Which of the following equations has a slope of 4 and passes through point (2, 5)?
0000
y = 4x + 2
y = 4x + 5
y = 4x - 3
y = 4x - 8

Answer: \(y=\dfrac12 x\) .

Step-by-step explanation:

We know that \(a f (x)\)  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by \(\dfrac12\).

Then, the equation of the new function is \(y=\dfrac12 F(x)=\dfrac12 x\) .

i.e. \(y=\dfrac12 x\) .

Answer:

The train travels 75 mph.

Step-by-step explanation:

Hope this helps!

Answer:

(75, 1)

Step-by-step explanation:

One way we can figure out how fast the train goes, is bylooking at what we have. We know that the train travels 450 miles in 6 hours. When we divide, we get 75. So, we know that the train is going at 75 miles per hour. We can check our work by looking at the second relationship on there. When 675 is divided by 9, we get 75. So for every hour, the train travels 75 miles.

I hope that this helps you out :)

831 in the standard form can be represented as

8.31 × 10²

Given, a number 831

we have to write the number in its standard form

Now, writing a number in standard form is useful when we have value is either very large or very small.

Formally, the standard form is defined by,

a × b^n

So, 831 in the standard form is

8.31 × 10²

Hence, 831 in the standard form can be represented as

8.31 × 10²

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Answer:

4/9 or 0.4

Step-by-step explanation:

Answer:

4/9-1/5

=11/45

Step-by-step explanation:

The required scale factor between the building and toy model is given as 900.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900

Thus, the required scale factor between the building and the toy model is given as 900.

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The mean points of the team is the average points per game

Dom's claim is wrong

The number of players in the team is:

n = 8

The mean score per game is:

Mean = 12

The mean of a dataset is calculated as:

\(Mean = \frac{Total}n\)

So, we have:

\(12= \frac{Total}8\)

Multiply both sides by 8

\(Total = 96\\\)

When Dom's point is removed, we have:

\(Points = 96 - 33\)

\(Points = 63\)

There are 7 players left.

So, the mean point is:

\(Mean = \frac{63}7\)

\(Mean = 9\)

The mean score is not 10.

Hence, Dom's claim is wrong

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Answer:

9.8978999e+98

Step-by-step explanation:

Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel. Therefore,

QT = PS = 3y ...(1)

PT + TR = PS

y + 2x + 1 = 3x + 9

2x - y = 4 .....(2)

PR = QT = 3y

PR = SQ = 3x + 9 ....(3)

From equations (1) and (3), we can see that:

3y = 3x + 9

y = x + 3

Substitute this value of y in equation (2):

2x - (x + 3) = 4

x = 7

To find the value of y, we can substitute x = 7 in equation (2):

2(7) - y = 4

y = 10

Therefore, x = 7 and y = 10.

Answer:

The answer is 28y + 63

Step-by-step explanation:

7(4y+9)

=28y+63

To schedule the tasks on two machines in a way that minimizes the time for both machines to finish their tasks, we can use the "Longest Processing Time" algorithm.

1. Sort the list of times in descending order: (18, 16, 12, 8, 6).

2. Assign the tasks one by one to the machine with the currently shorter total processing time.

  Machine 1: (18) -> Total time: 18

  Machine 2: (16) -> Total time: 16

  Machine 1: (12) -> Total time: 30

  Machine 2: (8) -> Total time: 24

  Machine 1: (6) -> Total time: 36

3. The best time for both machines to finish their tasks is the maximum of the two total times: 36.

the correct answer is:

D) 35 (Incorrect)

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Answer:

b=6

Step-by-step explanation:

line b + 14.5 is parallel to line 20.5

so 20.5= b + 14.5

b=6 when you subtract the 14.5

Answer:

A. y = 3x.

Step-by-step explanation:Relation 2 is a straight line that does not pass through the origin, so it is a partial variation.

Answer:

Original angle = 122*

Supplementary angle = 58*

Step-by-step explanation:

A supplementary angle is one of two angles that make up 180*

If one angle is 30*, its supplementary angle is 150*. 30 + 150 = 180.

So in this case we have two angles, the original and the supplementary angle. The original angle is 64* more than the supplementary angle. The key word is MORE.

The formula to figure it out would look like this:  x + (x + 64) = 180

x is the supplementary angle

x + 64 is the original angle (64 MORE than its supplementary angle)

180 is the total measure of the two angles because they are supplementary and we know that supplementary angles always equals 180* when added together.

