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3 years ago

Describe the domain and range for

Mathematics

2 answers:

swat323 years ago

7 0

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain
Domain: [-4,∞),{x | x ≥ -4}
Range: [0,∞),{y | y ≥ 0}

larisa86 [58]3 years ago

6 0

Square root functions domain have to be set greater than or equal to zero, so we can set x+4 greater than or equal to zero.
$x + 4 \geqslant 0 \\ x \geqslant - 4 \\ \\$
[-4, + infinity)

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PLEASE HELP ASAP

Crank

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts $(-2,0)$ and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points $(-2,0)$ , $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$ , we get,

$4a -2b+c=0$ -----------(1)

$16a +4b+c=0$ ----------(2)

$a-b+c=10$ -----------(3)

Subtracting (1) and (2), we get,

$\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \ \ -12a-6b=0$ -----------(4)

Subtracting (2) and (3), we get,

$16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10$ ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

$-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2$

Thus, the value of a is $a=-2$

Substituting $a=-2$ in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is $b=4$

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is $c=16$

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$ , we get,

$y=-2x^{2} +4x+16$

Taking out the common term as -2 we get,

$y=-2(x^{2} -2x-8)$

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

7 0

3 years ago

I don’t get 15a. The t^5 is confusing me

kondor19780726 [428]

15a is non-exponential because the variable is not in the exponent

Instead, this is a polynomial function. It can also be called a power function as power functions are in the form a*x^b where 'a' and 'b' are fixed numbers.

3 0

3 years ago

Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device.

alex41 [277]

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

6 0

3 years ago

What temperature is 15 degrees lower than 7degrees

BabaBlast [244]

15 degrees lower than 7 degrees means that we have to subtract.

So we have 7 degrees and it wants 15 degrees lower, so we would do 7 - 15

And so 7-15 = -8

So 15 degrees lower than 7 degrees would be -8 degrees. :)

8 0

3 years ago

Read 2 more answers

WILL GIVE EXTRA POINTS<br>Assignment name: Segment Addition

rjkz [21]

Answer:

the measure of AB equals the measure of BC

2x+1=3x-4

4+1=3x-2x

5=x

BC=3x-4=3*5-4=15-4=11

AB=2x+1=2*5+1=10+1=11

AC=AB+BC=11+11=22

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers