Which equation and number line show that a number and its opposite are additive inverses?

Which equation and number line show that a number and its opposite are additive inverses?

Answer:

m = 0

Step-by-step explanation:

- 10 = - 10 + 7m ( add 10 to both sides )

0 = 7m ( divide both sides by 7 )

0 = m

Step-by-step explanation:

f(g(x)) means g(x) is embedded in f(x) as the argument or input value for f(x).

therefore,

f(g)x)) = 4(x² - 1) - 7 = 4x² - 4 - 7 = 4x² - 11

c. is the right answer

g(f(x)) is now the other way around. now f(x) is the only value for g(x) :

g(f(x)) = (4x - 7)² - 1 = 16x² - 56x + 49 - 1 = 16x² - 56x + 48

a. is the right answer

The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.

Given X is not a negative number and conjecture X is a positive number.

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.

Given X is not a negative number

Conjecture X is a positive number

If X is 0, which is neither positive nor negative.

So, the statement is false.

The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.

To learn more about the conjecture visit:

https://brainly.com/question/24881803.

#SPJ1

Area of rectangle is length times of width. Thomas is painting the wall at a warehouse blue. He painted in 6 hours of area 240 square feet.

Area of rectangle is length times of width.

Area=Length*width.

From the given figure the length is 12 ft and width is 5 ft in 1.5 hrs.

area he covered painting= 12ft*5ft

=60 square feet.

In 1 and half hour he painted 60 square feet.

Now for 6 hours we have to calculate.

4*(1 and half hrs)=6 hrs

So we have to multiply 4 with 60 to get the area in 6 hours.

4*60=240square feet.

Therefore 240 square feet area Thomas painted.

To learn more on Area of rectangle click:

https://brainly.com/question/20693059

#SPJ1

a: The centripetal acceleration of the child = 1.60 m/s².

b: The net horizontal force exerted on the child = 40N.

The parameters provided;

Part a: The child's centripetal acceleration is calculated as follows:

a = v²/r

Put the values;

a = 1.65²/1.7

a = 1.60 m/s²

Thus, the child's centripetal acceleration is 1.60 m/s².

Part b: The child's net horizontal force is calculated as follows:

F = ma

F = 25×1.60

F = 40 N

Thus, child's net horizontal force is 40 N.

To know more about the centripetal acceleration, here

https://brainly.com/question/79801

#SPJ9

The complete question is-

A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.

a. Calculate the centripetal acceleration of the child

b. Calculate the net horizontal force exerted on the child

Mass of child = 25 kg.

The cost of running only half of the fleet for 6 hours each would be $7687.2 .

The company runs full fleet of 16 trucks at 8 hours each.

Which means total hours of running on full fleet = 128 Hours

So, The cost of running 128 hours =  $20,500

Then, cost of running 1 hour = $20,500 ÷ 128

                                             = $160.15

Now we will determine the cost of running trucks on half fleet for 6 hours each.

As we already know that

Full fleet = 16 Trucks

Then, Half fleet = 8 Trucks

Total hours of trucks running on half fleet = 8 × 6

                                                                 = 48

The cost of running 48 hours = 48 × $160.15

                                              =  $7687.2

To learn more about Truck Running questions visit : https://brainly.com/question/13803816

#SPJ9

Answer: x∈[-4,3)     y∈(-5,5)

Step-by-step explanation:

[tex]Domain:x\in[-4,3)\\Range\ of\ y:\ y\in(-5,5)[/tex]

The equation in slope-intercept form is y = x - 6.

What is in slope-intercept form?

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line p is

y = 8x + 2

Comparing with the slope intercept form, slope = 8

If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8

To determine the y intercept, we would substitute m = 8, x = - 1 and

y = -2 into y = mx + c. It becomes

-2 = 8 × - 1 + c

-2 = - 8 + c

c = - 8 + 2 = -6

The equation becomes

y = x - 6

Learn more about slope intercept form

brainly.com/question/9682526

#SPJ9

Using Bernoulli's principle, the thing that we know about the ocean and the coast is that E. There is more air pressure over the ocean than over the coast.

According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy.

The Bernoulli principle establishes a connection between a fluid's elevation and speed and its pressure. In water, air, or any other fluid with a very low viscosity, these characteristics can be approximated using Bernoulli's equation.

Since the weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean, it implies that there is more air pressure over the ocean than over the coast.

Learn more about Bernoulli's principle on;

https://brainly.com/question/13344039

#SPJ1

Based on the given task content, the quotient of - 80 and - 16 is 5

Quotient refers to the number resulting from the division of one number by another. Such as: the quotient of 12 divided by 4 is 3.

The divisor

The number or expression that another is to be divided by.

In "42 ÷ 3" the divisor is the 3.

The dividend

These refers to numbers or expressions that is to be divided by another.

In "42 ÷ 3" the dividend is the 42.

= - 80 / - 16

= 5

Therefore, the quotient of -80 and -16 is 5

Complete question:

what is the quotient of -80 and -16

Read more about quotient:

https://brainly.com/question/629998

#SPJ1

The expression that best represents the cost of shirts plus shipping is 20b + 5.

An expression is a statement that is made up of at least two numbers or variables and at least one mathematical operation. An expression usually does not have an equal to sign.

The first step is to determine the cost of a shirt and the cost of shipping.

a + b = 25 equation 1

a + 2b = 45 equation 2

Where:

a = cost of shipping

Subtract equation 1 from equation 2

b = 20

a = 25 - 20

a = 5

Thus, the cost of one shirt is 20. The cost of shipping is 5. The cost of shirts increases with the number of shirts bought while the cost of shipping remains constant.

The expression is: 20b + 5

To learn more about mathematical expressions, please check: https://brainly.com/question/11980704

#SPJ1

The liters of the 5% and the 40% solutions is

x= 4.3L

This is further explained below.

You have been tasked with creating a solution with a concentration of 20% in a volume of 10 liters by combining solutions of 5% and 40%. It seems as if there may be more than one response to this question. If you assume that the combined volume of the 5% and 40% solutions equals 10L, then you may calculate the required volume of solution. The formula ought to go as follows:

10 L= 40% solution volume+ 5% solution volume

10 L= x + 5% solution volume

5% solution volume= 10l-x

In conclusion, The formula for calculating volume would look like this then:

Volume 0.2*concentration 0.2= volume 0.4*concentration 0.4 + volume 0.05*concentration 0.05

10 * 0.2= x *0.4 + (10- x) *0.05

10l * 0.20= x  * 35% + 10*0.05

x *35 = 10l * 20 - 10 *5= 10 *15

x = 10l *15/35

x= 4.28 L

x= 4.3L

Read more about volume

https://brainly.com/question/13338592

#SPJ1

Answer:

7

Step-by-step explanation:

3 goes into 21 7 times leaving no remainder which means: 3 x 7 = 21

The weight of each baby based on the information will be:

Martin = 2.9 kg

Daniel = 3.5kg

Kevin = 3.9 kg

Martin = x

Daniel = x + 0.6

Kevin = x + 1

Total weight = 10.3 kg

Therefore, this will be solved as:

x + x + 0.6 + x + 1 = 10.3

3x + 1.6 = 10.3

3x = 10.3 - 1.6

3x = 8.7

Divide

x = 8.7 / 4

x = 2.9

Therefore, the weights will be:

Martin = x = 2.9 kg

Daniel = x + 0.6 = 2.9 + 0.6 = 3.5kg

Kevin = x + 1 = 2.9 + 1 = 3.9 kg

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

Answer:

Step-by-step explanation:

Round each number individually,

276.93 Rounded up -> 277

69.24 Rounded Down -> 69

102.56 Rounded up -> 103

73.69 Rounded up -> 74

Total = 523

Anything 0.50 to 0.99 gets rounded up

Anything 0.01 to 0.49 gets rounded down

When to the nearest dollar

Based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex]

The product rule of exponents says that if two quantities that are multiplied together have the same base, we will add their exponents together to get the product.

Given the following:

a^4 * a^6

Applying the product rule of exponents, we will have:

a^4 * a^6 = a[tex]^{(4 + 6)}[/tex]

a^4 * a^6 = [tex]a^{10}[/tex].

Therefore, based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex].

Learn more about the product rule of exponents on:

https://brainly.com/question/847241

#SPJ1

The projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that : the baggage weight projected was 2,182 1/4 lbs and the actual weight of all bags totaled 2,095 1/3 lbs.

Now, to find out by how much was the projected weight overstated we subtract weight projected with actual weight of baggage :

weight overstated = weight projected - actual weight

weight overstated = 2,182 1/4 lbs  - 2,095 1/3 lbs

weight overstated = 87 - 1/12 lbs

weight overstated = 86(11/12) lbs

Therefore, the projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.

Read more about subtraction at:

https://brainly.com/question/2346316

#SPJ1

Answer:

-1/8

Step-by-step explanation:

So to start you already have the denominator equal, which helps a lot. So you do whatever operation is on top which in this case would be 5 + -7. Which you end up with -2/16. Then you simplify and end up with -1/8. Hope this helps. Have a great night. :)

Answer:

d equals to -3, so in every expression we substitute d with -3.

2d(-3d)

2(-3) x (-3x-3)

-6 x 9 = -54

12d - 28

12(-3) - 28

-36-28 = -64

-3d

-3x(-3) = 9

-5d-8

-5x(-3)-8

15-8 = 7

8d+14

8x(-3) + 14

-24 + 14 = -10

hope it helps.

There is enough information to find the surface area of the​ pyramid

A polyhedron formed by connecting a polygonal base and a point, called the ape-x is known as a pyramid.

The formula for calculating the volume of a pyramid is expressed as:

Volume = BH/3

From the given question, the pyramid is square based. Since we are given the length of the base to be 4.8m and the  height of each triangular face of the pyramid is 6m, we can simply determine the height of the pyramid using Pythagoras theorem and then calculate the volume.

Learn more on volume of a pyramid here: https://brainly.com/question/218706

#SPJ1

The constant of variation k for the direct variation in 4x = –6y will be 1.5.

It should be noted that a direct variation simply means the mathematical relationship that exists between two variables which can be expressed by an equation such that a variable is equal to another one.

Therefore, the constant of variation k for the direct variation in 4x = –6y will be:

4x = –6y

Divide through by 4

4x / 4 = -6y / 4

x = -1.5y

Therefore, the constant of variation is 1.5.

Learn more about variation on:

brainly.com/question/6499629

#SPJ1

Trymaine is 20 years old and Sunny is 13 years old.

GIven, Trymaine is 7 years older than Sunny.

In 3 years the sum of their ages will be 39.

Let the age of Trymaine be a and age of Sunny be b.

we have,

a = b ₊ 7

a ₊ 3 ₊ b ₊ 3 = 39

a ₊ b = 39 ₋ 6

a ₊ b = 33 .... eq(2)

therefore a = b ₊ 7

a ₋ b = 7 ....eq(1)

solve eq (1) and eq(2)

2a = 40

a = 20

and a ₋ b = 7

20 ₋ b = 7

₋b = 7 ₋ 20

₋b = ₋13

b = 13

hence Trymaine is 20 years old , whereas Sunny is 13 years old.

hence we get the ages of Trymaine and Sunny as 20 and 13 respectively.

Learn more about Linear equations here:

brainly.com/question/4074386

#SPJ9

Answer:

-16

Step-by-step explanation:

pretty sure its the right answer, we did this a week ago in class so it may be wrong.

so first u gotta find the derivative of s(t) to get the vel equation. the derivative of s(t):

s(t)'= -4t, which is the vel equation

s(t)'=v(t)

v(4)=-4(4)

which equals -16

The instantaneous velocity of the ball at t = 4 seconds is -16 feet per second.

