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3 years ago

What is the equation for this line ?

Mathematics

1 answer:

konstantin123 [22]3 years ago

7 0

(-2,7)(0,-1)
slope = (-1 - 7) / (0 - (-2) = -8/2 = -4

y = mx + b
slope(m) = -4
use either ofur points (0,-1)...x = 0 and y = -1
now we sub and find b, the y int
-1 = -4(0) + b
-1 = b

so ur equation is : y = -4x - 1 or if u need it in standard form, it is
4x + y = -1

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PLEASE HELP I NEED THIS ASAP Find the vertex of y=x^2-7x+4

Goshia [24]

Answer:

$\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)$

Step-by-step explanation:

$y=x^2-7x+4\\\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\\\mathrm{The\:parabola\:params\:are:}\\a=1,\:b=-7,\:c=4\\x_v=-\frac{b}{2a}\\x_v=-\frac{\left(-7\right)}{2\cdot \:1}\\\mathrm{Simplify}\\x_v=\frac{7}{2}\\\mathrm{Plug\:in}\:\:x_v=\frac{7}{2}\:\mathrm{to\:find\:the}\:y_v\:\mathrm{value}\\y_v=\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4\\$

$\mathrm{Simplify\:}\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4:\quad -\frac{33}{4}\\y_v=-\frac{33}{4}\\Therefore\:the\:parabola\:vertex\:is\\\left(\frac{7}{2},\:-\frac{33}{4}\right)\\\mathrm{If}\:a0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\\a=1\\\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)$

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3 years ago

For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

3 0

3 years ago

Find the value of 1415×211 Although these numbers aren't quite as nice as the ones from the example, the procedure is the same,

BabaBlast [244]

Answer:

298565

Step-by-step explanation:

Given problem,

1415 × 211

∵ Direct multiplication is quite tough so we can split the number into smaller one for making the multiplication easier,

= (1400 + 15) × (210 + 1)

By using distributive property,

= 1400 × (210 + 1) + 15(210 + 1)

Again by distributive property,

= 1400 × 210 + 1400 + 15 × 210 + 15

Simplifying,

= 294000 + 1400 + 3150 + 15

= 298565

Hence, 1415 × 211 = 298565

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3 years ago

(K3+2k2-82k-28)/(k+10)

Ne4ueva [31]

So for this, we will be using synthetic division. To set it up, have the equation so that the divisor is -10 (since that is the solution of k + 10 = 0) and the dividend are the coefficients. Our equation will look as such:

(Note that synthetic division can only be used when the divisor is a 1st degree binomial)

-10 | 1 + 2 - 82 - 28
---------------------------

Now firstly, drop the 1:

-10 | 1 + 2 - 82 - 28
↓
-------------------------
1

Next, you are going to multiply -10 and 1, and then combine the product with 2.

-10 | 1 + 2 - 82 - 28
↓ - 10
-------------------------
1 - 8

Next, multiply -10 and -8, then combine the product with -82:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80
-------------------------
1 - 8 - 2

Next, multiply -10 and -2, then combine the product with -28:

-10 | 1 + 2 - 82 - 28
↓ -10 + 80 + 20
-------------------------
1 - 8 - 2 - 8

Now, since we know that the degree of the dividend is 3, this means that the degree of the quotient is 2. Using this, the first 3 terms are k^2, k, and the constant, or in this case k² - 8k - 2. Now what about the last coefficient -8? Well this is our remainder, and will be written as -8/(k + 10).

Putting it together, the quotient is $k^2-8k-2-\frac{8}{k+10}$ 

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3 years ago

I need help with math

sergey [27]

Everyone needs help in math

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3 years ago