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3 years ago

Find the coordinates of the vertex of the graph of the quadratic equation below. Identify the vertex as a minimum or a maximum.

Mathematics

1 answer:

Mama L [17]3 years ago

5 0

Answer: Vertex= (0,-8) [Maximum]

Step-by-step explanation:

The Vertex is the lowest or highest point On the graph. In this case it is -8 is the highest point.

it is maximum Because the graph is pointing downward. If it was pointing upward it would have a minimum.

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Which of the following questions describes the equation = -20? What number, when multiplied by four, is equal to negative twenty

love history [14]

Answer:

An equation contains an equal sign so -20 is not an equation, I think it's a typing error

3 0

3 years ago

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Suppose a random variable X has the following probability density function:f(x)=1/x, 1≤x≤C, or f(x)=0 otherwise a) what must the

Sergeeva-Olga [200]

Answer:

a) $C=e^1=e$

b) $P(X$

c) $E(X) =\int_{1}^e x \frac{1}{x} dx =x \Big|_1^e \ =e-1$

$E(X^2) =\int_{1}^e x^2 \frac{1}{x} dx =\frac{x^2}{2} \Big|_1^e \ =\frac{1}{2}(e^2 -1)$

$Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242$

Step-by-step explanation:

a) what must the value of C be so that f(x) is a probability density function?

In order to be a probability function we need this condition:

$\int_{1}^C \frac{1}{x} dx =1$

And solving the left part of the integral we have:

$ln(x) \Big|_1^C \ =1$

$ln(C)-ln(1)=1$ , so then $C=e^1=e$

b) find P(X<2)

We can find this probability on this way using the density function:

$P(X$

c) find E(X) and Var(X)

We can find the expected value on this way:

$E(X) =\int_{1}^e x \frac{1}{x} dx =x \Big|_1^e \ =e-1$

In order to find the Var(X) we need to find the second moment given by:

$E(X^2) =\int_{1}^e x^2 \frac{1}{x} dx =\frac{x^2}{2} \Big|_1^e \ =\frac{1}{2}(e^2 -1)$

And now we can use the following definition:

$Var(X)=E(X^2)-[E(X)]^2= \frac{1}{2}(e^2 -1) -(e-1)^2 = 0.242$

5 0

4 years ago

Simplify completely the quantity 14 times x to the 5th power times y to the 4th power plus 21 times x to the third power times y

timofeeve [1]

We have to simplify the given expression:

$\frac{14x^5y^4+21x^3y^2}{7x^3y}$

Dividing the terms of the numerator by the given term of denominator individually, we get

= $\frac{14x^5y^4}{7x^3y}+\frac{21x^3y^2}{7x^3y}$

By using the laws of exponent, $a^m \div a^n = a^{m-n}$ , we get

= $\frac{7 \times 2 x^5y^4} {7x^3y} + \frac{7 \times 3 x^3y^2}{7x^3y}$

= $\frac{2 x^5y^4} {x^3y} + \frac{3 x^3y^2}{x^3y}$

= ${2 x^{5-3}y^{4-1}} + 3 y^{2-1}$

= ${2 x^{2}y^{3}} + 3 y$

Therefore, the simplification of the given expression is ${2 x^{2}y^{3}} + 3 y$ .

So, Option 3 is the correct answer.

6 0

3 years ago

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Where is -2,1.5 plotted in a coordinate plane

vazorg [7]

Here is an image of (-2,1.5) in a coordinate plane. Hope this helps!

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3 years ago

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<img src="https://tex.z-dn.net/?f=%20-%2020x%20-%205" id="TexFormula1" title=" - 20x - 5" alt=" - 20x - 5" align="absmiddle" cla

Aloiza [94]

It equals 4 hhnug flight

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3 years ago