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Nikitich [7]
3 years ago
11

Find the value of x and simplify completely.

Mathematics
1 answer:
jok3333 [9.3K]3 years ago
7 0

Answer:

<h2>x=9√10</h2>

Given: A right triangle in which an altitude is drawn from the right angle vertex to the hypotenuse.

To find: 'x' the larger leg of triangle

Solution,

Using let rule for similarity in right triangle:

\frac{leg}{part}  =  \frac{hypotenuse}{leg}  \\ or \:  \frac{x}{27}  =  \frac{3 + 27}{x}  \\ or \: x \times x = 27(3 + 27) \\ or \: x \times x = 81 + 729 \\ or \:  {x}^{2}  = 810 \\ or \:  {x}^{2}  = 81 \times 10 \\ or \:  {x}  =  \sqrt{81 \times 10}  \\ or \: x =  \sqrt{81}  \times  \sqrt{10}  \\ or \: x =  \sqrt{ {(9)}^{2} }  \times  \sqrt{10}  \\  \: x = 9 \sqrt{10}

Hope this helps...

Good luck on your assignment..

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Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR= 5 m and diagonal QS
svet-max [94.6K]

Answer:

Given the statement: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P.

Properties of Kite:

  • The diagonals are perpendicular
  • Two disjoint pairs of consecutive sides are congruent by definition of kite
  • One diagonal  is the perpendicular bisector to the other diagonal.

It is given that: Side QR = 5m and diagonal QS = 6m.

Then, by properties of kite:

QP = \frac{1}{2}QS

Substitute the value of QS we get QP;

QP = \frac{1}{2}(6) = 3 m

Now, in right angle \triangle RPQ

Using Pythagoras theorem:

QR^2= RP^2 +QP^2

Substitute the given values we get;

(5)^2= RP^2 +(3)^2

or

25= RP^2 +9

Subtract 9 from both sides we get;

16= RP^2

Simplify:

RP = \sqrt{16} = 4 m

Therefore, the length of segment RP is, 4m


5 0
3 years ago
Read 2 more answers
Tell whether the pair of polygons is similar. Explain why or why not.
Savatey [412]

9514 1404 393

Answer:

  not similar

Step-by-step explanation:

Similar polygons have all corresponding angles congruent, and corresponding sides proportional.

The sides lengths guarantee the polygons are parallelograms, so one pair of angles being congruent is sufficient to ensure that all corresponding angles are congruent.

The ratio of side lengths in the left polygon is 13/8, and the ratio of side lengths in the right polygon is 5.2/2.4 = 13/6. These are different ratios, so the corresponding sides are NOT proportional.

The figures are NOT SIMILAR.

7 0
2 years ago
Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ<br>​
lilavasa [31]

Answer:

30°

Step-by-step explanation:

\because \:  \sin(90 \degree -  \theta) =  \cos \theta \\ \therefore \:  \sin(90 \degree - 5 \theta) =  \cos 5\theta....(1) \\  \\ \sin(90 \degree - 5 \theta) = \cos(180 \degree -  \theta)...(2) \\ from \: (1) \: and \: (2) \\ \cos 5\theta = \cos(180 \degree -  \theta) \\ 5 \theta = 180 \degree -  \theta \\  5 \theta  + \theta= 180 \degree  \\ 6\theta= 180 \degree  \\  \theta =  \frac{180 \degree}{6}  \\  \\  \huge \red{ \boxed{\theta = 30 \degree}}

8 0
3 years ago
Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression.
MrRa [10]

Answer:

<em> The numbers are 6, 18, and 30 </em>

Step-by-step explanation:

If the three numbers are in the ratio of 3:9:10,

let the numbers be 3x, 9x and 10x.

<em>If 10 is added to the last number to form an arithmetic progression</em>

<em>Then, 3x 9x (10x+10) are the progression</em>

The common difference of an arithmetic progression (d) = T₂ - T₁ = T₃ - T₂

T₂-T₁ = T₃ - T₂ .............. Equation 1

Where T₁ = first term of the progression, T₂ = Second term of the progression, T₃ = third term of the progression

<em>Given: T₁ = 3x, T₂ = 9x, T₃ = 10x +10</em>

<em>Substituting these values into equation 1</em>

<em>9x-3x = (10x+10)-9x</em>

<em>Solving the equation above,</em>

<em>3x = 10+x</em>

<em>3x-x = 10</em>

<em>2x = 10</em>

<em>x = 10/2</em>

<em>x = 2.</em>

<em>Therefore the numbers are 6, 18, and 30 </em>

<em />

7 0
3 years ago
Jason begins at the start of a path and rides his bike 11 12 miles on the path. The path is 12 14 miles long. Enter the distance
nikitadnepr [17]

Answer:

Number of miles remaining for Jason to reach end of the path = 3/4 miles

Step-by-step explanation:

Total distance of the path = 12 1/4 miles

Distance reached by Jason's bike on the path = 11 1/2 miles

Enter the distance, in miles, Jason must ride to reach the end of the path.

Number of miles remaining for Jason to reach end of the path = Total distance of the path - Distance reached by Jason's bike on the path

= 12 1/4 miles - 11 1/2 miles

= 49/4 - 23/2

= (49-46) / 4

= 3/4 miles

Number of miles remaining for Jason to reach end of the path = 3/4 miles

6 0
2 years ago
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