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Rufina [12.5K]
4 years ago
8

Xavier said the product of a monomial and a binomial will always be a trinomial. Explain the error in his reasoning.

Mathematics
2 answers:
sergejj [24]4 years ago
5 0

All that is needed is a single counter-example.

One counter-example is to multiply the monomial x^3 with the binomial x^7-10x^4

We then get...

x^3*(x^7-10x^4) = x^3*x^7 + x^3*(-10x^4)

x^3*(x^7-10x^4) = x^10 - x^7

The result we get is a binomial as there are still only two terms here. We would need three terms to have a trinomial.

drek231 [11]4 years ago
4 0

Answer:

See below.

Step-by-step explanation:

Each term in the binomial ( there are 2 terms, by definition) is multiplied by the single term (monomial) so the answer will be  another binomial.

For example:

2x (x - 6)

= 2x^2 - 12x.

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Find the chart that shows an increase of 4 feet for every second the balloon travels.

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2 years ago
Find the radius or diameter of each circle with the given dimensions.<br><br> d=30 m
Alex_Xolod [135]

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Step-by-step explanation:

C=pi`d

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3 years ago
Currently they sell a tub of popcorn for $10. SHOW or EXPLAIN what the cost of the cone of popcorn should be. Door context: The
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Answer:

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The cost of per unit volume is

$10/540.473

The cost of cone of popcorn is

\frac{10}{540.473}\times 140.035\\\\2.59

7 0
3 years ago
Derive the equation of the parabola with a focus at (3,1) and a directrix of y = 5
serg [7]
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because the parabola opens downwards, "p" is negative, and thus, -2

now, let's plug all those fellows in then

\bf \begin{array}{llll}&#10;(x-{{ h}})^2=4{{ p}}(y-{{ k}})\\&#10;\end{array}&#10;\qquad &#10;\begin{array}{llll}&#10;vertex\ ({{ h}},{{ k}})\\&#10;{{ p}}=\textit{distance from vertex to }\\&#10;\qquad \textit{ focus or directrix}&#10;\end{array}\\\\&#10;-----------------------------\\\\&#10;&#10;\begin{cases}&#10;h=3\\&#10;k=3\\&#10;p=-2&#10;\end{cases}\implies (x-3)^2=4(-2)(y-3)\implies (x-3)^2=-8(y-3)&#10;\\\\\\&#10;-\cfrac{(x-3)^2}{8}=y-3\implies \boxed{-\cfrac{1}{8}(x-3)^2+3=y}

5 0
4 years ago
Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths. X2 y2 − 2x 2y −
Colt1911 [192]

Circles (represented by their equations in general form) in ascending order of their radius lengths can be arranged as first-fifth-second-forth-third-seventh-sixth.

<h3>What is the equation of circle?</h3>

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

(x-h)^2+(y-k)^2=r^2

Here (h,k) is the center of the circle and (r) is the radius of the circle.

Lets arrange the first equation, in standard form of equation of circle as,

x^2 +y^2 - 2x+ 2y -1 = 0 \\(x^2 - 2x) +(y^2+ 2y )= 1\\(x^2 - 2x+1) +(y^2+ 2y +1)= 1+1+1\\(x-1)^2+(y+1)^2=(\sqrt{3})^2

The radius of this circle is √(3).

Lets arrange the second equation, in standard form of equation of circle as,

x^2 +y^2 - 4x+ 4y - 10 = 0  \\(x^2 - 4x) +(y^2+ 4y )= 10\\(x^2 - 4x+4) +(y^2+ 4y +4)= 10+4+4\\(x-2)^2+(y+2)^2=(\sqrt{18})^2

The radius of this circle is √(18).

Lets arrange the third equation, in standard form of equation of circle as,

x^2 +y^2 - 8x - 6y - 20 = 0   \\(x^2 - 8x) +(y^2-6y )= 20\\(x^2 - 8x+16) +(y^2- 6y +9)= 10+16+9\\(x-4)^2+(y-3)^2=(\sqrt{45})^2

The radius of this circle is √(45).

Similarly, radius of the forth, fifth, sixth and seventh circle is √(23), √(5), √(117) and √(46) units.

Hence, the circles (represented by their equations in general form) in ascending order of their radius lengths can be arranged as first-fifth-second-forth-third-seventh-sixth.

Learn more about the equation of circle here;

brainly.com/question/1506955

3 0
2 years ago
Read 2 more answers
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