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3 years ago

If f(x)=x+2,g=(x)=4x-1,fg(2)?

Mathematics

1 answer:

zysi [14]3 years ago

8 0

Answer:

$f(x) = x + 2 \\ g(x) = 4x - 1 \\ find \: fg(2) \\ therefore \: fg(2) = 2 + 2 + 4(2) - 1 \\ fg(2) =8(2)-1 \\fg(2)=16-1 \\ fg(2)= 15$

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1. Given the following diagram. (a) Name the minor arc __________ Name the major arc ___________ (b) If the minor arc is 112°, w

Dmitriy789 [7]

Answer:

a) XY , XVY

b) 248°

c) UV , UY

d) 6√5 = 13.42

Step-by-step explanation:

a) The minor arc is XY

The major arc is XVY

b) ∵ The measure of the minor arc is 112°

∵ The measure of the circle is 360°

∴ The measure of the rest arc = 360 - 112 = 248°

c) UV is the tangent to the circle

UY is the secant to the circle

d) ∵ UV is a tangent to the circle at V

∵ UY is a secant to the circle

∴ (UV)² = (UX) × (UY)

∵ UX = 9 and XY = 11 ⇒ ∴ UY = 11 + 9 = 20

∴ (UV)² = 9 × 20 = 180

∴ UV = √180 = 6√5 = 13.42

6 0

3 years ago

The function g(x)=(x-2)^2. The function f(x)=g(x)+3. How much is f(x) shifted horizontally and vertically from g(x)?

Vilka [71]

For this case we have the following function transformation:
Vertical displacement.
Assume k> 0
If f (x) is the original function, f (x) + k is the original function with a vertical displacement k units up.
Answer:
Part 1:
C. The function is not shifted horizontally from g (x)
Part 2:
A. 3 units up from g (x)

5 0

3 years ago

Micah is writing a function that models the height a dolphin reaches when it propels itself from underwater to the surface, leap

stepladder [879]

Answer:

The dolphin will be above the surface of the water for 2 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

The height of the dolphin after t seconds is given by:

$h(t) = -16t^2 + 96t - 128$

According to Micha's model, how long will the dolphin be above the surface of the water?

It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which $h(t) = 0$ it crosses the surface upwards, and then the second time for which $h(t) = 0$ it crosses the surface downwards.