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FrozenT [24]
3 years ago
9

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. f(x)

= 5x + 4 h(x) = x2 + 8x + 24
x = -3
x = 3
x = 4
x = 5
Mathematics
2 answers:
WINSTONCH [101]3 years ago
6 0
The exponential function is f(x)= 5^{x} +4
The polynomial function is h(x)= x^{2} +8x+24 

We want a value of x as such that f(x)\ \textgreater \ h(x), so

5^{x}+4 > x^{2} +8x+24

We are provided with four possible value of x. By process of trial and error, we will narrow down two values of x when the statement is changing from false to true

first, we try x=-3 by substituting into f(x) and h(x)

f(-3)=5^{-3}+4 = 4.008 and h(-3)= (-3)^{2}+8(-3)+24=9
so f(x)>h(x) which is not the inequality wanted

We try x=3 by substituting into f(x) and h(x)
f(3)= 5^{3}+4=129 and h(3)= (3)^{2}+8(3)+24=57, 
so f(x) > h(x) as wanted

We know that any values of x greater than three will give f(x) greater than h(x), so we narrow down to two values that make the statement changes from false to true.

There is one value between -3 and three that makes f(x) greater than h(x). From here we use the method of trial and error. 

We can start with the mid value between -3 and three which is 0
f(0)= 5^{0}+4=5
h(0)= 0^{2}+8(0)+24=24
f(x) is less than h(x) which isn't the inequality we want so here we narrow down the value of x must be between 0 and 3

We can try mid-value between 0 and three which is 1.5
f(1.5)= 5^{1.5}+4=15.18
h(1.5)= (1.5)^{2}+8(1.5)+24=38.25
f(x) is still less than h(x), so we now narrow down the value of x between 1.5 and 3

We try again using the mid-value between 1.5 and three which is 2.25
f(2.25)= 5^{2.25}+4=41.38
h(2.25)= 2.25^{2}+8(2.25)+24=47.0625
We still have f(x) less than h(x) so we can narrow down further the value of x between 2.25 and 3 (which is quite a short interval already)

We can keep trying by choosing a value of x says x=2.6
f(2.6)= 5^{2.6}+4=69.66
h(2.6)= 2.6^{2}+8(2.6)+24=51.56
We have f(x) greater then h(x) 

The narrowing down process continues where we now have the interval of x between 2.25 and 2.6. Keeping to one decimal place we can find the 
value of x=2.4 is the approximate value where f(x) is greater than h(x).

Answer: x=2.4
enyata [817]3 years ago
5 0

The correct answer is x = 5.

Trust me, I just did the quiz.

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Hello : 
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7 0
3 years ago
A line goes through the points (5, -1) and (7, -5). What is a possible equation to a new line that is perpendicular?
Leya [2.2K]

<em>Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."  </em>

<em> </em>

<em> </em>

<em> </em>

<em>  5x+4y=2 </em>

<em> </em>

<em>-5x     -5x  (subtract 5x from both sides to move it to the right side of your equation) </em>

<em> </em>

<em>4y = 2 - 5x </em>

<em> </em>

<em>/4  /4  /4 (divide all the terms by 4 to get "y" by itself) </em>

<em> </em>

<em>y = (1/2) - (5/4)x  ... I suggest leaving your slope as a fraction. </em>

<em> </em>

<em> </em>

<em> </em>

<em>Now, we know that our slope, m , is going to be -(5/4).  </em>

<em> </em>

<em> </em>

<em> </em>

<em>Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know: </em>

<em> </em>

<em> </em>

<em> </em>

<em>y = 5 </em>

<em> </em>

<em>m = -(5/4) </em>

<em> </em>

<em>x = 7 </em>

<em> </em>

<em> </em>

<em> </em>

<em>y=mx+b </em>

<em> </em>

<em>5=(-5/4)(7) + b  -> I plugged in what we knew for y, m, and x.  </em>

<em> </em>

<em>5 = -(35/4) + b  -> I multiplied the numbers in the numerator (5 x 7) to get 35/4 </em>

<em> </em>

<em>20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4) </em>

<em> </em>

<em>+(35/4) +(35/4)  -> I add (35/4) to both sides to isolate b </em>

<em> </em>

<em>55/4 = b ... or b = 13.74 </em>

<em> </em>

<em> </em>

<em> </em>

<em>Answer:  </em>

<em> </em>

<em>m = -(5/4) </em>

<em> </em>

<em>b = 13.75</em>

7 0
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leonid [27]
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8 0
3 years ago
The depth of Nathan's binder is 2 5/12 inches. what is the measurement as a decimal?
masya89 [10]
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6 0
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