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3 years ago

Match the range of the function f(x) = x2 2x − 1 to its domain.

1 answer:

Ivan3 years ago

7 0

F(x) = x^2 + 2x -1

Domain all real number

Range: all real numbers equal or greater than -2.

To find the range you need to find the vertex of the parabole, which is (-1,-2) and use the fact that, given that the coefficient of x^2 is positive, the funcion open upwards (which means that the vertex is a global minimum).

To find the vertex you use the quadratic formula to find the roots and then the x-coordinate of the vertex is in the middle of the two roots.

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the coordinates of the endpoints of AB are A (-8, -2) and B(16,6). Point P is on AB what are the coordinates of point P such tha

garri49 [273]

We have that
<span>A (-8, -2) and B(16,6)

step 1
find the distance AB in the x coordinates
dABx=(16-(-8))-----> 24 units

step 2
find coordinate x of P (Px)
Px=Ax+(3/5)*dABx------> Px=(-8)+(3/5)*24----> 6.4

step 3
F</span>ind the distance AB in the y coordinates
dABy=(6-(-2))-----> 8 units

step 4
find coordinate y of P (Py)
Py=Ay+(3/5)*dABy------> Py=(-2)+(3/5)*8----> 2.8

the coordinates of P are (6.4,2.8)

see the attached figure

6 0

3 years ago

3x-4y=11 <br>3x+2y=2<br>please help, I need to find what the answer is for x and y

Zielflug [23.3K]

Answer:

I have attached a picture of me solving the equation.

Now you must be wondering how I got the answer, well first simplify the expression in y = mx + b. Then graph it on demos. Do the same thing for the other expression. Pick any point that lies on the line. That is your solution to the equation.

The green line is the expression of 3x - 4y = 11. I simplify the equation in y = mx + b giving me y = 3/4x - 11/4.

The orange line is the expression of 3x + 2y = 2. I simplify the equation in y = mx + b giving me y = -3/2x + 1.

Hope this helps, thank you !!

3 0

3 years ago

.Choose the equation that represents the line that passes through the point (−1, 6) and has a slope of −3.

leonid [27]

Y=-3+3 answer do I need to explain?

5 0

2 years ago

An object is heated to 100°. It is left to cool in a room that

stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one. It involves natural logs and being able to solve equations that require natural logs. The formula is as follows:

$T(t)=T_{1}+(T_{0}-T_{1})e^{kt}$ where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value. That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

$80=30+(100-30)e^{5k}$ which simplifies to

$50=70e^{5k}$ Divide both sides by 70 to get

$\frac{50}{70}=e^{5k}$ and take the natural log of both sides:

$ln(\frac{5}{7})=ln(e^{5k})$

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared). That gives us:

$-.3364722366=5k$