what linear function can be represented by the set of ordered pairs? {(−4, 15), (0, 5), (4, −5), (8, −15)} enter your answer in the box. f(x)=

Answer:

y = (x-1/x+2)(x-1)

y = -3(x-1)

y = -3x+3

-3x y = 3

x y = -1

x(0) y = -1

y = -1

Step-by-step explanation:

Answer:

Theta = 37.9 degrees

AC = 11.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan theta = 7/9

tan ^ -1 tan theta = tan ^-1 (7/9)

theta =37.87498

To 1 decimal place

Theta = 37.9 degrees

We use the Pythagorean theorem to find AC

a^2 + b^2 = c^2

7^2 + 9^2 = AC^2

49+81 = AC^2

130 = AC^2

Taking the square root of each side

sqrt(130) = sqrt(AC^2)

AC = 11.40175

Rounding to 1 decimal place

AC = 11.4

Answer:

31.4

Step-by-step explanation:

the diameter of the cookie is 5. use 3.14x 5 then multiply that by 2

Step-by-step explanation:

\( \dashrightarrow \quad \rm {a = \dfrac{v -u}{t} } \\ \)

\( \dashrightarrow \quad \rm {a = \dfrac{9 -7}{2} \; m \: s^{-2}} \\ \)

\( \dashrightarrow \quad \rm {a = \dfrac{2}{2} \; m \: s^{-2}} \\ \)

\( \dashrightarrow \quad \underline{\boxed{\bf {a = 1 \; m \: s^{-2}}}} \\ \) (Answer)

Answer:

£735,000

Step-by-step explanation:

we can keep the first three numbers and then round the rest (284). since the first number (2) is less than 5, we round to 0. thus, 284 -> 000 and 735,284 -> 735,000. note that the first 3 numbers do not include a zero, so we don't have to do anything fancy here.

 Answer: the answer to this question is 49

Step-by-step explanation:  because (a+b)2 = a2 + 2ab +b2 = Perfect square trinomial

(b) 145, 143, 145, and 147 must have the smallest standard deviation.

A statistical measurement called standard deviation examines how distant a set of numbers is from the mean. Simply said, standard deviation quantifies the degree of dispersion between numbers in a data set. The square root of the variance is used to construct this metric. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

Given,

(b) 145, 143, 145, and 147 must have the smallest standard deviation.

Due to the near proximity of all the values, this particular data set has the lowest standard deviation.

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It took 1700 J of work to stretch a spring from its natural length of 2 m to a length of 6 m. The spring constant k will be 212.5 N/m.

The potential energy stored in a spring is given by the formula:

PE = (1/2) kx^2

where k is the spring constant, x is the displacement from the equilibrium position, and PE is the potential energy.

In this problem, the spring is stretched from its natural length of 2 m to a length of 6 m, so the displacement is x = 6 m - 2 m = 4 m.

The work done on the spring is equal to the change in potential energy, so:

Work = PE final - PE initial

1700 J = (1/2) k(4² - (1/2) k(0)²

1700 J = 8k

k = 212.5 N/m

Therefore, the spring constant is 212.5 N/m.

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The speed of the train is 45 mi/h hence the correct answer is option G. 45 mi/h.

Let's assume the speed of the train is x mi/h.

Since the car is traveling 15 mi/h faster than the train, the speed of the car is (x + 15) mi/h.

The distance traveled by train in 2 hours is 2x miles (since speed * time = distance).

The distance traveled by the car in 2 hours is 2(x + 15) miles.

According to the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse represents the distance between the train and the car, which is approximately 150 miles.

Using the Pythagorean theorem, we can set up the equation:

\((2x)^2 + [2(x + 15)]^2 = 150^2\\4x^2 + 4(x + 15)^2 = 150^2\)

Simplifying and solving the equation, we find:

\(4x^2 + 4(x^2 + 30x + 225) = 22500\\4x^2 + 4x^2 + 120x + 900 = 22500\\8x^2 + 120x + 900 - 22500 = 0\\8x^2 + 120x - 21600 = 0\)

Dividing the equation by 8 to simplify:

\(x^2 + 15x - 2700 = 0\)

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Factoring is the easiest method in this case:

(x + 60)(x - 45) = 0

Setting each factor equal to zero, we have:

x + 60 = 0  or  x - 45 = 0

x = -60  or  x = 45

Since the speed cannot be negative, we discard the solution x = -60.

