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Answer:

- 8x > 24

Step-by-step explanation:

Given

- 6x - 10 > 14 + 2x ( subtract 2x from both sides )

- 8x - 10 > 14 ( add 14 to both sides )

- 8x > 24 ← required missing step

Divide both sides by - 8, reversing the symbol as a result of dividing by a negative quantity.

x < - 3 ← is the solution

Answer:

(x,y) = (0,  1/3)

Step-by-step explanation:

  [1]    2x + 3y = 1

  [2]    4x - 6y = -2

Graphic Representation of the Equations :

   3y + 2x = 1        -6y + 4x = -2  

Solve by Substitution :

Solve equation [2] for the variable  x  

 [2]    4x = 6y - 2

 [2]    x = 3y/2 - 1/2

Plug this in for variable  x  in equation [1]

  [1]    2•(3y/2-1/2) + 3y = 1

  [1]    6y = 2

Solve equation [1] for the variable  y

  [1]    6y = 2  

  [1]    y = 1/3  

By now we know this much :

   x = 3y/2-1/2

   y = 1/3

Use the  y  value to solve for  x  

   x = (3/2)(1/3)-1/2 = 0

The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality shows the non equal comparison of two or more numbers and variables.

Given the inequality y > x + 3 and y < -x + 2.

The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.

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Answer:

-3

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.

Given-

Kylie uses the number 400 to represent 400 miles north of the equator.

Kylie uses the number -2000 to show 2000 miles south of the equator.

What is the direction?

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.

As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.

Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

Answer:

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Step-by-step explanation:

(2x + 3) (3x – 5)=

6x²+9x-10x-15=

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Answer:

I think its 19.1

Step-by-step explanation:

14 + 5.1

Maybe try

Considering point Q (x, y) to be (1, 2), and translating it by (x-3, y+4), the image of point Q, say Q' will be positioned at (-2, 6), which is plotted in the reference image attached hereby.

As per the question statement, we are required to plot the image of point Q(x, y) under the translation (x-3, y+4).

Let us assume the point Q to be (1, 2). Therefore, a translation of (x-3, y+4) on (1 , 2) will result in a new position, which will be:

3 units to the left of (1, 2) along the x-axis, and then 4 units upwards along y-axis.

Hence, the position of the image of Q (1, 2) after a translation of (x-3, y+4) will be Q' \([(1-3), (2+4)]=(-2, 6)\).

Both the points Q(1, 2) and its image after the translation of (x-3, y+4), Q'(-2, 6) are plotted in two separate graphs, attached hereby for reference.

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Answer:

24

Step-by-step explanation:

knowing a parallelogram, JK = ML

so,

14 + 2x = 5x – 1

2x – 5x = –14 –1

–3x = –15

3x = 15

x = 5

substitute x=5 into 14 + 2x

14 + 2(5) = 24

Answer:

not sure sorry

Step-by-step explanation:

you prob gotta do it

Answer:

$16

Step-by-step explanation:

she has $14 now

her parents let her earn 6

so $14 - $6 = $8

so thats what was left over from her allowance. she spent half of her allowance to get to $8 so you double the money

$8 * 2 = $16

$16 is her weekly allowance

Answer:

The median of the scores in this stem-and-leaf plot is 78

Step-by-step explanation:

The total data set represented by Stem and leaf in order from the least to the greatest are as following:

58, 59, 64, 64 , 66, 68, 72, 74, 75, 76, 78, 79, 83, 84, 86, 87, 88, 91, 93, 93, 95

The number of data is 21

The median of the data at the place number 11

So, median = 78

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

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Answer:

f⁻¹(x) = 1/2 x -3/2

Step-by-step explanation:

f(x) = 2x-3    ... y = 2x -3

replace x and y:    x' = 2y' -3

solve y':  y' = 1/2 x' - 3/2

f⁻¹(x) = 1/2 x -3/2

Answer:   \(6\sqrt{3}\)

Reason:

For any 30-60-90 triangle, the long leg is exactly \(\sqrt{3}\) times as long compared to the short leg.

In other words,

\(\text{long leg} = (\text{short leg})*\sqrt{3}\)

In this case, the short leg is 6 units long. The short leg is always opposite the smallest angle 30 degrees. Once again, this only applies to 30-60-90 triangles.

A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

Let X be an uncountable set and A be a countably infinite subset of X. We need to show that X - A is uncountable. By contradiction, assume that X - A is countable. Since A is countably infinite, we can list its elements in a sequence as {a1, a2, a3, ...}. Now, consider the following sequence of sets:S1 = X - {a1}S2 = S1 - {a2}S3 = S2 - {a3}...Sn = Sn-1 - {an}...Observe that each Si is obtained by removing a finite set from X, and hence Si is uncountable. Moreover, Si is a subset of Si-1 for each i, so we have an infinite descending chain of uncountable sets. This contradicts the fact that X is uncountable. Therefore, X - A must be uncountable.Note that this argument works for any uncountable set X, regardless of its cardinality. We only need to assume that A is countably infinite. If A is finite, then X - A is clearly uncountable (since it has the same cardinality as X). If A is countable but not infinite, then X - A is still uncountable (since it has the same cardinality as X). Thus, the only interesting case is when A is countably infinite.

