Principal= 4500

Rate= 2.5%

Time= 3 years

Using Simple Interest

SI = ( P x R xT)/100

SI = (4500 x 2.5 x 3) /100

SI = 33750/100

SI = $337.50

Hence, the interest earned is $337.50

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Answer:

how can I help u sir...???