Find the length of side xx in simplest radical form with a rational denominator.

Find The Length Of Side Xx In Simplest Radical Form With A Rational Denominator.

Answers

Answer 1
Answer:  6

Explanation:

For any 30-60-90 triangle, the hypotenuse is always twice as long compared to the short leg. The short leg is always opposite the 30 degree angle.

Answer 2

The length of x is 6.

What is a right-angled triangle?

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given problem,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = [tex]\frac{perpendicular}{hypotenuse}[/tex]

∅ = 30°

⇒ sin30 = [tex]\frac{3}{x}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{x}[/tex]  [ sin30 = [tex]\frac{1}{2}[/tex] ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ 6² = 3² + Base²

⇒ 6² - 3² = Base²

⇒ Base² = 25

⇒ Base = √25

⇒ Base = 5

Hence, we can conclude the value of x to be 6.

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Related Questions

Jing jing works in a store and she spends some of her time organizing the stationary section. If there are nine different items on the rack, how many ways can she organize the rack so that the two most expensive items are not together?

Answers

Answer:

282240 ways

Step-by-step explanation:

number of items = 9 different items

Ranking based on worth

determine number of ways to arrange the 9 items such that the 2 most expensive are apart

first step: consider the 2expensive items as 1

∴ number of permutation = [ ( 9 - 2 ) + 1 ]!  * 2!

                                          = [ 8 ] ! * 2!  = 80640

Total number of permutation/arrangement = 9! = 362880

hence to arrange the 9 items without having the two most expensive items together

= 362,880 - 80640

= 282240 ways

In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?

Answers

The ratio of the sine of

Find the measure of the missing angle using the exterior angle sum theorm.

Answers

Step-by-step explanation:

the correct answer for the question is 85

We know that, in a triangle,

Exterior angle = Sum of interior opposite angles

So,

missing angle = 45° + 40°

=> missing angle = 85°

I really need some help with this question also.

A) 2/5

B) 3/5

C) 11/25

D) 14/25

Answers

the answer to this problem is B 3/5

Why is lowering the interest rate on reserves considered an expansionary monetary policy? A. It encourages banks to lend money instead of keeping it in reserve.
B. It pressures investors to spend more money on treasury securities.
C. It prevents investors from withdrawing too much money from banks.
D. It causes banks to increase their prime interest rate in response.​

Answers

Step-by-step explanation:

The reserve ratio is the central bank's mandate for banks to keep a certain reserve requirements, which are excess cash deposits that must be kept on hand and not loaned out.

Raising the ratio is contractionary since less loans can be made, but this also solidifies banks' balance sheets.

If the Federal Reserve instead lowers the reserve ratio through an expansionary monetary policy, commercial banks are required to hold less cash on hand and can make more loans.

The lowering of the interest rate on reserves, considered an expansionary monetary policy, as it encourages banks to lend money instead of keeping it in reserve.

Hence, option 1 is correct.

Lowering the interest rate on reserves is considered an expansionary monetary policy because it incentivizes banks to lend out their excess reserves rather than keeping them idle in reserve accounts. When the central bank reduces the interest rate on reserves, it effectively lowers the opportunity cost for banks to hold reserves.

As a result, banks are more inclined to lend money to consumers and businesses at lower interest rates, which stimulates borrowing and spending in the economy. Increased lending and spending contribute to economic expansion and growth, making it an expansionary monetary policy.

Thus, lowering the interest rate encourages banks to lend money instead of keeping it in reserve.

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Micheal is selling lemonade.He sold 6 large lemonades at $3 each and 5 small lemonades at $2 each. How much money did he earn ?

Answers

Answer:

$28

Step-by-step explanation:

Answer:

6=$3

5=$2

6x3=18

5x2=10

18+10= 28

=$28

Step-by-step explanation:

Lily bought a pair of gloves and a shirt.
The gloves cost £4
She sold the gloves and the shirt for a total of £48
She made 100% profit on the cost of the gloves.
20% profit on the total cost.
Work out her percentage profit on the cost of the skirt.
Answer 1 decimal place.

