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3 years ago

The variables A, B, and C represent polynomials where A = x + 1, B = x2 + 2x − 1, and C = 2x. What is AB + C in simplest form?

Mathematics

2 answers:

topjm [15]3 years ago

3 0

AB + C
= (x + 1)(x^2 + 2x - 1) + 2x
= x^3 + 2x^2 - x + x^2 + 2x - 1 + 2x
= x^3 + 3x^2 + 3x - 1

allsm [11]3 years ago

3 0

Answer:

Step-by-step explanation:

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A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

4 0

3 years ago

Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram A

valentina_108 [34]

<h3><u>Answer:</u></h3>

The formula determine the distance from C to D is:

$\sqrt{(0-a)^2+(-b)^2}=\sqrt{a^2}=a$

<h3><u>Step-by-step explanation:</u></h3>

The formula that can be used to determine the distance from point C to point D is:

$\sqrt{(0-a)^2+(-b)^2}=\sqrt{a^2}=a$

We know that distance between two points A(a,b) and B(c,d) is equal to the length of the line segment AB and is calculated by the help of the formula:

$\sqrt{(c-a)^2+(b-d)^2}$

So, here we have:

(a,b)=(a,b) and (c,d)=(0,b)

3 0

3 years ago

Find the first term and the common ratio <br>third term =6 and seventh term= 96

mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: $a_n= a_1r^{n-1}$

We are given: third term = 6 i,e

$a_3=a_1r(3-1)\\6=a_1r^2----eq(1)$

Seventh term = 96

$a_7=a_1r(7-1)\\96=a_1r^6----eq(2)$

Dividing eq(2) and eq(3)

$\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}$