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Gala2k [10]
3 years ago
8

Find a counterexample to show each conjecture is false​

Mathematics
1 answer:
ANEK [815]3 years ago
7 0

Answer:

I am 85.9% sure the answer is number 15.

Step-by-step explanation:

You might be interested in
F(x)=<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2-4%7D" id="TexFormula1" title="\sqrt{x^2-4}" alt="\sqrt{x^2-4}" align="abs
hammer [34]

Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :

√(<em>x</em> ² - 4) = 1

<em>x</em> ² - 4 = 1

<em>x</em> ² = 5

<em>x</em> = ±√5

We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.

This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If <em>f(a)</em> = <em>b</em>, then  (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.

We have

<em>f(x)</em> = √(<em>x</em> ² - 4)   →   <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)

So if <em>a</em> = -√5 and <em>b</em> = 1, we get

(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)

(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.

3 0
3 years ago
Seiko spent $98.34 on a pair of shoes and 3 pairs of fancy shoestrings. The shoes cost $45.99. How much was EACH pair of shoestr
Marina86 [1]

Answer:

$17.45

Step-by-step explanation:

$17.45*3=52.35

$52.35+$45.99=$98.34

7 0
3 years ago
At a company picnic, 1/2 of the people are employees. 2/5 are employees' spouses. What percent are neither?​
kupik [55]

Answer:

10% of the people at the picnic are neither.

Step-by-step explanation:

To get the answer,

1/2 + 2/5 = 9/10

10/10 - 9/10 = 1/10

1/10 = 10%

Thanks, I hope I got this right!

7 0
3 years ago
Find g(x), where g(x) is the translation 1 unit right of f(x)=x2.
jeyben [28]

Step-by-step explanation:

this is the answer (y2 - y1) = m (x2 - x1)

4 0
2 years ago
Read 2 more answers
Simplify to using laws of exponents<br><br> (-2)^2(-2)^5
MAVERICK [17]

Answer:

-128

Step-by-step explanation:

(-2)^2  *  (-2)^5 <---

First, add the exponents

(-2)^7<----

If you evaluate this you will get

-128

7 0
2 years ago
Read 2 more answers
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