Sadie runs a farm stand that sells bananas and grapes. Yesterday Sadie sold 13 pounds of bananas and 15 pounds of grapes for a t
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The question clearly seeks the highest values from both functions, meaning the vertices of each.
<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,
(h,k) = (1.5, 7.5)
Where (h,k) represents the vertex's location.
Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:
a = -2</span>
b = 5
Consequently,
x = - 5 ÷ - 4
x = 5 / 4
x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4
y = - 3.125 + 6.25 + 4
y = 7.125
Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s
<span>football attains a higher height.</span>
<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,
(h,k) = (1.5, 7.5)
Where (h,k) represents the vertex's location.
Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:
a = -2</span>
b = 5
Consequently,
x = - 5 ÷ - 4
x = 5 / 4
x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4
y = - 3.125 + 6.25 + 4
y = 7.125
Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s
<span>football attains a higher height.</span>
Answer:
2.30 years
Step-by-step explanation:
The fish population increased threefold in the first year, resulting in 240 * 3 = 720 fish.
(a) The logistic equation can be represented as follows
where P0 = 240 denotes the initial fish count; substituting P = 720 and t = 1 allows us to determine the constant k
b) By applying the formula below
with P set to 3000, P0 as 240, and k equal to 1.1, we can compute the duration needed for the population to reach 3000 fish
Answer:
C. The hypotenuse measures twice the distance of the shorter leg.
B. The longer leg is √3 times the length of the shorter leg.
Step-by-step explanation:
A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:
The hypotenuse of a right triangle is always opposite to the right angle. If we designate as the shorter leg, the sine law affirms that the hypotenuse is:
This indicates that the hypotenuse is double the length of the shorter leg
The longer leg, which we can call , can be determined with the Pythagorean Theorem:
Thus, it is accurate that the longer leg is √3 times longer than the shorter leg.