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3 years ago

Describe the graph of the function. y = |x – 4| – 7

Mathematics

1 answer:

Lemur [1.5K]3 years ago

5 0

Answer:

This is always ''interesting'' If you see an absolute value, you always need to deal with when it is zero:

(x-4)=0 ===> x=4,

so that now you have to plot 2 functions!

For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:

|x-4| = -(x-4)=4-x

Then:

for x<=4, y = -x+4-7 = -x-3

for x=>4, (x-4) is positive, so no changes:

y= x-4-7 = x-11,

Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11

In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:

x=4 and x= 3 for y=-x-3

And just x=5 for y=x-11

The reason is that the absolute value is continuous, so x=4 works for both:

x=4===> y=-4-3 = -7

x==4 ====> y = 4-11=-7!

abs() usually have a cusp int he point where it is =0

Step-by-step explanation:

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3 years ago

How many solutions does the equation x_1 +x_2+x_3+x_4+x_5=21 have where x_1, x_2, x_3, x_4, and x_5 are nonnegative integers and

omeli [17]

Step-by-step explanation:

$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 21\\$ (given)

Let us consider :

$x_{1}$ = $t_{1} + 1$

$x_{2}$ = $t_{2}$

$x_{3}$ = $t_{3}$

$x_{4}$ = $t_{4}$

$x_{5}$ = $t_{5}$

Now, by substituting the above considerations in the above equation, we get:

$t_{1} + 1 + t_{2} + t_{3} + t_{4} + t_{5} = 21\\$

$t_{1} + t_{2} + t_{3} + t_{4} + t_{5} = 20\\$

where,

$t_{i}$ $\geq$ 1

then it follows

n = 20

r = 4

then no. of solutions for the eqn = $_{r}^{n + r}\textrm{C}$

= $_{4}^{24}\textrm{C}$

= 10626

Answer :

no. of solutions for the eqn 10626

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3 years ago

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Table C is a function because there is one x-value for every y-value.

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3 years ago

You are given an unfair coin (i.e. a coin where the probability of it landing on either side is NOT 1/21/2) and told that the pr

andrey2020 [161]

Here we have a problem of probability, we will find that the probability of landing in heads is M/N = 1/3, then we have:

M + N = 1 + 3 = 4.

Let's see how we got that:

Let's define:

p = probability of landing on tails

q = probability of landing on heads.

The probability of getting at least one tails in 3 tosses is 26/27

This means that the probability of not getting tails in the 3 tosses is:

P = 1 - 26/27 = 1/27

And the case where you do not get any tails in the 3 tosses, means that in all the 3 tosses you got heads.

The probability of getting 3 heads in a row is:

P = q^3 = 1/27

Solving for q, we get:

q = ∛(1/27) = 1/3

Now we want to express q = M/N = 1/3

then we have:

M = 1

N = 3

Now we want to compute M + N = 1 + 3 = 4

If you want to learn more about probability, you can read:

brainly.com/question/24369877

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