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2 years ago

Select the correct answer from each drop-down menu. In the figure, x = , y = , and z = .

Mathematics

2 answers:

alexdok [17]2 years ago

8 0

X= 95
z=180
y=147

based on from making sure each triangle added up to 180 degrees and with the outer angles

Gekata [30.6K]2 years ago

7 0

Answer:

x=95

y=147

z=128

Step-by-step explanation:

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V\Researchers periodically survey a few thousand of the patients taking a certain medication in order to make connections betwee

yanalaym [24]

Answer:

The correct answer is - an observational study.

Step-by-step explanation:

It is given that, Researchers periodically survey a few thousand of the patients. These are taking specific medicine patients and researchers taking this survey to find the connection between that medication and the subjects' general health.

So, it can say that the researchers observed the patient's health by the effect of the medication, therefore, the Observational Study is the given method of gathering data.

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2 years ago

How is this solved using trig identities (sum/difference)?

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

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2 years ago

What is the sum of 1/3 + 5 3/4 as a mixed number in simplest form

mart [117]

6 1/12 would be the answer

Rewriting our equation with parts separated

1/3+5+3/4

Solving the fraction parts

1/3+3/4=?

Find the LCD of 1/3 and 3/4 and rewrite to solve with the equivalent fractions.

LCD = 12

4/12+9/12=13/12

Simplifying the fraction part, 13/12,

13/12=11/12

Combining the whole and fraction parts

5+1+1/12=6 1/12

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2 years ago

Sum or products of 4x47

andrezito [222]

You multiply 4 and 47 so 188 would be the answer. Hope this helps! :)

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Diano4ka-milaya [45]

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Step-by-step explanation:

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2 years ago