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3 years ago

an equation that is perpendicular to x-3y=3 and pases through the point (5,-9) in slope-intercept form

Mathematics

1 answer:

Tatiana [17]3 years ago

8 0

Answer:

y = - 3x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x - 3y = 3 ( subtract x from both sides )

- 3y = - x + 3 ( divide all terms by - 3 )

y = $\frac{1}{3}$ x - 1 ← in slope- intercept form

with slope m = $\frac{1}{3}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{1}{3} }$ = - 3, then

y = - 3x + c ← is the partial equation

To find c substitute (5, - 9) into the partial equation

- 9 = - 15 + c ⇒ c = - 9 + 15 = 6

y = - 3x + 6 ← equation of perpendicular line

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Given a function <img src="https://tex.z-dn.net/?f=f%28x%29%3D3x%5E4-5x%5E2%2B2x-3" id="TexFormula1" title="f(x)=3x^4-5x^2+2x-3"

Levart [38]

Answer:

$\huge\boxed{f(-1) = -7}$

Step-by-step explanation:

In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

$3(-1)^4 = 3$

WAIT! How is this possible? $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$ , not 3!

It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use $-2^2$ as an example.

What your calculator did was follow BEMDAS since it wasn't explicitly told not to.

BEMDAS:

- Brackets

- Exponents

- Multiplication/Division

- Addition/Subtraction

Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.

So rather than being "-2 squared" - it's "the negative of of 2 squared."

Tying this back into our problem, the squared method would only be true if it looks like $-1^4$ . However, since we're substituting in -1, it looks like $(-1)^4$ , so the expression reads out as "-1 to the fourth."

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$ .

Applying this logic to our original term, $3(-1)^4$ :

$3(-1\cdot-1\cdot-1\cdot-1)$
$3(1)$
$3$

Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

$-5(-1)^2$

Applying the same logic from our first term:

$-5(-1 \cdot -1)$
$-5(1)$
$-5$

Third term: $2x$

$2(-1) = -2$

-3 is just -3, no influence of x.

Combining our terms, we have $3-5-2-3$ .

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is -7.

Hope this helped!

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3 years ago

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What is the volume? 7 mm 7 mm 7 mm cubic millimeters

Oksanka [162]

$\Huge\bf\overbrace{\underline{ \underbrace{\blue \dag \orange{Answer}}}} \blue\dag$

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$\huge\bf\mapsto{\underline{\green{ {7}^{3} }}}$

$\Large\bf\leadsto{\underline{\purple{ \: 7 \times 7 \times 7 = 343}}}$

6 0

3 years ago

David buys a new racing bike for £x he then sells it for £1584 making a loss of 12% find x

Sholpan [36]

Answer:

x=1800

Step-by-step explanation:

x-1584/x=0.12

x-1584=0.12x

x-0.12x=1584

0.88x=1584

x=1800

Hope this helps plz hit the crown :D

3 0

2 years ago

Help. I've been staring at this math question for hours. I can't figure it out.

kogti [31]

All the numbers are tilted at a 90 degree angle, except for the number 4 which it tilted at an angle of 89 degrees, hoped this helps

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3 years ago

( 1 0 3) + (4 1 7) The first entry of the resulting matrix is:

Mamont248 [21]

Hello!

When adding matrices you add the numbers that are in the same position

1 + 4 = 5

0 + 1 = 1

3 + 7 = 10

The answer is (5 1 10)

Hope this helps!

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3 years ago

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