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2 years ago

Using the technique in the model above, find the missing segments in this 30°-60°-90° right triangle. AB = 8 BC = 4 CD =

Mathematics

2 answers:

sattari [20]2 years ago

7 0

simpler version of answer above / below me

2 square root(3)

zimovet [89]2 years ago

6 0

For a 30-60-90 triangle the sides always have the same relationship
Short leg = a
Long leg = a√3
Hypotenuse = 2a

BC is the short leg of ∆ABC

Given BC = 2
BC = a
Therefor
a = 2
AB = 2a = 4
AC = a√3 = 2√3

For ∆ACD
As above AC = 2√3
Since AC is the hypotenuse of ∆ACD
2a = 2√3
a = √3

CD = a = √3
AD = a√3 = 3

For ∆BCD
As above
BC = 2
CD = √3
Since BC is the hypotenuse of ∆BCD
2a = 2
a = 1

DB = a = 1

You might be interested in

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal pla

svp [43]

Here is the correct computation of the question given.

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.

Men aged 20-29: 117 122 129 118 131 123

Men aged 60-69: 130 153 141 125 164 139

Group of answer choices

Men aged 20-29: 4.8%

Men aged 60-69: 10.6%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.4%

Men aged 60-69: 8.3%

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Men aged 20-29: 7.6%

Men aged 60-69: 4.7%

There is more variation in blood pressures of the men aged 20-29.

Answer:

(c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Step-by-step explanation:

From the given question:

The coefficient of variation can be determined by the relation:

$coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69

To start with;

The coefficient of men age 20 -29

Let's first find the mean and standard deviation before we can do that ;

SO .

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{117+122+129+118+131+123}{6}$

Mean = $\dfrac{740}{6}$

Mean = 123.33

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{161.3334}{5}}$

Standard deviation = $\sqrt{32.2667}$

Standard deviation = 5.68

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{5.68}{123.33}*100$

Coefficient of variation = 4.6% for men age 20 -29

For men age 60-69 now;

Mean = $\dfrac{\sum \limits^{n}_{i-1}x_i}{n}$

Mean = $\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}$

Mean = $\dfrac{852}{6}$

Mean = 142

Standard deviation $= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }$

Standard deviation = $\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }$

Standard deviation = $\sqrt{\dfrac{1048}{5}}$

Standard deviation = $\sqrt{209.6}$

Standard deviation = 14.48

The $coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100$

$coefficient \ of \ variation = \dfrac{14.48}{142}*100$

Coefficient of variation = 10.2% for men age 60 - 69

Thus; Option C is correct.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

4 0

2 years ago

on the grid below, draw and label an aquarium shaped like a rectangular prism with a volume of 8,000 cubic inches. (Hint: A cube

n200080 [17]

If you want an aquarium in shape of a cube with volume of 8000, then use the formula for volume of cube to find the length of one side:
V = s^3
where
s = side length
Substitute,
8000 = s^3
s = cuberoot(8000)
s = 20 inches

Well, if you have to draw this on a graphing paper, you should first make a scale to fit the drawing, like 1 inch = 0.5 cm, so a side length of 20 inches is equivalent to 10 cm on your graphing paper.

Hope this helped!

3 0

2 years ago

In which diagram are angles 1 and 2 vertical angles?

Solnce55 [7]

<u>Answer</u>

First diagram shows 1 and 2 vertical angles

<u>Explanation</u>

From the all four diagrams,we get the diagram first shows the vertically opposite angles.

angle 1 and angle 2 are vertically opposite angles

vertically opposite angles are equal in measurements. when two lines are intersect each other form four angles, out of this four angles two pairs of vertically opposite angles are there.

All other figures angle 1 and 2 shows adjacent angles.

6 0

2 years ago

Read 2 more answers

Nina has x coins. Clayton has 5 fewer coins than six times the number of coins Nina has. Write an expression for the total numbe

DedPeter [7]

Answer:

7x - 5

Step-by-step explanation:

Let

Nina = x coins

Clayton = 6x - 5 coins

Expression for the total number of coins Nina and Clayton have altogether.

Nina + Clayton

= x + (6x - 5)

= x + 6x - 5

= 7x - 5

The correct answer and expression is 7x - 5

7 0

2 years ago

Read 2 more answers

Lorena calculated the slope of the linear function that is represented by the table of values as shown. x y –10 15 –8 27 –6 39 –

Anvisha [2.4K]

She made a mistake when she subtracted x1 from x2.

Step-by-step explanation:

Step 1 :

The formula used by Lorena to calculate the slope between 2 points is correct

So the statement given in option 1 is not the reason for her mistake

Step 2:

She has taken the fourth and fifth point and correctly used the x and y co ordinates to calculate the slope

Hence the statement in second option is not true

Step 3:

While calculating the slope the denominator is -2 - (-4) . This gives 2 as the answer. But she has made a mistake in this subtraction giving -6 as the answer.

Hence she has made a mistake in subtracting x1 from x2 and this statement is true

Step 4:

She has not made any mistake in subtracting y1 from y2. Hence this statement is not true

4 0

2 years ago

Read 2 more answers