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Kisachek [45]
4 years ago
6

Find the missing side lengths. Leave your answers as radicals in simplest form.

Mathematics
1 answer:
sattari [20]4 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

To find x use the sine ratio in the right triangle and the exact value

sin60° = \frac{\sqrt{3} }{2} , then

sin60° = \frac{opposite}{hypotenuse} = \frac{14\sqrt{3} }{x} = \frac{\sqrt{3} }{2} ( cross- multiply )

x \sqrt{3} = 28\sqrt{3} ( divide both sides by \sqrt{3} )

x = 28

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

To find y use the tangent ratio in the right triangle and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{14\sqrt{3} }{y} = \sqrt{3} ( multiply both sides by y )

14\sqrt{3} = y \sqrt{3} ( divide both sides by \sqrt{3} )

y = 14

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Jakes class were numbered in order from 1 to 24 and jake was asked to choose a classmate numbered with multiples of 5 to be in h
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4 0
3 years ago
half of an integer exceeds one _ third of the next integer by unity .Find the integer. please ask fast​
gulaghasi [49]

9514 1404 393

Answer:

  8

Step-by-step explanation:

If the integer is n, half of it is n/2. The next integer is (n+1) and 1/3 of it is (n+1)/3. You want ...

  n/2 - (n+1)/3 = 1

  n(1/2 -1/3) -1/3 = 1

  n/6 = 4/3 . . . . . . . . add 1/3, simplify

  n = 6(4/3) = 8

The integer is 8.

6 0
3 years ago
Which of the following represents a function?
Gwar [14]

Answer:

A

Step-by-step explanation:

This is because each x coordinate is mapped to a y coordinate.

3 0
3 years ago
The guttering hold up to 20 litre of rain water. Work out the length of guttering in meters if the diameter is 11.5cm.
bazaltina [42]

Answer:

1107.0213 cm

Step-by-step explanation:

Assuming this gutter is half a cylinder,

Volume of half a cylinder = 0.5(πr²l)²

where, Volume = 20l, π = 3.142, r = 0.5(11.5) and l = ?

But, the other units are in cm while the Volume is in liters, so let's convert the liters to cm³

It would be easier to convert the liters to m³ then to cm³ rather than converting directly. So,

1000 L = 1 m³

     1 L = ?

1 ÷ 1000 = 0.001 m³

      1 m³ = 1,000,000cm³

0.001 m³ = ?

0.001 x 1,000,000 = 1000 cm³

So, if 1 L = 1000 cm³

      20 L = ?

20 x 1000 = 20,000 cm³

Thus, 20,000 = 0.5(3.142 x 0.5(11.5) x l)

20,000 = 0.5(3.142 x 5.75 x l)

20,000 = 18.0665l

Make l the subject and divide both sides by 18.0665

length = 1107.0213 cm

6 0
3 years ago
Please answer this is only algebra 1
Alexeev081 [22]

The numeric values for the given functions are as follows:

  • f(1/3) = 1/9.
  • g(4) = 8.
  • g(-3) = -6.

<h3>How to find the numeric value of a function or of an expression at a given point?</h3>

To find the numeric value of a function at x = a, we replace each instance of the variable, usually x, in the function by the desired value of a.

Function f(x) is defined by:

f(x) = x².

For the numeric value at x = 1/3, we replace the lone instance of x by 1/3, hence:

f(1/3) = (1/3)² = 1/9.

Function g(x) is defined by:

g(x) = 2x.

For the numeric value at x = 4, we replace the lone instance of x by 4, hence:

g(4) = 2(4) = 8.

For the numeric value at x = -3, we replace the lone instance of x by -3, hence:

g(-3) = 2(-3) = -6.

More can be learned about the numeric values of a function at brainly.com/question/28367050

#SPJ1

6 0
1 year ago
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