Natalie was asked to find the angle measures of a triangle that has the ratio 1:3:5 . Natalie made a mistake in her work. Find the mistake and correct it.

Answer: Qualititative, Nominal and Categorical

Explanation:

The variable is qualitative since it does not involve numerical data (i.e. numbers). Rather we're dealing with names or labels.

Since names or labels are involved, and there isn't really inherent order to them, we consider this qualitative data to be nominal.

We can also consider it categorical since each label is a category.

a) From the Pythagorean theorem, we have

AC² = AB² + BC² = a² + a²   ⇒   AC = √2 a

and

AK² = AB² + BK² = a² + (2a)²   ⇒   AK = √5 a

ABCD and BKLC are perpendicular, so AC and CL are perpendicular and ∆ACL is a right triangle. By the Pythagorean theorem, we have

AL² = AC² + CL² = (√2 a)² + (2a)²   ⇒   AL = √6 a

Now,

AK² + LK² = (√5 a)² + a² = 6a² = (√6 a)² = AL²

which means ∆AKL satisfies the Pythagorean theorem and is a right triangle, so ∠AKL = 90°.

b) We know AC = √2 a and AK = √5 a. By the Pythagorean theorem, we find

CK² = BC² + BK² = a² + (2a)²   ⇒   CK = √5 a

By the law of cosines, we have

AK² = AC² + CK² - 2 AC CK cos(∠AKC)

6a² = 2a² + 5a² - 2√10 a² cos(∠AKC)

cos(∠AKC) = 1/(2√10)

∠AKC = arccos(1/(2√10)) ≈ 80.9°

Answer:

Step-by-step explanation:

1/3 of 12 = 2/3 of ?

1/3 of 12 =

(12 : 3) =

4

4 * 2 = 8

8 + 4 =

12

Answer:

B.

Step-by-step explanation:

Answer:

45.8 m^2

Step-by-step explanation:

area = π x 3.82^2

area ≈ 45.8

hope this helps

have a good day

Answer:

Step-by-step ef(x)=-2x+5……i

and f(-3x)=?

let x=-3x so that

-2x+5=-3x

x=5

substitutinx x into… i

f(x)=-10+5=-5

f(5)=-5………ii

now f(–3x)=f(-15)

scrutinizing… ii ,we can propose that

f(-15)=15.

Thus f(-3x)=15xplanation:

f times x would equal to fx=2x+5 and i think we move the x move to the other side which makes it f=3x+5 and then we plug this equal into f(3x) (i think)  which makes it f(3x+f=3x+5)

Answer:

7 watermelons were in each row.

Answer:

Step-by-step explanation:

Discussion

You have to rearrange the equation so that y is all by itself on the left and it must be positive. Stay tuned to get the rest of the rule.

x - y = 3                       Multiply the whole equation by -1

-1(x - y = 3)                   Remove the brackets. This gets y to be +

-x + y = - 3                   Add x to both sides of the equation.

-x+x + y = -3 + x           Combine the left. Notice the x's disappear on the left

y = - 3 + x

Now for the rest of the rule. The number in front of the x is the slope. But, you say, there is no number. Well there is. It's 1.

Answer

The slope of the line is 1.

Answer:

2/3

Step-by-step explanation:

p(B/A)=[P(A&B)]/p(A)

2/3=[P(A&B)]/(1/2)

P(A&B)=2/3 *1/2=1/3

P(A&B)=P(A)*P(B)

1/3=1/2*P(B)

P(B)=1/3*2/1=2/3

Answer:

60

Step-by-step explanation:

The mean of a set of numbers is calculated by adding them all together and then dividing the sum by the amount of values in the data set. In this scenario, we know the mean is 30, and there are 3 numbers in the data set, 10, 20, and an unknown number (x).

Let's set up an equation with the information we have.

30 = (10 + 20 + x) / 3

Now we can multiply both sides by 3 ==>

90 = 10 + 20 + x

Combine like terms ==>

90 = 30 + x

Subtract 30 from each side ==>

60 = x

And now you have your answer!

The value of x = 60 would make the mean of the data set 30.

Answer:

16.1 cm (nearest tenth)

Step-by-step explanation:

Pythagoras’ Theorem

[tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for c:

[tex]\implies 16^2+2^2=c^2[/tex]

[tex]\implies 256+4=c^2[/tex]

[tex]\implies c^2=260[/tex]

[tex]\implies c=\sqrt{260}[/tex]

[tex]\implies c=2\sqrt{65}[/tex]

[tex]\implies c=16.1 \sf \: cm\:(nearest\:tenth)[/tex]

16.1 is rounded to the nearest tenth

Answer:

the game is fair because the probability of winning is equal to 50%

Step-by-step explanation:

If Louis needs to secure his tent. He will use a rope to go down the edge of the tent, straight out to a post and back to the starting think fastener then total length of rope is 36 ft.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that Louis needs to secure his tent.