Answers

Answer:

Profit % = 11,11 %

Step-by-step explanation:

Answer:

14% profit on shirt/skirt?...

actually as written the question can not be answered....

the start of the problem has gloves, and SHIRT... at the end you want the

profit on a SKIRT

Step-by-step explanation:

gloves sold for 8

shirt sold for 40

.2(48) = 9.60 profit

9.60 - 4 = 5.60 profit of shirt

x(40) = 5.60

14% profit on shirt

The midpoint, M , of segment AB has coordinates (2,−1) . If endpoint A of the segment has coordinates (−3,5) , what are the coordinates of endpoint B ?

The coordinates of endpoint B are?

Answers

the coordinates of endpoint B are (7,7)

Answer:

Solution given:

M(x,y)=(2,-1)

A[tex](x_{1},y_{1})=(-3,5)[/tex]

Let

B[tex](x_{2},y_{2})=(a,b)[/tex]

now

by using mid point formula

x=[tex]\frac{x_{1}+x_{2}}{2}[/tex]

$ubstituting value

2*2=-3+a

a=4+3

a=7

again

y=[tex]\frac{y_{1}+y_{2}}{2}[/tex]

$ubstituting value

-1*2=5-b

b=5+2

b=7

the coordinates of endpoint B are (7,7)

Surveying Indiana high school students about virtual learning or e-learning by sampling all of the students from only some of the online schools in Indiana would be a type of sampling known as cluster sampling.

True
False

Answers

Answer: True

Each high school in Indiana is considered a cluster. Let's say there are 1000 high schools in that state. That would mean there are 1000 clusters.

You would then randomly select say 5 clusters. Once those selections are made, you would then survey every student at those five schools selected. The number of clusters selected will depend on the situation of course.

If a^2 -b^2 =12 and a-b=4 what is the bay of a +b

Answers

Answer:

a+b = 3

Step-by-step explanation:

a = b+4

a^2 = (b+4)(b+4) = b^2 + 8b +16=-b^2 = 12

8b=-4

b = - 1/2

a = 3.5

rization
Vhat is the prime factorization of 180?
Select a composite number to break into factors. Continue
factoring until all factors are prime.
22•2•3•3.5
2.2.45
2.3.3.5
480
2.9.5

Answers

Answer:

5 3 3 2 2

Step-by-step explanation:

180

90 2

45 2 2

15 3 2 2

5 3 3 2 2

Answer:

180 = 5 × 3² × 2²

Step-by-step explanation:

Starting with 180, the prime factors are in bold

180 = 90 × 2

      = 45 × 2 × 2

      = 15 × 3 × 2 × 2

      = 5 × 3 × 3 × 2 × 2

Then

180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²

SOMEONE PLEASE HELP ME! IM SO CONFUSED, NEED THIS VERY BADLY!

Answers

Answer:

115°

Step-by-step explanation:

in a parallelogram vertically opposite angles are equal.

m∠MNK=m∠KLM=115°

they help me ? is the last someone please

Answers

The 3rd one because the integer is greater then or equal 0

6. Don Juan compro un terreno con las dimensiones que se muestran en la figura el cual se va acondicionar para realizar eventos sociales, por lo que desea instalar césped en la region sombreada. ¿Cuantos metros cuadrados de césped requiere? Considera rt=3.14 16 m O 50 24 m2 0 205 76 m2 256 00 m2 0 5504 m2​

Answers

Answer:

Not sure but I think it might be A

Step-by-step explanation:

Took the test

The following are the last 10 run scores Colin got in cricket:
28, 13, 4, 12, 32, 22, 13, 22, 26, 32
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 16 runs.
What is his new mean score?
Give your answers as decimals.

Answers

Answers:

a) Mean = 20.4b) New mean = 20

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

Explanation:

To get the mean, we add up the scores and divide by 10 (because there are 10 scores at first)

28+13+4+12+32+22+13+22+26+32 = 204

204/10 = 20.4

The mean is 20.4

------------

For part b), we redo those steps shown above, but tack 16 onto the list. So we'll add up all the values (including that 16 at the end) and divide by 11 this time.

28+13+4+12+32+22+13+22+26+32+16 = 220

220/11 = 20

The new mean is 20.

The new mean is slightly smaller than the old mean. Notice how 16 is smaller than 20.4, so this new score pulls down the mean just a little bit.

