is y = |x| a function

the maximum height of a ballon is 58 after 1 sec

Answer:

3, 10, -2/3

Step-by-step explanation:

I don't speak spanish, so I hope i did this right.

Problem 1

set equal to each other

2x+1=x+4

-4         -4

2x-3=x

-2x     -2x

-3=-x

times -1 to get a positive x

3=x

Problem 2

repeat steps

4x-5=3x+5

+5            +5

4x=3x+10

-3x    -3x

x=10

Problem 3

repeat steps

x=4x+2

-4x  -4x

-3x=2

divide

x=- 2/3

to find the y's, go back and plug in

Prob 1: y=(3+4) =7

Prob 2: y=[3(10)+5] =35

Prob 3: y=(-2/3) =-2/3

Answer:

1.)

y = 2x + 1

y = x + 4

Substitute

2x + 1 = x + 4

Subtract 1 on both sides

2x + 1 - 1 = x + 4 - 1

2x = x + 3

Subtract x on both sides

2x - x = x - x + 3

x = 3

Now that we have x we can use that for finding y

y = x + 4

y = 3 + 4

y = 7

x = 3

y = 4

( 3, 4 )

__________________________________________________________

2.)

y = 4x - 5

y = 3x + 5

Substitute

4x - 5 = 3x + 5

Add 5 on both sides

4x - 5 + 5 = 3x + 5 + 5

4x = 3x + 10

Subtract 3x on both sides

4x - 3x = 3x - 3x + 10

x = 10

Now that we have x, we can use that to find y

y = 3x + 5

y = 3 (10) + 5

y = 30 + 5

y = 35

x = 10

y = 35

( 10, 35)

__________________________________________________________

3.)

y = x

y = 4x + 2

Substitute

x = 4x + 2

Subtract 4x on both sides

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

-3x = 2

Divide -3 on both sides to isolate the variable

-3x/-3 = 2/-3

x = -2/3

Now that we have that we can use it to find y

y = x

y = -2/3

x = -2/3

y = -2/3

( -2/3, -2/3)

Hope this helped!

Have a supercalifragilisticexpialidocious day!

(2,-1), (-4,17).

Step-by-step explanation:

Equate the equation A and equation B

Convert the quadratic equation in factored form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

Square root both sides

Find the values of y

Substitute the value of x in the equation B

We find that option 1, -3(x^2 + 4), is the only expression that is equal to -3x^2-12.

The expression -3x^2-12 can be simplified by factoring out a common factor from both terms. Let's analyze the given options to determine which one is equal to the expression.

Option 1: -3(x^2 + 4)

If we distribute the -3, we get -3x^2 - 12. Therefore, this option is equal to the given expression.

Option 2: -3(x^2 - 4)

If we distribute the -3, we get -3x^2 + 12. This option is not equal to the given expression.

Option 3: -3(x^2 + 12)

If we distribute the -3, we get -3x^2 - 36. This option is not equal to the given expression.

Option 4: -3(x^2 - 12)

If we distribute the -3, we get -3x^2 + 36. This option is not equal to the given expression. ( option 1)

For such more questions on expression

https://brainly.com/question/1859113

#SPJ8

Note- The complete question is "Which of the following expressions is equal to -3x^2-12:

-3(x^2 + 4)

-3(x^2 - 4)

-3(x^2 + 12)

-3(x^2 - 12)

Answer: The length, breadth, and height of the rectangular prism are:

Length = 3x + y cm

Breadth = 2x + 2y cm

Height = 3y cm

The volume of the rectangular prism is given by the formula:

Volume = Length x Breadth x Height

Substituting the values, we get:

Volume = (3x + y) x (2x + 2y) x (3y)

Simplifying the expression, we get:

Volume = 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3

Therefore, the volume of the rectangular prism is 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3 cubic cm.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Point given:

Translation rule:

Image is:

The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs

The histogram is not given and the data represented on the histogram are not properly presented

This means that the histogram cannot be interpreted

Here, we have

Ketchup = 63

Mustard = 27

Chili = 60

So, we have

Mustard = 27/(63 + 27 + 60) * 5000

Evaluate

Mustard = 900

This means that 900 people prefer mustard

Given that

Data = Milligrams of Vitamin C from 100 different gummy vitamins sold

This data can be represented using a box plot because the five-summary data can be easily identified from the dataset

From the five-summary, the median can be derived

In this case, the graph to use is a circle graph

This is so because the circle graph would show the proportion of the student's preferences

Read more about graphical representation at

https://brainly.com/question/28350999

#SPJ1

Answer:

d

Step-by-step explanation:

The sum of the angles of a triangle is ALWAYS 180 degrees.

