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shusha [124]
3 years ago
13

What is the vertex of the graph of the function below? y=x^2-10x+24

Mathematics
2 answers:
adoni [48]3 years ago
4 0
\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
\begin{array}{llcccl}
y = & 1x^2& -10x& +24\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad 
\left(-\cfrac{ b}{2 a}\quad ,\quad   c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{-10}{2(1)}~~,~~24-\cfrac{(-10)^2}{4(1)} \right)\implies \left(5~~,~~24-25  \right)\implies (5~,~-1)
cupoosta [38]3 years ago
3 0
The vertex of the equation is (5,-1). Rewrite in standard form. (h,k)
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What is the slope of the line that passes the points(6,2) and (12,-2)​
Levart [38]
The slope is -2/3.

You have to do -2-2 and you get -4.
Then you do 12-6 and you get 6.
The final step is to do -4 divide 6 and you get -2/3.
5 0
2 years ago
A bank's loan officer rates applicants for credit.
Artist 52 [7]

Answer:

a=200 +0.253*50=212.65

So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.7.  

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 loan officer rates applicants for a credit of a population, and for this case we know the distribution for X is given by:

X \sim N(200,50)  

Where \mu=200 and \sigma=50

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

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

P(X>a)=0.40   (a)

P(X   (b)

Both conditions are equivalent on this case.

As we can see on the figure attached the z value that satisfy the condition with 0.60 of the area on the left and 0.40 of the area on the right it's z=0.253. On this case P(Z<0.253)=0.60 and P(z>0.253)=0.4

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

P(X  

P(Z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.253

And if we solve for a we got

a=200 +0.253*50=212.65

So the value of height that separates the bottom 60% of data from the top 40% is 212.65. And rounded would be 212.7.  

5 0
3 years ago
If a and b are positive numbers, find the maximum value of f(x) = xa(7 â x)b on the interval 0 ⤠x ⤠7.
algol [13]
Given f(x)=x^a(7-x)^b on the interval 0 ≤ x ≤ 7, for maximum value, f'(x) = 0.

f'(x)=0 \\  \\ \Rightarrow -bx^{a}(7-x)^{b-1}+ax^{a-1}(7-x)^b=0 \\  \\ \Rightarrow ax^{a-1}(7-x)^b=bx^{a}(7-x)^{b-1} \\  \\ \Rightarrow a(7-x)=bx \\  \\ \Rightarrow (a+b)x=7a \\  \\ \Rightarrow x= \frac{7a}{a+b}
8 0
3 years ago
IF YOU DON'T KNOW OR NOT SURE DON'T ANSWER!!
Aneli [31]

Answer:

c

Step-by-step explanation:

because i got 11

5 0
2 years ago
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kompoz [17]

Answer:

186.

Step-by-step explanation:

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8 0
3 years ago
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