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Remeber we know that the original angle is 64 more than the supplementary angle, so we'll add the 64 to the value of x and we get 122.

x + 64 = 122

Check our work:

x + (x + 64) = 180

58 + 58 + 64 = 180

Given :

⠀

To Find :

⠀

Solution :

Now,

⠀

According to the Question :

⠀

\(\longrightarrow\qquad \sf{{x + (x + 64) {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x + x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {180}^{ \circ} - 64 {}^{ \circ}}}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {116}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x = \dfrac{{116}^{ \circ}}{2} }}\)

⠀

\(\longrightarrow\qquad \mathfrak{\pmb{{x = {58}^{ \circ} }}}\)

⠀

Therefore,

⠀

Henceforth ,

The distribution of the mean, median, and mode values will depend on how skewed the distribution is. As a result, mean or mode may be larger than or less than mode.

correct answer is D.

Different measures of the center in a set of numerical data include mean, median, and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.

The "mean" value is obtained by summing all the data points and dividing the result by the total number of data points.

The middle number, or median, is obtained by placing all data points in order and choosing the middle one (or, if there are two middle numbers, the mean of those two figures).

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Answer:

3 or -3

Step-by-step explanation:

What number multiplied by itself will give you 9

1*1 =1

2*2 =4

3*3 =9

Also note that negative times negative will be positive so

-1*-1=1

That means -3*-3 = 9

Answer:

3^2 0r (-3)^2

Step-by-step explanation:

let the number be x

x^2=9

x=\(\sqrt{9\)

x=\(\sqrt{3*3\)

x=3

there fore x=plus or minus 3.since it is a sqauring a number if u square (-3)^2 along will the number sign also gets multiplied and (-*-)=+ so u we get positive number.

therefore if u square 3 then u will get 9

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Answer:

180 D

Step-by-step explanation:

The Wronskian of the functions y₁ = e²ˣsin(9ˣ) and y₂ = e²ˣcos(9ˣ) is zero on (-∞, ∞), indicating that they are linearly dependent. Therefore, they do not form a fundamental set of solutions for the differential equation D²y - 4Dy + 85y = 0 on (-∞, ∞).

:

The Wronskian of two functions y₁ and y₂ is defined as W(y₁, y₂) = y₁Dy₂ - y₂Dy₁, where Dy represents the derivative of y with respect to x. In this case, we have y₁ = e²ˣsin(9ˣ) and y₂ = e²ˣcos(9ˣ).

Calculating the derivatives, we have Dy₁ = (2e²ˣsin(9ˣ) + 9e²ˣcos(9ˣ)) and Dy₂ = (2e²ˣcos(9ˣ) - 9e²ˣsin(9ˣ)).

Now, we can compute the Wronskian:

W(y₁, y₂) = y₁Dy₂ - y₂Dy₁

= e²ˣsin(9ˣ)(2e²ˣcos(9ˣ) - 9e²ˣsin(9ˣ)) - e²ˣcos(9ˣ)(2e²ˣsin(9ˣ) + 9e²ˣcos(9ˣ))

Simplifying further, we find that W(y₁, y₂) = 0 on (-∞, ∞).

Since the Wronskian is zero, the functions y₁ and y₂ are linearly dependent, which means they do not form a fundamental set of solutions for the given differential equation.

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The derivative of the function \(g(x) = ∫[1, x^3] t^3 dt is g'(x) = (3/4) x^11.\)

To find the derivative of the function \(g(x) = ∫[1, x^3] t^3\)dt using the Fundamental Theorem of Calculus, we can apply Part 1 of the theorem, which states that if the function g(x) is defined as the integral of a function f(t), then its derivative g'(x) can be found by evaluating f(x) at the upper limit of integration and multiplying it by the derivative of the upper limit.

In this case, the upper limit of integration is\(x^3\), so we have:

\(g'(x) = d/dx ∫[1, x^3] t^3 dt\)

Using the power rule for integration, we can integrate \(t^3\) to obtain (1/4) \(t^4\). Applying the Fundamental Theorem of Calculus, we have:

\(g'(x) = d/dx [(1/4) (x^3)^4]\)

Simplifying, we get:

\(g'(x) = d/dx [(1/4) x^12]\)

Taking the derivative using the power rule, we have:

\(g'(x) = (1/4) * 12x^(12-1)g'(x) = (3/4) x^11\)

Therefore, the derivative of the function \(g(x) = ∫[1, x^3] t^3 dt is g'(x) = (3/4) x^11.\)

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Rewritten form of equations in exponential form will be:\(log_{25}(5) = 1/2:Exponential form: 25^{1/2} = 5\quad \\log_{64}(1/2) = -1/6:Exponential form: 64^{-1/6} = 1/2\quad\\log_{(1/17)}(1/289) = 2:Exponential form: (1/17)^2 = (1/289)\quad , \\log_6(216) = 3:Exponential form: 6^3 = 216\)

\(log_{25}(5) = 1/2\)

Identify the base (b) as 25, the logarithmic expression as \(log_{25}(5) = 1/2\), and the result (y) as 1/2.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 25^(1/2) = 5.

\(log_{64}(1/2)=\frac{-1}{6}\)

Identify the base (b) as 64, the logarithmic expression as log_64(1/2), and the result (y) as -1/6.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 64^(-1/6) = 1/2.

\(log_{(1/17)}(1/289) = 2\)

Identify the base (b) as 1/17, the logarithmic expression as log_(1/17)(1/289), and the result (y) as 2.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: (1/17)^2 = 1/289.

\(log_6(216) = 3\)

Identify the base (b) as 6, the logarithmic expression as log_6(216), and the result (y) as 3.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 6^3 = 216.

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The exponential form of the equation is :

15) \(25^{(1/2)} = 5.\)

16)  \(64^{(\frac{-1}{6})} = \frac{1}{2}.\)

17)  \((\frac{1}{17})^2 = \frac{1}{289}.\)

18)  \(6^3 = 216.\)

How to determine exponential form of equation?

15) \(log_{25}5=\frac{1}{2}\)

Identify the base (b) as 25, the logarithmic expression as , and the result (y) as \(\frac{1}{2}\).

Apply the definition of logarithms:  \(log_b x=y\) if and only if  \(b^y = x\).

Rewrite the equation using the exponential form: \(25^{(1/2)} = 5.\)

16)\(log_{64}\frac{1}{2}=-\frac{1}{6}\)

Identify the base (b) as 64, the logarithmic expression as \(log_{64}\frac{1}{2}\), and the result (y) as -\(\frac{1}{6}\).

Apply the definition of logarithms:  \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form:  \(64^{(\frac{-1}{6})} = \frac{1}{2}.\)

17)\(log_{\frac{1}{17}}\frac{1}{289}=2\)

Identify the base (b) as 1/17, the logarithmic expression as \(log_{\frac{1}{17}}\frac{1}{289}\), and the result (y) as 2.

Apply the definition of logarithms:  \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form: \((\frac{1}{17})^2 = \frac{1}{289}.\)

18) \(log_6216=3\)

Identify the base (b) as 6, the logarithmic expression as \(log_6216\), and the result (y) as 3.

Apply the definition of logarithms:   \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form: \(6^3 = 216.\)

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One important consequence of migration is remittances.

Migration can have a significant impact on remittances, which refers to the money or resources that migrants send back to their home countries. When individuals migrate to other countries for employment or better opportunities, they often send a portion of their earnings or resources back to support their families or invest in their home communities.

These remittances can play a crucial role in the economic development of the receiving countries, providing a source of income and contributing to poverty reduction. Remittances can also stabilize the economies of the home countries, boosting consumption, investment, and overall economic growth.

Additionally, remittances can help improve access to education, healthcare, and other essential services for the families left behind by migrants.

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Answer:

JRQ = 56

Step-by-step explanation:

SRQ - SRJ = JRQ

166 - 110 = 56

The probability of assigning 7 black vans on a day when there are 20 drivers is approximately 0.0035 or 0.35%.

We have,

The total number of ways to select 7 black vans out of 8 is given by the combination formula:

C(8, 7) = 8! / (8 - 7)! 7! = 8

The total number of ways to assign 20 drivers to 26 vans (12 white + 10 silver + 4 remaining black) is given by the combination formula:

C(26, 20) = 26! / (26 - 20)! 20! = 230,230.

The probability is calculated by dividing the favorable outcomes by the total outcomes:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Probability = C(8, 7) / C(26, 20)

Probability ≈ 8 / 230,230 ≈ 0.0035 (rounded to four decimal places)

Therefore,

The probability of assigning 7 black vans on a day when there are 20 drivers is approximately 0.0035 or 0.35%.

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There are 72 different bracelets with 4 identical red beads, 4 identical orange beads, and 2 yellow beads, after flipping a bracelet.

To find the number of different bracelets, we can use the concept of permutations.

First, let's consider the red beads.

Since there are 4 identical red beads, the number of ways to arrange them in a line is 4! (4 factorial).

However, since rotating the bracelet does not change it, we need to divide by 4 to account for the different rotations of the same arrangement.

So, the number of arrangements of the red beads is 4!/4 = 6.

Next, let's consider the orange beads.

Similarly, there are 4!/(4 * 2) = 12 different arrangements of the orange beads.

Again, we divide by 4 to account for the different rotations.

Lastly, we have the yellow beads. Since there are 2 identical yellow beads, there is only 1 arrangement for them.

To find the total number of different bracelets, we multiply the number of arrangements for each type of bead:

6 * 12 * 1 = 72.

Therefore, there are 72 different bracelets with 4 identical red beads, 4 identical orange beads, and 2 yellow beads, if rotating or flipping a bracelet does not change it.

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Answer:

The correct answer is B.

A histogram, because the class organizes the data into intervals or ranges.

Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16