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Rashid [163]
2 years ago
5

The two triangles shown are congruent. Find the value of x

Mathematics
1 answer:
shusha [124]2 years ago
4 0

Answer:

x = 11

Step-by-step explanation:

right triangle ABC

using Pythagoras' identity

BC² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )

BC = \sqrt{625} = 25

Since the triangles are congruent then corresponding sides are congruent.

ST = BC , that is

3x - 8 = 25 ( add 8 to both sides )

3x = 33 ( divide both sides by 3 )

x = 11

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GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
2 years ago
g Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether event
vagabundo [1.1K]

Answer:

There is not sufficient evidence to support the claim.

Step-by-step explanation:

The claim to be tested is:

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To test this claim the hypothesis can be defined as follows:

<em>H₀</em>: The mean respiration rate of students is 32, i.e. <em>μ</em> = 32.

<em>Hₐ</em>: The mean respiration rate of students is less than 32, i.e. <em>μ</em> < 32.

The sample mean  respiration rate of students is 31.3.

According to the claim the sample mean is less than 32.

The sample mean value is not unusual if the claim is true, and the sample mean value is also not unusual if the claim is false.

Thus, there is not sufficient evidence to support the claim.

7 0
3 years ago
-4x^4 - 3x^3 - 29x^2 - 114 where x= -4
tatiyna

Answer: -1410

Step-by-step explanation:

Let's start by subbing in -4 for x

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Now we can solve

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5 0
3 years ago
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Dmitry [639]

Answer:

The height of the giraffe is 27.432 decimeters.

Step-by-step explanation:

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6 0
2 years ago
How to find the answer
Shalnov [3]

its 90 measurement CBG (I think) is corresponding to measurement DAE

7 0
3 years ago
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