What is the length of the diagonal of the rectangle?

10.625

126.4375

29.75

21.25

Answer:

you mean trigonometry i'm assuming

but essentially:

soh = sin theta (the angle) = opposite length/hypotenuse length

cah = cos theta (angle) = adjacent length/hypotenuse length

toa = tan theta (angle) = opposite length/adjacent length

Step-by-step explanation:

Answer:

the missing pencil length is 13.5 cm

Step-by-step explanation:

The computation of the length of the missing pencil is shown below:

Let us assume the missing pencil be x

Now

(12.4 cm + 12.6 cm + 13 cm + 13.4 cm + 13.5 cm + 13.3 cm + x) ÷ 7 = 13.1 cm

(78.2 cm + x) ÷ 7 = 13.1 cm

78.2 cm + x = 91.7 m

So, x would be

= 91.7 cm - 78.2 cm

= 13.5 cm

hence, the missing pencil length is 13.5 cm

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

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to choice A as the final answer

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An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

The percentage reduction in Caroline's earnings if she decides to go ahead with her plan is 30%.

Since Caroline works 8 hours each day for 5 days a week and she's earns £11 per hour. The amount earned for the week is:

= (80 × 5 × £11)

= £440

When she is planning on reducing her working schedule and only work 7 hours each day for 4 days a week. The amount will be:

= (4 × 7 × £11)

= £308

The percentage reduction will be:

= Difference on amount / Old amount × 100

= (440 - 308) /440 × 100

= 132/440 × 100

= 0.3

= 30%

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Caroline works 8 hours each day for 5 days a week. She's earns £11 per hour. Caroline is planning on reducing her working schedule and only work 7 hours each day for 4 days a week work out the percentage reduction in Caroline's earnings if she decides to go ahead with her plan

Answer:

The answer is A. x= -13

Step-by-step explanation:

The way that you solve it is change the positive 3 to negative and adding the negative 3 to negative 10.

The new data set's range must be greater than the original data set's range. which is the correct answer would be an option (C).

The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.

Let m be the smallest value in the original data collection.

Given that the original data set's range = 84 -m

A new data set is made up of 26 positive integers and 96 from the existing data set.

As a result, the new data set's range is 96-m.

We can now determine the difference between two ranges by subtracting them :

⇒ (96 - m) - (84 - m)

⇒ 96 - m - 84 + m

⇒ 12

As a result, the new data set's range must be greater than the original data set's range.

Hence, the correct answer would be an option (C).

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Answer:

The exact value of x will be [tex]\sqrt{52}[/tex] or 7.2111

Step-by-step explanation:

Hope this Helped

Answer:

George should charge 1.70$ for each frame to break-even.

Step-by-step explanation:

Variable cost for the frames:

Wood + polishing = $100 + $50 = $150

Variable cost per frame would be:

$150/ 500 = $0.30

The fixed cost of the operation is $700.

George has to make 500 frames.

Fixed cost / (Selling price per unit – variable cost per unit) = 500

$700 / (Selling price per unit - $0.30) = 500

700 = 500 (Selling price per unit – 0.30)

700 = 500 * Selling price – 500 * 0.3

700 = 500 * Selling price – 150

(700 + 150) / 500 = Selling price

850 / 500 = 1.7

Answer:

+9.2=7.6x

x+9.2=38x

______

5

Solution

=1.393939393

Answer: See explanation

Step-by-step explanation:

Sita bought a sofa set for Rs 30,000 and sold the sofa set at a loss of 5%. The loss on the sofa will be:

= 5% × 30000

= 5/100 × 30000

= 0.05 × 30000

= 1500

Selling price of the sofa = 30000 - 1500 = 28500

Sita bought a dining set for Rs 20,000 and made a profit of 5% on the dining set. The selling price of the dining set will be:

= 20000 + (5% × 20000)

= 20000 + (0.05 × 20000)

= 20000 + 1000

= 21000

The cost price of the sofa and dining set will be:

= Rs 20000 + Rs 30000

= Rs 50000

The selling price of the dining set will be:

= Rs 28500 + Rs 21000

= Rs 49500

The net result of the transaction is will be:

Selling price - Cost price

= 49500 - 50000

= -500

There's a net loss of $500

Answer:

Step-by-step explanation:

x+x+9=65

2x=56

x=28

28,37

Answer:

one number= 28, other number= 37

Step-by-step explanation:

9+x+x=65

9+2x=65

2x=56

x=28

Answer:

192

Step-by-step explanation:

on edge

Answer:

116.1

Step-by-step explanation:

Answer:

-3>=x this is because the circle is closed as well as the arrow going the opposite from -3

Step-by-step explanation:

Answer:

While statistics are extremely valuable, they are also notorious for being a means that people use to make false and misleading arguments. Also far too often statistics are obtained by taking a sample from a larger group and assuming the whole group has the same characteristics as the sample.

A sample provides a smaller set of the population for review, that delivers data that is useful to represent the whole population. Surveying a smaller sample, as opposed to the entire population, can save precious time for researchers and offer urgent data.

Step-by-step explanation:

Hope it is helpful.....

Answer:

from what i remember it should be b≤24

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠BEF = ∠ABE   {Alternate interior angle}

∠BEF = 60

∠EQR = ∠ BEF         {Corresponding angles}

∠EQR = 60

In ΔEQR

∠QER + ∠EQR + ∠ERQ = 180 {angle sum property}

80 + 60 +x = 180

140 + x = 180

          x = 180- 140

x = 40

Answer:

so 240-90cm he cut off=195cm. Then 45x2=80cm so 195-90cm=105cm.

Therefore, 105 divided by 40=2.625 so he cut off 6 pieces of 40cm lengths overall

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

X and XY

Step-by-step explanation:

When you expand and compare the result to (X+Y)^2, you will see that the only terms different are those with the variable X. This means that the only terms affected are X and XY.

9514 1404 393

Answer:

  13.609°

Step-by-step explanation:

The csc^-1 function is the arccosecant function. It gives the angle whose cosecant is given. If we let A represent that angle, your statement is ...

  A = csc^-1(4.25)

It is used to solve the relation ...

  4.25 = csc(A)

__

Some calculators can give you the value directly (see attached). Most cannot. In any event, you need to make sure the angle mode for the calculator is set to degrees.

When your calculator does not have the csc^-1 function, you can make use of the trig identity ...

  csc(x) = 1/sin(x)

In the above equation, this becomes ...

  4.25 = 1/sin(A)

  sin(A) = 1/4.25 . . . . . solve for sin(A)

All scientific and graphing calculators will have the inverse sine (arcsine) function.

  A = sin^-1(1/4.25)

  A ≈ 13.609° . . . . . . . calculator mode in Degrees

_____

Additional comment

For inverse functions, especially inverse trig functions, I find it useful to read them as ...

  csc^-1(x)   ⇒   "the angle whose cosecant is x"

  sin^-1(x)   ⇒   "the angle whose sine is x"

This reminds me that the value it gives is an angle (degrees or radians), and the argument it takes is a pure number (one with no units).

Answer:

32÷2= 16 so just do 16×12

Step-by-step explanation:

192

Answer:

6

Step-by-step explanation:

Ez

Answer:

A. 106

B. 25

Step-by-step explanation:

A. 33 times 2 = 66

66 Plus the 40 for the membership

66 + 40 = 106

B. 90 - 40 = 50  (40 from the membership)

50 divided by 2 = 25

Answer:

You can solve 1.2 word problems per minutes

Step-by-step explanation:

If 6 word problems were solved in 5 minutes, you must put this into a fraction. We're looking for how many word problems could be solved per minute, so we divide 5 by itself to get 1 and whatever you do to the bottom, you must do to the top, so 6 divided by 5 is 1.2

Hope this helped ;)

Answer:

yum

Step-by-step explanation: