The endpoints of CD are C(3,−5) and D(7, 9). The coordinates of the midpoint M of CD are?

Explanation:

Step-by-step clarification:

Referring to step 6

(b² — 4ac) / 4a² = (x + b/2a)²

The mistake in the question is that it should be (x + b/2a)²

According to step 7

±√(b² —4ac) /2a = x + b/2a

The error in the question is that it should be divided by 2a, not 1a.

1. The transition from step 6 to step 7 involves taking the square roots of both sides

(b² — 4ac) / 4a² = (x + b/2a)²

Taking the square of both sides

√(b²—4ac) / √4a² = √(x + b/2a)²

√(b²—4ac) / 2a = x + b/2a

This forms step 7 correctly.

Next, subtracting b/2a from both sides

√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a

√(b²—4ac) / 2a — b/2a = x

(√(b²—4ac)  — b)/2a = x

x = [—b ± √(b²—4ac)] / 2a

This gives the desired formula.

The discriminant is D = b²—4ac.

FV = P(1 + r/t)^nt, where P denotes the principal amount, r is the interest rate, t is the frequency of compounding per year, and n is the total number of years.

Calculating: FV = 7650(1 + 0.05/4)^(9 x 4) = 7650(1 + 0.0125)^36 = 7650(1.0125)^36 = 7650(1.564) = $11,964.17

Answer:

Step-by-step explanation:

Provided

Height = 10cm

Refer to the attachment for the complete question

Required

Calculate the volume of the circle

Volume is determined as follows:

We'll take

Thus; Volume now becomes

Insert 10 for h

Given that the radius is unspecified;

The volume of the circle is:

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.

Answer: Option C - Construction Y, as point E serves as the circumcenter of triangle LMN.

Point E is ideal for the warehouse since it maintains equal distances from the three stores located at L, M, and N.

Step-by-step explanation:

To effectively tackle an algebra problem, establishing a geometric illustration frequently proves beneficial. Geometry states that three points define a circle; meaning, there is one unique circle encompassing all three non-collinear points. Identifying the point equidistant from these three points corresponds to finding the circle's center that passes through them (as all points on the circle share equal distance from the center).

Considering our points L, M, and N, draw the segments LM, LN, and MN to outline a triangle. Construct the perpendicular bisectors of any two line segments, and their intersection, point E, will indicate the center of this circle.

As illustrated in Construction Y, E represents the circumcenter of triangle LMN.

This makes it the most suitable place for the warehouse, being equidistant from all three stores at L, M, and N.

QED!