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3 years ago

Write a proof for the biconditional using the inverse and contrapositive.

1 answer:

7 0

I don’t really understand the question at hand but let me try to help

X is equal to 4 we know this because because the sign in between the number means greater than or equal to so 3 x 4 equals 12 and that makes the equation on right true and on the left x is also equal to for which also makes the statement on the right true as well so I think X = 4

I hope I was able to help and If not I’m sorry

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Consider the following function. f(x) = |x − 9| Find the derivative from the left at x = 9. If it does not exist, enter NONE. -1

nydimaria [60]

Answer with Step-by-step explanation:

We are given that

$f(x)=\mid x-9\mid$

$f(x)=-(x-9)$ when x<9

$f(x)=x-9$ when $x\geq 9$

LHD

$\lim_{x\rightarrow 9-}f'(x)$

= $-\lim_{x\rightarrow 9-}(x-9)=-1$

RHD

$\lim_{x\rightarrow 9+}f'(x)$

$=\lim_{x\rightarrow 9+}(x-9)=1$

$LHD\neq RHD$

Hence, the function is not differentiable at x=9

8 0

2 years ago

To the nearest millimeter, a cell phone is 82 mm long and 36 mm wide. What is the ratio of the width to the length?

iVinArrow [24]

<h2>The ratio of the width to the length of a cell phone is 18 : 41.</h2>

Step-by-step explanation:

Given,

The length of a cell phone(l) = 82 mm and

The width of a cell phone(b) = 36 mm

Find, the ratio of the width to the length of a cell phone = ?

∴ The ratio of the width to the length of a cell phone

= 36 mm : 82 mm

= 36 : 82

Divided by 2, we get

= $\dfrac{36}{2}$ : $\dfrac{82}{2}$

= 18 : 41

Thus, the ratio of the width to the length of a cell phone is 18 : 41.

3 0

2 years ago

Find all values of c such that c/(c - 5) = 4/(c - 4). If you find more than one solution, then list the solutions you find separ

Deffense [45]

Answer:

$\large\boxed{\bold{NO\ REAL\ SOLUTIONS}}\\\boxed{x=4-2i,\ x=4+2i}$

Step-by-step explanation:

$Domain:\\c-4\neq0\ \wedge\ c-5\neq0\Rightarrow c\neq4\ \wedge\ c\neq5\\\\\dfrac{c}{c-5}=\dfrac{4}{c-4}\qquad\text{cross multiply}\\\\c(c-4)=4(c-5)\qquad\text{use the distributive property}\\\\c^2-4c=4c-20\qquad\text{subtract}\ 4c\ \text{from both sides}\\\\c^2-8c=-20\qquad\text{add 20 to both sides}\\\\c^2-8c+20=0\qquad\text{use the quadratic formula}$

$\text{for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x^2-8x+20=0\\\\a=1,\ b=-8,\ c=20\\\\b^2-4ac=(-8)^2-4(1)(20)=64-80=-16$

$\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\\text{therefore}\ \sqrt{b^2-4ac}=\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4i\\\\x=\dfrac{-(-8)\pm4i}{2(1)}=\dfrac{8\pm4i}{2}=\dfrac{8}{2}\pm\dfrac{4i}{2}=4\pm2i$