He will use a rope to go down the edge of the tent, straight out to a post and back to the starting think fastener

We have to find the length of the rope by using pythagoras theorem

12²+9²=x²

144+81=x²

225=x²

Take square root on both sides

x=√225

x=15

The total length is 12+9+15=36 ft

Hence, if Louis needs to secure his tent. He will use a rope to go down the edge of the tent, straight out to a post and back to the starting think fastener then total length of rope is 36 ft.

To learn more on trigonometry click:

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Answer:

Statements B and E are true.

Step-by-step explanation:

B is true

E is true

In the above scenario, for question 1 and 2, we can say that relationship does depict or appear to be fairly strong and also linear as the points on the graph doesn't move far from a line.

Other answers are:

The  Interpretation of the slope of the line of best fit in the context of this problem is that the additional person added to the party will  bring or add about $11.15 to the bill above.

 The variability can be shown or explained by the differences that is seen in what the parties in the graph has ordered to eat or drink.

Since the party of 8 paid were said to have paid (95 - 82.50 =12.50) therefore, 12.50  is known to be less than the predicted amount.

Learn more about relationship from

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Answer:

y= between 9-10 patients, round down to 9

Step-by-step explanation:

y= 9/4x + 5

y = 9/4(2) + 5

y = 9.5

y= between 9-10 patients, round down to 9

Answer:

$1,200

Step-by-step explanation:

$15 x 20 = $300/week; $300 x 4 weeks = $1,200

Answer:

A.)$1,200 a month

Step-by-step explanation:

it's the same as before. but, if you're looking for multiple weeks, just do the same thing, but multiply it by how many weeks there are. Ex. $15 an hour times 20 hours is $300, and there are 4 weeks in a month, so you would multiply it by 4 to get $1,200

Answer:

4.5 step by step

Step-by-step explanation:

6 × 6 = 36 ÷ 8 = 4.5

Answer:

graph c

Step-by-step explanation:

it's coordinate (0,2) satisfy the equation

Answer:

t = time

42 + 8.8t < 112.40

8.8t < 70.4

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Answer: t = 4

Step-by-step explanation:

(x) - (y) = (t)

78.00 - 41.00 = 37.00

7.40 x 5 = 37

t = 4

Any amount of time under 5 hours would work.

Answer:

400

83 000 000

600,000

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

483,600,000 miles

Answer:

(5,5) Remember, the bottom line always goes first since it is the X axis, and the one going up and down goes second because it is the Y axis :D

Step-by-step explanation:

Answer:

flip it around 9/13 reciprocal would be 13/9

For A it is 6240 / 20% for B it is 6240 x 15%

Answer: A. .20x640=128

                   128+640=768

B. .15x640=96

     640-96

Step-by-step explanation:

Answer:

= CL : SL

= 28 cm : 20 cm

= 1,4 cm

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\color{magenta}{\rule{10pt}{20pt}}\purple{\rule{10pt}{20pt}}\red{\rule{10pt}{20pt}}\orange{\rule{10pt}{20pt}}\color{yellow}{\rule{10pt}{20pt}}\color{lime}{\rule{10pt}{20pt}}\color{green}{\rule{10pt}{20pt}}\color{blue}{\rule{10pt}{20pt}}\color{indigo}{\rule{10pt}{20pt}}\color{violet}{\rule{10pt}{20pt}}\color{aquamarine}{\rule{10pt}{20pt}} \\\color{magenta}{\rule{10pt}{20pt}}\purple{\rule{10pt}{20pt}}\red{\rule{10pt}{20pt}}\orange{\rule{10pt}{20pt}}\color{yellow}{\rule{10pt}{20pt}}\color{lime}{\rule{10pt}{20pt}}\color{green}{\rule{10pt}{20pt}}\color{blue}{\rule{10pt}{20pt}}\color{indigo}{\rule{10pt}{20pt}}\color{violet}{\rule{10pt}{20pt}}\color{aquamarine}{\rule{10pt}{20pt}}\end{gathered}\end{gathered}\end{gathered}[/tex]

[tex]\text{In}~ \triangle ABC,\\\\~~~~~~~~\sin 45^{\circ} =\dfrac{BC}{AC} \\\\\implies \dfrac 1{\sqrt 2} = \dfrac{BC}{6\sqrt 2}\\\\\\ \implies BC= 6\\\\\text{Now, In}~ \triangle BCD\\\\~~~~~~\cos 60^{\circ} = \dfrac{BD}{BC}\\\\\ \implies \dfrac 12 = \dfrac{x}{6}\\\\\\\implies x = \dfrac 62\\\\\\\implies x = 3[/tex]

Answer:

x = 3

Step-by-step explanation:

using the sine ratio in right triangle ABC and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{6\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

BC × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

BC = 6

using the cosine ratio in right triangle BCD and the exact value

cos60° = [tex]\frac{1}{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BD}{BC}[/tex] = [tex]\frac{x}{6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

The correct answer is graph A.