Answer: y²z⁴ / x¹²
Explanation:
1) The expression to simplify:
2) Rule: power of a power:
3) Rule: product of powers with identical bases
4) Add up the exponents
5) Transfer the negative exponent to the denominator:
The exponent attached to x is 12, for y it is 2, and for z it is 4.
In the first month, she made a payment of $1451
In the second month, she paid one-third of that, which amounts to:
1451/3 = 483.66
For the third month, she pays one-third of 483.66 as indicated, meaning she takes one-third of the prior month's payment.
483.66/3 = 161.22
In the fourth month, her payment was
161.22/3 = 53.74
Altogether, her total payments amounted to:
$2149.62 - B.
Hope this information is helpful:)
The domain refers to all potential input values, specifically represented by the x-axis on a graph. Conversely, the range includes all possible output values, depicted along the y-axis.
The graph clearly extends horizontally from (-∞,∞) on the x-axis, indicating that its domain is (-∞,∞).
Similarly, it can be seen that the graph stretches vertically from (-∞,∞) on the y-axis, denoting that the range is also (-∞,∞).
This indicates the function includes an infinite array of values. Therefore, there are no limitations on either the domain or the range for this function.
Answer:
You need to purchase 3 shirts to be able to use your coupon.
Step-by-step explanation:
Each shirt originally costs $17.99.
There is a 20% discount on this specific brand of shirts.
$17.99 × 0.2 = $3.60 (discount per shirt)
Subtracting the discount from the original price:
$17.99 - $3.60 = $14.39 (price per shirt after discount)
To qualify for the $10 off coupon which requires a $40 minimum purchase:
$40 ÷ $14.39 ≈ 2.779, rounded up to 3 shirts
Therefore, you must buy 3 shirts.
3 shirts × $14.39 = $43.17, surpassing the $40 minimum needed to apply the $10 discount.
Since this parabola intersects the center, its formula is:
y = ax². Given that it opens downward, the coefficient a must be negative.
Thus, the equation can be expressed as:
y = - ax², with the axis of symmetry located at x = 0.
The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:
y = - ax²
84 = - a(21)²
84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.
Therefore, the final equation is: y = -4/21 x².
