Find the equation of the lines given the two points.

a) (-8, 3) and (-6, 0)

b) (5, 4.5) and (5, -1)

2. A rental car costs $18 plus a fixed charge per mile driven. The total charge for 180 miles of use was $80. Write an equation for the cost, C (in dollars), in terms of the miles driven, x.

Solve the linear systems.

3. 5x -2y = 7
x = 2y-5

4. 4x + v=5
v = 2x - 10

The quadratic equation y2 + 7y - 2 = 0 can be solved using the quadratic formula, which states that the solutions for x in the equation ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

We can apply the quadratic formula to this equation by letting a = 1, b = 7, and c = -2:

y = (-7 ± √(7^2 - 4 * 1 * -2)) / 2 * 1

y = (-7 ± √(49 + 8)) / 2

y = (-7 ± √57) / 2

So the solutions to the equation y2 + 7y - 2 = 0 are:

y = (-7 + √57) / 2

y = (-7 - √57) / 2

The solutions to the equation are y = (-7 + √57) / 2 and y = (-7 - √57) / 2.

Answer:

sampling distribution

Step-by-step explanation:

:)

X = -3 and its substitution into the first equation results in 3y = 9, which can be written as y = 3. As a result, the system of equations' solution's y-coordinate is 6.

Equation is a mathematical and physical statement that describes physical phenomena and the relationship between various physical quantities.

It usually consists of a simple variable that presents the physical quantity, followed by a personal variable that may be a personal variable that is focused on the energy.

The system of equations has a solution, and its y-coordinate is 6. This is obtained by solving for x and then putting the specified y-value (2/3) into the equation -x+3y=9. In particular, -x+3(2/3) = 9 becomes -x = 3 when -x+3(2/3) = 9.

Therefore, The system of equations has a solution, and its y-coordinate is 6.

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The height that a ladder reaches is determined by the length of the ladder and its distance from the base of the building.

The ladder can be thought of as the hypotenuse of a right triangle, with the height that the ladder reaches up the building being one of the other sides and the distance of the ladder from the building being the other side.

So, the formula for the height that a ladder reaches can be expressed as:

Height =

Where "Ladder Length" is the length of the ladder, and "Distance from Base" is the distance of the ladder from the building.

Using this formula, we can calculate the height that the 14-foot ladder reaches when set up 4 feet from the base of the building:

Height = ([tex]14^2 - 4^2)^0.5[/tex]

= [tex](196 - 16)^0.5[/tex]

= [tex]180^0.5[/tex]

= 13.416407864

Rounding to the nearest tenth of a foot, the height the ladder reaches is 13.4 feet.

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The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

What is a function?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.

To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:

g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0

Therefore, the g-intercept of the function g(n) is 0.

To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.

We can factor out a common factor of 2n² to simplify the equation:

2n²(n² + 10n + 21) = 0

This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

Hence,

The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

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The label covers approximately 4,800 square centimetres of the wheel of cheese.

What is the lateral surface area of a cylinder?

The lateral surface area of a cylinder can be found using the formula:

L = 2πrh

where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.

In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:

L = 2 x (22/7) x 30 x 20

L = 4,800 square centimetres

This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.

The area of a circle can be found using the formula:

A = πr²

where A is the area of the circle, and r is the radius of the circle.

In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:

2 x (22/7) x 30²

= 56,400/7 square centimeters

Subtracting this from the total surface area, we get:

4,800 - 56,400/7

= 33,600/7 square centimeters

= 4,800 square centimeters (rounded to the nearest whole number)

Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.

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The population in the year 2040 is 31800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 4 is an equation.

We have,

The exponential equation is y = m[tex]a^t[/tex].

Where t is a variable

Now,

In 2007 (t = 0). the population was 12,000.

y = 12000

This means,
12000 = m[tex]a^0[/tex]

12000 = m

And,

In 2019 (t = 12). the population was 23,000.

y = 23000

23000 = m[tex]a^{23}[/tex]

23000 = 12000 [tex]a^{23}[/tex]

23000/12000 = [tex]a^{23}[/tex]

1.92 = [tex]a^{23}[/tex]

[tex]1.036^{23}[/tex] = [tex]a^{23}[/tex]

a = 1.03

Now,

y = 12000 [tex]1.03^t[/tex]

The population in the year 2040.

i.e

t = 33

y = 12000 x [tex]1.03^{33}[/tex]

y = 12000 x 2.65

y = 31800

Thus,

31800 is the population in the year 2040.

