Consider the quadratic equations

2 answers:

6 0

Consider the two functions as
<span>y1(x) =3x^2 - 5x,
y2(x) = 2x^2 - x - c

The higher the value of c, father apart the two equations will be.
They will touch when the difference, i.e. y1(x)-y2(x)=x^2-4*x+c has a discriminant of 0.
This happens when D=((-4)^2-4c)=0, or when c=4.
(a)
So when c=4, the two equations will barely touch, giving a single solution, or coincident roots.
(b)
when c is greater than 4, the two curves are farther apart, thus there will be no (real) solution.
(c)
when c<4, then the two curves will cross at more than one location, giving two distinct solutions.

It will be more obvious if you plot the two curves in a graphics calculator using c=3,4, and 5.

</span>

laila [671]3 years ago

3 0

Can you please make this more clear

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Can someone please help me on this question

klemol [59]

C = 31.4 (10pi)

The radius is half of the diameter
To find the circumference multiply the diameter by pi (3.14 )
The radius is 5 so the diameter is 10
3.14•10=31.4

6 0

2 years ago

Combine like terms to complete the equivalent expression. 2 1/2 z² + 4 1/2 + 7z - 4 +5z - 1/2 z² = ( _ z² - _z²) + ( 7z + _ z) +

postnew [5]

Step-by-step explanation:

z is 1 and 2 is 2

8 0

3 years ago

In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean

Otrada [13]

Answer:

$a=1050 -0.126*218=1022.532$

So the value of height that separates the bottom 45% of data from the top 55% is 1022.532.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the consumption levels of a population, and for this case we know the distribution for X is given by:

$X \sim N(1050,218)$

Where $\mu=1050 kWh$ and $\sigma=218kWh$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.55$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.45 of the area on the left and 0.55 of the area on the right it's z=-0.26. On this case P(Z<-0.126)=0.45 and P(z>-0.126)=0.55

If we use condition (b) from previous we have this:

$P(X$