Consider the polynomials p(x) = 3x + 27x^2 and q(x)= 2 . Find the x -coordinate(s) of the point(s) of intersection of these two polynomials. What is the sum of these x -coordinates? (If there is only one point of intersection, give the corresponding x -coordinate.)

Answers

Answer 1

Answer:

Answer:

The x -coordinate(s) of the point(s) of intersection of these two polynomials are $x=(2)/(9)\approx0.2222,\:x=-(1)/(3)\approx-0.3333$

The sum of these x -coordinates is $(2)/(9)+\left(-(1)/(3)\right)=-(1)/(9)$

Step-by-step explanation:

The intersections of the two polynomials, p(x) and q(x), are the roots of the equation p(x) = q(x).

Thus, $3x + 27x^2=2$ and we solve for x

$3x+27x^2-2=2-2\n27x^2+3x-2=0\n\left(27x^2-6x\right)+\left(9x-2\right)\n3x\left(9x-2\right)+\left(9x-2\right)\n\left(9x-2\right)\left(3x+1\right)=0$

Using Zero Factor Theorem: = 0 if and only if = 0 or = 0

$9x-2=0\n9x=2\nx=(2)/(9)$

$3x+1=0\n3x=-1\nx=-(1)/(3)$

The solutions are:

$x=(2)/(9)\approx0.2222,\:x=-(1)/(3)\approx-0.3333$

The sum of these x -coordinates is

$(2)/(9)+\left(-(1)/(3)\right)=-(1)/(9)$

We can check our work with the graph of the two polynomials.

Related Questions

Write the formula for Newton's method and use the given initial approximation to compute the approximations x_1 and x_2. f(x) = x^2 + 21, x_0 = -21 x_n + 1 = x_n - (x_n)^2 + 21/2(x_n) x_n + 1 = x_n - (x_n)^2 + 21 x_n + 1 = x_n - 2(x_n)/(x_n)^2 + 21 Use the given initial approximation to compute the approximations x_1 and x_2. x_1 = (Do not round until the final answer. Then round to six decimal places as needed.)
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What’s the correct answer for this?
For the function y=ln(x-1)+2 which of the following statements is truea. the domain is all real numbers and the range is [2, infinity)b. the domain is (-1, infintity} and the range is all real numbersc. the domain is (1, infinity) and the range is [2, infinity)d. the domain is (1, infinity) and the range is all real numbers
A circle with a diameter of 36 inches is shown.circle with diameter of 36 inches What is the area of the circle using π = 3.14? 113.04 in2 452.16 in2 1,017.36 in2 4,069.44 in2

The solution to a system of equations is any ordered pair that
makes both equations true/false

Answers

the answer to the question is true

Answer: false

Step-by-step explanation:

Which of the following is the equation of the line that is parallel toy= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2

Answers

Answer:

Step-by-step explanation:

We want to write the equation of a line that is parallel to:

$y=(3)/(5)x+8$

And also passes through (-10, 4).

Remember that parallel lines have the same slope.

The slope of our old line is 3/5.

Therefore, the slope of our new line is also 3/5.

We know that it passes through (-10, 4). So, we can use the point-slope form:

$y-y_1=m(x-x_1)$

Where m is the slope and (x₁, y₁) is a point.

So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:

$y-(4)=(3)/(5)(x-(-10))$

Simplify:

$y-(4)=(3)/(5)(x+10)$

Distribute on the right:

$y-4=(3)/(5)x+6$

Add 4 to both sides:

$y=(3)/(5)x+10$

So, our answer is C.

And we're done!

Step-by-step explanation:

Hey there!

The equation of a st.line passing through point (-10,4) is ;

(y-y1)= m1(x-x1) [one point formula]

Put all values.

(y - 4) = m1( x + 10)..........(i)

Another equation is; y = 3/5 + 8.............(ii)

From equation (ii)

Slope (m2) = 3/5 [ By comparing equation with y = mx+c].

As per the condition of parallel lines,

Slope of equation (i) = slope of equation (ii)

(i.e m1 = m2 )

Therefore, the value of m1 is 3/5.

Putting value of slope in equation (i).

$(y - 4) = (3)/(5) (x + 10)$

$(y - 4) = (3)/(5) x + (3)/(5) * 10$

$(y - 4) = (3)/(5) x + 6$

$y = (3)/(5) x + 10$

Therefore the required equation is y = 3/5x + 10.

Hopeit helps...

A drawer contains 3 tan sweaters and two black sweaters. You randomly choose two sweaters. What is the probability that both sweaters are black?

Answers

A = event that you select a black sweater
P(A) = 2/5 since there are 2 black out of 2+3 = 5 total

After you make a selection, we have the event
B = event that you select another black sweater assuming event A has happened already

P(B) = 1/4 because there's 1 black sweater left out of 5-1 = 4 left over

Multiply the probabilities
P(A and B) = P(A)*P(B)
P(A and B) = (2/5)*(1/4)
P(A and B) = 2/20
P(A and B) = 1/10

The answer as a fraction is 1/10
In decimal form, it is 0.1
As a percent, the answer is 10%

Based on the scatterplot of the transformed data and the residual plot, which type of model is appropriate for estimating print publication each year? A linear model is appropriate because the residual plot does not show a clear pattern. A power model is appropriate because the scatterplot of years and the log of circulation is roughly linear. An exponential model is appropriate because the scatterplot of years and the log of circulation is roughly linear and the residual plot shows no distinct pattern. Both an exponential and a power model would be appropriate because the log of circulation was used to develop the model.

Answers

Answer:

Step-by-step explanation:

Answer: c

Step-by-step explanation:

I just took the test and got it correct

Х
If two lines do not intersect, then
they are parallel.

Answers

If it is not intersect they are not parallel

Determine whether the improper integral converges or diverges, and find the value of each that converges.∫^0_-[infinity] 5e^60x dx

Answers

Answer:

The improper integral converges.

$\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12)$

General Formulas and Concepts:
Calculus

Limit

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_(x \to c) x = c$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = (x^(n + 1))/(n + 1) + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Method: U-Substitution

Improper Integral: $\displaystyle \int\limits^(\infty)_a {f(x)} \, dx = \lim_(b \to \infty) \int\limits^b_a {f(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = 5 \int\limits^0_(- \infty) {e^(60x)} \, dx$
[Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) 5 \int\limits^0_(a) {e^(60x)} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = 60x$
[u] Differentiate [Derivative Properties and Rules]: $\displaystyle du = 60 \ dx$
[Bounds] Swap: $\displaystyle \left \{ {{x = 0 \rightarrow u = 0} \atop {x = a \rightarrow u = 60a}} \right.$

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) \int\limits^0_(a) {60e^(60x)} \, dx$
[Integral] Apply Integration Method [U-Substitution]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) \int\limits^0_(60a) {e^(u)} \, du$
[Integral] Apply Exponential Integration: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1)/(12) e^u \bigg| \limits^0_(60a)$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = \lim_(a \to - \infty) (1 - e^(60a))/(12)$
[Limit] Evaluate [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1 - e^(60(-\infty)))/(12)$
Rewrite: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12) - (1)/(12e^(60(\infty)))$
Simplify: $\displaystyle \int\limits^0_(- \infty) {5e^(60x)} \, dx = (1)/(12)$