A right triangle has side lengths 8, 15, and 17 as shown below.
Use these lengths to find sin.X, tanX, and cos.X.

the only value of x where the tangent line has the largest slope is x = 0.

To find the value(s) of x on the curve y = -240x^3 - 3x^5 where the tangent line has the largest slope, we need to find the maximum of the derivative of y with respect to x.

Let's calculate the derivative of y with respect to x:

y' = d/dx (-240x^3 - 3x^5)

  = -720x^2 - 15x^4

To find the maximum slope, we set the derivative equal to zero and solve for x:

-720x^2 - 15x^4 = 0

Factoring out x^2, we have:

x^2 (-720 - 15x^2) = 0

Setting each factor equal to zero, we get two solutions:

x^2 = 0   -->   x = 0 (repeated solution)

-720 - 15x^2 = 0   -->   x^2 = -720/15   -->   x^2 = -48   (no real solutions)

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Answer:

A) 6 x² - 7x - 20

Step-by-step explanation:

Explanation:-

Given p(x) = 2 x-5 and r (x) = 3 x +4

(pr)(x) = p(x) r(x)

         = (2x -5)( 3 x +4)

        = 2x(3x +4) -5( 3x +4)

       = 6 x² + 8x - 15 x - 20

       =  6 x² - 7x - 20

(pr)(x) = 6 x² - 7x - 20

Answer:

8/27

Step-by-step explanation:

Answer:

300

Step-by-step explanation

LxWxH

Answer:

You flip a coin 4 times, with 2 possibilities every flip, heads or tails. So, every time you throw there's a 50% chance you'll throw tails. so it would be 1/2

The probability of getting at least 2 tails is 0.688.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Given that, a fair coin is tossed 4 times.

So, sample space is

S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

Now, total number of outcomes =16

Number of favorable outcomes = 11

Probability =11/16

= 0.6875

≈ 0.688

Therefore, the probability of an event is 0.688.

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To factor quadratics with leading coefficients other than 1, you can follow these steps:

Check your factoring by expanding the factored form to see if it simplifies back to the original quadratic equation.

Remember that factoring quadratics with leading coefficients other than 1 may involve more complex algebraic techniques, and in some cases, the quadratic equation may not factor easily. In such cases, you can resort to using the quadratic formula to find the roots of the equation.

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The length of the side of the smaller square is 7 inches.

Let x be the length of the side of the smaller square.

The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is

(x + 3) inches.

The area of the smaller square is

x^2 square inches.

The area of the larger square is

(x + 3)^2 square inches.

We can set up the equation:

x^2 + (x + 3)^2 = 149

Expanding and simplifying the equation gives:

x^2 + x^2 + 6x + 9 = 149

Combining like terms:

2x^2 + 6x - 140 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2

x = (-6 ± √(36 + 1120)) / 4

x = (-6 ± √(1156)) / 4

x = (-6 ± √(596)) / 4

x = (-6 ± 34) / 4

x = -10 or x = 7

The side length of the smaller square can't be negative, so x = 7 inches.

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Answer: The number is 1.

Step-by-step explanation:

Let the number be x

5-x = 1+3x

or, 5 = 1+3x+x

or, 5 = 1+4x

or, 5-1 = 4x

or, 4x = 4

or, x = 4/4

so, x = 1

The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

The average total cost can be found by dividing the total cost by the quantity produced. In this case, the total cost function is given as C = 90 + 35Q + 25Q^2 + 10Q^3, and we want to find the average total cost when Q = 2.

To find the average total cost, we need to calculate the total cost when Q = 2. Plugging Q = 2 into the cost function, we get:
C = 90 + 35(2) + 25(2^2) + 10(2^3)
C = 90 + 70 + 100 + 80
C = 340

Next, we divide the total cost by the quantity produced:
Average Total Cost = Total Cost / Quantity
Average Total Cost = 340 / 2
Average Total Cost = 170

Therefore, the value of average total cost when Q = 2 is $170.

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Answer: A-True B-False C-True D-True E-False

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

X-X

=0

Adaptations are distinct characteristics of an organism that allow it to survive in the environment. Adaptation can be classified into three mainly - structural, behavioural and and psychological.

A structural adaptation is a modification in the body of an organism. They are special attributes to the body of an organism.

Four examples of structural adaptations are

(1) Thick white fur in Polar bears : This fur helps the Polar bear to withstand the harsh cold climate. Also the white fur enable them to be not easily visible protecting it from its predators.

(2) Blubber in marine animals : It is a thick layer of fat beneath the skin. It helps in insulation of heat, storing energy and increasing buoyancy.

(3) Hump in camels : It helps to store fat which can be broken down into energy and water during scarcity of food and water. It also helps in better thermoregulation allowing them to live in extreme environments.

(4) Thorns in cacti : The entire leaf of a cactus is spine reducing the surface area of leaf and thereby decrease loss of water in evaporation. It also protect it from herbivores.

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Differentiation - The change of perimeter = dP/dt= 40/7m/h

What is differentiation?

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics.

what is area?

It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.

let the area of the square be "A" of sides "S"

area of the square

A = S²

differentiating with respect to "t" time

dA/dt = d(S²)/dt

= dA/dt = 2S*ds/dt

dA/dt=2S*ds/dt

=20m²/h

since we are given dA/dt=20

2Sds/dt=20

and at that instant A=49m sq.

