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3 years ago

15

Can you help me with the bottom three please?

1 answer:

nika2105 [10]3 years ago

6 0

Answer:

6= 66.67%

7=25%

8=70%

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Graph the following piecewise function on a separate piece of graph paper and upload your graph below.

Alecsey [184]

ANSWER

To graph the function

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

follow the steps below.

1. Find y- intercept by plugging in $x=0$ .

$x=0$ is on the interval, $-4\leq x$ , so we substitute in to

$f(x)=x+4$

$\Rightarrow f(0)=0+4$

$\Rightarrow f(0)=4$

Hence the y-intercept is $(0,4)$

2. Find x-intercept by setting $f(x)=0$

This implies that

$x+4=0,$ on $-4\leq x$

or

$2x-1=0$ on $3\leq x$

We now solve for $x$ on each interval,

$x=-4,$ on $-4\leq x$

or

$x=\frac{1}{2}$ on $3\leq x$

But observe that

$x=\frac{1}{2}$ does not belong to $3\leq x$

This means it can never be an intercept for this piece-wise function.

Hence our x-intercept is $(-4,0)$

3. Plotting the boundaries of the interval.

For $f(x)=x+4$ on $-4\leq x$

$f(-4)=-4+4$

$\Rightarrow f(-4)=0$ .

This point $(-4,0)$ coincides with the x-intercept.

$f(3)=3+4$

$f(3)=7$

So we have the point $(3,7)$ . But note that $x=3$ does not belong to this interval so we plot this point as a hole.

For $f(x)=2x-1$ on $3\leq x$

$f(3)=2(3)-1$

$\Rightarrow f(3)=5$

So we plot $(3,5)$

$f(6)=2(6)-1$

$\Rightarrow f(6)=11$

So we plot $(6,11)$ also as a hole.

Plotting all these points we can now graph the function,

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

See attachment for graph.

7 0

3 years ago

Read 2 more answers

A pond is freshly stocked with 6 brown trout and 18 lake trout. The first fisherman in the area catches and releases a trout. He

Andreas93 [3]

Number of brown trout = 6

Number of lake trout = 18

Total number of trouts = $6+18=24$

Probability to catch a lake trout first time = $\frac{18}{24}$

As the fisherman let the trout go, so probability for the second time is =

$\frac{18}{24}$

Hence, the probability becomes=

$\frac{18}{24}\times\frac{18}{24}=\frac{324}{576}$

= $\frac{9}{16}$

The probability to find the brown trout is $\frac{1}{16}$

as , $\frac{6}{24}\times\frac{6}{24}=\frac{36}{576}$

= $\frac{6}{96}=\frac{1}{16}$

8 0

3 years ago

Read 2 more answers

-3/4 + 7/2 help me l

yawa3891 [41]

11 over 4

(Decimal: 2.75)

4 0

3 years ago

The product of the page numbers on two facing pages of a book is 156. Find the page numbers

Gnoma [55]

Let x be the page number then x+1 would be the other page number (because the pages are two facing pages which means they follow on consecutively)

Then

(x)(x+1) = 156

x^2 + x - 156 = 0

x = 12 or x = -13( but x can't be a negative number)

so x = 12

and the next page is 13

3 0

3 years ago

Determining a Number of Solutions

MatroZZZ [7]

Answer:

No Solution

Step-by-step explanation:

<u>For one solution;</u>

it will be consistent and independent ( example, x = 1 and y = 2)

<u>For no solution;</u>

it will be inconsistent and independent ( example, 0 = 2)

<u>For many solution;</u>

it will be consistent and dependent ( example, 1 = 1, 2 = 2, y = y, x = x)

Given;

3x - 2y = 3 -------------- equation (1)

6x - 4y = 1 --------------- equation (2)

6: 18x - 12y = 18 -------------equation (3)

3: 18x - 12y = 3 --------------- equation (4), <em> subtract (4) from (3)</em>

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

0 - 0 = 15

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

0 = 15

The solution is inconsistent and independent, because zero (0) cannot be equal to 15

Thus, the system has no solution

6 0

4 years ago

Read 2 more answers