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The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.

We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.

Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.

In a week there are 20 hours

So, in 4 weeks, there will be 80 hours

Take - home pay before deductions = 80 * $11.66 = $932.8

Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94

This is equal to ¢ 68094.

Hence, the monthly take-home pay is ¢ 68094.

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100%, If 12 of all  12 marbles are blue, its 100%

Answer:

Step-by-step explanation:

here's a step-by-step explanation with more detail:

The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a,

where a = 1, b = 1, and c = 8.

Plugging in the values, we get:

X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1

X = (-1 ± √(-31)) / 2

Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.

X = (-1 ± i * √31) / 2

So, the two solutions to the equation are:

X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2

And these are the two solutions expressed in terms of the imaginary unit i.

Step-by-step explanation:

-1 1/2 = -3/2

1/4 × (x - 2/5) = -3/2

let's multiply both sides by 4 to remove the first fraction on the left side :

x - 2/5 = -12/2

x = -12/2 + 2/5 = -6 + 2/5

-6 = -6 × 5/5 = -30/5

so,

x = -30/5 + 2/5 = -28/5 = -5 3/5 = -5.6

please pick any form you need for your result.

Reciprocal of 0.0002 is:

Reciprocal of c/d:

Reciprocal of 1 2/3 is:

Use identity x² - y² = (x - y)(x + y) to solve the following questions.

Evaluate  173² - 127²:

Evaluate (8.70)²- (8.60)²:

Evaluate 1003²- 9​:

Answer:

D

Step-by-step explanation:

Count total dots => 30

Amount of dots under x>=5 => 21

21/30 = 7/10 = 70%

On solving the provided question we can say that here trigonometry  y = Asin(Bx + C)+D

Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.

(x)=sin(x) consider y = Asin(Bx + C)+D adjusts the amplitude of the function (how high or low it is).

if you want to

B determines how many full wavelengths will occur during a certain time period, and C determines the phase shift (left/right on the axis) (positive values will shift left)

The vertical shift, or D, is up or down. For example, a +3 would move the entire function up 3 units.

In your situation, the amplitude is 4 since you wish to stretch vertically.

Additionally, you want to move it right three units. C = -3 (always the opposite of the direction you wish to go) (always the opposite of the direction you want to go)

g(x) = 4sin(x - 3)

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Answer:

61

Step-by-step explanation:

using the rule to find the fifth term from the fourth term 29

5th term = 2 × 29 + 3 = 58 + 3 = 61

Answer:

20000*4*5/100=4000

Step-by-step explanation:

Hope this helps!

Answer:32768/7

Step-by-step explanation:

double every term

Answer:c

Step-by-step explanation:

Andre borrowed 350,000 from the bank and the bank will charge him 6% interest per month. To calculate the amount he has to pay for one month of interest, we can use the following formula:

Interest = Capital * Interest rate

In this case, the capital is 350,000 and the interest rate is 6%. So, we can plug in the values:

Interest = 350,000 * 0.06

Interest = 21,000

Therefore, Andre has to pay 21,000 for one month of interest.

The integral f(x, y, z) dV E as an iterated integral can be expressed in six different ways, where E is the solid bounded by the given surfaces.

To express the integral as an iterated integral, we need to determine the limits of integration for each variable.

First, we can find the limits of integration for z The plane z = 0 is the xy-plane, and the plane y + 4z = 16 can be rewritten as z = (16 - y)/4. So the limits of integration for z are 0 to (16 - y)/4.

Next, we can find the limits of integration for y  The surface y = x^2 bounds the solid from below in the y direction, and the plane y + 4z = 16 bounds the solid from above in the y direction. So the limits of integration for y are x^2 to 16 - 4z.

