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3241004551 [841]
3 years ago
12

Find the length of x. Assume the triangles are similar.

Mathematics
1 answer:
Veronika [31]3 years ago
6 0

Answer:

  x = 32

Step-by-step explanation:

The longest side is double the length of the shortest side, so x is 2·16 = 32.

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Evaluate the function:<br><br> f(x)=4x−1, find f(9)
Eddi Din [679]

Answer:

f(9) = 35

Step-by-step explanation:

To solve this, you can take 9 and replace both x's with it and then complete the equation;

f(x) = 4x - 1

f(9) = 4(9) - 1

f(9) = 36 - 1

f(9) = 35

Hope this helps!

3 0
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Find csc 0, sin 0, and cot 0, where is the angle shown in the figure. Give exact values, not decimals approximations. (LISTING B
dexar [7]

Answer:

sup

Step-by-step explanation:

sup

4 0
3 years ago
Which of the following ordered pairs represents the solution to the system given below?
pentagon [3]
(3,-1) just fill it in and the only one that makes sense is the first one 
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3 years ago
How do I factor 2x^2 + 11x +5
ASHA 777 [7]
(2x+1)(x+5) is the answer.
4 0
3 years ago
I dont understand how to do this precalc question
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

6 0
2 years ago
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