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UNO [17]
3 years ago
7

Which statement describes the end behavior of the exponential function f(x)=2^x-3

Mathematics
1 answer:
notsponge [240]3 years ago
6 0

I believe it's A. Hope it helps :)

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Which function models the area of a rectangle with side lengths of 2x - 4 units and x + 1 units?
aalyn [17]

Answer:

Area of rectangle, f(x)=2x^2-2x-4.

Step-by-step explanation:

We are given with side lengths of a rectangle are (2x-4) units and (x+1) units. It is required to find the area of rectangle.

The area of a rectangle is equal to the product of its length and breadth. It is given by :

A=L\times B

Let us consider, L = (2x-4) units and B = (x+1) units

Plugging the side lengths in above formula:

A=(2x-4)\times (x+1)

A=2x^2+2x-4x-4\\\\A=2x^2-2x-4

So, the function that models the area of a rectangle is f(x)=2x^2-2x-4.

5 0
3 years ago
A (-5,3)
stellarik [79]

Answer:

- 3/4

Step-by-step explanation:

m = difference of y / difference of x = (3 - (-3)) / (-5 -3) = 6 / -8 = - 3 / 4

6 0
3 years ago
Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.
NeTakaya

Answer:

Option B

Step-by-step explanation:

Complex roots occur as conjugate pairs so the third root is -3 - i ( note that the sign changes from + to -).

So in factor form we have:-

(x - 2)(x - (-3 + i))(x - (-3 - i)) = 0    Let's expand the last 2 factors first:-

(x - (-3 + i))(x - (-3 - i))

= (x + 3 - i)(x + 3 + i)

= x^2 + 3x +ix + 3x + 9 + 3i - ix - 3i - i^2

= x^2 + 6x + 9 - (-1)

= x^2 + 6x + 10

Now multiplying by (x - 2):-

(x - 2)(x^2 + 6x + 10) = 0

x^3 + 6x^2 + 10x - 2x^2 - 12x - 20 = 0

x^3 + 4x^2 - 2x - 20 = 0    (answer)

Option B

5 0
3 years ago
Diagram below shows the curve of a quadratic function
uranmaximum [27]

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of  -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The  r  is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

=  -6.

3 0
3 years ago
Solve for x : x-m/q = t
Ipatiy [6.2K]

Answer:

x - m/q = t

x = m/q + t is the answer

7 0
3 years ago
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