factorise this expression as fully as possible:

4x²+x³

Answer:

It is a function

Step-by-step explanation:

for a relation to be a function, every X must have one and only one y. That is true for the given values

The equation of the line will be equal to y = -x + 3.

The equation of the line in slope intercept form is expressed as

y = mx + c

where m is the slope of the line, c is the y-intercept and x and y are independent and dependent variables respectively.

We have the equation of the line as y = x + 5 and we need to find equation of line perpendicular to this line. The slope of the line is 1.

If two lines are perpendicular then the relation in their slope is expressed as

m₁ × m₂ = -1 and we have m₁ = 1 and m₂ = m so we get

1 × m = -1

=> m = -1

Now, the equation of the line will be

y = (-1)x + c

Also, the line passes through (1, 2) so on putting these values

2 = -1 + c

=> c = 3

So, the complete equation of line will be

y = -x + 3

Learn more about Slope-intercept form at:

brainly.com/question/1884491

#SPJ4

Complete Question:

Write the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5.

The interquartile range of the data is equal to 2.18.

The interquartile range is a measure of where a data set's "middle fifty" is located. Whereas a range is a measure of where the start and end of a set are, an interquartile range is a measure of where the majority of the values are.

Given data is { 1.56,1.77,2.22,2.35,2.45,2.77,3.26,4.35,5.23,6.02}.

The upper limit is, and the median is 2.22.

{ 1.56,1.77,2.22,2.35,2.45,2.77}

The lower limit is, and the median is 4.35.

{2.77,3.26,4.35,5.23,6.02}

The interquartile range will be calculated as,

IQR = 4.35 - 2.22

IQR = 2.18

To know more about interquartile range follow

https://brainly.com/question/21270410

#SPJ1

7 is initially represented by 7 units to the right, Now, if we remove 5 from 7, we must move 5 units to the left, arriving at unit 2.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

On the number line, 7 is represented 7 units right from the origin.

Now subtracting 5 from 7 implies we have to go 5 units to the left so we end up in unit 2.

The graphical representation is illustrated in the attached image.

learn more about number line here :

https://brainly.com/question/13425491

#SPJ1

Dilate any given figure by a scale factor 2/3 represents the new image contracted by scale factor 2/3 or 0.667% times image get contracted.

Explanation :

Therefore, the dilate a given figure by scale factor 2/3 represents the figure gets contracted by 0.667%.

The complete question is:

How do you dilate a figure by scale factor 2/ 3?

Learn more about dilation here

brainly.com/question/13176891

#SPJ4

Answer: $1925 is the commission she gets from the merchandise, which means if you add 1,500 + 1925 = $3425. $3425 is what she got for that month.

Step-by-step explanation: if its wrong tell me

The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".

What is Principle of specificity ?

According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.

if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.

This an example of  "Principle of specificity or specific adaption to imposed demands (SAID Principle) "

Tenet according to which the body will adjust to the unique demands imposed upon it.

Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.

To learn more about the Principle of specificity from the given link

https://brainly.com/question/1631588

#SPJ4

The function that represent the company's profit is (2.52x - 700).

As per the known formula, Profit = Revenue - Cost

Now keeping the functions of revenue and cost to find the function of profit.

Profit = 2.9x - (0.38x + 700)

Performing subtraction on Right Hand Side of the equation to find the profit of company

Profit = 2.9x - 0.38x - 700

Performing subtraction on Right Hand Side of the equation to find the profit of company

Profit = 2.52x - 700

Thus, the the profit of company will be represented by the function 2.52x - 700.

Learn more about functions -

https://brainly.com/question/25638609

#SPJ4

The complete question is -

The costs of a company are represented by the function c(x)=0. 38x+700. Its revenues are represented by the function r(x)=2. 9x. Find the function that represent the company's profit.

A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ4

By using the concept of mode, it can be calculated that-

Mode number of hours spent on the computer is 11 hours.

What is mode?

Mode of a data set is that value which occurs most number of times in the data set. In other words, the value whose frequency is the largest is the mode of the data set.

The number of hours that 9 students spend on the computer on a typical day: 2 5 5 7 11 11 11 14 15

Here 11 occurs most number of times (3 times)

Mode number of hours spent on the computer is 11 hours.

To learn more about mode, refer to the link-

https://brainly.com/question/27951780

#SPJ4

Answer:

A. Here are three more equations that are true based on the information you provided:

1. 3w + 2 = 2w + 6

2. 5w - 6 = 4w - 8

3. 7w - 5 = 6w - 7

B. To find the value of 2w, we need to first solve for w in the original equation 7w + 4 = 5w + 12. We can do this by subtracting 5w from both sides of the equation, which gives us 2w + 4 = 12. Then we can subtract 4 from both sides to get 2w = 8. Therefore, the value of 2w is 8.

C. To find the value of w, we can divide both sides of the equation 2w = 8 by 2, which gives us w = 4. Therefore, the value of w is 4.

The graph of function f(x) = log 1/8(x) is shown in figure with x - intercept

(8, 0).

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The function is,

⇒ f (x) = log 1/8 (x)

Now,

Since, The function is,

⇒ f (x) = log 1/8 (x)

Hence, The x - intercept = (8, 0)

And, The graph is show in figure.

Thus, The figure is shown in figure.

Learn more about the line segment visit:

https://brainly.com/question/280216

#SPJ1

The length of the shadow of man is 0.8 m/s.

How to solve word problems?

Here are some actions to take:

1. Recognize the issue.

Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.

2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.

3. Put the strategy into action and find a solution.

dx/dt  =1.2 m/s

4.5 / x+ y = 1.8 / y

1.8x + 1.8y = 4.5y

1.8x = 2.7y

2x = 3y

3 dy/dt = 2dx/ dt = dy/dt = 2/3

​ =0.8

Hence, The length of the shadow of man is 0.8 m/s

To know more about word problem check the below link:

https://brainly.com/question/13818690

#SPJ4

Answer: 30 combinations

Step-by-step explanation:

Multiply 3x2x5 to get 30.  

Answer:

---------------------------

Verify the equations:

The rate of change of the graphs are as follows:

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Therefore,

rate of change = change in y / change in x

Hence,

rate of change = y₂ - y₁ / x₂ - x₁

let's find the rate of change of the graphs.

a.

using (-5, -1) and (5, 7)

rate of change = 7 + 1 / 5 + 5

rate of change = 8 / 10

rate of change = 4 / 5

b.

using (0, 3)(-4, 0)

rate of change = 0 - 3 / -4 - 0

rate of change = - 3 / - 4

rate of change = 3 / 4

learn more on rate of change here: https://brainly.com/question/29518179

#SPJ1

By using some exponent properties, we will see that the equivalent expression to √(x⁵*y⁶) is:

x²*y³*√x

So the correct option is the first one.

Here we need to remember 3 properties about exponents that we will need to use.

These are:

√x = x¹´²

Also remember that:

(xⁿ)ᵃ = xⁿ*ᵃ

And that:

√(a*b) = √a*√b

Well, our expression is:

√(x⁵*y⁶)

We can rewrite this as:

√x⁵*√y⁶

And using the first and second properties we can rewrite.

√x⁵ = x⁵´² = x⁴´²*x¹´² = x²*√x

√y⁶ = y⁶´² = y³

Replacing all that we get:

√(x⁵*y⁶) =  x²*y³*√x

Thus, the correct option is the first one.

Learn more about equivalent expressions:

https://brainly.com/question/2972832

#SPJ1

The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5

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

0.5 ( x +3)

Write the expression properly

So, we have the following representation

0.5 (x + 3)

Express the brackets as products

So, we have the following representation

0.5 (x + 3) = 0.5 * (x + 3)

Open the brackets using products i.e. distributive property

So, we have the following representation

0.5 (x + 3) = 0.5 * x + 0.5 * 3

Evaluate the products

So, we have the following representation

0.5 (x + 3) = 0.5x + 1.5

Hence, the expression as a sum is 0.5x + 1.5

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

Answer:

1. 0.5x + 1.5

2. are not

Answer:

The inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality can be derived by first calculating the total cost of renting the car for 2 days at $39.90 per day and $0.20 per mile. This gives us a total cost of $79.80 for the rental plus $0.20 per mile for the number of miles Henry drives. Since Henry has $150.00 to spend, we can set up the following inequality to represent the maximum number of miles he can drive:

150.00 >= 79.80 + 0.20m

We can then solve for m by subtracting 79.80 from both sides of the inequality and dividing both sides by 0.20, which gives us:

m <= 550.5

Therefore, the inequality that represents how many miles Henry can drive the car is "m <= 550.5". This inequality states that Henry can drive the car for a maximum of 550.5 miles.

Step-by-step explanation:

the upper bound is 54.2.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

31 pts for the data given below, we construct a 90% confidence interval for the population mean.

42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 .

MEAN = 50.94

varience = 48.55

s.d = √48.55 = 6.96.

C=0.90,α= 1-0.90=0.10

t=ta/2.df = 1.771 (using t value table)

90% confidence interval

(47.6378,54.2336)

Hence the upper bound is 54.2.

Learn more about confidence intervals, by the following link.

https://brainly.com/question/17097944

#SPJ4

Answer: Record

Step-by-step explanation:

The ordered pair which is solution to this system of inequalities is (1.75, -0.0625).

The system of inequalities are 5x−4y≥9 and 6x+8y≤10.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The intersection consists of the elements that are contained in all of the intervals.

Here, 5x−4y≥9 -------(I) and 6x+8y≤10 -------(I)

Now, y ≤ 5/4 x+(-9/4); y ≤ -3/4 x+5/4

⇒ 5/4 x+(-9/4) ≤ -3/4 x+5/4

⇒ 5/4 x+3/4 x ≤ 5/4+9/4

⇒ 2x≤ 3.5

⇒ x≤ 1.75

Substitute x=1.75 in y ≤ 5/4 x+(-9/4), we get

y ≤ 1.25(1.75)-2.25

y ≤ 2.1875-2.25

y ≤ -0.0625

Two inequalities are intersect at (1.75, -0.0625)

Therefore, the ordered pair which is solution to this system of inequalities is (1.75, -0.0625).

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

A  compound inequality 45 ≤ t ≤ 75 which represents the union of all values larger than or equal to 45 minutes and less than or equal to 75 minutes is the time, denoted by the notation t.

The time Mo takes to mow the lawn is between 45 minutes and 75 minutes, inclusive, which means that the time is either 45 minutes, 46 minutes, 47 minutes, and so on, up to and including 75 minutes. This is a range of values that includes all the times from 45 minutes to 75 minutes.

This statement represents a union, which is the combination of two or more sets of values. In this case, the union is the combination of all the values from 45 minutes to 75 minutes.

To write this statement as a compound inequality, you can use the symbols "≥" (greater than or equal to) and "≤" (less than or equal to) to indicate that the time is greater than or equal to 45 minutes and less than or equal to 75 minutes:

45 minutes ≤ t ≤ 75 minutes

This compound inequality can also be written as:

45 ≤ t ≤ 75

This means that the time, t, is a member of the union of all values that are greater than or equal to 45 minutes and less than or equal to 75 minutes.

Learn more about inequalities here:

brainly.com/question/20383699

#SPJ1

The logarithm of (789.5) elevated to the power 1/8 is given as follows:

log(789.5)^(1/8) = 0.36216901679.

The logarithm in this problem is defined as follows:

log(789.5)^(1/8).

It has a power, hence the power can be moved to the front of the logarithm expression applying the power rule, as follows:

log(789.5)^(1/8) = 1/8 x log(789.5).

Then a calculator is used to obtain the logarithm of 789.5, which is the number that is elevated to the base 10 to obtain 789.5, hence:

log(789.5) = 2.89735213434.

Thus the numeric value of the logarithmic expression in this problem is calculated as follows:

log(789.5)^(1/8) = 1/8 x log(789.5) = 1/8 x 2.89735213434 = 0.36216901679.

More can be learned about logarithmic expressions at https://brainly.com/question/237323

#SPJ1

The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.

In the question ,

it is given that ,

the system of 2 linear equations in 2 variables .

we know that the linear equations represent a line .

(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .

(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .

(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .

Therefore , the number of solutions of linear equation is explained above .

Learn more about Linear Equations here

https://brainly.com/question/84787

#SPJ4

The percent error of Ira’s guess for the number of buttons is 25%

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Ira’s guess is 200 buttons but the actual number of buttons is 250.

The net amount error is (250 - 50) = 50 buttons.

Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,

= (50/200)×100%.

= 25%

So, the percentage error is 25%.

Learn more about percentages here :

https://brainly.com/question/24159063

#SPJ1

The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.

Given that:

The probability of pulling a red marble at random is 1/10

Probability of not pulling red marble is = 1-(1/10)= 9/10

The odds of pulling red marble is (1/10)/(9/10)

The probability of odds of pulling red marble is 1/9.

To learn more about probability visit: https://brainly.com/question/14069444

#SPJ4

Answer:

2 gallons

Step-by-step explanation:

1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4

Then:

5/4 gallons ⇒ 5/8 fence

x  gallons ⇒ 8/8 fence

x = (5/4)(8/8) / (5/8)

x = ((5*8)/(4*8)) / (5/8)

x = (5/4) / (5/8)

x = (5*8)/(4*5)

x = 40/20

x = 2

Answer:

the answer is

-3/2

I hope that helps

The value of x from the expression 2x + 6 = 38 is 16.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x + 6 = 38

Subtracting 6 on both sides.

2x = 38 - 6

2x = 32

Divide both sides by 2.

x = 16

Thus,

The value of x is 16.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1