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3 years ago

Which of the following have both 2 and -5 as solutions.

2 answers:

5 0

$x_1=2\ \ \ and\ \ \ x_2=-5\\\\ \Rightarrow\ \ \ (x-x_1)(x-x_2)=(x-2)(x+5)=x^2+5x-2x-10=\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =x^2+3x-10\ \ \ \Rightarrow\ \ \ Ans.\ a.$

Stella [2.4K]3 years ago

3 0

$x_1=2;\ x_2=-5\\\\(x-2)(x-(-5))=(x-2)(x+5)=x^2+5x-2x-10=x^2+3x-10\\\\Answer:a.$

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Ostrovityanka [42]

The answer is A and B

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3 years ago

a. I have five coins in my pocket – four are fair, and the other is weighted to have a 70% chance of coming up heads. I pull one

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Answer:

The conditional probability that I get four heads given I pulled out the weighted coin = 0.2401

Step-by-step explanation:

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But given that it is the weighted coin that is pulled out,

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4 years ago

If the measure of angle 3=122, then the measure of angle 2 =?

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A = 122

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6 0

3 years ago

How are the solutions to the inequality -2x ≥ 10 different from the solutions to -2x > 10?

CaHeK987 [17]

Answer:

First lets find the solutions to each inequality.

-2x $\geq \\$ 10 and -2x>10 (divide both sides by -2 to solve)

x $\leq$ -5 and x<-5

x $\leq$ -5 tell us that x could be -5 or less.

x<-5 tells us that x could be -6 or less.

The first one is less than or equal to which tells you that there is a possibility that the number is shows is could be an answer

Hope this helps ;)

4 0

4 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago