Solve this system of equations by graphing. First graph the equations, and then type the solution.

A point that lies in the middle of a line and is equally spaced from its ends is the line's midway. The formula for the line's midpoint is [(x)1 + (x)2]/2, [(y)1 + (y)2]/2 if the line's endpoints are (x)1, (y)1, and (x), (y), respectively.

Using the equations [(x)1 + (x)2]/2, [(y)1 + (y)2]/2, one may get the midway. Here, the coordinates of two points are (x), (y), (x)2, (y)2, and the midway is a location that is equally spaced from both of these positions.

The exact middle number between two numbers is referred to as the midway. The midpoint calculation is the same as the two-number average calculation. Therefore, by adding any two numbers together and dividing by two, you may find the halfway between any two integers.

The distance formula, which is derived from the Pythagorean Theorem, is employed to determine the separation between two points in the plane. The Pythagorean Theorem is based on a right triangle where the angles are a and b.

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The probability that the life span of the monitor will be more than 15,240 hours = 0.055

Given,

Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance σ^2 = 1,960,000 of  and a mean life span of μ = 13,000 hours.

Here, σ = [tex]\sqrt{1,960,000}[/tex] = 1,400

Let x represents  the life span of a monitor.

Then , the probability that the life span of the monitor will be more than 15,240 hours will be :-

= P(x > 15,240) = P[(x - μ)/σ >  (15,240 - 13,000)/ 1,400 ]

= P (z > 1.6) =  1 - P(z ≤ 1.6)  [∵ P(Z > z ) = 1 - P(Z ≤ z) ]

= 1 - 0.9452  = 0.0548 ~ 0.055

Hence, the probability that the life span of the monitor will be more than 15,240 hours = 0.055

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Answer:

522 1/2  revolutions

Step-by-step explanation:

First convert 13 3/4 into improper fraction

13 3/4 = (13 x 4 + 3)/4 = 55/4

Since these many revolutions are made in 1 minute, to find total number of revolutions made in 38 minutes, simply multiply 55/4 x 38

==> 55/4 x 38 = (55 x 38)/4 = 2090/4

Divide by 2 both numerator and denominator

==> (2090 ÷ 2)/(4 ÷ 2) = 1045/2 = 522 1/2

The resulting complex number is -10 - 10i.

             z₁ - z₂ = (a + ib) - (c + id)

                       =  (a - c) + i(b - d)

Given complex number: -4-(1+i)-(5+9i)

-4-(1+i)-(5+9i)

Remove the parentheses and combine the real and the imaginary parts respectively.

(- 4 -1 -5) - i(1 + 9)

-10 - 10i

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The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

A customer has 40 gallons of a cleaning solution that contains 20% soap.

The company sells a cleaning solution that contains 50% soap.

The customer wishes to create a 40% solution.

Solution:

By mixture and allegation method,

1 gallon                              1 gallon

  50%                                   20%

                         40%

  20                                       10

To create a 40%Soap solution, one must mix 20 gallons of 50%  soap solution and 10 gallons of  20% Soap solution.

Therefore, the ratio is 20 : 10 = 2:1

The customer has 40gallons of a cleaning solution that contains 20% soap, therefore in a 2:1 ratio, 1 part is 40 gallons.

Then for 2 parts = 2*40 = 80 gallons.

The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

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Betty spent $90 and Nan spent $ 30

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that :While shopping, Betty spent three times as much as Nan. And they spent a total of $120,

Let the Betty spent total $x and Nan spent total $Y

then,

x = 3y ....(i)

x +y =120 .....(ii)

put value of c from i equation to equation ii

4y = 120

y = 30

x = 90

Hence Betty spent $90 and Nan spent $ 30

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f(2) = 3

f⁻¹(2) = 1

f⁻¹(0) = -1

(f⁻¹o f)(1) = 1

The graph of f(x) is given. Here, f(x) = y and f⁻¹(y) = x.

That is, f(x) are y values corresponding to the given x-values and f⁻¹(y) is the x-value corresponding to the given y-value.

From the graph, f(2) is the y value when x = 2.

So, f(2) = 3

Now f⁻¹(2) is the x-value when y = 2.

So, f⁻¹(2) = 1

Also f⁻¹(0) =-1

Since f(1) = 2,

(f⁻¹o f)(1) = f⁻¹(f(1)) = f⁻¹(2) = 1

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Cans of paint (k) = Birdhouses painted

x= cans of paint

y= Birdhouses painted

y= kx

Where k is the constant of proportionality.

