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3 years ago

Use absolute value to express the distance between 8 and -5

Mathematics

1 answer:

tankabanditka [31]3 years ago

6 0

Answer:

The distance between points 8 and -5 is 13

Step-by-step explanation:

We need to find distance between points 8 and -5

The formula used to find the distance is: $Distance=|b-a|$

Absolute value is used to get only positive values. i.e |-1|=1 if required.

We are given: b=8 and a=-5

Putting values and finding distance

$Distance=|b-a|\\Distance=|8-(-5)|\\Distance=|8+5|\\Dstance=|13|\\Distance=13$

So, the distance between points 8 and -5 is 13

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Can someone please help!!!

RideAnS [48]

Answers:

System 1: x = 3 and y = -5
System 2: x = 1 and y = 2

==========================================================

Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

The x terms subtract to 7x-x = 6x
The y terms subtract to 0 and go away
The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

----------------------------

Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

$\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}$

Now we have the same situation as before: Subtract straight down, solve for x.

The x terms subtract to 7x-(-2x) = 7x+2x = 9x
The y terms go away when subtracting
The right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2

6 0

2 years ago

One of the solutions of the system of equations shown in the graph has an x-value of –4. What is its corresponding integer y-val

jeka57 [31]

The solution is (-4, -1

7 0

3 years ago

Read 2 more answers

If the equation of the line is y=1/2x-3, find the x-coordinate of the Lundy whose y coordinate is 5.

Anna71 [15]

Y=1/2x -3 find the x coordinate of the point whose y

coordinate is 5

y = 5. Write the equation as:

1/2F2x - 3 = 5

multiply both sides by 2, and you have

x - 6 = 10

x = 10 + 6

x - 16

Check solution in original equation, replace x with 16

y = 1/2F2(16) - 3

y = 8 - 3

y = 5

5 0

3 years ago

A fair coin is continually flipped until heads appears for the 10th time. Let X denote the number of tails that occur. Compute t

Ierofanga [76]

Answer:

The probability mass function is expressed as:

P(x) = [(x+r-1)C(r-1)]*[p^r]*[(1-p)^x]

Step-by-step explanation:

This is not a binomial distribution. It is actually a negative binomial distribution. The probability mass function is expressed below:

P(x) = [(x+r-1)C(r-1)]*[p^r]*[(1-p)^x]

where:

x = number of failures

r-1 = number of successes (10 in this scenario)

p = probability of a success

nCr = n!/[r!(n-r)!]

The main formula difference in the positive binomial versus negative binomial is this: With respect to the negative binomial, it is obviously known that the last event will be: when we reach our 10th "head", we stop .

Thus, the last flip will ALWAYS be a "head".

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3 years ago

4z = 2(z + 4)<br> Please help me solve this

mezya [45]

$4z = 2(z + 4)\\
4z=2z+8\\
2z=8\\
z=4$

6 0

3 years ago