Finally, we can find the limits of integration for x There are no explicit surfaces that bound the solid in the x direction, so we can use the limits of integration for y to determine the limits of integration for x.

With these limits of integration, we can express the integral in six different ways over dz dy dx:

∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫x^2^(16 - 4z) ∫0^g(x, y) f(x, y, z) dz dy dx

where g(x, y) = (16 - y)/4

∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^16-4z ∫0^g(x, y) f(x, y, z) dz dx dy

where g(x, y) = (16 - y)/4

∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^g(x, y) ∫0^(16 - 4z) f(x, y, z) dz dy dx

where g(x, y) = 16 - 4z

∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^g(x, y) f(x, y, z) dy dx dz

where g(x, y) = (16 - 4z)

∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫0^(16 - 4z) ∫y^(1/2)^4 f(x, y, z) dy dz dx

∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^(16 - 4z) f(x, y, z) dz dy dx

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The area of the shaded region is given as follows:

As = 324(2π - 1) in².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:

A = π x [tex](18\sqrt{2})²[/tex]

A = 648π in².

The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:

A = 18²

A = 324 in².

Hence the area of the shaded region is given as follows:

As = 648π - 324

As = 324(2π - 1) in².

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Answer:

See below

Step-by-step explanation:

You should just use a graphing calculator or an online graphing site to do this

If you were to do this manually on  a graph sheet, here is how you proceed

Given line is

y = -x - 4

We need to find 2 points to plot a straight line

Choose x = 0 ==> y = - 0 - 4 = -4

So (0, - 4) is one point

Choose another value for x. x = -4 is a good point
At x = - 4, y = -(-4) - 4 = 0

So (-4, 0) is another point.

Plot these two points on the graph and draw a straight line through those points

The attached graph shows this all

Answer:

$2,000

Step-by-step explanation:

Interest = Principal x Rate x Time

840 = .06(7)p

840 = 0.42p

p = 2000

Answer:

The area of the sign is 706.5 cm^2.

Step-by-step explanation:

We know,

The formula of area of a circle,

A = πr^26

Here A is area and r is radius.

Here we have radius is 15 cm, so we can put the values in the above equation and find the area,

A = π * 15^2

A = 3.14 * 225

A = 706.5

The area of the sign is 706.5 cm^2.

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

The average thickness of the metal sheet is 0.0423 inches.

In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.

Mean = (sum of all values) / (number of values)

For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:

Mean = (5 + 7 + 9 + 11 + 13) / 5

Mean = 9

Therefore, the mean of this data set is 9.

The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.

To find the average thickness of the sheet, we need to add the five measurements together and then divide by 5 (the number of measurements):

Average thickness = (0.0401 + 0.0417 + 0.0462 + 0.0407 + 0.0428) / 5

Average thickness = 0.0423 in

Therefore, the average thickness of the metal sheet is 0.0423 inches.

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Using equations, they sold 165 tickets before both accounts had the same amount of money.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The variables that must be included in the equation are also known as the unknowns.

Given that, Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket.

and Erik had $480 in his school account and sold tickets for the fundraiser at a cost of $6 per ticket.

Let they sold x tickets and they have the amount in their account is y.

After sold tickets, Jaelyn accounts had the amount is

y = 150 + 8x

After sold tickets, Erik accounts had the amount is

y = 480 + 6x

the amount in their account is same, so we compare both equation to find x

150 + 8x = 480 + 6x

arranging like terms in same side

8x - 6x = 480 - 150

2x = 330

divide both sides by 2 we get,

x = 330/2

x = 165

So, they sold 165 tickets before both accounts had the same amount of money.

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Answer:

Below

Step-by-step explanation:

From the image below you can see that

90 F  + 60 L   = 160 miles

and given F + L = 2 hours       re arrange to  F = 2 - L  

                                      and substitute this "F" into the first equation

90 (2-L )  + 60 L = 160           Solve for L

180  - 90 L     + 60 L     = 160

180 - 30 L = 160

- 30 L = -20

L = 2/3 hr       then   F = 1  1/3  hr       ( because they add to '2' )