Answer:

a. 29

b. 0.25

c. 75

d. 64

Step-by-step explanation:

You just basically plug in the number for x and solve.

The lateral area, total area, and volume of Cylinder 1 are 36π cm², 22π cm², and 36π cm³, respectively, and the lateral area, total area, and volume of Cylinder 2 are 58.24π m², 88.96π m², and 459.39π m³, respectively.

What is lateral area?

We can use the formulas for the lateral area, total area, and volume of a right circular cylinder to solve these problems. The formulas are:

Using these formulas and rounding off the answer to two decimal places, we get:

Cylinder 1:

Lateral area = 2πrh = 2π(2 cm)(9 cm) = 36π cm²

Total area = 2πr(r+h) = 2π(2 cm)(2 cm + 9 cm) = 22π cm²

Volume = πr²h = π(2 cm)²(9 cm) = 36π cm³

Cylinder 2:

Lateral area = 2πrh = 2π(4 m)(7.3 m) = 58.24π m²

Total area = 2πr(r+h) = 2π(4 m)(4 m + 7.3 m) = 88.96π m²

Volume = πr²h = π(4 m)²(7.3 m) = 459.39π m³

Therefore, the lateral area, total area, and volume of Cylinder 1 are 36π cm², 22π cm², and 36π cm³, respectively, and the lateral area, total area, and volume of Cylinder 2 are 58.24π m², 88.96π m², and 459.39π m³, respectively.

To know more about lateral area, visit:

https://brainly.com/question/29089726

#SPJ1

Complete question is: The lateral area, total area, and volume of Cylinder 1 are 36π cm², 22π cm², and 36π cm³, respectively, and the lateral area, total area, and volume of Cylinder 2 are 58.24π m², 88.96π m², and 459.39π m³, respectively.

Answer:

B

Step-by-step explanation:

The explanation is attached below.

Therefore, the transfer function of the system is:

G(s) = Y(s) / U(s) = U(s) / (s^3 + 0.25s + 1.25)

In summary, the differential equation depicting the dynamics of a fourth Single-Input-Single-Output (SISO) system is y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t), and the transfer function of the system is G(s) = U(s) / (s^3 + 0.25s + 1.25).

The differential equation describing the dynamics of a single-input-single-output (SISO) system is given by ddy(t) + ay'(t) + by(t) = cdu(t), where y(t) is the output of the system, u(t) is the input of the system, and d, a, b, and c are constant coefficients representing the system dynamics.

For the given differential equation, which is the dynamics of four Single-Input-Single-Output (SISO) systems, we have:

\(y(t) + ay'(t) + by''(t) + cy'''(t) = u(t)\)
Here, we have the third-order differential equatior : \(y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t)\)

The given equation is a third-order, linear, time-invariant (LTI) differential equation. In control theory, a differential equation that relates the input u(t) to the output y(t) of a system is known as the transfer function.

The transfer function of the given system can be found by applying the Laplace transform to the differential equation:

s^3Y(s) + 0.25sY(s) + 1.25Y(s) = U^2(s)

where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.

Solving for Y(s), we get:

Y(s) = U^2(s) / (s^3 + 0.25s + 1.25)

for such more questions on Laplace transform

https://brainly.com/question/2272409

#SPJ11

Answer:

Hope this is correct

Average rate of change gives us the slope of the secant line that connects the two points on the graph of g(t) corresponding to t = a and t = b. This can help us understand how quickly the function is changing over the interval and can be useful in many applications.

We need to use the formula:

average rate of change = (g(b) - g(a))/(b - a)

Here, g(b) represents the value of the function at t = b and g(a) represents the value of the function at t = a.

We can use this formula to calculate the average rate of change of g(t) over the given interval. Just substitute the values of g(a), g(b), a, and b into the formula and simplify the expression to get the answer.

Learn more about average rate of change.

brainly.com/question/28744270

#SPJ11

The total amount of fees for each bank is First state bank = $8, National bank = $12.50, and third city bank = $9.

