A horizontal line includes the points (0,-5) and (2,-5). Find the slope of the line

Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

Sum of the interior angles of a rectangular polygon of 18 sides​ IS 2880°

Given,

Rectangular polygon of 18 sides.

The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180.

Then,

S=(n-2)*180°

n = Number of sides

So,

S=(18-2)(180°)

S=16(180°)

S=2880°

A polygon with 18 sides has an interior angle sum of 2880 degrees.

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Answer:

Divisors of 78 1,2,3,6,13,26,39,78

Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

x = ~2.17 (rounded)

Step-by-step explanation:

First, combine like terms (terms with the same amount of the same variable):

5x + 1 + 18x + 11 = 62

(5x + 18x) + (1 + 11) = 62

(23x) + (12) = 62

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, &  =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 12 from both sides:

23x + 12 (-12) = 62 (-12)

23x = 62 - 12

23x = 50

Divide 23 from both sides to isolate the variable, x:

(23x)/23 = (50)/23

x = 50/23 = 2 4/23 = ~2.17 (rounded to the nearest hundredths).

Answer:

x= -2.17 (rounded to nearest hundredth)

Step-by-step explanation:

5x + 1 + 18x + 11 = 62

     -1            -11      -12

subtract 1 and 11 from both sides which leaves you with:

5x + 18x = 50

add 5x and 18x and you get:

23x = 50

now divide both sides by 23 and get:

x=-2.17

The rectangular coordinates will be (2.999, -0.1239)

The Cartesian Coordinate system is not sufficient to locate points in a plane , therefore some other systems like polar coordinates , spherical coordinates , cylindrical coordinate systems are used.

Polar coordinates are given in the question and we need to determine rectangular coordinates for the same.

The equations used to convert from polar coordinates to rectangular coordinates.

x=rcosθ

y=rsinθ

z=z

For the polar coordinates

(3-√2.37)

r = 3

\(\rm \theta \\\) = -√2.37

x = 3cos (-√2.37)

x = 3 *0.999

x =2.999

y = 3 sin.(-√2.37)

y = 3*(-0.0413)

y = -0.1239

Therefore the rectangular coordinates will be (2.999, -0.1239)

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Answer:

  Adult market

  Junior market

  Total profit: 13000

  Total consumer surplus: 14600

Step-by-step explanation:

Given Adult (a) and Junior (j) demand equations Pa = 200 -Qa and Pj = 160 -Qj, and cost equation C = 20Q, you want to find the price in each market that maximizes profit, the sales in each market, and the consumer surplus, and a graph of profit-maximizing sales and prices.

Each demand equation is of the form P = Pmax -Q, where P is the price that will result in sales of Q tickets. The revenue (R) in each case is the product of numbers of tickets sold (Q) and the price at which they are sold (P).

  R = QP = Q(Pmax -Q)

The profit is the difference between revenue and cost.

  Profit = R - C = Q(Pmax -Q) -20Q

  Profit = Q(Pmax -20 -Q)

Writing the demand equation in terms of P, we find ...

   Q = Pmax -P

Substituting this into the Profit equation gives ...

  Profit = (Pmax -P)(Pmax -20 -(Pmax -P))

  Profit = (Pmax -P)(P -20)

The profit function describes a downward-opening parabolic curve with zeros at P=Pmax and P=20. The maximum profit is on the line of symmetry of this curve, halfway between these values of P:

  Price for maximum profit = (Pmax +20)/2 = Pmax/2 +10

In the adult market, Pmax = 200, so the profit-maximizing ticket price is ...

  Pa = 200/2 +10 = 110 . . . . price for maximum profit in Adult market

In the Junior market, Pmax = 160, so the profit-maximizing ticket price is ...

  Pj = 160/2 +10 = 90 . . . . price for maximum profit in Junior market

Using the revenue equation, we find the sales in each market to be ...

  Qa = 200 -Pa = 200 -110 = 90

  Ra = Qa·Pa = 90(110) = 9900 . . . . sales in Adult market

  Qj = 160 -Pj = 160 -90 = 70

  Rj = Qj·Pj = 70(90) = 6300 . . . . sales in Junior market

The profit in each market is ...

  Adult market profit = 90(110 -20) = 8100

  Junior market profit = 70(90 -20) = 4900

The overall profit will be the sum of the profits in each market:

  Overall profit = 8100 +4900 = 13000

The consumer surplus in each market is the area below the demand curve and above the price point. It is half the product of the maximum price and the quantity actually sold.

  CSa = (1/2)(200)Qa = 100(90) = 9000

  CSj = (1/2)(160)(Qj) = 80(70) = 5600

The total consumer surplus is ...

  CS = CSa +CSj = 9000 +5600 = 14,600 . . . . total consumer surplus

The first attachment shows the sales (output) in each market (red=Adult, purple=Junior) as a function of ticket price. It also shows the corresponding profit (orange=Adult, blue=Junior). The profit-maximizing price point is marked on each curve. You will note that it is different from the output-maximizing price point.

The second attachment illustrates the consumer surplus in each market. That graph has price on the vertical axis, and quantity on the horizontal axis. The colors correspond to the colors on the graph in the first attachment.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The horizontal shift is to the right.

The exact period is 8/7.

In a trigonometric function, written of the form

y = A csc (Bx - C)

the parameters are interpreted as follows

A is the amplitude

B is period / 2π

C is the horizontal shift

comparing with the equation y = 2 csc (7π/4x - 21π/2). we have that

horizontal shift = -21π/2 since it is positive it is to the right

The exact period is

Period = 2π / (7π/4)

= 8/7

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Answer:

If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).

To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.

The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.

For the matrix

2 1 -1

3 2 -3

3 1 -2

the characteristic equation is

(2 - λ)(3 - λ) - 3 = 0

which gives us λ = 1 and λ = 3 as the eigen values.

The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.

For λ = 1, the eigen vector is (1, -1, 1).

For λ = 3, the eigen vector is (-1, 2, 1).

If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.

Answer:

25, 20

Step-by-step explanation:

35-15

       =25

35-15

       =20

If Logan decided to buy 5 drinks, so the possible value the number of tacos that he could buy is $20 and the number of tacos that could be purchased is 10 units by the help of equation.

An equation in algebra is a mathematical statement demonstrating algebra, an equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

In the given instance, Logan and his children went into a restaurant and where they sell drinks for $3 each and tacos for $2 each. The number of Drinks denoted by x and number of tacos denoted by y.

The price of each drink is $3 and tacos is $2 respectively and the total amount that Logan can spend is $35. Since following equation can be made:

3x + 2y = 35

If value of x = 5

then the value of y,

3 × x + 2y = 35

15 + 2y = 35

y = 20 ÷ 2

y = 10

If value of y = 5

then the value of x,

3x + 2 (5) = 35

3x + 10 = 35

3x = 25

x = 8.33 (Approx.)

Therefore the value of tacos that could be acquired by logos are $20 and $25 respectively with the help of solving equation.

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Answer:

There will be 42 trees in each row.

Step-by-step explanation:

672 divided by 4 = 168 rows

168 rows divded by 4 = 42 trees in each row

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Solid will this lesson focus on the regular square pyramid

Regular square pyramid.

The justification is stated below:

Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.

By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.

Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).

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Answer:

86.53

Step-by-step explanation:

Area of Triangle Formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Step 1: Draw altitude and label numbers

If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:

3² + b² = 29²

b² = 29² - 3²

b = √832 = h

Step 2: Plug in known variables into area formula:

A = 1/2(√832)(6)

A = 3√832

A = 86.5332

Answer:

\(\widehat{GF}=49\) degrees

Step-by-step explanation:

In the figure attached, EG is the diameter of the circle and a point F is located on the circle.

Measure of \(\widehat{GF}\) = 8.5 inches

Radius HF = 10 inches

Formula to get the length of arc = \(\frac{\theta}{360}\times (2\pi r)\)

8.5 = \(\frac{\theta}{360}(2\pi)(10)\)

θ = \(\frac{360\times 8.5}{20\pi }\)

  = 48.7°

  ≈ 49°

Since central angle = measure of the intercepted arc

Therefore, \(\widehat{GF}=49\) degrees will be the measure of the given arc GF.                                  

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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The inequality x ≤ 3 indicates how many different bicycle outfits she can purchase.

She has $560 to spend at a bike shop on new accessories and clothing for riding.

For $425.05. she spends on a brand-new bicycle.

She spends $15.19 for each of four bicycle reflectors and $15.79 on a pair of cycling gloves.

She intends to use all or part of the remaining funds to purchase new bicycle clothing at $29.20 each.

The disparity that can be used to calculate how many garments she can purchase for her budget is as follows:

let

x = the number of garments

Therefore,

425.05 + 15.19(4) + 15.79 + 29.20x ≤ 560

425.05 + 60.76 + 15.79 + 29.20x ≤ 560

29.20x ≤ 560 - 425.05 - 60.76 - 15.79

29.20x ≤ 58.4

Divide the difference between the two sides by 29.20.

x ≤ 58.4 / 19.20

x ≤ 3.04166666667

x ≤ 3

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Answer:

\(\frac{1}{x} ; x > 2\)

Step-by-step explanation:

A fraction less than one half would have to be one out of a larger number than two.

Basically, let's change the denominator to "x"

\(\frac{1}{x}\) -> for this fraction to be less than 2, x always has to be greater than two

Answer:

5

Step-by-step explanation:

On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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Answer:

90-35=55

x=55

Step-by-step explanation:

Answer:

x = 55

Step-by-step explanation:

x and 35 must = 90 degrees because of the Angle Addition Postulate. So if you subtract 90 and 35, you get x.

Answer: 8.4375 U.S. dollars2

Step-by-step explanation:

Answer:

$8.44

Step-by-step explanation:

From the question it self we know that 1 pound of chicken costs $3.75. In order to solve this question we just need to find out how much 1 pound does fit into 2.25 pounds and then multiple the result by $3.75. We can find that out by dividing 2.25 by 1, and we get 2.25. Then we do the following....

2.25 x $3.75 = $8.4375

We got $8.4375 as an answer but we have to remember that when we are talking about money and we have to round to the nearest cent (which is equal to 1 hundredth of a dollar). So now we just have to round to the nearest hundredth, and we get $8.44 as our answer.

The slope of the costs and choose the most accurate statement are captured in the below option:

D.) Costs are increasing at a rate of $51 per item

What is the slope cost?

The slope of a line is the degree of change in y coordinates(costs) with respect to change in x coordinates(volume of output).

The formula for slope of the costs is as given below:

slope=(new costs-old costs)/(new quantity-old quantity)

new costs=$58,100

old costs=$55,040

new quantity=1000

old quantity=940

slope=($58,100-$55,040)/(1000-940)

slope=$51.00

This implies that for every additional new electronic part, the cost goes up by $51.00

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Answer:

8

Step-by-step explanation:

Answer: the answer is 8

Step-by-step explanation: hope this helps :)