Find the domain and range

Answer:

So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.

Step-by-step explanation:

To find the equation of a line perpendicular to y=-x-7, we need to find its slope first, which is the coefficient of x, which is -1 in this case. The slope of a line perpendicular to this line will be the negative reciprocal of this slope, so the slope of our line will be 1.

To find the equation of the line in point-slope form, we can use the formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. We are given the point (-2, -6), so we can substitute these values into the formula and get:

y - (-6) = 1(x - (-2))

Simplifying this equation gives:

y + 6 = x + 2

Subtracting 6 from both sides gives:

y = x - 4

So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.

Answer:

Maria earned €600 each week, and she spent 1/4 of her money on food.

So, Maria spent:

(1/4) * €600 = €150 on food each week.

To find how much she earned in 4 weeks, we can simply multiply her weekly earnings by 4:

€600/week * 4 weeks = €2400

Therefore, Maria earned €2400 in 4 weeks.

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The expression that is shown on the number line is 5/6 - 1/6.

Expression is a combination of words and/or symbols that conveys a meaning or an idea. It can take many forms, including verbal, written, and nonverbal communication. Expressions can be used to describe emotions, thoughts, and feelings, and they can be used to explain why something happened or how something works. Expression is a powerful tool that allows people to communicate with each other, build relationships, and understand one another.

The expression that is shown on the number line is C: 5/6 - 1/6. To reach this answer, we must evaluate the points located on the number line. Starting from the left, the first point is 0, followed by -1/6, -2/6, -3/6, -4/6, -5/6, and -1. We can see that the difference between 5/6 and 1/6 is 4/6. Therefore, the expression that is shown on the number line is 5/6 - 1/6.

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In your fourth year on the job, you can expect to earn $41,327.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that;

In this case, P = 34,000, r = 0.05, and n = 4.

Plugging these values into the formula, we get:

A = 34,000(1 + 0.05)^4

A = 34,000(1.05)^4

A = 34,000(1.2155)

A = 41,327

Therefore, by the simple interest the answer will be $41,327.

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Answer: 35

Step-by-step explanation:

The formula is there

a=(41+29)/2= 35

Lucy's new unpaid balance is $694.28 to the nearest cent.

Lucy's minimum payment can be calculated by multiplying her unpaid balance by the minimum payment percentage:

Minimum payment = 3% of $700 = 0.03 x $700 = $21

So, Lucy's minimum payment for the month is evaluated at $21.

As per the given information,

Monthly interest rate = 27% / 12 = 0.0225 / month

The interest charged for the month is then calculated by multiplying the monthly interest rate by the unpaid balance:

Interest charged for the month = 0.0225 x $700 = $15.75

So, Lucy will be charged $15.75 in interest for the month.

Finally, we can calculate Lucy's new unpaid balance after making the minimum payment and paying the interest charged for the month. This is given by:

Unpaid balance = (unpaid balance - minimum payment) x (1 + monthly interest rate)

Unpaid balance = ($700 - $21) x (1 + 0.0225) = $694.2775

Therefore, Lucy's new unpaid balance is $694.28.

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Expression which represents the distance between point J and point K is d) |-10| + |5|.

The distance between two points is the length of the straight line segment that connects them in Euclidean space.

The distance formula between two points in a coordinate plane is given by:

d = [tex]\sqrt{(x_{2}- x_{1} )^{2} + (y_{2}-y_{1} )^{2} }[/tex]

where ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are the coordinates of the two points.

Using this formula, the distance between point J(-10,-15) and point K(5,-15) is:

d = [tex]\sqrt{(5-(-10))^{2}+(-15-(15))^{2} }[/tex]

= [tex]\sqrt{(5+10)^{2}+0^{2} }[/tex]

= [tex]\sqrt{15^{2} }[/tex]

= 15

Therefore, the correct expression that represents the distance between point J and point K is:

d) |-10| + |5|

Correct Question :

Which expression represents the distance between point J and point K?​

a) |-10| - |5|

b) |5| + |-15|

c) |-15| - |-10|

d) |-10| + |5|

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Answer: C

Step-by-step explanation:

cos ∅ = adj/ hyp = XZ/ZY

the inverse cos is how you find angle

[tex]cos^{-1}\frac{XZ}{YZ}[/tex]  none of these are your choices so try sin

sin∅ = opp/hyp = xy/yz

[tex]sin^{-1}\frac{XY}{YZ}[/tex]

so answer is C

The area of the circle rounded to the nearest whole number is A 50 ft²

We see that the diameter of the circle in diagram is 8 feet. The area of the circle is calculated by the formula -

Area = πr², where r is the radius of the circle. Now, we know that radius is half the diameter. Thus, radius = 8/2

Divide the value

Radius of circle = 4 feet

The area of circle = 3.14 × 4²

Take square and multiply the value on Right Hand Side of the equation

Area of circle = 50.24 square feet

Rounding the number to the nearest whole number, we get 50 square feet

Hence, the area of the circle is A 50 ft².

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The question is attached in figure.

Answer:

Step-by-step explanation:

8 possible books, you plan to take 7 with you on vacation. How many different collections of 7 books can you take

Answer:

1. He sold 5 erasers in January

2. He sold 130 erasers.

Step-by-step explanation:

1. ₹1 per eraser = ₹5 for 5 erasers

2. if you add opposites you get 0 So, ₹2 by selling one marker pen, loss of ₹1 per eraser. 65*2 is 130. So 130 erasers.

Answer:

- 2/5 + 4/5 would give you 2/5

Step-by-step explanation:

think of it as (positive) + 4/5 (subtracted by) - 2/5 then you get 2/5!

If, the cylinder has a radius of x and a height of y. The cone has a radius of 13x. Then, the height of the cone in terms of y is h = (3/169)y.

The volume of a cylinder will be given by the formula V_cylinder = [tex]πr^{2h}[/tex], where r is the radius and h is the height. The volume of a cone is given by the formula V_cone = (1/3)[tex]πr^{2h}[/tex], where r is radius and h is height.

If the cylinder and cone have the same volume, then we can equate their volume formulas;

[tex]πX^{2y}[/tex] = (1/3)[tex](π13X)^{2h}[/tex]

Simplifying, we get;

[tex]πX^{2y}[/tex] = π169[tex]X^{2h/3}[/tex]

Dividing both sides by [tex]πX^{2}[/tex], we get;

y = 169h/3

Therefore, the height of the cone in terms of y is h = (3/169)y.

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Answer:

Six of the plants grew to a full height of 16 to 17 inches.

Step-by-step explanation:

A major problem in South Africa since the end of apartheid is B. The failure of government policies to address the race-based wealth gap.

Since the termination of apartheid in South Africa in 1994, the nation has endured numerous social and financial struggles throughout the consecutive decades.

Specifically, a major problem is the long-standing inequity and destitution that putatively affects black South Africans, plausibly due to the lingering impact of past apartheid initiatives. Despite attempts by the government to tackle these problems via Black Economic Empowerment (BEE) policies, the degree of headway achieved appears to be tardy and spotty.

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25 times out of 50 times the die will land on greater than 3.

We have,

A 6 sided die is rolled 50 times.

So, the probability of getting greater than 3 on first trial

= 3/6

= 1/2

Now, if the die rolled 50 times then the chances of getting greater than 3 is = 1/2 x 50

= 25 times

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Using the tangent line to f(x) at x=1, the linear approximation of 1/1.001 is approximately equal to 0.999.

Linear approximation is a method used in calculus to approximate the value of a function near a given point by using the tangent line to the function at that point. The tangent line is a straight line that "touches" the function at the given point and has the same slope as the function at that point. By using the equation of the tangent line, we can approximate the value of the function for values of x that are very close to the given point. Linear approximation is useful for estimating values of complicated functions that are difficult or impossible to calculate directly.

