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2 years ago

The triangle below is equilateral. Find the length of side x in simplest radical

Mathematics

1 answer:

Verdich [7]2 years ago

3 0

Answer:

x = 10

Step-by-step explanation:

In an equilateral triangle, the altitude, or height is also the median and angle bisector. So, we can say a side of the equilateral triangle is 2 x 5 or 10. Every side of an equilateral triangle is congruent, so x is 10.

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2 years ago

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Alexeev081 [22]

Answer:

x-intercept: (-0.1, 0)
Horizontal Asymptote: y = -3
Exponential <u>growth</u>

(First answer option)

Step-by-step explanation:

<u>General form of an exponential function</u>

$y=ab^x+c$

where:

a is the initial value (y-intercept).
b is the base (growth/decay factor) in decimal form:
If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function.
y=c is the horizontal asymptote.
x is the independent variable.
y is the dependent variable.

Given <u>exponential function</u>:

$y=4(10)^x-3$

<h3><u>x-intercept</u></h3>

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0. To find the x-intercept, substitute y = 0 into the given equation and solve for x:

$\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}$

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

<h3><u>Asymptote</u></h3>

An <u>asymptote</u> is a line that the curve gets infinitely close to, but never touches.

The <u>parent function</u> of an <u>exponential function</u> is:

$f(x)=b^x$

As<em> </em>x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form $f(x) = ab^x+c$ always has a horizontal asymptote at y = c.

Therefore, the horizontal asymptote of the given function is y = -3.

<h3><u>Exponential Growth and Decay</u></h3>

A graph representing exponential growth will have a curve that shows an <u>increase</u> in y as x increases.

A graph representing exponential decay will have a curve that shows a <u>decrease</u> in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).

If b > 1 then it is an increasing function.
If 0 < b < 1 then it is a decreasing function.

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

Learn more about exponential functions here:

brainly.com/question/27466089

brainly.com/question/27955470

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