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What is the equation for the line in
slope-intercept form?
Enter your answer in the box.

When finding the area of a rectangle, it is correct to use the formula "length x width" or "width x length."

These two expressions are interchangeable because the multiplication operation is commutative, meaning the order of multiplication does not affect the result.

The reason why "length x width" or "width x length" is used to calculate the area of a rectangle is based on the definition of area. The area of a rectangle represents the amount of two-dimensional space enclosed within its boundaries.

The length of a rectangle refers to the longer side or dimension, while the width refers to the shorter side or dimension. By multiplying the length and width together, we are essentially determining the product of the two dimensions, which represents the total area of the rectangle.

For example, if we have a rectangle with a length of 6 units and a width of 4 units, the area can be calculated as follows:

Area = Length x Width = 6 units x 4 units = 24 square units

In summary, it is correct to use "length x width" or "width x length" to find the area of a rectangle because the order of multiplication does not affect the result, and the product of the dimensions represents the total enclosed space within the rectangle.

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The graph of the function g(x) = x + 3 is a straight line that passes through the point (0, 3) on the y-axis and has a slope of 1.

To understand how to plot the graph, let's consider a few points on the line.

We can choose any values for x and calculate the corresponding values for g(x).

Let's start with x = 0.

Substituting this value into the function, we get g(0) = 0 + 3 = 3.

So, the point (0, 3) is on the graph.

Next, let's choose x = 1.

Substituting this value into the function, we get g(1) = 1 + 3 = 4.

This gives us another point on the line, (1, 4).

Similarly, we can choose more values for x and calculate the corresponding values for g(x).

For example, if we let x = -1, we get g(-1) = -1 + 3 = 2, giving us the point (-1, 2).

By connecting these points and extending the line in both directions, we obtain a straight line that represents the graph of g(x) = x + 3.

The line has a positive slope of 1, which means it rises by 1 unit vertically for every 1 unit it moves horizontally.

Overall, the graph of g(x) = x + 3 is a straight line that passes through the point (0, 3) and has a slope of 1.

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To find the volume of the cube, Brayden has to multiply the area of one face by the width

Answer:

10 x 10 x 10 x 10.

Step-by-step explanation:

2(5)^4

10^4

Expanded form; 10*10*10*10.

Answer:

10 x 10 x 10 x 10

Step-by-step explanation:

Answer:

7 is the answer

Step-by-step explanation:

28+14=7 (4+2)

Step-by-step explanation:

\(s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} \)

The shaded region represents 1.5 grids

\(1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} \)

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

Answer:

\(y=\dfrac{5}{4}x^3+10\)

Step-by-step explanation:

Given information:

Create two equations by substituting the given points into the given equation:

Equation 1:  point (0, 10)

\(\implies a(0)^3+d=10\)

\(\implies 0+d=10\)

\(\implies d=10\)

Equation 2:  point (2, 20)

\(\implies a(2)^3+d=20\)

\(\implies 8a+d=20\)

Substitute Equation 1 into Equation 2 and solve for a:

\(\implies 8a+d=20\)

\(\implies 8a+10=20\)

\(\implies 8a+10-10=20-10\)

\(\implies 8a=10\)

\(\implies \dfrac{8a}{8}=\dfrac{10}{8}\)

\(\implies a=\dfrac{10}{8}\)

\(\implies a=\dfrac{5}{4}\)

Finally, substitute the found values of a and d into the original formula:

\(\implies y=\dfrac{5}{4}x^3+10\)

Check by substituting the x-values of the two given points into the found equation:

\(x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}\)

\(x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}\)

Put(0,10)

Now

Put again (2,20) this time

Answer:

it is correct I think it's right

Step-by-step explanation:

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer: 0.500001

Step-by-step explanation: Hope that helps!

Answer:

1011011101012

Step-by-step explanation:

Converting 2933 to base 10.

2*103=2000

9*102=900

3*101=30

3*100=3

Adding all to get Ans=293310

Step2 converting 293310 to 2

The equation calculation formula for 293310 number to 2 is like this below.

2|2933

2|1466|1

2|733|0

2|366|1

2|183|0

2|91|1

2|45|1

2|22|1

2|11|0

2|5|1

2|2|1

2|1|0

2|1|1

Ans:1011011101012

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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Answer:

RIP to all those kings!!

Step-by-step explanation:

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

hope this helps a little

Answer:

1.

The explanatory variable is the level of education.

response variable is Rate of motor vehicle crash deaths

2. b

3. A) Without an experiment, no causal relationship can be made.

Step-by-step explanation:

1.

The explanatory variable is the level of education.

The explanatory variable tells us that more education among people over 25 years, brings about a reduction in motor deaths.

The response variable is the rate of motor vehicle deaths.

This variable actually responds to the changes in the explanatory variable. The rate of motor vehicle deaths could increase or decrease based on the level of education.

2.

They are lurking variables. option B

These variables are not known primarily as explanatory variables here in this relationship but they have the ability to affect the result of the study.

3. We have to carry out an experiment first in order to carry out a causal relationship.

Answer:

33

Step-by-step explanation:

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The first step to solve the present question is to determine each of the equations to determine the number of each accessory as a function of the number of boxes, If d is the number of boxes, Nt is the number of Turbo Jet Pack, Nx is the number of X-Ray Vision Glasses, and Ni is the number of invisible shields, we have the following:

Now, we can use it to solve the question.

Part A

It Nl is the number of Laser Sabers sold, let's transform the statement into a math equation, we have the following:

If we substitute the expressions we have from the previous-developed expressions, we have the following:

Part B

Let's assume the value of a single Laser Saber is given by Vl, then the total value for the value of a unity times the number of sold Laser Sabers, as follows:

Answer:

Yes, 9 is the answer.

Step-by-step explanation:

This is a one step equation so you only have to preform one operation to solve. You do the inverse operation of what the equation is doing. In this case you are multiplying, which means you will divide to solve.

63/7 = 9

The percentage change of the population is P = 1.7 %

Given data ,

To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.

Population increase = 7,375 - 7,250 = 125

Percent increase = (Population increase / Initial population) * 100

Percent increase = (125 / 7,250) * 100 ≈ 1.7241

Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.

Hence , the percentage change is P = 1.7 %

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Answer:

The answer should be 2 but it won't let me post it with less than twenty characters so yeah