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4 years ago

What is the linear function equation represented by the graph? f(x)=

Mathematics

1 answer:

algol [13]4 years ago

3 0

The x-intercept is 2 and the y-intercept is 1, so the equation can be written in intercept form as
.. x/2 +y/1 = 1

Putting this in the form you want gives
.. f(x) = -1/2*x +1

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An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125, . . . What is the sum, S, of the infinit

dezoksy [38]

Answer: $\dfrac{5}{4}$

Step-by-step explanation:

Given: The first term of Geometric series : a=1

The seconds term of Geometric series : $ar=\dfrac{1}{5}$

The common ratio between the terms is given by :-

$r=\dfrac{ar}{a}=\dfrac{\frac{1}{5}}{1}=\dfrac{1}{5}$

We know that the sum of infinite geometric series is given by :-

$S_{\infty}=\dfrac{a}{1-r}\\\\\Rightarrow\ S_{\infty}=\dfrac{1}{1-\frac{1}{5}}=\dfrac{1}{\frac{4}{5}}\\\\\Rightarrow\ S_{\infty}=\dfrac{5}{4}$

Hence, the sum of the given infinite series = $\dfrac{5}{4}$

7 0

3 years ago

F(x)=2x-3 and g(x)=x^2-5, find (fog) (x) and (gof) (x)

Alexxandr [17]

F(g(x)) = 2(x^2-5)-3
= 2x^2-13

g(f(x)) = (2x-3)^2 - 5
= 4x^2 + 9 -12x -5
= 4x^2 -12x + 4

6 0

3 years ago

What is the mean of the following data values 22,37,49,15,72

nexus9112 [7]

Mean simply means average
so just add them all up and divide by 5

22 + 37 + 49 + 15 + 71 = 195
195/5 = 39

mean = 39

3 0

4 years ago

Read 2 more answers

What is x. Please show *all* the steps.

Zolol [24]

The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation

The value of x is 8 or 1

<h3>How to determine the value of x?</h3>

The equation is given as:

5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Rewrite as:

-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0

Take the LCM

[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0

Expand

[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0

Evaluate the like terms

[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0

Multiply through by x^2 - 4

x^2 - 12x+ 3x + 8 = 0

Evaluate the like terms

x^2 -9x + 8 = 0

Expand

x^2 -x - 8x + 8 = 0

Factorize

x(x -1) - 8(x - 1) = 0

Factor out x - 1

(x -8)(x - 1) = 0

Solve for x

x = 8 or x = 1

Hence, the value of x is 8 or 1