f(x) = 1/3x + 1; h(x)= -f(x)

What is the Distribution Property?

The distribution property in math is a process that allows an equation to be simplified to help easily solve problems. Expressions that qualify to use the distributive property are usually written in the format: a(b +c)

a is then distributed to both b and c, rewriting the equation as ab +ac, where a has been multiplied to both values.

In this problem, you can distribute -15 to both 5x and 6y.

This will leave you with and equation that resembles this:

(-15×5x) + (-15×6y)

Multiply -15 to the coefficient attached to the variable to get your answer.

Your answer is -75x + -90y or -75x-90y

The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

The coordinates of the point = (9,1)

The equation of the line is

y = 2x + 3

Here the slope of the line is 2

The shortest distance between the point and the second line will be the perpendicular distance between the point and line

The perpendicular line slope will be -(1/m)

= -(1/2)

This perpendicular line will pass through the point (9, 1)

The point slope form is

y - 1 = -(1/2)(x - 9)

y - 1 = -(1/2x) + 9/2

y = -(1/2)x + 9/2 + 1

y = -(1/2)x + 11/2

Solve the equation

y = 2x + 3

y = -(1/2)x + 11/2

0 = (2 + 1/2)x -5/2

5/2 x = -5/2

x = -5/2 / 5/2

x = -1

Then

y = 2(-1) + 3

y = -2 + 3

y = 1

The distance between the point (9,1) and (-1, 1)

= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

= [tex]\sqrt{(-1-9)^2+(1-1)^2}[/tex]

= [tex]\sqrt{100}[/tex]

= 10 units

Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

Learn more about distance between the points here

brainly.com/question/14364020

#SPJ9

Answer:

what is ur questions we cant see them

Answer:

350 seconds to jog 5 laps.

Step-by-step explanation:

One lap of a running track is 350m Kyle jogs 5 complete laps at an average speed of 5 m/s. How long does it take him in seconds?

First, to run one lap:

350m / 5 meters per second = 70 seconds

Now, solve for five laps:

70 seconds * 5 laps = 350 seconds to jog 5 laps.

An equation for the curve that passes through the point (1,0) and whose slope at (x,y) is xe^y is y = -1/x -1.

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches. The slope is nothing more than the tangent to the angle formed with the x-axis measured. As a result, it is simply an angle's measurement.

Given,

The curve that passes through the point (1,0) and whose slope at (x,y) is xe^y.

Since x-2 is equal to the slope of the function f(x), we can express that as

dy/dx = x^-2

dx multiplication and integration of both sides:

y = -1/x + C

Connecting the provided point:

0 = -1/1 + C

C = -1

Consequently, the curve's equation is

y = -1/x -1

To learn more about slope, visit:

https://brainly.com/question/3605446

#SPJ4

Answer:

Below

Step-by-step explanation:

3ax = (m+n)       divide both sides by 3 a

x = (m+n) / 3a       that's it

Answer: 32 bracelets

First multiply each bracelet by 4 to get the correct amount:

3x4=12

4x5=20

Then, add the two.

12+20=32

Step-by-step explanation:

The product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

What is a matrix?

A rectangular matrix is a set of numbers arranged into a predetermined number of rows and columns. The rows of a matrix are formed when the elements are placed in a horizontal matrix. The columns of a matrix are formed by the elements when they are stacked in the matrix vertically.

Here, we have given a matrix that is

A = [tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex]       B = [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

We have to find the product of this matrix

[tex]\left[\begin{array}{ccc}5&5\\-2&3\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-4&9\\8&7\end{array}\right][/tex]

First, we multiply the first row of matrix A with the first column of matrix B then continue in this manner, we get

[tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

Hence, the product of the given matrix is  [tex]\left[\begin{array}{ccc}20&80\\32&3\end{array}\right][/tex]

To learn more about the matrix from the given link

https://brainly.com/question/1279486

#SPJ1

The term used to describe an error that occurs when numbers are moved to the right or left in an amount column is "Slide".

Slide:

An accounting slide is a mistake that happens when the decimal point of a number is moved to the left or right of where it should be.

For instance, a bookkeeper would enter $1,200.50 in place of $12,005 in the revenue account or $250.75 in place of $2,507.50 in the monthly insurance expenses. In general, bookkeeping mistakes and accounting blunders lead to financial record misstatements.

"Slide" is the name for a mistake that happens when numbers are moved to the right or left in an amount column.

To learn more about decimal point click here:

brainly.com/question/20753759

#SPJ4

The function (f-g)(x) = x²+3x+5

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable

Given: f(x) = √16x⁴ = 4x² and g(x) = 3x²-3x-5

To evaluate (f-g)(x) such g(x) from f(x). Thus:

(f-g)(x) = 4x²-(3x²-3x-5)

          = 4x²-3x²+3x+5

          = x²+3x+5

Therefore, (f-g)(x) is x²+3x+5. The 4th option is the answer

Learn more about function on:

https://brainly.com/question/11735394

#SPJ1

well, the population before the increase was "x", which oddly enough is the 100%, now if it increased by 16% that means 100% + 16% = 116%, and we happen to know that's 667

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 667& 116 \end{array} \implies \cfrac{x}{667}~~=~~\cfrac{100}{116} \\\\\\ \cfrac{x}{667}=\cfrac{25}{29}\implies 29x=(25)(667)\implies x=\cfrac{(25)(667)}{29}\implies x=575[/tex]

The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Given:

A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.

x be the number of small animals and y be the number of large animals

The number of small animals = 10x

Number of large animals = 6y

The equation:

= 10x + 6y = 12.

Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Learn more about the inequalities here:

https://brainly.com/question/28823603

#SPJ4

Answer:

Absolute value is to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Hope this helped, good luck on your homework!

Answer:  how far a number is from zero

Step-by-step explanation: Cannot be a negative. The absolute value of -12 is 12.

Answer: -6a-48

Step-by-step explanation:

-6(a+8)
distribute and you get
-6a-48

By using the concept of dilution factor, it is obtained that the number of cells in the original sample is 36 per ml

What is dilution factor?

Suppose there is a solution. The volume of the solution present in the total volume is the dilution factor of the solution.

Here, the concept of dilution factor is important

Dilution factor = 1 [Undiluted solution]

Number of colonies = 36

Volume of the sample = 1 ml

Number of cells in the original sample = [tex]\frac{Number \ of \ colonies \times Dilution \ factor}{Volume\ of\ the \ solution}[/tex]

                                                                = [tex]\frac{36\times 1}{1}[/tex]

                                                                = 36 per ml

To learn more about dilution factor, refer to the link-

https://brainly.com/question/24881505

#SPJ4

Answer:

m<M = 76°

m<N = 76°

LN = 18 in

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

triangle LMN is an isosceles triangle and the measure of M is equal to N and LM = LN.

Now the measure of missing angle:

m<M + m<N + 28 = 180 subtract 28 from both sides

m<M + m<N = 152 since the measure of M is equal to N divide 152 by 2

152 ÷ 2 = 76 each angle is 76°

The probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2[tex]p^{2} (1-p)[/tex] + 3/3 [tex]p^{3}[/tex].

= 3([tex]1-e^-2)^2[/tex][tex]e^-2[/tex] + ([tex]1-e^-2)^3[/tex]

= [tex](1-e^-^2)^2[3e^-^2 - e^-^2+1][/tex]

= [tex](1-e^{-2} )^2[2e^-2+1][/tex]

Therefore the probability that the equipment will operate for at least 200 hours without failure is [tex](1-e^{-2} )^2[2e^-2+1][/tex].

Learn more about the probability here:

https://brainly.com/question/11234923

#SPJ4

Answer:

1/6

Step-by-step explanation:

[tex]36^{-1/2}=\frac{1}{36^{1/2}}=\frac{1}{\sqrt{36}}=\frac{1}{6}[/tex]

Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies then,

Here, given data as the first batch was 120 gingerbread cookies and the second batch consist of 150 shortbread cookies.

And, the same fractions of cookies from each batch were saved.

Let x parts of each of cookies were saved.

Then, the number of the saved gingerbread cookies = 120 x

While, the number of the saved shortbread cookies = 150 x

And, Again according to the question, the number of the saved shortbread cookies is 20 more than the number of the saved shortbread cookies.

That is equal to 150 x - 120 x = 20

⇒ 30 x = 20

⇒ x = 2/3

Hence the answer is, Mrs. Nicholas saved 2/3 part of each cookies.

To learn more about fractions click here https://brainly.com/question/17220365

#SPJ9

The distance travelled by the car in 34 minutes is 22.667 miles.

We are given a car. The car is travelling at a steady speed. It travels 1.5 miles in 2.25 minutes. We need to find the distance travelled by the car in 34 minutes. First of all, we need to find the speed of the car. The speed of the car is the ratio of the distance travelled and the corresponding time taken.

v = s/t

v = 1.5/2.25

v = 0.667

Hence, the speed of the car is 0.667 miles per minute. The speed of the car remains constant throughout its journey. Let the distance travelled by the car be denoted by "d" . The distance travelled in 34 minutes is calculated below.

d = v*t

d = 0.667*34

d = 22.667

Hence, the distance travelled by the car in 34 minutes is 22.667 miles.

To learn more about distance, visit :

https://brainly.com/question/15172156

#SPJ1

The equation that gives the value of k in terms of x and y is  k = y*x  .

In the question ,

it is given that ,

the variation is an inverse variation .

So , equation representing the inverse proportionality is

y ∝ 1/x ,

to remove the proportionality sign (∝) , we introduce

the constant k which is called as Constant of Proportionality .

So , the equation becomes

y = k * 1/x

y = k/x

Simplifying further , we get

k = y*x

Therefore , The equation that gives the value of k in terms of x and y is  k = y*x  .

Learn more about Inverse Proportion here

https://brainly.com/question/28054205

#SPJ1

The value of z is 1.23.

Given:

the value of Z such that 0.11 of the area lies to the right of Z.

0.11 = 11%

z score is calculated :

z = x - μ / σ

where μ=0 and σ=1

so z value is equal to 1.23.

More details in the image uploaded.

Learn more about the value here:

https://brainly.com/question/14316282

#SPJ4

Answer:

its A

Step-by-step explanation:

Answer: twenty eight-twelfths (or seven-thirds in the simplest form)

Step-by-step explanation:

The statement which correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' is "Trapezoid ABCD ≅ trapezoid A'B'C'D'.

The correct answer option is option C

The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1).

The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

Given trapezoid ABCD:

Parent coordinates of ABCD = A (2,6), B (5,6), C (7,1), and D (-1,1)

Translated coordinates of A'B'C'D' = A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

Based on the reflection rule:

Reflection across x axis (x , y) -> ( x , -y) and rotating it 90°clockwise (x , y) -> ( -y, x).

Therefore, if trapezoid ABCD is reflected across the x-axis and then rotating it 90°clockwise

ABCD ≅ trapezoid A'B'C'D'

Complete question:

The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?

A. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then across the y-axis.

B. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.

C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Read more on trapezoid:

https://brainly.com/question/11804542

#SPJ1

Answer:

Step-by-step explanation:

If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The mean of the normal distribution = 4

Standard deviation of the normal distribution = 1.5

The value of x = 5.5

The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution

Substitute the values in the equation

The z-score of the normal distribution  = (5.5 - 4) / 1.5

Substract the terms

= 1.5 / 1.5

= 1

Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The complete question is:

suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5

Learn more about z-score here

brainly.com/question/15016913

#SPJ4

The monthly payment To pay off $170,000 in 9 years at 8.5%

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula of monthly payment is given as

M = PJ / 1- (1 + J)^-n

M = $2257.49

The monthly payment on this loan is $2257.49

Learn more on monthly payment here;

https://brainly.com/question/25599836

#spj1

Answer:

HCE or ECH

Explanation:

Supplementary is angle that add up to 180° (A line)

Answer: HCE

Step-by-step explanation:

A supplementary angle is an angle that when added to another angle, equals 180 degrees, or a straight line.

Angles HCE and ECF add up to 180 degrees.

Answer:

x = 4

Step-by-step explanation:

-x + 5 - x = -3  Combine like terms

-2x + 5 = -3  Subtract 5 from both sides

-2x = -8  Divide both sides by -2

x = 4