Replace with a set of points and solve for k

(x,y) = (3,15)

15= k 3

15/3 = k

k=5

The function's domain and range are (-3, -3, 2, 4) and (-2, 7, 1, 6) correspondingly.

The value of the independent function for which the function exists is referred to as the function's domain.

The value of the dependant function, for which the function exists, is referred to as the function's range.

The values in the x-column of the provided table are the domain, and the values in the y-column are the range.

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Answer: A. 1.152 pounds.

Step-by-step explanation:

Add vertically

 0.320

+0.832

[tex]2+0=2[/tex]

 0.320

+0.832

         2

[tex]2+3=5[/tex]

 0.320

+0.832

      52

Since [tex]3+8=11[/tex] , the one Carries Over to the ones place.

 1

 0.320

+0.832

    .152

[tex]1+0+0=1[/tex]

 1

 0.320

+0.832

  1.152

Therefore, 1.152 pounds is the correct answer.

Answer: 64

Step-by-step explanation:

If angle A is 116, then the angle C is also 116. As the sum of the angles of a parallelogram is 360, the sum of B and D should be 360 - 2*116 = 132. Hence, the angles B and D should be each 132/2 = 64

Dean's bike moved a total distance of 93.7 kilometers on Thursday and Friday

From the question, we have the following parameters:

Thursday = 88 kilometers

Friday = 5.7 kilometers

The total distance moved by Dean bike altogether on Thursday and Friday is the sum of the distance moved on Thursday and on Friday

Substitute the known values in the above equation

So, we have

Total distance = Distance moved on Thursday + Distance moved on Friday

Substitute the known values in the above equation

So, we have

Total distance = 88 kilometers + 5.7 kilometers

Evaluate the sum

So, we have

Total distance = 93.7 kilometers

Hence, the total distance moved by the bike is 93.7 kilometers

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When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.

It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.

The constant rate will be:

7 / 3 1/2 = 2

Now we can then write the relationship and this is illustrated as:

B = 2R

where B is the distance biked

R = the distance that's run.

We want to find the missing value of A. This is illustrated as:

5 1/2 = 2 × A

2A = 5 1/2

A = 2 3/4

Therefore, based on the information given, the correct option is C.

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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.

Complete the table for A

A 2 1/4

B 2 2/4

C 2 3/4

D 3 3/4

Sears offers them an installment loan at 15% (add-on rate) and if at Sears costs $1,500 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 2 years, the monthly payment will be $75.47     using the interest and percentage formulas.

As per the question statement, Karen and Wayne need to buy a refrigerator because theirs just broke but their savings account is depleted and they will need to borrow money in order to buy a new one. The Sears offers them an installment loan at 15% ( add-on-rate), If the refrigerator at Sears costs $1,500 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 2 years. We are supposed to find the monthly payment made by them using the interest formula and percentage formula.

5% of $1500 = $75

Total amount borrowed is 1500 + 75 = $1575.00

Sears charges 15% to borrow the money

15% of 1575 = $236.25

total amount is 1575 + 236.25 = $1811.25

There are 24 months present in 2 years so,

The monthly payment = 1811.25 / 24 = $75.47

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Answer:

In point-slope form: y + 4 = -2(x + 1)

In slope-intercept form: y = -2x - 6

In standard form: 2x + y = -6

Step-by-step explanation:

y + 4 = -2(x + 1)

y + 4 = -2x - 2

y = -2x -6

2x + y = -6

Answer: g=-16.3

Step-by-step explanation:

ya welcome

The relationship between the input and output variables in the given table of values are;

Question 1

Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour

Question 2;

x; 1, 2, 3, 4, 5

y; 140, 280, 420, 560

Question 3

No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent

Question 4

No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3

Question 5

Yes, it is a proportional relationship because it is a line that intersects with the origin

Question 6

The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned

Question 7

Yes because the ratio of the miles per hour are all equivalent to 1.75

A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.

