How do you write 2m as a verbal expression

Mathematics

1 answer:

Maksim231197 [3]3 years ago

7 0

When you say "2m," you say "two meters," since the letter "m" represents meters.

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The perpendicular distance of p (3,4) from the y - a x is _____

solmaris [256]

Answer:

Step-by-step explanation:

The perpendicular distance from the y- axis is the value of the x- coordinate, so

perpendicular distance is 3 units

8 0

3 years ago

WILL MARK BRAINLIEST!!! Given p(x)=x3−4x2+15x+k and the remainder of the division of p(x) by (x+1) is equal to −8, what is the r

balandron [24]

Use the polynomial remainder theorem. If $p(x)$ is a polynomial of degree $n>1$ , then we can divide by a linear term $x-c$ to get a quotient $q(x)$ and remainder $r(x)$ of the form

$\dfrac{p(x)}{x-c}=q(x)+\dfrac{r(x)}{x-c}\iff p(x)=(x-c)q(x)+r(x)$

Then when $x=c$ , we get $p(c)=r(c)$ . In other words, the value of $p(x)$ at $x=c$ tells you the value of the remainder upon dividing $p(x)$ by $x-c$ .

So given that $p(x)=x^3-4x^2+15x+k$ , and the remainder upon dividing $p(x)$ by $x+1$ is -8, we know that $r(-1)=-8$ , so

$\dfrac{x^3-4x^2+15x+k}{x+1}=q(x)-\dfrac8{x+1}$
$\dfrac{x^3-4x^2+15x+k+8}{x+1}=q(x)$

Since $q(x)$ is a polynomial (not a rational expression), then we know that $x+1$ divides $x^3-4x^2+15x+k+8$ exactly. In particular, the remainder term of this quotient is 0. We can use long or synthetic division to determine $q(x)$ . I prefer typing out the work for synthetic division:

-1   |   1   -4   15    k + 8
.     |        -1     5       -20
- - - - - - - - - - - - - - - - - -
.     |   1   -5    20    k - 12

The remainder here has to be 0, so $k-12=0\implies k=12$ .

Finally, we can get the remainder upon dividing $p(x)$ by $x-1$ by evaluating $p(1)$ , which gives $p(1)=24$ .

6 0

3 years ago

Read 2 more answers

Select the two values of x that are roots of this equation.

charle [14.2K]

Answer:

$x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2}$

Step-by-step explanation:

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 + - \sqrt{9 + 24} }{2} \\ x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2}$