1. Simplify (Write each expression without using the absolute value symbol. )


|120+x| if x<-120


2. Simplify (Write each expression without using the absolute value symbol. )


|x-120| if x<-120


3. Simplify (Write each expression without using the absolute value symbol. )


|x-(-12)| if x>-12


4. Simplify (Write each expression without using the absolute value symbol. )


|x-(-12)| if x<-12

Answer:

Step-by-step explanation:

graph attached

Answer:

graph y

Step-by-step explanation:

Answer:

5.32⋅10−6

Step-by-step explanation:

Answer:

5320000

Step-by-step explanation:

standard notation form : 5320000

9514 1404 393

Answer:

  1. line b is perpendicular to the other two, which are parallel

  2. line a is perpendicular to the other two, which are parallel

Step-by-step explanation:

1. The differences between coordinates (∆x, ∆y) are ...

  (-2, 3) -(1, -1) = (-3, 4) . . . line a

  (-3, 1) -(1, 4) = (-4, -3) . . . line b

  (0, 2) -(3, -2) = (-3, 4) . . . line c

When the (∆x, ∆y) values are identical, the lines are parallel. If the values are swapped, and one differs in sign, the lines are perpendicular.

  line b is perpendicular to lines a and b, which are parallel

__

2. When all of the equations are written in standard form, they are ...

As above, when the x- and y-coefficients are identical, the lines are parallel. If they are swapped and one is negated, the lines are perpendicular.

  line a is perpendicular to lines b and c, which are parallel

__

In the attached graph, the lines of part 1 are blue; those of part 2 are red.

Using a calculator to evaluate the compositions of functions can be a convenient and efficient way to determine whether two functions are inverses. Just make sure to select a calculator that allows for function evaluation and composition.

To determine whether two functions are inverses of each other, you can use a calculator by following these steps:

1. Choose a calculator that supports function evaluation and composition.

2. Identify the two functions you want to test for inverse relationship. Let's call them f(x) and g(x).

3. Input a value for x, and calculate f(x) using the calculator.

4. Take the result obtained in step 3 and input it into the calculator to calculate g(f(x)).

5. Compare the result from step 4 with the original value of x. If g(f(x)) is equal to x for all values of x, then f(x) and g(x) are inverses of each other.

For example, let's say we want to determine whether f(x) = 2x and g(x) = x/2 are inverses of each other.

1. Choose a calculator with function evaluation capabilities.

2. Take the value of x, let's say x = 3.

3. Calculate f(x): f(3) = 2 * 3 = 6.

4. Calculate g(f(x)): g(f(3)) = g(6) = 6/2 = 3.

5. Compare the result with the original value of x. In this case, g(f(x)) = 3, which is equal to x.

Since g(f(x)) equals x for all values of x, we can conclude that f(x) = 2x and g(x) = x/2 are inverses of each other.Using a calculator to evaluate the compositions of functions can be a convenient and efficient way to determine whether two functions are inverses. Just make sure to select a calculator that allows for function evaluation and composition.

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If Sam needs 2/5 pound turkey to make one sandwich, then to make 7 sandwiches, he will need:

(2/5) x 7 = (2 x 7)/5 = 14/5 = 2.8 pounds of turkey

Therefore, Sam needs 2.8 pounds of turkey to make 7 sandwiches.

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Answer:

The slope is 1/3

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

The expression represented by 50 added to half of a number, c is 50 + c/2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

50 added to half of a number, c

half of a number, c means divide c by 2

So, we have

50 added to half of a number, c  => 50 added to c/2

Added to means +

So, we have

50 added to half of a number, c  => 50 + c/2

Hence, the expression represented by the statement is  50 + c/2

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The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.

Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs

Step 1: Calculate the circumference of the original circle.

Circumference of a circle = 2πr

Circumference of the circle with a radius of

7 cm = 2πr = 2 × 22/7 × 7 = 44 cm

Step 2: Calculate the perimeter of each semicircular shape disc.

The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.

Perimeter of each semicircular shape disc

= 44 cm/2

= 22 cm

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The slope of the line passing through the origin and makes an 4π/7 angle with the positive x-axis is tan(4π/7).

To find the slope of the line passing through the origin which forms an angle of 4π/7 with the positive x-axis, we can use trigonometric ratios. Trigonometry is a branch of mathematics that deals with the study of relationships involving lengths and angles of triangles.

In the given problem, the line passes through the origin and forms an angle of 4π/7 with the positive x-axis. We need to find the slope of the line. Slope is defined as the ratio of the change in y to the change in x. That is, If we have two points (x1, y1) and (x2, y2), then the slope is given by:

m = (y2 - y1)/(x2 - x1)

Since the line passes through the origin, one point is (0, 0). Now we need to find another point on the line. Let's say this point is (x, y). We know that the angle between the line and the positive x-axis is 4π/7.

Therefore, we can write, tan(4π/7) = y/x

We can solve for y by multiplying both sides by x.

y = x tan(4π/7)

Now we have two points on the line, (0, 0) and (x, y). We can find the slope by using the slope formula.

m = (y2 - y1)/(x2 - x1)m = (y - 0)/(x - 0)m = y/xm = x tan(4π/7)/x

Canceling out the x terms, we get

m = tan(4π/7)

Therefore, the slope of the line passing through the origin which forms an angle of 4π/7 with the positive x-axis is tan(4π/7).

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Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

\(a = 144\) --- Initial Population

\(r = 8\%\) --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

\(f(x) = a(1-r)^x\)

Substitute values for a and r

\(f(x) = 144(1-8\%)^x\)

Convert % to decimal

\(f(x) = 144(1-0.08)^x\)

\(f(x) = 144(0.92)^x\)

Next, we calculate the average rate of change for both intervals using:

\(Rate = \frac{f(b) - f(a)}{b-a}\)

For 1 to 5:

\(Rate = \frac{f(5) - f(1)}{5-1}\)

\(Rate = \frac{f(5) - f(1)}{4}\)

Calculate f(5) and f(1)

\(f(x) = 144(0.92)^x\)

\(f(1) = 144*0.92^1 =144*0.92=132.48\)

\(f(5) = 144*0.92^5 =144*0.66=95.04\)

\(Rate = \frac{95.04 - 132.48 }{4}\)

\(Rate = \frac{-37.44}{4}\)

\(Rate = -9.36\)

For 6 to 10:

\(Rate = \frac{f(10) - f(6)}{10-6}\)

\(Rate = \frac{f(10) - f(6)}{4}\)

Calculate f(6) and f(10)

\(f(x) = 144(0.92)^x\)

\(f(6) = 144*0.92^6 =144*0.61=87.84\)

\(f(10) = 144*0.92^{10} =144*0.43=61.92\)

\(Rate = \frac{61.92-87.84}{4}\)

\(Rate = \frac{-25.92}{4}\)

\(Rate = -6.48\)

So, we have:

\(Rate = -9.36\) for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

\(Rate = -6.48\) for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

\(f(x) = a(1-r)^x\)

Substitute values for a and r

\(f(x) = 144(1+8\%)^x\)

Convert % to decimal

\(f(x) = 144(1+0.08)^x\)

\(f(x) = 144(1.08)^x\)

Next, we calculate the average rate of change for both intervals using:

\(Rate = \frac{f(b) - f(a)}{b-a}\)

For 1 to 5:

\(Rate = \frac{f(5) - f(1)}{5-1}\)

\(Rate = \frac{f(5) - f(1)}{4}\)

Calculate f(5) and f(1)

\(f(x) = 144(1.08)^x\)

\(f(1) = 144(1.08)^1 = 144*1.08= 155.52\)

\(f(5) = 144(1.08)^5 = 144*1.47= 211.68\)

\(Rate = \frac{211.68 - 155.52}{4}\)

\(Rate = \frac{56.16}{4}\)

\(Rate = 14.04\)

For 6 to 10:

\(Rate = \frac{f(10) - f(6)}{10-6}\)

\(Rate = \frac{f(10) - f(6)}{4}\)

Calculate f(6) and f(10)

\(f(x) = 144(1.08)^x\)

\(f(6) = 144(1.08)^6 = 228.52\)

\(f(10) = 144(1.08)^{10} = 310.89\)

\(Rate = \frac{310.89-228.52}{4}\)

\(Rate = \frac{82.37}{4}\)

\(Rate = 20.59\)

So, we have:

\(Rate = 14.04\) for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

\(Rate = 20.59\) for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.

the television station can show 10 45-second commercials per hour.

To convert hours into minutes, you simply multiply the number of hours by 60, since there are 60 minutes in an hour.

So, if you want to convert 3 hours into minutes, you would do:

3 hours x 60 minutes/hour = 180 minutes

Therefore, 3 hours is equivalent to 180 minutes.

There are 60 minutes in an hour, and 7 1/2 minutes is equal to 7.5 minutes.

So, the television station shows commercials for 7.5 minutes per hour.

We can convert 45 seconds to minutes by dividing it by 60:

45 seconds ÷ 60 = 0.75 minutes

To find out how many 45-second commercials the television station can show per hour, we can divide the total number of minutes of commercials by the length of each commercial:

7.5 minutes ÷ 0.75 minutes/commercial = 10 commercials

Therefore, the television station can show 10 45-second commercials per hour.

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Answer:

Step-by-step explanation:

The visitor might be exactly 54 inches or above 54 inches.

The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

Answer:196 inches

Step-by-step explanation:196 inches. Step-by-step explanation: We have been given that an ant can travel at a constant speed of 980 inches in every 5 minutes.

The derivative of -3e⁴u with respect to x is -3e⁴u * du/dx.

To find the derivative of the given function, we can apply the chain rule. The derivative of a function of the form f(g(x)) is given by the product of the derivative of the outer function f'(g(x)) and the derivative of the inner function g'(x).

In this case, we have: f(u) = -3e⁴u

Applying the chain rule, we have: f'(u) = -3 * d/dx(e⁴u)

Now, the derivative of e⁴u with respect to u can be found using the chain rule again: d/dx(e⁴u) = d/du(e⁴u) * du/dx

The derivative of e⁴u with respect to u is simply e⁴u, and du/dx is the derivative of u with respect to x.

Putting it all together, we have: f'(u) = -3 * e⁴u * du/dx

So, the derivative of -3e⁴u with respect to x is -3e⁴u * du/dx.

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Answer:

big money

Step-by-step explanation:

Answer:

get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.

:D thanks :D

Therefore, the probability of landing on land would be higher than landing on water, with a ratio of approximately 1:3.

If you were dropped at a completely random spot on the planet, the chances of landing on land would be one in three, or approximately 33.33%. This is because approximately 71% of the Earth's surface is covered by water, while the remaining 29% is land.

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Answer:

The answer is x = 9.19

Step-by-step explanation:

I used the pythagorean theorem to solve for x.

12^2 - 7.71^2 = x^2

#teamtrees #WAP (Water and Plant)

Answer:

What is a mean?

A mean is the average of all the numbers in a data set.

How can I find mean?

to find mean you add up all the numbers in the data set; and divide them by the amount of numbers there are.

103+3+41+7=154

154÷4=38.5

The mean is 38.5

Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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points , pi represents point that you can earn .

Answer:

The answer selected is correct

Step-by-step explanation:

"Myra is 5 years younger than her sister Talat" as an equation should be written as: B. m = t - 5.

In an experiment, there are two (2) main types of variables and these include:

An independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and mostly represented by x.

Translating the word problem into an algebraic equation, we have;

m = t - 5

In conclusion, "Myra is 5 years younger than her sister Talat" as an equation should be written as m = t - 5.

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