Question 1

A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant

Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12

Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour

Question 2;

The points on the graph are;

(0, 0), (5, 700), (6, 840), (7, 980)

Therefore;

y = (5/700)•x = (1/140)•x

The table is therefore;

x; 1, 2, 3, 4

y; 140 280 420 560

Question 3;

The ratio of the dozens of cookies to cups of flour, gives;

Recipe 1; R = 2/1.5 dozen per cup of flour

Which gives;

Approximately 1.33 dozens per cup of flour

Recipe 2, R = 3/3 dozens per cup of flour

Which gives;

Recipe 3, R = 4/4.5 dozens per cup of flour

Therefore;

No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent

Question 4

The ratio of the terms are;

18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3

Therefore;

No it is not proportional because 18.26/36.5 is not equal 21.1/63.3

Question 5

Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;

Yes, it is a proportional relationship because, it is a line that intersects with the origin

Question 6

The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned

Question 7

The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75

Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75

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Answer:

The relationship between the input and output variables in the given table of values are;

Question 1

Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour

Question 2;

x; 1, 2, 3, 4, 5

y; 140, 280, 420, 560

Question 3

No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent

Question 4

No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3

Question 5

Yes, it is a proportional relationship because it is a line that intersects with the origin

Question 6

The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned

Question 7

Yes because the ratio of the miles per hour are all equivalent to 1.75

What is a proportional relationship?

A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.

Question 1

A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant

Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12

Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour

Question 2;

The points on the graph are;

(0, 0), (5, 700), (6, 840), (7, 980)

Therefore;

y = (5/700)•x = (1/140)•x

The table is therefore;

x; 1, 2, 3, 4

y; 140 280 420 560

Question 3;

The ratio of the dozens of cookies to cups of flour, gives;

Recipe 1; R = 2/1.5 dozen per cup of flour

Which gives;

Approximately 1.33 dozens per cup of flour

Recipe 2, R = 3/3 dozens per cup of flour

Which gives;

Recipe 3, R = 4/4.5 dozens per cup of flour

Therefore;

No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent

Question 4

The ratio of the terms are;

18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3

Therefore;

No it is not proportional because 18.26/36.5 is not equal 21.1/63.3

Question 5

Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;

Yes, it is a proportional relationship because, it is a line that intersects with the origin

Question 6

The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned

Question 7

The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75

Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75

Step-by-step explanation:

Answer:

Yes, the side lengths

Explanation:

To be able to determine if the given side lengths of the triangle will form a right triangle, we'll have to apply the Pythagorean Theorem which states, in a right-angled triangle, the square of the hypotenuse(the longest side) must be equal to the sum of squares of the other two sides.

So let's go ahead and confirm;

Since the Pythagorean theorem is obeyed as we can see above, then the side lengths will form a right triangle.

It depicts horizontal linear equation, as the slope is 0.

The slope of horizontal lines is zero. Consequently, m = 0 in the slope-intercept equation y = mx + b. Y = b, where b is the y-coordinate of the y-intercept, results in the equation.

The y-coordinate of every point on a horizontal line is the same. The line's equation is y=b if two points share the same y coordinate, b. The point (0,b) is the y-intercept of the horizontal line y=b. Horizontal lines don't have an x -intercept other than the line y=0.

A horizontal line is a line that is perpendicular to the x-axis. Because the value of x never changes, the graph of a relation of the form x = 5 is a line parallel to the y-axis.

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The function for profit given the conditions for  revenue and expense is P = $20a - $1,600.

The first claim is incorrect because profit is $400

The first claim is incorrect because profit is $4,400.

Profit is revenue less total cost. Total cost consists of fixed cost and variable cost. Fixed cost is the cost that does not change with the level of output. Variable cost is the cost that changes with output. It increases as the level of output increases. Revenue is output multiplied by price per unit.

Profit = revenue - total cost cost

Profit = (price x output) - fixed cost - variable cost

P = ($45 x a)  - $1,600 - ($25 x a)

P = $45a - $1,600 - $25a

P = $20a - $1,600

Where:

P = profit

a = output

Profit when 100 units is sold:

P = (20 x 100) - $1,600

$2,000 - $1,600 = $400

Profit when 300 units are sold

P = (300 x 20) - $1600

$6,000 - $1,600 = $4,400

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-1000 represents Jenny's change in elevation.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.

Given Data

Jenny ended a hike at an elevation of 3, 000 feet above sea level.

She had started at an elevation of 2, 000 feet above sea level.

Hike remaining = 3000 - 2000

Hike remaining = 1000

-1000 represents Jenny's change in elevation.

