Newton and his friends were watching a movie. They watch 50% of the movie and then take a break. Then they watch the remaining 65 minutes of the movie. How long was the whole movie

Answers

Answer 1
Answer:

The length of the whole movie was 130 minutes.

Let's call the length of the whole movie "x". According to the problem, Newton and his friends watch 50% of the movie before taking a break. This means they watched 0.5x minutes of the movie.

After the break, they watch the remaining 65 minutes of the movie. So the total time they watched the movie is:

0.5x + 65

But we know that the total time they watched the movie is the same as the length of the whole movie "x". So we can set these two expressions equal to each other and solve for "x":

0.5x + 65 = x

Subtracting 0.5x from both sides, we get:

65 = 0.5x

Dividing both sides by 0.5, we get:

x = 130

Therefore, the length of the whole movie was 130 minutes.

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Solve for x. (Round to the nearest thousandth.)
3x - 8 = 15

Answers

Answer:x = 7.667

Step-by-step explanation:

3x - 8 = 15

     + 8 = 23

3x = 23

divide 3 by 3 and 23 so you get x by itself

answer = 7.667

Answer:

x = 7.667

Step-by-step explanation:

3x - 8 = 15 (Rearrange expression)

-8 - 15 = -3x (Combine like terms)

-23 = -3x (Divide)

x = 7.667

He sum of two numbers is 46 and the difference is 2 . What are the numbers?large number is
the small number is

Answers

a + b = 46
a-b = 2

solve one of the equations for a...
a + b = 46
a = b + 2

solve for "b" using substitution...
(b + 2) + b = 46
2b + 2 = 46
2b = 44
b = 22

solve for "a" with substitution...
a + (22) = 46
a = 24

Smaller Number: 22
Bigger Number: 24
Let us condense your question in the form of system of equations,

x + y = 46
x - y = 2

Now, x = 46 - y

Thus,

46-y - y = 2

46 - 2y = 2

-2y = -44

Thus, y = 22.

x + y = 46

x + 22 = 46

Thus, x = 24.

Thus, the greater number is 24 and smaller number is 22.

Solve for x:
- 11x + 32.5 < 82

Answers

Answer:

x>-4.5

Step-by-step explanation:

- 11x + 32.5 < 82

Subtract 32.5 from each side

- 11x + 32.5-32.5 < 82-32.5

- 11x  < 49.5

Divide each side by -11. remembering to flip the inequality since we are dividing by a negative

-11x/-11 > 49.5/-11

x>-4.5

Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. Explain also.

Answers

Answer:

1) For  y=5x

A)  Domain=(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept = 0

D) Asymptote= No asymptote

2) For   y=log_5x

A)  Domain=Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept =  None

D) Vertical Asymptote:   x=0

Step-by-step explanation:

Given : y=5x and y=log_5x

Refer the graph attached.

1)  In equation (1)  y=5x

The domain is the set of all possible values in which function is defined.  

y=5x is a linear polynomial defined on all real numbers.

Domain=(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

Range is the set of all values that function takes.

It also include all real numbers.

Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

→y-intercept- Value of y at the point where the line crosses the y axis.

put x=0 in equation y=5x we get, y=0

Therefore, y-intercept = 0 (We can see in the graph also)

→An asymptote is a line that a curve approaches, but never touches.

Asymptote= No asymptote

2) Now in equation (2) y=log_5x

Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

because log function is not defined in negative.

Range=  (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

y-intercept - None

Vertical Asymptote:   x=0

1)

A)  Domain= (-∞, ∞) for all x

B) Range= (-∞, ∞) for all y

C) y-intercept = 0

D) Asymptote= No asymptote

2)

A)  Domain=(0, ∞) for all x > 0

B) Range= (-∞, ∞) for all y

C) y-intercept =  None

D) Vertical Asymptote:   x=0

Here, we have,

Function 1: y = 5x

Domain: The domain of this function is all real numbers because there are no restrictions on the values that x can take.

Range: The range of this function is also all real numbers because for every value of x, we can find a corresponding y value by multiplying it by 5.

Y-intercept: To find the y-intercept, we set x = 0 and solve for y. Substituting x = 0 into the equation, we get y = 5(0) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: There are no asymptotes in this linear function.

Function 2: y = log₅x

Domain: The domain of this function is all positive real numbers because the logarithm function is only defined for positive values of x.

Range: The range of this function is all real numbers because the logarithm function can produce any real number output.

Y-intercept: To find the y-intercept, we set x = 1 and solve for y. Substituting x = 1 into the equation, we get y = log₅(1) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: The logarithmic function has a vertical asymptote at x = 0 because the logarithm is undefined for x ≤ 0. Additionally, there is no horizontal asymptote.

When plotting these functions on the same set of axes, we will observe that the graph of y = 5x is a straight line passing through the origin (0, 0) with a slope of 5.

The graph of y = log₅x will appear as a curve that starts at the point (1, 0) and approaches the vertical asymptote x = 0 as x approaches zero.

The two graphs will intersect at the point (1, 0) because log₅1 = 0.

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If UX=34 and VX=37, what is WX? Write your answer as a whole number or as a decimal rounded to the nearest hundredth. *

Answers

The calculated length of the segment WX is 40.26 units

How to determine the length of the segment WX

From the question, we have the following parameters that can be used in our computation:

The right triangle

Using the ratio of proportional sides, we have

VX/UX = WX/VX

This gives

WX = VX * VX/UX

Substitute the known values into the equation

WX = 37 * 37/34

Evaluate

WX = 40.26

Hence, the length of the segment WX is 40.26 units

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Final answer:

Without specific relationships or equations that relate UX, VX, and WX, it is not possible to determine the value of WX with the given values, UX=34 and VX=37.

Explanation:

The question is missing information necessary to accurately determine the value of WX. With the given values, UX=34 and VX=37, we do not have a specific relationship or equation that relates UX, VX, and WX. If there was a relationship or equation provided, such as VX = UX + WX, we could then substitute the known values to calculate WX.

However, without the necessary information, determining the value of WX is not possible. Recheck your problem statement, and make sure all the relevant details are included. Ensuring the question provides all the necessary information from your problem will aid in obtaining an accurate answer.

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a model car has a scale of 3 cm : 2 m. The length of the actual hood of the car is 1 m. What is the length of the model?

Answers

1.5 cm is the length of the model.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

a model car has a scale of 3 cm : 2 m.

The length of the actual hood of the car is 1 m.

Now,

Set up a proportion:

3cm/2m = x/1m

Cross-multiply:

2x=3

Divide by 2:

x=1.5 cm

Hence, 1.5 cm is the length of the model.

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Set up a proportion:
3cm/2m = x/1m
Cross-multiply:
2x=3
Divide by 2:
x=1.5 cm