A maple tree loses 384 leaves during the first week of fall, and 3/2 as many each successive week. At the end of 7 weeks, all th

Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x denote the smaller number and y denote the larger number.

Part 1

The equation presented indicates that four times some number added to three times a larger number equals 31.

This translates to:

• 4x + 3y = 31

From here, solving for y yields:

• 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

This indicates the correct response for this scenario:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

The statement that seven subtracted from the larger number equals twice the smaller number translates to:

y-7= 2x

Further, solving for y yields:y-7= 2x ⇒

y= 2x+ 7

The correct answer for this equation is:

y = 2 x + 7

You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)

The precise distance between the two points is calculated to be 10.

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>

Answer:

According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.

Consequently, a single whole stick of butter will suffice to prepare $100$ cupcakes.