In the given question,

To find the equation of the tangent line to f(x) at a point near 1.001, we first need to find the derivative of f(x):

f(x) = 1/x

f'(x) = -1/x²

Now, let's choose a "nice" point near 1.001, such as x = 1. We can find the equation of the tangent line to f(x) at x = 1 using the point-slope form:

y - f(1) = f'(1)(x - 1)

Substituting in the values for f(1) and f'(1):

y - 1 = (-1/1²)(x - 1)

y - 1 = -x + 1

y = -x + 2

This is the equation of the tangent line to f(x) at x = 1.

To approximate 1/1.001 using this tangent line, we plug in x = 1.001 and solve for y:

y = -x + 2

y = -(1.001) + 2

y = 0.999

Therefore, using the linear approximation, 1/1.001 is approximately equal to 0.999.

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Answer:

The answer is (x+2) + (y-2)=2²

(-2,2)

Step-by-step explanation:

x= -2,y=2

(x-h) + (y-k)=R²

C(h,k)

where C is Centre

x+2=0,y-2=2²

(x+2)² + (y-2)²= 2²

The probability that you get both of them right but guessing is 1/16 or 6.25%.

The likelihood of getting both multiple-choice questions right when speculating can be calculated by increasing the likelihood of getting each address right together. Since there are four reply choices for each address.

The likelihood of speculating the proper reply for one address is 1/4. In this manner, the likelihood of getting both questions right is (1/4) x (1/4) = 1/16 or 6.25%.

This implies that in case you were to guess randomly on both questions, there's as it were a 6.25% chance that you just would get both of them right.

This illustrates that speculating isn't a solid strategy for replying to multiple-choice questions and it is superior to utilize information and thinking to create educated choices. 

Hence, the likelihood of speculating both questions accurately is (1/4) x (1/4) = 1/16. In other words, there's a 1 in 16 chance of getting both questions right fair by speculating.

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Answer:

Let's assume that the colors on the cube are numbered as follows:

Red

Blue

Green

Yellow

Purple

Orange

Without loss of generality, we can assume that the face numbered 1 is painted red. We can then use the following table to determine the colors of the other faces:

Face Number Color Opposite Face Number Opposite Color

1 Red 6 Orange

2 Blue 5 Purple

3 Green 4 Yellow

4 Yellow 3 Green

5 Purple 2 Blue

6 Orange 1 Red

We can start by choosing the color for face number 2, which must be one of the colors opposite to red (i.e., purple, green, or yellow). Let's say we choose purple. Then, the color for face number 5 must be one of the colors opposite to blue (i.e., green or yellow). Let's say we choose green. Then, the color for face number 3 must be one of the colors opposite to yellow (i.e., purple or orange). Let's say we choose orange. Now, the remaining three colors must be the ones that have not been used yet, which are blue, green, and yellow. We can then assign them to faces 4, 6, and 1, respectively.

Therefore, the numbering of the faces is as follows:

Face Number Color

1 Yellow

2 Purple

3 Orange

4 Green

5 Green

6 Blue

Note that we could have started by choosing green for face number 2 instead of purple, which would have led to a different numbering. However, we would have ended up with the same set of six colors.

In general, there are 3 choices for the color of face number 2, 2 choices for the color of face number 5, and 2 choices for the color of face number 3. After those choices are made, there is only one way to assign the remaining three colors to the remaining three faces. Therefore, there are:

3 x 2 x 2 x 1 = 12

different ways to number the faces of the cube as described in the problem.

Step-by-step explanation:

please leave thanks

Note that the probabilities that the engineer will win:

Let's denote the even of winning a contract as W and the event of not winning a contract as NW.

Thus, where we have:

P(W1) =1/2

P (NW1) = 1 - P(W1) = 1-1/2  1/2

P(W2) = 1/3

P(NW2) = 1-P(W2) = 1-1/3 = 2/3

1) To win both contracts, engineer need to have won contracts 1 and 2. Thus,

P(W1 and W2) = P(W1) *P(W2) = (1/2) * (1/3) = 1/6

2) To win only one contract, the engineer can either win contract 1 or contract 2 or vice versa.

