Ixl . R.8 Trigonometric ratios : Find a side length
Help please

Find FG

9514 1404 393

Answer:

  4

Step-by-step explanation:

If the unknown leg is represented by x, then the Pythagorean theorem tells you ...

  x² + 3² = 5²

The sum of the squares of the legs equals the square of the hypotenuse.

Solving for x, we have ...

  x² = 5² -3² = 25 -9 = 16

  x = √16 = 4 . . . . . . . only the positive root is of interest

The missing leg length is 4 units.

_____

Additional comment

This exercise shows you that the triple (3, 4, 5) will form a right triangle. It is the smallest integer "Pythagorean triple", and the only one that is an arithmetic sequence (the differences between the numbers are the same). You will see this a lot, sometimes multiplied by various factors: 6, 8, 10, for example. It is worth remembering.

Answer:

4

Step-by-step explanation:

Correct answers:

$4$

Let a represent the length of the leg and label a on the figure.

The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.

The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.

Using the Pythagorean Theorem with b=3, c=5, and solving for a, we have

a2+b2a2a2a2a2aa=c2=c2−b2=52−32=25−9=16=16−−√=4

The length of the leg is 4.

Answer: I think f

Step-by-step explanation:

The value of a must be 1 in order for the equation to hold true .

If a * b = b, we can find the value of a by isolating it on one side of the equation .

Given that a * b = b, we can divide both sides of the equation by b :

( a * b ) / b = b / b

This equation simplifies to form :

a = 1

For a = 1 the equation is true .

Therefore, the value of a must be 1 in order for the equation to hold true .

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Answer:

Triangle 1 and triangle 3 have same area.

Step-by-step explanation:

Given:

Triangle  Base  Height

1                30         16

2               60        40

3               20        24

Find:

Same area triangle

Computation:

Area of triangle = (1/2)(b)(h)

Area of triangle 1 = (1/2)(30)(16)

Area of triangle 1 = 240 unit²

Area of triangle 2 = (1/2)(60)(40)

Area of triangle 2 = 1200 unit²

Area of triangle 3 = (1/2)(20)(24)

Area of triangle 3 = 240 unit²

So,

Triangle 1 and triangle 3 have same area.

Answer:

x = 28 y = 122

Step-by-step explanation:

Transversal Lines would be 112 and 4x

112 / 4 = 28

x = 28

y and 122 are alternate interior angles

so y = 122

hope this helps ^^

Answer:

the answer is the same.....

[tex]\frac{1}{c^2+8}[/tex]

Answer:

C and E

Step-by-step explanation:

Expressions does not contain any equal or less than greater than sign

So C and E are the right answers

Answer:

The answer is 5 times

Step-by-step explanation:

1/6*1/6*180=5

Answer:

Enter the amount of money you are investing. Start Year. Enter the year in which the money was first invested. End Year. Enter the future year on which you want to base your calculation. Annual Interest Rate. Enter the annual compound interest rate you expect to earn on the investment. The default value (2.0%) equals the rate currently paid on five-year Guaranteed Investment Certificates

Step-by-step explanation:

Answer:

A 234.11

Step-by-step explanation:

[tex]= 234.11148454551 feet^{3}[/tex]  is what you get lol

Answer:

[tex]90 in^{2}[/tex]

Step-by-step explanation:

Base is an equilateral triangle

slant hight= 12 in

side of base= 5 in

so, perimeter of base = 3(5)=15 in

lateral area = 1/2 pl =1/2 (15)(12) in

=90 in²

--------

hope it helps..

have a great day!!

Answer:

Step-by-step explanation:

lateral area = 1.5*12*5 =90

Answer: $ 1 710

Step-by-step explanation:

Area of parallelogram = base x height = 27 x 20 = 540ft2

Area of triagne = 1/2 x base x height = 1/2 x 3 x 20 = 30ft2

total = 540 + 30 = 570ft2

570 ft2 x $3 = $1 710

Answer: yes

Step-by-step explanation: so smart I think

Answer: 200 miles

Step-by-step explanation:

Answer:

±6

Step-by-step explanation:

Given the mathematical expression;

√36 < √42 < √49

But, √36 = 6 * 6 = 6²

√49 = 7 * 7 = 7²

Simplifying further, we would substitute the new values respectively;

±[6] < √42 < ±[7]

Therefore, evaluating √36 is equal to ±6.

Answer:

19

Step-by-step explanation:

Given average of 3 numbers = 17 Total of 3 numbers = 17×3 = 51. Given average of 2 numbers = 16 Total of 2 numbers = 16×2 = 32 Therefore, Third Number = 51–32 = 19

Answer:

a) 0.19

b) 0.9689

c) ≈ 6 cars

Step-by-step explanation:

Rate at which cars arrive = 12 cars/hour = 1/5 cars/minute

time needed by each car to complete ATM transaction = 6 minutes = 1/6 car/minute

capacity of lane = 10 car

n = 10

a) Calculate the probability of an arriving not using the ATM because the line is full

p ( not using the ATM ) = 0.19

b) probability that a car will not be able to use the ATM machine immediately on arrival

P ( n > 0 ) = 1 - Po

                 = 1 - 0.0311 = 0.9689

c) Average number of cars in the lane

Lq = 5.74 ≈ 6 cars

attached below is the detailed solution

Answer:

Step-by-step explanation:

It's the magnitude of the average rate of change that's important here.

| -12.5 | is greater than | 10 |.  The negative sign tells us that the function is decreasing on the given interval.

Answer:

Step-by-step explanation:

Given equation:

Cylinder A has:

Using the given values find k:

The equation now is:

Find the volume of cylinder B:

Answer:

Step-by-step explanation:

[tex]0.25=\frac{x}{140} \\140*0.25=\frac{x}{140}*140\\35=x[/tex]

1st box: 140

2nd box: 140

3rd box: 35

Answer:

-1.5

Step-by-step explanation:

The Z - score of a person who scored 240 on the exam will be - 1.5.

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

On a standardized exam,

The mean of scores = 300

Standard deviation = 40

Score on the exam = 240

Now,

Since, The Z - score is defined as;

Z - score = (X - μ) / σ

Where, μ is mean of scores and σ is Standard deviation.

Substitute all the values , we get;

Z - score = (X - μ) / σ

Z - score = (240 - 300) / 40

Z - score = - 60 / 40

Z - score = - 1.5

Therefore,

The Z - score of a person who scored 240 on the exam will be - 1.5.

Learn more about the Z - score visit:

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Answer:

100%

none are greater than 80

Step-by-step explanation:

the answer can be that they can have a common denominator at 9/60 and 12/60?

Answer:

c

Step-by-step explanation:

Answer:

Ralphie's dad can eat 8 fruit bars without going over his calorie allotment.

Answer:

( 6 x 9  ) + ( 6 x 8) = 102

Step-by-step explanation:

The answer 102

Hope this helped!

Answer:

102

Step-by-step explanation:

6 times 9 is 54

8 times 6 is 48

Then add to get 102!!!

Answer:

B  I think

Step-by-step explanation:

Here we want to make a system of equations and solve it, in this way, we will see that there are 8 black sheep.

first, let's define the variables:

x = number of black sheep

y = number of white sheep.

We know that:

"there are 56 sheep"

Then we can write:

[tex]x + y = 56[/tex]

We also know that there are 6 times as many white sheep than black sheep, this means that:

[tex]y = 6 \cdot x[/tex]

Then we have a system of equations:

[tex]x + y = 56[/tex]

[tex]y = 6\cdot x[/tex]

To solve this we need to start by isolating one of the variables in one of the equations. Here, we can see that the variable y is already isolated in the second equation, so we can use that.

Now we can replace that variable in the other equation:

[tex]x + y = 56[/tex]

[tex]x + 6\cdot x = 56[/tex]

Now we can solve this for x, the number of black sheep:

[tex]7\cdot x = 56\\\\x = 56/7 = 8[/tex]

There are 8 black sheep.

If you want to learn more, you can read:

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Answer:

1.35

Step-by-step explanation:

45 x .03