Therefore, the speed of the train is 45 mi/h hence the correct answer is option G. 45 mi/h.

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

-1

Step-by-step explanation:

because is the answer

The inverse function theorem states that if f is a differentiable function with a nonzero derivative at a point x, then there exists a neighborhood of x where f is invertible and the inverse function g is also differentiable.

If f has k continuous derivatives, then we can apply the theorem k times to obtain a neighborhood of x where f is k times differentiable and invertible with a k times differentiable inverse function g. To show that g also has k continuous derivatives, we can use induction.

For k = 1, we know that g'(y) exists and is continuous by the inverse function theorem. Now assume that g has k continuous derivatives, and let's show that g has (k+1) continuous derivatives. By the chain rule, we have (g o f)(x) = x, which implies that (g' o f)(x) f'(x) = 1. Differentiating both sides with respect to x, we get (g'' o f)(x) f'(x)^2 + (g' o f)(x) f''(x) = 0. Solving for (g'' o f)(x), we obtain (g'' o f)(x) = - (g' o f)(x) f''(x) / f'(x)^2.

Since f has k continuous derivatives, we know that f'' is continuous. By the induction hypothesis, g' o f has k continuous derivatives. Since f' is nonzero, we know that f' is continuous and hence 1/f'(x)^2 is also continuous. Therefore, (g'' o f) is continuous as a product of continuous functions, and g has (k+1) continuous derivatives.

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Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

Given that equation  \(\frac{16x+12}{2}=100\)  and asked to evaluate the value of x in the given equation

⇒ \(\frac{16x+12}{2}=100\)(given equation)

To solve the given equation, need to use the various mathematical  operations i.e division and subtraction)

⇒8x+6=100 ( using the operation division)

⇒8x=100-6 (using the operation subtraction)

⇒8x=94

⇒x=\(\frac{94}{8}\)(using the operation division)

⇒x=11.825

By using the mathematical  operations i.e division and subtraction the value of x came as 11.825

⇒Therefore, The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

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Answer:

Step-by-step explanation:

a) 4/9*x^4

b) 2/y

Answer:

% = 50

Step-by-step explanation:

%       9

--   =   --

100    18

Multiply 9 times 100, that equals 900. Divide 900 by 18, which = 50.

If the metal strip goes around the bench, then we are looking for the perimeter.

P = 2L + 2W

P = 2(9) + 2(4)

P = 18 + 8

P = 26 feet

Then, we know that the stripping costs $5 per foot, and we need 26 feet of the stripping.

26 x 5 = 130

Total cost = $130

Hope this helps!

The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.

To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).

Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.

1 - 0.04 = 0.96

Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.

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Answer:

37.5 units²

Step-by-step explanation:

Please see the attached pictures for full solution.

*The shoelace method can be used to find the area of any polygons given its coordinates. Ensure that if the polygon has x number of points, (x+1) coordinates are written down in the formula, in which the last coordinate written down is the same as the 1st coordinate. (A triangle has 3 points so 4 coordinates were written down)

In method 2, the length/ height/ base/ breadth can be found by subtracting its x and y coordinates. Alternatively, count the number of squares. Each square would be 1 unit.

Answer:

x = 4 and y = 10

Step-by-step explanation:

-5y + 8x = -18

5y + 2x = 58

First you will want to get rid of y from both equations, so you add both equations together.

You will get 10x = 40, then subtract 10 from both sides and you get x = 4.

Now substitute x as 4 in any of the equations to get y.

-5y + 32 = -18

-5y = -50

y= 10

Answer:

x = 4

y = 10

Answer:

Step-by-step explanation:

x + 7 ≤ -9 subtract 7 from both sides

x≤-16  this is your answer

If you're plotting it will be (-∞,-16]

Answer:

Step-by-step explanation:

For this equation, all it is asking is to replace the unknown value with a number that completes the equation. However, the number must make the equation valid. Here is a few examples that could be a valid solution to this problem:

1. -55 + 7 < -9

(you don't need to solve this equation to tell that it's less than negative nine.)

2. 22 + (-98) + 7 < -9

(this is more complicated, but you can still tell that the sum is less than negative nine.)

So, basicly all that you have to do is replace the missing value with a number that gives the eqquation a sum less than negative nine. Hope this helped!!! :)

The value of x in the given equation 3x + 5 = 2(2x + 4) is x = -3.

How to solve the value of x in equation?

3x + 5 = 2(2x + 4)

3x = 4x + 8 - 5

3x - 4x = 3

-x = 3

x = -3

Hence, the value of x in the given equation 3x + 5 = 2(2x + 4) is x = -3.

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Answer:

25 and 13

Step-by-step explanation:

sum of ages of Farhan and his cousin = 38

7 years ago Farhan thrice of his cousin = 3:1

7 year ago the sum of their ages = 38-14 = 24( 7 years for each)

3:1 = 4 units = 24

1 unit =6

ages of Farhan and his cousin 7 years ago  = 6*3= 18 and 6*1 = 6

so the present age of Farhan = 18+7 = 25 and his cousin 6+7 = 13

Answer:

length is 19 width is 15

Step-by-step explanation:

The area of the classroom floor in the scale drawing is 247 square inches.

The area of Rectangle is length times of width.

We need to find the scale of the drawing, which is the ratio of the length in the drawing to the actual length:

19 inches / 38 feet = 0.5 inches/foot

Now we can use the scale to find the dimensions of the classroom floor in the scale drawing:

Length in scale drawing = Actual length ×  Scale

Width in scale drawing = Actual width ×  Scale

Length in scale drawing = 38 feet ×  0.5 inches/foot = 19 inches

Width in scale drawing = 26 feet ×  0.5 inches/foot = 13 inches

So the dimensions of the classroom floor in the scale drawing are 19 inches by 13 inches.

To find the area in square inches, we can multiply the length by the width:

Area in scale drawing = Length in scale drawing × Width in scale drawing

= 19 inches× 13 inches

= 247 square inches

Therefore, the area of the classroom floor in the scale drawing is 247 square inches.

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Answer:

The model on the top right.

Answer:

your answer would be the top right one

Step-by-step explanation:

I don't really know how to explain how I got my answer in words sorry.

Hope this helps! Have a great day ahead. Tell me if im wrong :) Stay Safe <3

Answer:

21/29

Step-by-step explanation:

Sin = hypotenuse side / opposite side to the angle

then: Sin (C) = 21 / 29

By answering the presented question, we may conclude that As a result, probability the chance of receiving heads and 4 is 1/12.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Here is an example space diagram that depicts all of the possible outcomes when Leo flips a coin and rolls a dice:

Each row represents the outcome of rolling the dice, and each column indicates the outcome of flipping the coin. The table entries represent the combined outcome of rolling the dice and flipping the coin. For example, the occurrence of receiving heads on the coin flip and rolling a 1 on the dice is represented by the outcome in the top left corner (H1).

As a result, the chance of receiving heads and 4 is 1/12.

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Answer:

Smallest number = 15

Second number = 177

Third number =     109

Step-by-step explanation:

Givens

Let the first number = x

Let the second number = 12x - 3

Let the third number = 7x + 4

Equation

x + 12x - 3 + 7x +4 = 301                 Combine like terms

Solution

20x + 1 = 301                                  Subtract 1 from both sides

20x = 301 - 1                                  Combine

20x = 300                                      Divide by 20

x = 300/20

x = 15

Answer:

The flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

Step-by-step explanation:

We can use the following formula to calculate the flow rate:

Flow rate (mL/hr) = Volume to be infused (mL) / Time of infusion (hr)

First, we need to convert the total volume of 2 liters to mL:

2 liters = 2000 mL

Next, we can plug in the values:

Flow rate = 2000 mL / 16 hours

Flow rate = 125 mL/hr

Therefore, the flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.