Helppppp and explain tooo pls and thankyouuu

Answers

Answer:

---            ---

|  -5     -2   |

|   4      12  |

---           ----

Step-by-step explanation:

A matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions . To add two matrices, just add the corresponding entries, and place this sum in the corresponding position in the matrix which results.

PLEASE HELP! Use the substitution method to solve the system of equations.

A. (-30,11)

B. (5,-3)

C. (10,-5)

D. (0,1)

Answers

Hello,

[tex]\left\{\begin{array}{ccc}2x+5y&=&-5\\x+3y&=&3\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\6-6y+5y&=&-5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\y&=&11\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&-30\\y&=&11\\\end{array}\right.\\\\[/tex]

Answer A

If AABC IS REFLECTED across the y axis what are the coordinates of A

Answers

Answer:

A. (-1, 3)

Step-by-step explanation:

When reflecting across the y-axis: (x, y) ⇒ (-x, y).

Therefore, A(1, 3) ⇒ A'(-1, 3).

Find the equation of the line through the points (6, -9) and (-2, -1).

Answers

The answer is y= -x - 3

Evaluate the question in the photo attached please. ASAP

Answers

The answer is 29 I think
The answer is 29

——————————

Explanation:

X^2 = 4^2 when we replace x with 4, 4^2 is 16

And 3x = 3*4 which makes 12

We can then add these sums together to get 28

28 - 7 = 21 and 21 + 8 = 29


Hope this helps, have a great day

Determine the period

Answers

The period is 11

Explanation

Answer:

It's 10, on acellus :)

Step-by-step explanation:

If a window is to be 6 feet wide, how high should it be, to the nearest tenth of a foot, to be a golden rectangle

Answers

Answer:

3.7 feet

Step-by-step explanation:

A golden rectangle is a rectangle in which the length and the width are in the ratio 1 : 1.618

If the width of the rectangle is 6, the length = 6 / 1.618 = 3.708 ft

= 3.7 (to the nearest tenth)

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

If 'a' is a number lying between 0 and 1. then which of the following is in increasing order? a) a², a, √a b) a √a ,a² c) a²,√a,a d) a, a², √a ​

Answers

Hello,

[tex]0\leq a\leq 1 \Longrightarrow 0*a\leq a*a\leq 1*a \Longrightarrow 0 \leq a^2 \leq a\\\\0\leq a^2\leq a \Longrightarrow \sqrt{0} \leq \sqrt{a^2} \leq \sqrt{a} \\\\The\ function\ y=x^2\ is\ increasing\\\\Answer A\\\\ex: a=0.5 \\\\a^2=0.25\\\\\sqrt{a}=\dfrac{\sqrt{2}}{2}\approx{0.7071...}\\\\and\ 0.25\leq 0.5 \leq 0.7071...[/tex]

What are equivalent expressions please explain

Answers

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

(a+1)(b+2)
please help me!!!

Answers

Answer:

(a + 1) (b + 2 ) = 2a + b + ab + 2

Step-by-step explanation:

[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]

Answer:

[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]

Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]

Method Used:

↦ Distributive Property.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

What should be done first to evaluate the expression?

3 + (5 - 3)2 × 4

Answers

Answer:

19

Step-by-step explanation:

19 is the answer I think so

what is the measure of < B ? help !!

Answers

The choose (C) 60

The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°

According to general equation for conditional probability, if P(A^B) = 2/3 and P(B) = 3/4, what is P(A|B)?

Answers

Answer:

a

Step-by-step explanation:

ok

Answer:

D. 8/9

Step-by-step explanation:

Which of the following describes point D?

Answers

Point g I hope it helps

The coordinates that describe the point D are: Option C: (0, 4)

How to find the coordinates of the graph?

The graph shows that the vertical axis is labelled as the y-axis while the horizontal axis is labelled as the x -axis.

Normally, the coordinate system of writing the given points of the graph is (x, y)

Thus, the point D on the graph is seem to be 4 units on the positive y-axis and 0 units on the positive x-axis and as such, we can say that the coordinates of point D are:

D(0, 4)

Read more about Graph Coordinates at: https://brainly.com/question/11337174

Complete question is:

Which of the following describes point D?

(-4, 0)

(0, -4)

(0, 4)

(4, 0)

What is the measure of Arc E B C?

Answers

Answer:

The measure of arc (EBC) is 220°.

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