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Answer:

The answer is 2.

Step-by-step explanation:

2 appears three times while the others appear only twice

A person leaves their home at noon walking toward a restaurant located 16 miles away If the person walks constantly at 2.5 miles per hour, the person arrive at the restaurant at 6:24 PM.

To determine the time it will take for the person to arrive at the restaurant, we can use the formula:

Time = Distance / Speed

Given:

Distance to the restaurant = 16 miles

Walking speed = 2.5 miles per hour

Substituting these values into the formula, we can calculate the time:

Time = 16 miles / 2.5 miles per hour

Time = 6.4 hours

Since we know the person leaves their home at noon, we can add the calculated time to noon to find the arrival time:

Arrival Time = Noon + 6.4 hours

To express the arrival time in a standard 12-hour clock format, we convert 6.4 hours into hours and minutes:

0.4 hours * 60 minutes/hour = 24 minutes

So, the person will arrive at the restaurant at approximately 6 hours and 24 minutes after noon.

Therefore, the person will arrive at the restaurant at approximately 6:24 PM.

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Answer:

C. 180-degree rotation counterclockwise followed by a translation of 5 units to the left

Step-by-step explanation:

Answer:

180° counterclockwise rotation about the origin followed by a translation 5units left

Step-by-step explanation:

Rule for 180° counterclockwise rotation is

Take any point to prove

let it be A

Rotate

Translate 5 units left(change in x)

Yes verified

We use the change of variables formula to obtain the PDF of X in terms of the PDF of Y:

\(f(x) = f_Y(ln(x)) * |d(ln(x)) / dx|\)

where f_Y is the PDF of Y and |d(ln(x)) / dx| is the absolute value of the derivative of the transformation.

Yes, that's correct. A continuous random variable X is said to have a log-normal distribution with parameters μ and σ^2 if its natural logarithm, ln(X), follows a normal distribution with mean μ and variance σ^2. This is denoted as X ~ LogN(μ, σ^2).

The probability density function (PDF) of X can be expressed as:

\(f(x) = (1 / (x * σ * √(2π))) * e^(-(ln(x) - μ)^2 / (2σ^2))\)

where x > 0 is the value of the random variable X.

This PDF is derived using the transformation method, where we start with the PDF of the normal distribution and apply the transformation to obtain the PDF of the log-normal distribution. Specifically, we use the transformation:

ln(X) = Y

where Y follows a normal distribution with mean μ and variance σ^2. Then, we use the change of variables formula to obtain the PDF of X in terms of the PDF of Y:

\(f(x) = f_Y(ln(x)) * |d(ln(x)) / dx|\)

where f_Y is the PDF of Y and |d(ln(x)) / dx| is the absolute value of the derivative of the transformation. This simplifies to the expression given above.

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The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

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After the evaluation of integral I = Sπ/6 0 2sin2x/cosx the result is -2 [Si(1) - Si(√3/2)], under the condition that the given integral is a form of infinite integral.

The  given integral I = ∫(π/6)0 2sin2x/cosx

can be evaluated by performing the principles of substitution method.

Then Let us consider u = cos(x),

then du/dx = -sin(x)

dx = -du/sin(x).

Staging these values in the integral

I = ∫(π/6)0 2sin2x/cosx dx

 = ∫(π/6)0 2sin2x/u (-du/sin(x))

 = -2 ∫u=cos(π/6)u=cos(0) sin(u)²/u du

 = -2 ∫u=√3/2u=1 sin(u)²/u du

 = -2 [Si(1) - Si(√3/2)]

here Si is the sine integral function.

After the evaluation of integral I = Sπ/6 0 2sin2x/cosx the result is -2 [Si(1) - Si(√3/2)], under the condition that the given integral is a form of infinite integral.

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The required ultimate tensile strength for 4130 steel quenched and tempered at 400F is 138,000 psi with a reliability of 90 percentage.

The ultimate tensile strength of 4130 steel quenched and tempered at 400F can be calculated using the data given in Appendix Table A-9. First, we need to calculate the standard deviation of the ultimate tensile strength of 4130 steel which is 16,000 psi. Then, we need to calculate the margin of error at a reliability of 90 percentage. This is done by multiplying the standard deviation by 1.645, which gives us a margin of error of 26,120 psi. Finally, we need to add the margin of error to the mean value of ultimate tensile strength, which is 112,000 psi. This gives us a required ultimate tensile strength of 138,120 psi with a reliability of 90%.

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Answer:

Concept: Linear systems

A graph of y - 2 = -3/4(x - 6) in the point-slope form is shown in the image attached below.

The point-slope form can be defined as an equation which is used when the slope of a straight line and one of the points on this line is known.

Mathematically, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Where:

Given the following point-slope form equation:

y - 2 = -3/4(x - 6)

From the above, we have:

Slope, m = -3/4

Point at x = 6.

Point at y = 2.

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