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Bogdan [553]
3 years ago
15

Let f be a linear function such that f(2) =5 and f(6) = -1. find an equation for f(x).

Mathematics
1 answer:
astra-53 [7]3 years ago
6 0
Using f(x) = y, we know that a graph of the function contains the (x,y) points (2,5) and (6,-1). first find the slope of that line,
m = (y2 - y1)/(x2 - x1) ⇒ -6/4⇒-3/2

then using either point (I'll use the first one) solve for b in y = mx + b.
5 = (-3/2)(2) + b⇒ 5 = -3 + b⇒ 8 = b.

So y = (-3/2)x + 8 ⇒ f(x) = (-3/2)x + 8.

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Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.
barxatty [35]

Answer:

x=9,-1  and x^2+(-8)x=9

Explanation:

we have been given with the quadratic equation x^2-8x-9

we compare the given quadratic equation with general quadratic equation

general quadratic is ax^2+bx+c=0

from given quadratic equation a=1,b= -8,c= -9

substituting these values in the formula for discriminant D=b^{2}-4ac

D=(-8)^2-4(1)(-9)=100

Now, to find the value of x

Formula is x=\frac{-b\pm\sqrt{D}}{2a}

Now, substituting the values we will get

x=\frac{-(-8)\pm\sqrt{100}} {2}= \frac{8\pm10}{2}=9,-1

And rewritting the given equation by  shifting 9 to right hand side of the given equation and taking minus inside the bracket so as to convert it in the form of

x^2+bx=c

4 0
3 years ago
Read 2 more answers
Below are the jersey numbers of 11 players randomly selected from a football team. Find the​ range, variance, and standard devia
padilas [110]

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

Range= 71

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

Mean value =58.7

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

Variance=546

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

Standard deviation= 23.4

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

5 0
2 years ago
The graph of the even function F(X) Has 5 x-intercepts if (6,0) is the one of the intercepts what set of points can be the other
alex41 [277]

f(x) being even means


f(x) = f(-x)


So the zeros come in positive and negative pairs. If there are an odd number of intercepts like there are here, it's because one of them is x=0 which is its own negation.


Given zero x=6 we know x=-6 is also a zero.


So we know three zeros, and know the other two zeros are a positive and negative pair.


The only choice with (-6,0) and (0,0) is A.


Choice A



3 0
2 years ago
Read 2 more answers
Find the area of the circle 3.6​
swat32

Answer:

The formula to get the area of a circle is: A = πr²

  • Area = pi × radius²
5 0
2 years ago
There will be 6 people at ellies pie party she wants to bake enough pie so each person can eat at least 1/5 of pie what is the m
tatyana61 [14]

Answer:

2

Step-by-step explanation:

She needs to have 6 portions of 1/5 pie size.

6 portions of 1/5 pie size is 6/5 of a pie.

6/5 of a pie is the same as 1 1/5 (one and one-fifth) pies.

Since she only bakes full pies, she must round up to the next higher whole number, so she must bake 2 pies.

8 0
3 years ago
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