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3 years ago

What is an equation of the line passing between(4, -6) and (12, -8)?*

Mathematics

1 answer:

I am Lyosha [343]3 years ago

4 0

Answer:

y= -1/4x - 5

Step-by-step explanation:

first you need to find the slope.

to do this you can use the equation: change in y/change in x which is also y2 - y1/x2-x1

-8 - (-6)/12-4

-2/8

-1/4 = slope

since the line's equation is y = mx + b, we still need to find the y-intercept. we can do this by just plugging in one of the points

-6 = -1/4(4) + b

-6 = -1 + b

-5 = b

so the final equation is y= -1/4x - 5

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3 years ago

Which polynomial function has a leading coefficient of 1 and roots /7 and - /3 with multiplicity 1?

VladimirAG [237]

Answer:

A. f(x) = (x - √2)(x + √3)

Step-by-step explanation:

Leading coefficient is 1, multiplicity is 1, roots are √2 and -√3. It means the function is the product of two binomials.

<u>The function with the roots of a and b is:</u>

f(x) = (x - a)(x - b)

<u>Substitute and and b:</u>

f(x) = (x - √2)(x - (-√3)) ⇒
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3 years ago

Read 2 more answers

Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H is a vector space. If

Verizon [17]

Answer:

Yes. It is a vector space over the field of rational numbers $\mathbb{Q}$

Step-by-step explanation:

An element $p$ of the set $H$ has the form

$p(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}$

where $a_{0},a_{1},a_{2},a_{3},a_{4}$ are rational coefficients.

The operations of addition and scalar multiplication are defined as follows:

$p(x)+q(x)=(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+x_{4}x^4)+(b_{0}+b_{1}x+b_{2}x^{2}+b_{3}x^{3}+b_{4}x^{4})=(a_{0}+b_{0})+(a_{1}+b_{1})x+(a_{2}+b_{2})x^{2}+(a_{3}+b_{3})x^{3}+(a_{4}+b_{4})x^{4}$

$\lambda p(x)=\lambda (a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4})=\lambda a_{0}+\lambda a_{1}x+\lambda a_{2}x^{2}+\lambda a_{3}x^{3}+\lambda a_{4}x^{4}$

The properties that $H$ , together the operations of vector addition and scalar multiplication, must satisfy are:

Conmutativity
Associativity of addition and scalar multiplication
Additive Identity
Additive inverse
Multiplicative Identity
Distributive properties.

This is not difficult with the definitions given. The most important part is to show that $H$ has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that $\mathbb{Q}$ is a field, then it is closed under sum and multiplication.

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3 years ago