Performance task trigonometric identities

Variation can be direct, inverse or joint.

The perimeter is 243 cm

Represent perimeter with P and side lengths with L.

So, we have:

[tex]\mathbf{P\ \alpha\ L}[/tex]

Express as an equation

[tex]\mathbf{P = kL}[/tex]

Where k is the constant of variation.

Make k the subject

[tex]\mathbf{k = \frac PL}[/tex]

So, we have:

[tex]\mathbf{\frac{P_1}{L_1} = \frac{P_2}{L_2}}[/tex]

Make P2 the subject

[tex]\mathbf{P_2 = L_2 \times \frac{P_1}{L_1} }[/tex]

Substitute the given parameters

[tex]\mathbf{P_2 = 81 \times \frac{153}{51} }[/tex]

[tex]\mathbf{P_2 = 81 \times 3 }[/tex]

[tex]\mathbf{P_2 = 243}[/tex]

Hence, the perimeter is 243 cm

Read more about variations at:

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Answer:

Given equation is (8/y) = 2/(y-2) +1

=> (8/y)- 2/(y-2) = 1

=> [8(y-2)-2y]/(y-2)y = 1

=> (8y-16-2y)/(y²-2y) = 1

=> (6y-16)/(y²-2y) = 1

=> y²-2y = 6y-16

=> y²-2y -6y+16 = 0

=> y²-8y+16 = 0

The standard form is y²-8y+16 = 0.

Answer:

-6

Step-by-step explanation:

8/y = 2/y - 2 + 1

8/y = 2/y - 1

8 = 2 - y

6 = -y

y = -6

Answer:

the √78 would be 8.832 so D

Answer:

n=0

Step-by-step explanation:

n+-5= -5

n-5= -5

n= -5 +5

n=0

Answer:

false

Step-by-step explanation:

the variable x is used in slope intercept

Answer:

False

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

as you can see in the pattern he adds 1 in each time to the height and 2 to the width

Answer:

0.75

Step-by-step explanation:

1. To change 3/4 into a decimal, you have to divide 3 by 4.

2. (Check out the image below to see how to divide 3 by 4.)

Answer:

3/4 is expressed as 0.75 in the decimal form.

Step-by-step explanation:

Fractions and decimals are two ways to represent the same numbers. A decimal number can be defined as a number whose whole number part and fractional part is separated by a decimal point. A fraction is represented as a numerical value that is defined as a part of a whole.

To convert any fraction to decimal form, we just need to divide the numerator by the denominator.

Here the fraction is 3/4 which means we need to divide: 3 ÷ 4.

* Use the attatched images for steps*

Therefore, 3/4 = 0.75.

Thus, 3/4 is expressed as 0.75 in the decimal form.

Answer:

X=13

Step-by-step explanation:

79=4x+27

-27       -27

52=4x  

x=13

Answer:

80

Step-by-step explanation:

Your 4 given numbers equal 295. 5x75 is 375. So take 375-295 and you get 80, your 5th number.

Answer:

.98 L / b   * .4 b   = .392 L         amount contained in sample

.99 L / b  * .25 b  = .248 L        this was rounded from .2475

1.00 L / b * .3 b   = .30 L

1.01 L / b * .05 b =   .05 L

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

3.98 L / 4 b * 1.0 b     = .99 L

Actual measurements might be 40 bottles at .98 L/b, 25 bottles at .99 etc

Then the total liters would be divided by the total number of bottles

Answers:

Domain is  [tex]0 \le d \le 100[/tex]

Range is  [tex]0 \le F(d) \le 150[/tex]

==============================================

Explanation:

The most money made from selling drinks is $150. Divide this over the cost per drink to get 150/(1.50) = 100; indicating that at most 100 drinks are sold per day. This is the largest that d can get because d represents the number of drinks sold.

The smallest d can get is d = 0 to mean that no drinks are sold.

In short: d is between 0 and 100, including both endpoints. We write [tex]0 \le d \le 100[/tex] to indicate this. This is the domain because the domain represents all the possible inputs allowed.

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

The range is the set of allowed outputs.

If we plugged in d = 0, then you would find F(d) = 0 as well. If you don't sell any drinks, then you earn $0. This is the smallest item in the range.

On the other side of things, the largest item in the range is 150 because this value was given to us. It's the upper limit or ceiling value of how much money is made from drinks. You can also find this by plugging d = 100, the largest domain value, into the function to get F(d) = 150.

