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Svetradugi [14.3K]
3 years ago
13

Please help. the semester isd almost over need this

Mathematics
1 answer:
Zolol [24]3 years ago
8 0
The answer is a because it is the only one that decreases without ever increasing
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What is lim x→3 x^2 - x - 6/ x - 3
Kisachek [45]
<h3>Answer: D) 5</h3>

=======================================================

Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, \frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2

Allowing us to say,

\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\

5 0
3 years ago
A measure that describes the typical value of a data set
jonny [76]

<u>e</u>

<u>measure of center</u>

as A measure that describes the typical value of a data set mean,median and mode.

6 0
2 years ago
Simplify: –3(y + 2)2 – 5 + 6yWhat is the simplified product in standard form?
sweet-ann [11.9K]

Answer by Mimiwhatsup:

\mathrm{Multiply\:the\:numbers:}\:3\cdot \:2=6\\=-6\left(y+2\right)-5+6y\\-6\left(y+2\right)\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=-6,\:b=y,\:c=2\\=-6y+\left(-6\right)\cdot \:2\\Apply\:minus-plus\:rules\\+\left(-a\right)=-a\\=-6y-6\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:6\cdot \:2=12\\=-6y-12\\=-6y-12-5+6y\\\mathrm{Simplify}\:-6y-12-5+6y\\Group\:like\:terms\\=-6y+6y-12-5\\\mathrm{Add\:similar\:elements:}\:-6y+6y=0\\=-12-5\\

\mathrm{Subtract\:the\:numbers:}\:-12-5=-17\\Answer is: =-17

6 0
3 years ago
480/X - 8 - 480/x = 3
Nataliya [291]

Answer:

i don't know its ans thank you

7 0
2 years ago
Read 2 more answers
A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur
Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

V=LWH

where

L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in

substitute

V=(7-2x)(2-2x)x

Convert to expanded form

V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

so

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0
3 years ago
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