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The attached figure shows the location of P' and R' in the figure, after the dilation

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The figure that completes the question is added as an attachment

From the figure, we have the following parameters

The image of dilation using the above parameters is the scaled factor of the given figure

As a general rule, the following are the properties of a scaled copy of another figure

The above means that

New lengths = Old lengths * Scale factor

So, we have

P'R' = PR * Scale factor

C'R' = CR * Scale factor

This gives

P'R' = 5 * 3

P'R' = 15

C'R' = 2.6 * 3

C'R' = 7.8

Using the above as a guide, the location of P' and R' are identifies in the figure

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For the given functions, we have that:

a) The numeric value of the division function at x = 4 is of (h/g)(4) = 81/21 = 3.86.

b) The value that is not in the domain of the division function is of x = -1.25.

In this problem, the functions that we are given are defined as follows:

To find the quotient function of h(x) and g(x), we just divide the function h(x) by the function g(x), that is:

h(x)/g(x) = [(x + 5)(x + 5)]/(4x + 5).

At x = 4, the numeric value is found replacing each instante of x by 4, hence:

(h/g)(4) = [(4 + 5)(4 + 5)]/(4(4) + 5)) = 81/21 = 3.86.

The denominator of a fraction cannot be zero, as division by zero does not exist, hence the value of x that is not on the domain of the division function is found as follows:

4x + 5 = 0.

4x = -5.

x = -5/4

x = -1.25.

The complete problem is given by the image at the end of the answer. There are lots of instances of this problem, just with different functions, so we use the functions given in this problem and not on the image.

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The equation of the lines are:

5. y - 5 = -3(x - 1)

6. y - 3 = 2(x + 4)

7. y - 6 = -4/3(x - 1)

8. y - 8 = -12/9(x + 2)

9. y = -5x + 1

10. y + 1 = -2(x - 2)

11. y - 1 = 2/3(x - 3)

For any given line, the equation that represents the line can be written as:

5. Substitute m = -3, and (a, b) = (1, 5) into y - b = m(x - a):

y - 5 = -3(x - 1) [equation in point-slope form]

6. Substitute m = 2, and (a, b) = (-4, 3) into y - b = m(x - a):

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

y - 3 = 2(x + 4) [equation in point-slope form]

7. Given the points, (4, 2) and (1, 6)

Find the slope (m):

Slope (m) = change in y/change in x = (6 - 2)/(1 - 4)

Slope (m) = -4/3

Substitute m = -4/3, and (a, b) = (1, 6) into y - b = m(x - a):

y - 6 = -4/3(x - 1) [equation in point-slope form]

8. Given the points, (-2, 8) and (7, -4)

Find the slope (m):

Slope (m) = change in y/change in x = (-4 - 8)/(7 -(-2))

Slope (m) = -12/9

Substitute m = -12/9, and (a, b) = (-2, 8) into y - b = m(x - a):

y - 8 = -12/9(x - (-2))

y - 8 = -12/9(x + 2) [equation in point-slope form]

9. y - 6 = -5(x + 1)

y - 6 = -5x - 5

y - 6 + 6 = -5x - 5 + 6 [addition property of equality]

y = -5x + 1 [equation in slope-intercept form]

10. Find the slope (m):

Slope of the line (m) = rise/run = -2/1

Slope (m) = -2

Substitute m = -2, and (a, b) = (2, -1) into y - b = m(x - a):

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

y + 1 = -2(x - 2) [equation in point-slope form]

11. Find the slope (m):

Slope of the line (m) = rise/run = 2/3

Slope (m) = 2/3

Substitute m = 2/3, and (a, b) = (3, 1) into y - b = m(x - a):

y - 1 = 2/3(x - 3) [equation in point-slope form]

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The initial value is the initial profits of the company, so:

Answer a: $25,000

The decay factor is the percentage in what the profits have been decreasing, so:

Answer b: 6% or 0.06

Finally, the profits every year can be calculated as:

Answer c: $15,239

Answer:

378.3 [tex]cm^{2}[/tex]

Step-by-step explanation:

a =[tex]\pi[/tex][tex]r^{2}[/tex] for a whole circle, but we only want the area for part of a circle

a = [tex]\frac{150}{360}[/tex] [tex]\pi[/tex][tex]17^{2}[/tex]

a = 378.3 [tex]cm^{2}[/tex] rounded to the nearest tenths place

Answer:

Hhhhhhhhhhhhhhhhhh : x=-2