=S²=49

since A=s²

S=√49

=±7

S=7

2SdS/dt=2*7ds/dt =20

ds/dt=20/14

=10/7

The perimeter of the square

P=4S

dP/dt =4dS/dt

=4*20/14

=4*10/7

thus the change of perimeter = dP/dt= 40/7m/h

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Answer:

The cost of 5 pounds of apples at $1.90 per pound is:

5 x $1.90 = $9.50

The cost of 1 1/2 dozen oranges at 50¢ an orange is:

1 1/2 dozen = 18 oranges

18 x $0.50 = $9.00

The cost of 6 avocados priced at 3 for a dollar is:

6 / 3 = 2 dollars

So we add everything they spend together:

$9.50 + $9.00 + $2.00 = $20.50

So the equation is:

$1.90(5) + $0.50(18) + $2(3) = $20.50

Answer:

Question 1: -3

Question 2: 5

Step-by-step explanation:

Question 1's value decreses by 3 so the answer is -3 :)

Question 2's value increases by 5 so the answer is 5 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

14

Step-by-step explanation:

Answer:72/97

Step-by-step explanation: took the test.

In the given scenario, the data described are of nominal type. Nominal data are variables that have distinct categories with no inherent order or rank among them.

They are categorical and do not have any numerical value, unlike ordinal data. In this case, the competitions at a company picnic are three-legged race, wiffle ball, egg toss, sack race, and pie eating contest. These competitions can be classified into distinct categories, and there is no inherent order or rank among them.

Therefore, the data described are of nominal type. The data described in the context of competitions at a company picnic are nominal. Nominal data refers to categories or labels that do not have any inherent order or ranking. In this case, the competitions listed (three-legged race, wiffle ball, egg toss, sack race, and pie eating contest) are simply different categories without any implied ranking or order.

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Answer:

16

Step-by-step explanation:

no image, but 6 + 2 + 2 + 6 = 16

Answer:

141

Step-by-step explanation:

First, you need to identify the pattern. As we have 3 terms, the pattern is +18 then +30. So, we can determine the next term is +18. 75 + 18 = 93. 93 is the 4th term. We can also determine the next term is +30. 93 + 30 = 123. 123 is our 5th term. Based off of what we know, we can determine the next term will be +18. 123 + 18 = 141. This proves our 6th term is 141.

I hope this helped. If this isn't correct, I apologize. This is based off of the 3 terms shown. If this helped, leave a heart and leave stars.

Answer:

24cu. cm

Step-by-step explanation:

Answer:

h= -15

Step-by-step explanation:

you have to move the negative from the h to the other side :)

Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

Answer: £2.33

Step-by-step explanation:

30% of 3.34 is 1.002

3.34-1.002=2.338

Answer:

For the first one if solving for y, y=−8x−16. If solving for x,

x= −1/8y-2

For the second one if solving for y, y=3x−5 and if solving for x,

x=1/3y +5/3

To find the break-even point, we need to find the point where the cost function and revenue function intersect, since at that point the profit will be zero.

So, we set the cost function equal to the revenue function:

180x + 8400 = 210x

Simplifying:

30x = 8400

x = 280

Therefore, the break-even point is at x = 280. To find the coordinates, we need to plug this value into either the cost or revenue function:

c(280) = 180(280) + 8400 = 50400

r(280) = 210(280) = 58800

So the break-even point is (280, 50400).
To find the coordinates of the break-even point, we need to determine the value of x when the cost of production (c(x)) is equal to the revenue (r(x)). In other words, we need to solve the equation c(x) = r(x).

Step 1: Set c(x) equal to r(x)
180x + 8400 = 210x

Step 2: Rearrange the equation to solve for x
210x - 180x = 8400
30x = 8400

Step 3: Divide both sides by 30 to find x
x = 8400 / 30
x = 280

Step 4: Find the break-even revenue by plugging x into either the cost or revenue function (we'll use r(x))
r(280) = 210 * 280 = 58800

So, the coordinates of the break-even point are (280, 58800), where 280 represents the number of cell phones produced and 58800 is the revenue generated.

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The linear equation y = -3x - 3, have a slope of -3 while the y intercept is -3.

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change (slope); and b is the y intercept

Given the equation:

y = -3x - 3

The slope of the graph is -3 while the y intercept is -3.

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Answer: Use a variable

w

to represent the width of the room.

From the given information find that

10

w

=

80

, hence

w

=

8

.

So the room is

8

meters by

32

meters.

Explanation:

Let

w

represent the width of the room in meters.

Then the length of the room is

4

w

.

So the perimeter of the room is

w

+

4

w

+

w

+

4

w

=

10

w

.

Given that the perimeter is

80

meters, that translates as:

10

w

=

80

Divide both sides by

10

to get

w

=

8

.

Hence the width of the room is

8

meters and the length is

4

w

=

32

meters.

Step-by-step explanation:

The dimensions of the room are 5 meters long and 5 meters wide.

The perimeter of a rectangular room is equal to twice the sum of its length and width. In this case, the perimeter of the rectangular room is equal to 2 x (length + width) =  10 meters.

Therefore, we can write:
2 x (L + W) = 10

To find the dimensions of the room, we need to solve the equation for L and W.
L + W = 5
L = 5 - W

Substitute this equation for L in the original equation:
2 x (5 - W + W) = 10
2 x (5) = 10
10 = 10

Therefore, L = 5 and W = 5, so the dimensions of the room are 5 meters long and 5 meters wide.

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