solve for x
2x/3 + 2 = 16

1) To find the inverse function we need to switch the values of the variables, that is, the x-values of the original function corresponds to the y-values of the inverse function, and the y-values of the original function corresponds to the x-values of the inverse function. Then, the table is:

x | 4 | 2 | 1 | 3 | 4 |

y | -2 | -3 | 6 | 7 | 5 |

2) The inverse is not a function because the input x = 4 has two different outputs, -2 and 5; and in a function, each input value can have only one input value.

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

L =  total number of slices for Luke

K = total number of slices for Kira

A = total number of slices for Ali

\(\stackrel{\textit{two thirds of all slices}}{\cfrac{2}{3}L}=4\implies 2L=12\implies L=\cfrac{12}{2}\implies L=6 \\\\\\ \stackrel{\textit{two thirds of all slices}}{\cfrac{2}{3}K}=6\implies 2K=18\implies K=\cfrac{18}{2}\implies K=9 \\\\\\ \stackrel{\textit{two thirds of all slices}}{\cfrac{2}{3}A}=8\implies 2A=24\implies A=\cfrac{24}{2}\implies A=12\)

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

For such more questions on Sprinter Race Time Calculation

https://brainly.com/question/18963548

#SPJ8

Answer:

21 hot dogs

9 pizza slices

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information:

\(\textsf{Equation 1}: \quad x + y = 30\)

\(\textsf{Equation 2}: \quad 2.5x+3.25y=81.75\)

Rewrite Equation 1 to make x the subject:

\(\implies x=30-y\)

Substitute this into Equation 2 and solve for x:

\(\implies 2.5(30-y)+3.25y=81.75\)

\(\implies 75-2.5y+3.25y=81.75\)

\(\implies 75+0.75y=81.75\)

\(\implies 0.75y=6.75\)

\(\implies y=9\)

Substitute the found value of y into the rewritten form of Equation 1 and solve for x:

\(\implies x=30-9\)

\(\implies x=21\)

Solution

Learn more about systems of equations here:

https://brainly.com/question/28281431

https://brainly.com/question/27034625

Answer:

Number of hot dogs purchased = 21

Number of pizza slices purchased = 9

Step-by-step explanation:

Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P

Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H

Since P slices of pizza were purchased and each slice of pizza costs $3,25,  total amount spent on hot dog purchase = $3,25P

Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75

So we have an equation in two variables

2.50H + 3.25P = 81.75      (1)

We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased

So

H + P = 30     (2)

Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30

2.50H + 2.50P = 75    (3)

Subtract equation (3) from equation (1) to eliminate the H terms

(1) - (3):

2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75

2.50H + 3.25P - 2.50H - 2.50P = 6.75

Collect like terms and simplify

==>  (2.50H -2.50H) + (3.25P - 2.50P) = 6.75

==>  0.75P = 6.75

Divide both sides by 0.75

==>  0.75P/0.75 = 6.75/0.75

==>  P = 9

So number of people who bought pizza slices = 9

This is the same as the number of pizza slices that were bought

Substitute for P in Eq (2) H + P = 30
==>  H + 9 = 30

Subtract 9 from both sides

==> H + 9 - 9 = 30 - 9

==>  H = 21

So number of people who bought hot dogs = 21

This is the same as the number of hot dogs purchased

There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

To know more about Inequalities here

https://brainly.com/question/28823603

#SPJ1

Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

Learn more about unit circle here: https://brainly.com/question/30403151

#SPJ1

282

Step-by-step explanation:

C=180-112=68

A=180-68-51=61

sum of exterior angles=112+119+51=282

Answer:

the answer is 9

Step-by-step explanation:

i used a caculator

The relationship between the interior and exterior angles of a polygon is they are supplementary.

What is a regular polygon?

If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

Here,

we have to show how the interior and exterior angles of a polygon relate to each other.

A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.

As a result, the interior angles of a regular polygon are all equal to 180 degrees minus the measure of the exterior angle(s).

Hence, the relationship between the interior and exterior angles of a polygon is they are supplementary.

To learn more about the regular polygon from the given link

https://brainly.com/question/1592456

#SPJ1

The land area of North America is 9,455,941.77 square miles.

Percentage can be described as the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %.

