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2 years ago

The explains why a x b = b x a and a + b = b + a.

1 answer:

6 0

Answer: The commutative property

Explanation: the commutative property of addition/multiplication states that no matter what order the expression is in it will equal the same thing.

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What's one third multiply 3

allsm [11]

Simple! 1/3 times 3 equals 3/3, or 1.

7 0

2 years ago

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What is the range of the function? f(x) = -2^x + 1

Readme [11.4K]

{y|1 > y}, (-∞, 1); you did not specifically mention what notation you needed, so I wrote both [Internal Notation and Set Notation].

6 0

2 years ago

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g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

6 0

3 years ago

Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula: a1 =

alexdok [17]

Answer:

D) The population alternates between increasing and decreasing

Step-by-step explanation:

correct on edge

4 0

1 year ago

The ratio of cassette to compact disc is 10 to 3 and the number of cassettes is 10 less than 5 times the number of compact discs

OlgaM077 [116]

There are 20 cassettes.

Step-by-step explanation:

Given,

Ratio of cassette to compact disc = 10:3

Let,

the number of cassettes = 10x

Number of compact disc = 3x

According to given statement;

the number of cassettes is 10 less than 5 times the number of compact discs.

10x = 5(Number of CD) - 10

$10x=3(5x)-10 \\10x=15x-10\\10=15x-10x\\10=5x\\5x=10$

Dividing both sides by 5

$\frac{5x}{5}=\frac{10}{5}\\x=2$

Number of cassettes= 10x = 10(2) = 20

There are 20 cassettes.

Keywords: variable, ratio

Learn more about variables at:

#LearnwithBrainly

5 0

2 years ago