To find the instantaneous velocity of the ball at t = 4 seconds, we need to calculate the derivative of the given function s(t) with respect to t, and then evaluate it at t = 4.

Given that s(t) = -2t² - 2, we can find the velocity function v(t) by taking the derivative of s(t):

v(t) = d/dt (-2t² - 2)

v(t) = -4t

Now, we can find the instantaneous velocity at t = 4 by substituting t = 4 into the velocity function:

v(4) = -4(4)

v(4) = -16

This means that at that specific moment, the ball is moving downward with a velocity of 16 feet per second. The negative sign indicates the direction of motion.

To learn more about velocity click on,

https://brainly.com/question/32801526

#SPJ2

Answer:

you to get my number 3 whole thing together

The value of x is 74

Surekha Washburn has scores of 61, 65, 77, and 81 on her algebra tests.

a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam

counts as two tests.

let score on final exam is x

two test are 2x

then we get the value of x

[tex]\frac{61 + 65 + 77 + 81 + 2x}{6}[/tex] = 72

[tex]\frac{284 + 2x}{6}[/tex]  = 72

284 + 2x =432

2x = 432 - 284

x = [tex]\frac{148}{2}[/tex]

x = 74

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Average Formula in Maths

The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:

Average = Sum of Values/ Number of values

Suppose, we have given with n number of values such as x1, x2, x3 ,….., x n. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+x n)/n

How to Calculate Average?

We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.

Average can be calculated using three simple steps. They are:

Step 1: Sum of Numbers:

The first step in finding the average of numbers is to find the sum of all the given numbers.

Step 2: Number of Observations:

Next, we have to count how many numbers are in the given dataset.

Step 3: Average Calculation:

The final step in calculating the average is to divide the sum by the number of observations.

Now, let us consider an example to calculate the average.

If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.

By average formula, we know,

Average = (Sum of values)/No. of values

= (20+21+23+22+21+20+23)/7

= 150/7

=21.42

learn more about Average here :  brainly.com/question/24057012

SPJ9

According to the given a two-column proof bellow the EFI = 40°

A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned with in right column.

Given:

GFI = 128°where

9x - 2 = 128°

EFI = 40° And

4x = 40

So,

GFI = 128°where

9x - 2 + 4x = 128°

13x = 130

x = 10

putting the value x = 10 in EFI = 40° And  4x = 40:

So,

4x = 40

4(10) = 40

40 = 40

To Know more about two-column proof visit:

https://brainly.com/question/12894994

#SPJ9

Answer:

3h+6 inches

Step-by-step explanation:

The values of the functions are:

f(-2) = -6

f(0) = 0

f(3) = 9

Given the function, f(x) = 3x, to find the values of f(-2), f(0), and f(3), solve as shown below.

Find f(-2) by substituting x = -2 into the function, f(x) = 3x:

f(-2) = 3(-2)

f(-2) = -6

The value of f(-2) for the given function is: -6

Find f(0) by substituting x = 0 into the function, f(x) = 3x:

f(0) = 3(0)

f(0) = 0

The value of f(0) for the given function is: 0

Find f(3) by substituting x = 3 into the function, f(x) = 3x:

f(3) = 3(3)

f(3) = 9

The value of f(3) for the given function is: 9

Thus, the values of the functions are:

f(-2) = -6

f(0) = 0

f(3) = 9

Learn more about functions on:

https://brainly.com/question/2284360

#SPJ1

Answer:

x = 7

x = -1

Step-by-step explanation:

2x - 6 = 8  Add 6 to both sides

2x = 14  Divide both sides by 2

x = 7

2x -6 = -8  Add 6 to both sides

2x = -2  Divide both sides by 2

x = -1