In order to determine the land area of North America, multiply the total land area of the Earth by the percentage of the land area of North America.

Land area of North America = percentage of the land area of North America x total land area

16.5% x  57,308,738

0.165 x 57,308,738 = 9,455,941.77 square miles

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

The vector having a magnitude √61 and direction 140.2° has been shown in the figure.

Given,

Let the vector v have an initial point at (4, 8) and a terminal point at

(-2, 3).

we are asked to  Plot the vector v .

Given that the initial point of the vector is (4,8) and the termination point of the vector is (-2,3).

So, the tail of the vector is at point (4,8) and the head of the vector is at (-2,3).

The vector , v, has been shown.

I v I = √(4-(-2))²+(8-3)²

= √(4+2)²+(8-3)²

= √(6)²+(5)²

= √36+25

= √61

The direction of a vector is the angle made by a vector with the positive direction of the x-axis.

θ =  180° tan⁻¹ I 3-8/-2-4I

θ = 180° tan⁻¹ (5/6)

θ = 180° - tan⁻¹(5/6)

θ = 180° - 39.80°

θ = 140.2°

Hence, the required vector having a magnitude √61  and direction  140.2° has been shown in the figure.

Learn more about Direction of vectors here:

brainly.com/question/3184914

#SPJ9

Answer:

the answer is 16000

because 4 × 3848 is the best estimate for 16000 its nearby 15 k

hopefully its correct

Answer:

In an hour the factory makes 3848 pencils

In four hours the factory will make four times as much

=4×3848=15392 pencils

the best estimate is 16000 pencils

Answer:

-0.38

Step-by-step explanation:

0.6-(0.7)(1.4)

0.6-0.98

-0.38

Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

I think its either 5 or 4 one of the 2

Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Answer:

15,18,21

Step-by-step explanation:

Answer:

15 18 21

Step-by-step explanation:

its skskskskskksksskskkssksksksk

Parallelogram area is base times height.  Base of 14, height of 10,

Answer: A = (14 ft)(10 ft)    second choice

Answer:

choice B

Step-by-step explanation:

Answer:

44 grams carbohydrates = 176 calories

36 gram of fat = 324 calories

37 gram of protien = 148 calories

44 grams of Carbohydrates = 176 calories

36 grams of Fat = 324 calories

37 grams of Protein = 148 calories

To calculate the number of calories from each macronutrient (carbohydrates, fat, and protein), you need to know the caloric content per gram for each nutrient.

The caloric content per gram is as follows:

- Carbohydrates: 1 gram = 4 calories

- Fat: 1 gram = 9 calories

- Protein: 1 gram = 4 calories

Now, let's calculate the number of calories for each macronutrient in the Wendy's Big Bacon Classic:

1. Carbohydrates:

Calories from Carbohydrates = 44 grams × 4 calories/gram

Calories from Carbohydrates = 176 calories

2. Fat:

Calories from Fat = 36 grams × 9 calories/gram

Calories from Fat = 324 calories

3. Protein:

Calories from Protein = 37 grams × 4 calories/gram

Calories from Protein = 148 calories

In total, the burger would have 176 + 324 + 148 = 648 calories.

To know more about Carbohydrates:

https://brainly.com/question/16646944

#SPJ2

The rate of change of the linear function is 5(option c).

What is a linear function?

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

We can get the x-values and y-values from the table.

We have to find the rate of change for the associated linear function.

From the table,

If x=1 , the value of y is 7.

If x=2, the value of y is 12.

If x=3, the value of y is 17.

If x=4, the value of y is 22.

If x=5, the value of y i 27.

The y values are in the interval of 5.

That is if x changes in 1 unit, the corresponding y value changes in 5 units.

Hence, the rate of change of the linear function is 5(option c).

Complete question :

The values shown represent the y-values that correspond to x-values from x = 1 through x = 5. What is the rate of change for the associated linear function?

(a) 9 (b)2 (c) 5 (d)10

Learn more about linear function here:

https://brainly.com/question/29281420

#SPJ1

Answer:

53.94$

Step-by-step explanation:

Answer:

53.94$

Step-by-step explanation:

Answer:

Step-by-step explanation:

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

For more such question on function. visit :

https://brainly.com/question/11624077

#SPJ8

Answer:

It is D

Step-by-step explanation: