Two lines are perpendicular. if one line has a slope of 0, what is the slope of the other line?

Answer:

C. (4, 3, 2)

Step-by-step explanation:

Given : [tex]3x+2y+z=20[/tex]

            [tex]x-4y-z=-10[/tex]

            [tex]2x+y+2z=15[/tex]

To Find: Solution:

[tex]3x+2y+z=20[/tex]   -1

[tex]x-4y-z=-10[/tex]      --2

[tex]2x+y+2z=15[/tex]   --3

Substitute the value of z from 1 in 2 and 3

So in 2 , [tex]x-4y-(20-3x-2y)=-10[/tex]  

[tex]x-4y-20+3x+2y=-10[/tex]  

[tex]4x-2y=-10+20[/tex]  

[tex]4x-2y=10[/tex]  ---4

So, in 3 ,  [tex]2x+y+2(20-3x-2y)=15[/tex]

[tex]2x+y+40-6x-4y=15[/tex]

[tex]-4x-3y=15-40[/tex]

[tex]-4x-3y=-25[/tex]   -5

Now solve 4 and 5

Substitute the value of x from 4 in 5

[tex]-4(\frac{10+2y}{4})-3y=-25[/tex]

[tex]-1(10+2y)-3y=-25[/tex]

[tex]-10-2y-3y=-25[/tex]

[tex]-10-5y=-25[/tex]

[tex]-5y=-15[/tex]

[tex]y=3[/tex]

Now substitute the value of y in 4

[tex]4x-2(3)=10[/tex]

[tex]4x-6=10[/tex]

[tex]4x=10+6[/tex]

[tex]4x=16[/tex]

[tex]x=4[/tex]

Now substitute the value of x and y in 1 to get value of z

[tex]3(4)+2(3)+z=20[/tex]

[tex]12+6+z=20[/tex]

[tex]18+z=20[/tex]

[tex]z=20-18[/tex]

[tex]z=2[/tex]

Thus The solution is (4,3,2)

Hence Option c is correct.

Answer:

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

The variable X represents the quantity.

Step-by-step explanation:

We are given that

The demand function for an auto parts manufacturing company is fiven by

f(x)=100000-25 x

Where x=Represents  price

f(x)= Represents quantity

We have to find inverse function [tex]f^{-1}(X)[/tex]

Let f(x)=X

[tex]X=100000-2500 x[/tex]

[tex]2500x=100000-X[/tex]

[tex]x=\frac{100000-X}{2500}[/tex]

Substituting the value of x then we get

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

Therefore, the inverse function

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

Where X= Represents the quantity

[tex]f^{-1}(X)[/tex]=Represents price

BE is [tex]7.73[/tex]

What is Square?

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

What is equilateral triangle?

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.

We have to find BE.

Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]

The angle EAB is [tex]90+60 = 150[/tex]°

Using the law of the cosines, we get

[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]

        [tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]

⇒[tex]BE=7.73[/tex]

Hence, we can conclude that BE is [tex]7.73[/tex]

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Answer:

Each share worth is $42.0672 .

Step-by-step explanation:

As given

You invest $3,756.00 and buy 100 shares of a company's stock.

Their value increases by 12%.

12% is written in the decimal form

[tex]= \frac{12}{100}[/tex]

= 0.12

Share value increase = 0.12 × Investment cost

                                   = 0.12 × 3756

                                   = $450.72

Total value of shares becomes after increases of 12% = Share value increase +  Investment cost .

Total value of shares becomes after increases of 12% = $3756+ $450.72

                                                                                          = $4206.72

[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]

[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]

Each shares worth = $42.0672

Therefore the each share worth is $42.0672 .

Answer:

Answer: 20°

Step-by-step explanation:

The area of a rectangle can be directly calculated using the formula:

A = l * w

Where l is the length or the depth while w is the width

Therefore,

A = 50 feet * 100 feet

A = 5000 square feet

Answer:

-4x+2y+-6 and y=3x-2

A +B = 181

A=181-B

4.70A+5.90B= 967.10

4.70(181-B) +5.90B =967.10

850.70-4.70B+5.90B=967.10

850.70+1.2B =967.10

1.2B=116.40

B =116.40/1.2 = 97

A=181-97 = 84 pounds of type A coffee

The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.

The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.

Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.

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For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.

In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the

perimeter

of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.

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need 2 numbers when added = 5 and when multiplied = -24

answer is D

-3+8 = 5

-3*8 = -24

Final answer:

Approximately $17.86 is spent on gas each day.

Explanation:

To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.

First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.

Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86

Therefore, approximately $17.86 is spent on gas each day.

Answer:

Step-by-step explanation:

Answer:

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.

Step-by-step explanation:

The average rate of a function f(x) on the interval [a,b] is defined as

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

The average rate of change from x = 2 to x = 3 is

[tex]m=\frac{f(3)-f(2)}{3-2}[/tex]             .... (1)

From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.

Put  f(2)=-3 and f(3)=-1 in equation (1).

[tex]m=\frac{-1-(-3)}{3-2}[/tex]

[tex]m=\frac{-1+3}{1}[/tex]

[tex]m=\frac{2}{1}[/tex]

[tex]m=2[/tex]

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.