Because they are independence,

P((W1 AND NW2) or (NW1 and  W2)) = P(W1 AND NW2) + P(NW1 and W2)

= P(W1) * P(NW2) + P(NW1 * P(W2)
= (1/2) * (2/3) + (1/2) * (1/3)

= 1/2

3) With regard to the contractor winning neighter 1 or 2:

P(NW1 and NW2) = P(NW1) * P(NW2) = (1/2) * (2/3) = 1/3

Hence, it is correct to state that:

that the probabilities that the engineer will win:

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Step-by-step explanation:

The 3.5% saltwater means that for every 100 gallons of saltwater, there are 3.5 gallons of salt and 96.5 gallons of purified water. Therefore, to find the number of gallons of salt mix that Julian should add to 30 gallons of purified water, we can set up the following proportion:

3.5 gallons of salt / 100 gallons of saltwater = x gallons of salt / 30 gallons of purified water

Simplifying this proportion, we get:

x = (3.5 gallons / 100 gallons) * 30 gallons / 96.5 gallons

x = 0.01078 gallons of salt mix

To find the number of pints of aquarium salt mix that Julian should use, we can set up another proportion:

1 gallon of salt mix / 8 pints of salt mix = 0.01078 gallons of salt mix / y pints of salt mix

Simplifying this proportion, we get:

y = (0.01078 gallons of salt mix / 1 gallon of salt mix) * (8 pints of salt mix / 1 gallon of salt mix)

y = 0.0862 pints of aquarium salt mix

Rounding to the nearest tenth, Julian should use approximately 0.1 pints of aquarium salt mix for 30 gallons of purified water.

Answer:

Answer: The area of rectangle is 4*m square unit.

Step-by-step explanation:

Answer:

If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s .

Step-by-step explanation:

Graph A shows the image of the quadrilateral WXYZ after a reflection over the x-axis and a translation of 2 units.

Option A is the correct answer.

We have,

From the figure,

The coordinates of WXYZ.

W = (5, -3)

X = (-6, 3)

Y = (-3, 1)

Z = (-2, 3)

Now,

After the reflection over the x-axis.

W = (-3, 5) = (-3, 5)

X = (-6, 3) = (-6, -3)

Y = (-3, 1) = (-3, -1)

Z = (-2, 3) = (-2, -3)

Now,

Translation to the right of 2 units.

W = (-3, 5) = (-3, -5) = (-1, 3)

X = (-6, 3) = (-6, -3) = (-4, -3)

Y = (-3, 1) = (-3, -1) = (-1, -1)

Z = (-2, 3) = (-2, -3) = (0, -3)

Thus,

Graph A shows the image of the quadrilateral WXYZ after a reflection over the x-axis and a translation of 2 units.

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1) 19.2% is the rate of return for each division.

2) The New South Wales divisional manager seems to be doing a better job.

1) How to compute the rate of return for each division?

To compute the rate of return for each division using the return on investment (ROI) formula stated in terms of margin and turnover, we can use the following formula:

ROI = Margin × Turnover

Where Margin = Net operating income / Sales and Turnover = Sales / Average operating assets.

a. Queensland division:

Margin = -$102,660 / $1,711,000 = -0.06

Turnover = $1,711,000 / -$590,000 = -2.90

ROI = -0.06 × (-2.90) = 0.174 or 17.4%

b. New South Wales division:

Margin = $113,280 / $2,832,000 = 0.04

Turnover = $2,832,000 / $590,000 = 4.80

ROI = 0.04 × 4.80 = 0.192 or 19.2%

2) The New South Wales divisional manager seems to be doing a better job based on given ROI as the ROI of the New South Wales division is higher than which of the Queensl and division.

The New South Wales division generated a 19.2% return on investment.

The Queensland division generated a 17.4% return on investment.

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