Therefore the range is [tex]0 \le F(d) \le 150[/tex] to indicate that F(d) is between 0 and 150 inclusive of both endpoints.

Answer:

SAS

Step-by-step explanation:

Answer:

1/7 km long

Step-by-step explanation:

The area of a square is any given one of the sides, squared. We can take this information and apply it to this problem. If the area is 1/49 km squared, we can take the square root of this to find the length of each side.

The square root of 1 is 1, and the square root of 49 is 7, so the answer is 1/7 km for each side.

If you have any further questions, let me know!

Answer:

[tex]\frac{1}{7}[/tex]

Step-by-step explanation:

Answer:

the answer is 30

when you substitute x = 4

solve for K

Step-by-step explanation:

the answer is 30

please brainlist

The corresponding roots of the quadratic equations are given.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

1. x² = 49

Find the square root.

x = ±√49 = ±7

2. x² - 27 = 0

x² = 27 = 9 × 3

x = √27 = √(9×3) = √9 × √3 = ±3√3

3. 3x² - 36 = 0

3x² = 36

Divide 3 on both sides.

x² = 12

x = √12 = √(4 × 3) = ±2√3

4. 9x² = 0

x = 0

5. 5x² - 15 = 0

5x² = 15

x² = 3

x = ±√3

6. 2x² - 144 = 0

2x² = 144

x² = 72

x = √72 = √(36 × 2) = ±6√2

7. (x + 3)² = 9

x + 3 = √9

x + 3 = ±3

x = 3 - 3 = 0 and x = -3 - 3 = -6

8. 4x² - 100 = 0

4x² = 100

x² = 25

x = ±√5

9. 5x² = 40

x² = 8

x = √8 = √(4 × 2) = ±2√2

10. 3x² - 12 = 0

3x² = 12

x² = 4

x = ±2

11. (x - 5)² = 121

x - 5 = √121

x - 5 = ±11

x = 11 + 5 = 16 or x = -11 + 5 = -6

Hence the solutions are found.

Learn more about Quadratic Equations here :

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Answer:

Let the numbers are

x, (x+2), (x-2) and (x+4)

Step-by-step explanation:

x + x +2 +x - 2+x+4 = 80

4x +4 = 80

4x =80-44x = 76

4x = 76

x = 76/4

x = 19x

x=19

(x+2) =19+2=21

(x-2) = 19-2=17

(x+4)=(19+4)=23

hope it helps

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Given : Kishore bought a basket containing 30 oranges for rs 310. If he sells the oranges at rs 12 each , what Would be it's profit or loss?

Solution :

Cost price of oranges = rs.310

As we know that each oranges cost rs.12

So, selling price of oranges is 30 × 12 = rs.360

Now, finding profit or loss

Profit = Selling Price - Cost Price

Profit = rs.360 - rs.310

Profit = rs.50

Answer:

domain - (-infinity,infinity)

range - (-infinity, 2]

axis of sym - x=-1

y int - (0,-1)

at what value (row 1) - (-1,2)

Step-by-step explanation:

domain is side to side, it never ends bc of the arrows

range is top to bottom, there is no bottom bc of the arrow, but it has a top at 2 (the value on the y axis)

the axis of sym is basically the line that runs through the vertex, it's where you could fold it in half and it would still match up

Answer:

Original = $200

Step-by-step explanation:

Original = x

Final = 172

Percent Decrease = 14%

Original = 100%

Final = 100% - 14%

172 = 86%

Solve:

172/86 * 100 = x

2 * 100 = 200

Original = 200

-Chetan K

$ 200 ( approximately )

Step-by-step explanation:

100% - 14% = 86%

100/86 × 172

Answer:

because it is larger than 0.5, but smaller than 0.6

Step-by-step explanation:

another way to write 0.6 is 0.60 and another way to write 0.5 is 0.50

if you ignore the 0.

55 is between 60 and 50

hope this helps :)

Answer:

-8/11=12/v

-8v / 11 = 12

-96v / 11 = 12

-96v = 132

v = 132 / -96

v = 1.375  OR

v = 1   3/8

Step-by-step explanation:

Answer:

The answer is 3x^2+2x+5

Step-by-step explanation:

I just simply factored and followed the long division method.