8x - 2y = 4 and x + 4y = -12

The absolute value function is defined as

[tex]|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}[/tex]

If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.

If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.

But if x = 0, the derivative doesn't exist!

In order for the derivative of a function f(x) to exist at x = c, the limit

[tex]\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}[/tex]

must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.

If x approaches 0 from below (so x < 0), we have

[tex]\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1[/tex]

whereas if x approaches 0 from above (so x > 0), we have

[tex]\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1[/tex]

But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.

Putting everything together, you can define the derivative of |x| as

[tex]\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}[/tex]

Answer:

y = –(1/2)x + 7

Step-by-step explanation:

Slope intercept form is y = mx + b

m is the slope

When the slope is the same the lines are parallel

here the slope is –1/2

therefor

y = –(1/2)x + 7 is parallel

Dilation and rotation.

Answer:

0, 1/18, and 1/36

Step-by-step explanation:

For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.

For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.

For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

We have,

The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."

Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.

Let's go through the cases:

i = 2 (only possible sum with two dice):

In this case, both dice must show a 1.

The probability of this happening on a fair 6-sided die is

(1/6) * (1/6) = 1/36.

i = 3: The combinations are (1, 2) and (2, 1).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 4:

The combinations are (1, 3), (2, 2), and (3, 1).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 5:

The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).

The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.

i = 6:

The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 7:

The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.

i = 8:

The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 9:

The combinations are (3, 6), (4, 5), and (5, 4).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 10:

The combinations are (4, 6) and (6, 4).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 11:

The combinations are (5, 6) and (6, 5).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 12:

The combination is (6, 6).

The probability of this happening is (1/6) * (1/6) = 1/36.

Now, sum up the probabilities for each case:

(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)

This simplifies to:

69/36 = 23/12

Thus,

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

Learn more about probability here:

https://brainly.com/question/14099682

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Answer:

y = 2x - (3/2)

standard equation is

y = mx + c

c is the y intercept

m is the gradient/slope

so

2 is the slope (m)

Answer:

Slope = 2

Step-by-step explanation:

Our equation: y = 2x - 3/2

=> Given equation: y = mx + b

Now, let's compare:

=> y = mx + b = y = 2x - 3/2

=> We can tell that the slope is m, which is 2.

Hoped this helped.

Answer:

y=11-2x           x + y =15

4x − y=7 and 2x − y=15 all have one solution

x=12 − 3y             2x + y=7

3x + 9y=24 and -4x=2y + 14 have no solution

you can just put the rest in infinite solutions

Step-by-step explanation:

Answer:

∡3 & ∡6 are same side interior angle.

∡4 & ∡6 are alternate interior angles.

∡2 & ∡8 are vertical angles.

∡1  & ∡5 are corresponding angles (because they are in the same spot).

∡1  & ∡3 are vertical angles (because they are the opposite angle of each other).

∡1 & ∡2 are supplementary angles (because they add up to 180°).

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + y - 1 = 0 ( subtract 3x - 1 from both sides )

y = - 3x + 1 ← in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + c ← is the partial equation

To find c substitute (1, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = - 3x + 7 ← equation of line in form y = mx + c

Answer:sadddddddddddddddddddddddddddddddddddddddddddddddddddd

Step-by-step explanation:

ddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

Answer: The cost of renting a car from Company A be the same as renting a car from company B in 17.5 miles

Step-by-step explanation:

y=2.30x +15

y=1.90x +22

0.4x +7 Divide 0.4 from both sides

x=17.5

y=2.30(17.5)+15

y=40.25+15

y=40.25-15

y=25.25

Answer:

1. Markup: $2.70, Retail: $20.70

2. Markup: $9.45, Retail: $31.95

3. Markup: $25.31, Retail: $59.00

4. Markup: $24.75, Retail: $99.74

5. Markup: $48.60, Retail: $97.20

6. Markup: $231.25, Retail: $416.25

Step-by-step explanation:

To get the markup price of an item, multiply it by the markup percentage as a decimal. To get the decimal of a percentage, divide the number by 100. For example, 15% would be 0.15. And then to find how much the item has been marked up by, multiply the current price by the decimal.

$18 * 0.15 = $2.70

So $2.70 is the markup. To find the retail price, you need to add the markup price to the current price given.

$18 + $2.70 = $20.70

So your retail price is $20.70. Repeat these steps for each question to get the answers above.

Hope this helps.

- BRAINLIEST ANSWERER

Answer:

Refer to the attachment

<ABC = [ 52° ]

not sure but

hope it helps!

Answer:

[tex] \: [/tex]

∆ ABC → 132 °

Step-by-step explanation:

Given : ∠DBC = 48°

Now we are going to use the property that the sum of angles of a linear pair always equal to 180∘

Therefore,

∠ABC + ∠DBC = 180°

∠ABC + 48 ° = 180° [ ∠DBC = 48° ]

∠ABC = 180° - 48°

∠ABC = 132°

Answer:

795$

Step-by-step explanation:

750 x 0.06 = 45

750 + 45 = 795

Answer:

3

Step-by-step explanation:

(8 + 4) / 2 - 3

12 / 2 -3

6 - 3

3

Answer:

3

Step-by-step explanation:

You do the parenthesis first (8+4)

Then you divide 12 by 2 if you are following Pemdas

6 - 3 = 3

Hope this helped!

Answer:

16.25, 20, 13.75, 12.5, 7.5

Step-by-step explanation:

1cm= 2.5m

6.5x2.5= 16.25

8x2.5= 20

5.5x2.5= 13.75

5x2.5= 12.5

3x2.5= 7.5

Let y = cos⁻¹(x), so that cos(y) = x.

For some angle y between 0 and π, cos(y) takes on some value between -1 and 1.

For the y in this range, we have cos(y) = -1/2 exactly when y = 2π/3.

Then

tan(cos⁻¹(-1/2)) = tan(2π/3) = sin(2π/3)/cos(2π/3) = (√3/2)/(-1/2) = -√3

Answer:

Well 5 times 1 is 2.5 which can't be and integer

so I looked it up an this is what I got How do you write 2.5 as an integer?

If this is the question, then Integer-Part[2.5] = 2, and the Fractional-Part[2.5] = . 5.

I would put 3 it because 2.5 as a hole number is 3

Step-by-step explanation:

Step-by-step explanation:

I assume "fair game" means that there is no profit and the expenses are equal to the income or sales.

we have clear expenses :

1× $100

3× $20

that is in total : $160

now we need to make sure that we generate exactly $160 by selling the tickets.

we have 100 tickets that should lead to $160.

how much should 1 ticket cost ?

well, 160/100 = $1.60

Answer:

B is the answer.

x = 1

y = 2

Step-by-step explanation:

In B, Multiply the second equation by 2

8y - 2x = 14                

Now add the first and the equation above.

8y - 2x = 14

3y +2X = 8

11y = 22        

Divide by 11

11y/11 = 22/11

y = 2

Use the given equation #2

4y - x = 7

4*2 - x = 7

-x = 7 - 8

-x = - 1               Multiply by - 1

-1*x = -1*-1

x = 1

Answer:

b. y=1/2x-2

Step-by-step explanation:

We can determine b by looking at the y intercept, which, in this case is (0,-2). Now we know that b is -2. To find the slope, we need to look a rise over run which is 1/2 here (1 up, 2 right). So, our final answer is y=1/2x-2

Answer:

A rectangle have 2 equal sides whilst the other 2 is also equal

So we can make length “l”

Whilst we can make width “w”

So the formula for a perimter is

2l+2w=p

In this case it’s 70

Now the length is 3 in longer then the width.

So l= 3+w

We can subsitute that in so we can solve the equation now

2(3+w) + 2w = 70

4w+6=70

Now solve

4w+6=70

4w= 64

w= 16

So width is 16

Lenght is 3 more then with so 16+3=19

Width is 16

Length is 19