If g(x)=4x^2-16 were shifted 5 units to the right and 2 down, what would the new equation be?

Let

x represent the cost per pound of ham
y represent the cost per pound of cheese

<span>1.3x + 0.8y = 11.28....(1)
1.5x + 1.2y = 14.76....(2)

Now, let's multiply equation (1) by -1.2
...and multiply equation (2) by 0.8

Then we obtain -1.56x - 0.96y = -13.536.....(3)
</span>...and 1.2x + 0.96y = 11.808.....(4)


Adding (3) and (4) results in

-0.36x = -1.728............> x = 4.8

Substituting x back into (1)

1.3(4.8) + 0.8y = 11.28

y = 6.3

Cost per pound of ham = x = 4.8
Cost per pound of cheese = y = 6.3

Answer:

Part A: During the interval from 0 to 2 seconds, the water balloon reaches a height of 75 feet from an initial height of 60 feet, showing an increase in height during [0,2]

Part B: Between 2 to 4 seconds, the height remains constant at 75 feet, indicating a stable height during [2,4]. Similarly, from 10 to 12 seconds, the height stays at 0 feet, thus remaining unchanged during [10,12] and from 12 to 14 seconds, it also remains at 0 feet, indicating stability during [12,14].

Part C: The water balloon height decreases most rapidly between the intervals [4,6], dropping by 35 feet. The other intervals that show a decrease, [6,8] and [8,10], drop by 20 feet each. Thus, it reveals that the decreasing interval [4,6] is the most significant, as 35 feet is a more considerable reduction compared to 20 feet.

Part D: I estimate that at 16 seconds, the height of the water balloon will be 0 feet. This correlates with the height of the balloon being 0 feet between 10 and 14 seconds. In real-life contexts, if the balloon rests on the ground at 0 feet, it stays on the ground because of gravitational force.

Step-by-step explanation:

I hope this offers some assistance! I can't confirm if everything is accurate, but I have researched thoroughly, so fingers crossed it is correct! Best of luck!

A single rose sells for 50 cents, so buying two will cost $1 (50 cents multiplied by 2).

With 2 roses per dollar, spending $20 allows for the purchase of 40 roses.

They make $6 profit on $20 sales, which means they spend $14 on the 40 roses ($20 minus $6).

Dividing $14 by 40 roses gives a cost of $0.35 per rose.

Therefore, the vendor pays 35 cents for each rose.

Approximately 2, I believe... I calculated it to be around 2.10. 

Response:

• Refer to the attached graph

• x₁ ≈ - 2.1

• x₂ ≈ 0.2

Clarification:

To analyze log (−5.6x + 1.3) = −1 − x visually, graph these equations on the same coordinate system:

• Equation 1: y = log (5.6x + 1.3)

• Equation 2: y = - 1 - x

The first equation can be graphed using these characteristics of logarithmic functions:

• Domain: values must be positive ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)

• Range: all real values (- ∞, ∞)

• x-intercept:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒ x = 0.3/5.6 ≈ 0.054

• y-intercept:

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

• Choose additional values to create a table:

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

• This graph is shown in the attached image: it's represented by the red curve.

Graphing the second equation is simpler as it forms a straight line: y = - 1 - x

• slope, m = - 1 (the coefficient of x)

• y-intercept, b = - 1 (the constant term)

• x-intercept: y = 0 = - 1 - x ⇒ x = - 1

• This graph is indicated by the blue line in the image.

The resolution to the equations corresponds to the points where the two graphs intersect. The graphing method thus allows you to determine the x coordinates of these intersection points. Ordered from smallest to largest, rounded to the nearest tenth, we have:

• x₁ ≈ - 2.1

• x₂ ≈ 0.2