The fundamentals of mathematics are arithmetic operations. Operations like addition, subtraction, multiplication, and division make up the majority of it. Sometimes referred to as mathematical operations, these. In daily life, we employ mathematical operations to calculate overall business revenue and costs, create monthly or yearly budgets, measure distances, and more. We use them nearly constantly throughout the day. For instance, we use them to calculate the overall amount of homework problems, time, money, the number of chocolates we ate, the total number of grades we received across all courses, etc.

Given that, one month you write 5 checks and use bank's ATM machine 3 times, you use a non bank ATM twice and your debit card 8 times

The total amount for first state bank is:

C = 5(1) + 3(1) = $8

The total amount for National bank is:

C = 12.50

The total amount for third city bank is:

C = 3(1) + 8(0.75) = 9

Hence, the total amount of fees for each bank is First state bank = $8, National bank = $12.50, and third city bank = $9.

Learn more about arithmetic operations here:

https://brainly.com/question/20595275

#SPJ1

Any expression that can be simplified to a ratio of two integers is a rational number.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. Therefore, any expression that can be simplified to a ratio of two integers is a rational number.

Expressions that represent rational numbers include:

1. 5/7 - This is a ratio of two integers (5 and 7) and can be simplified to a fraction.

2. -3/4 - This is a negative ratio of two integers (3 and 4) and can be simplified to a fraction.

3. 0.25 - This is a decimal, but it can be written as 1/4, which is a raio of two integers.

4. -6/8 - This is a negative ratio of two integers (6 and 8) and can be simplified to a fraction.

5. 1/2 + 1/3 - This is the sum of two ratios of integers (1/2 and 1/3), which can be combined and simplified to a fraction.

6. (2x + 3)/(x - 4) - This expression can be simplified to a ratio of two polynomials, but it still represents a rational number because polynomials are just combinations of integers.

In general, any expression that involves only arithmetic operations (+, -, x, ÷) with rational numbers or polynomials will represent a rational number.

Learn more about ratio brainly.com/question/13419413

#SPJ11

Answer:

I believe its A

Step-by-step explanation:

D. h(t) = -16(t - 5)² + 403 could be used to model this situation.

A baseball is hit from an initial height of 3 feet.

The baseball reaches a maximum height of 403 feet.

Here, h(t) indicates the height in feet after t seconds.

At the start, t = 0 & Initial height = 3 feet ,i.e. h(0) = 3

We have to verify options by putting t = 0

A.  h(t) = -16(t - 403)² + 3

So, h(0) = -16(0-403)² + 3 = -16(-403)² +3 = -2598544+3 = -2598541

B.  h(t) = -16(t - 5)² + 3

So, h(0) = -16(0-5)² + 3 = -16(-5)² + 3 = -400+3 = -397

C.  h(t) = -16(t - 3)² + 403

So, h(0) = -16(0-3)² + 403 = -16(-3)² + 403 = -144 + 403 = -259

D.  h(t) = -16(t - 5)² + 403

So, h(0) = -16(0-5)² + 403 = -16(-5)² + 403 = -400 + 403 = 3

Hence, in this function h(0) = 3 verified.

Therefore h(t) = -16(t - 5)² + 403 is the required function.

Learn more about function here :

https://brainly.com/question/27447037

#SPJ2

Answer:1.25/

Step-by-step explanation:

Answer:

by size,color,by first name, by last name, and by date purchased.

Step-by-step explanation:

Answer:

Step-by-step explanation:

9   1

12

3

- 1

The name of the figure that he drew is a ray SE.

Given that,

Oliver drew the figure shown to show light traveling from the sun to earth.

In the figure, there is a fixed starting point S from one side.

Then it goes on a direction to E and is going to infinity, that is it never ends.

Here S represents the sun and E represents the Earth.

A line is a straight figure which goes to infinity in both directions.

A ray is a straight figure which goes to infinity in one direction and the other end is fixed.

Here one direction is going to infinity and the other if fixed.

Hence the figure is a ray.

Learn more about Ray here :

https://brainly.com/question/13144568

#SPJ1

Answer:

It is a scalene triangle because it has unequal sides

Answer:

A scalene triangle

Step-by-step explanation:

I'm just a smart guy

Answer:

3x5

Step-by-step explanation:

15 is an integer and odd

Answer:

48a - 24

Step-by-step explanation:

6(8a - 4):

Distribute 6 into the terms inside the parenthesis:

6*8a = 48a

6 * -4 = -24

Therefore, the answer is 48a - 24.

Hey there!

The distributive property states the following:

a(b+c)=ab+ac

where

we distribute a by multiplying it times b and c

Now that we know the property, let's simplify

6(8a-4)

multiply

48a-24

And we're done!

Hope everything is clear.

Also, please let me know if you have any questions.

#LearningIsFun

Answer:

(c) A convenience sample error was made in this design. This type of sampling is only representative of one neighborhood and not the entire city population.

Answer:

2(m+8)

Step-by-step explanation:

5(m+2) -3(m-2)

= 5m+10-3m+6

= 2m+16

= 2(m+8)

Answer:

Step-by-step explanation:

\(\begin{aligned}& 5(m+2)-3(m-2) \\\\=& 5 m+5 \times 2-(3 m-6) \\\\=& 5 m+10-3 m+6 \\\\=&(5 m-3 m)+(10+6) \\\\=& 2 m+16\end{aligned}\)

Answer:

49

Step-by-step explanation:

To find the number we add to both sides to complete the square, we do b divided by 2 all squared.

(b/2)²

In this case, we have b = 14

(14/2)²

7²

49

Answer:   49  

Step-by-step explanation:

To complete the square, the second leading coefficient  divided by 2 squared will give you the number need to add to both sides.

For example,

14 is the second leading coefficient in the   so if you divide it by 2 you get 7  and 7 squared is 49.

Answer:

There are 30 girls

Step-by-step explanation:

The ratio is 3:5 so (3)*(6)= 18 boys , and (5)*(6)=30

30+18=48 members

There were 30 girls in swim team.

We have,

Total Members = 48

Ratio of Boys to Girls= 3:5

So, the number of boys are

= 3/8 x 48

= 3 x 6

= 18

and, the number of girls

= 5/8 x 48

= 5 x 6

= 30

Thus, 30 girls were in swim team.

Learn more about Ratio here:

https://brainly.com/question/13419413

#SPJ3

The probability that the high temperature on a randomly selected January day in Columbus, Ohio is between 15 and 25 degrees Fahrenheit is approximately 0.3811, or 38.11%.

To find the probability that the high temperature on a randomly selected January day in Columbus, Ohio is between 15 and 25 degrees Fahrenheit, we need to calculate the z-scores for the given values and use the standard normal distribution table.

The z-score represents the number of standard deviations a value is away from the mean. It can be calculated using the formula:

z = (x - μ) / σ

Where:

x = the given value (temperature in this case)

μ = the mean of the distribution (21 degrees Fahrenheit)

σ = the standard deviation of the distribution (10 degrees Fahrenheit)

For the lower limit of 15 degrees Fahrenheit:

z1 = (15 - 21) / 10 = -0.6

For the upper limit of 25 degrees Fahrenheit:

z2 = (25 - 21) / 10 = 0.4

Next, we use the standard normal distribution table or a calculator to find the area under the curve between these two z-scores. This area represents the probability of the high temperature being between 15 and 25 degrees Fahrenheit.

Using the standard normal distribution table, the area to the left of -0.6 is 0.2743, and the area to the left of 0.4 is 0.6554.

To find the area between these two z-scores, we subtract the smaller area from the larger area:

P(15 ≤ x ≤ 25) = 0.6554 - 0.2743 = 0.3811

Therefore, the probability that the high temperature on a randomly selected January day in Columbus, Ohio is between 15 and 25 degrees Fahrenheit is approximately 0.3811, or 38.11%.

To learn more about probability visit:

brainly.com/question/23417919

#SPJ11

There are no such pairs. The sum of the reciprocals of any two positive integers is always greater than\($\frac14$\).

The sum of the reciprocals of any two positive integers is \($\frac{1}{m} + \frac{1}{n}$\), which is always greater than \($\frac14$\). Therefore, there are no distinct ordered pairs of positive integers \($(m,n)$\) so that the sum of the reciprocals of m and n is \($\frac14$\)

For any two positive integers m and n, the sum of their reciprocals is \($\frac{1}{m} + \frac{1}{n}$\) which is always greater than \($\frac14$\) This is because \(\frac{1}{m}$ ,$\frac{1}{n}\) are both positive numbers, and so their sum must be greater than \($\frac14$\)Therefore, there are no distinct ordered pairs of positive integers \($(m,n)$\) so that the sum of the reciprocals of m and n is \($\frac14$\).

Learn more about sum here

https://brainly.com/question/641910

#SPJ4