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3 years ago

Thinking the perimeter of the rectangle is 3x + 2 + x + 3x + 2 + X.

1 answer:

7 0

They are both right because the first expression is the perimeter but expanded in terms of length.The second expression is shortened to be a factor expression but they both represent the length.
The benefit of the first one is you can see how it’s expanded and plug the numbers in and the second one is more easy to plug in the numbers with ease.

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(x2-2x+2)+(3x2-4x-10)

Angelina_Jolie [31]

Answer:

4x^2-6x-8

Step-by-step explanation:

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Use the hundreds try to find a mystery number The number has 2 even digits the number in the tens place is greater than the numb

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Step-by-step explanation:

2 even numbers and its sum is 12: 4, 8 and 6, 6

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What is 0.27 as a percent?<br> A)0.27%<br> B)27%<br> C)2.7%<br> D)270%

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Step-by-step explanation:

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2 years ago

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What is the value of x?

solniwko [45]

Answer:

x = 7.5

Step-by-step explanation:

Since we see that sides AD and DC are equal, as well as sides BE and EC, we can use this information to conclude that the value of 2x-7 is equal to double the value of DE.

2x - 7 = 4(2)

2x - 7 = 8

2x - 7 + 7 = 8 + 7

2x = 15

x = 7.5

5 0

2 years ago

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