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Margarita [4]
3 years ago
7

M is the midpoint of line segment AB. If the coordinates of M are (2, 6) and the coordinates of B are (5, 10), which of the foll

owing represents the coordinates of point A?
Mathematics
1 answer:
timama [110]3 years ago
4 0

Answer:

The coordinates of A would be (-1, 2)

Step-by-step explanation:

In order to find this, use the mid-point formula.

(xA + xB)/2 = xM

In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.

(xA + 5)/2 = 2

xA + 5 = 4

xA = -1

Now we can do the same using the midpoint formula and the y values.

(yA + yB)/2 = yM

(yA + 10)/2 = 6

yA + 10 = 12

yA = 2

This gives us the midpoint of (-1, 2)

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Evaluate each of the following. (a) P(11,5) (b) C(11,5) (a) P(11,5) = (Simplify your answer.) (b) C(11,5) = (Simplify your answe
Hunter-Best [27]
<h2>Answer:</h2>

(a)   P(11,5)= 55440

(b)  C(11,5)=462

<h2>Step-by-step explanation:</h2>

We know that the permutation is the number of ways of arranging r items out of a total of n items and is given by:

P(n,r)=\dfrac{n!}{(n-r)!}

and the combination is the number of ways of choosing r items out of a total of n items and is given by:

C(n,r)=\dfrac{n!}{r!\times (n-r)!}

(a)

               P(11,5)

P(11,5)=\dfrac{11!}{(11-5)!}\\\\P(11,5)=\dfrac{11!}{6!}\\\\P(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{6!}\\\\P(11,5)=11\times 10\times 9\times 8\times 7\\\\P(11,5)=55440

(b)

                 C(11,5)    

C(11,5)=\dfrac{11!}{5!\times (11-5)!}\\\\C(11,5)=\dfrac{11!}{5!\times 6!}\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{5\times 4\times 3\times 2\times 1\times 6!}\\\\C(11,5)=462

8 0
3 years ago
The volume of a rectangular prism can be computed using the formula V = lwh. What is the height of a prism that has a volume of
AnnZ [28]
18x11=198
198x12= 2376






4 0
3 years ago
Susan invests $Z at the end of each year for seven years at an annual effective interest rate of 5%. The interest credited at th
aleksley [76]

Answer:

2.02955

Step-by-step explanation:

Given that:

Susan invests $Z as each year ends for seven years.

So we assume that Z = 1

Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.

The cashflow interest:

The cashflow of Susan interest payments are:

Payments   Time

0                     1

0.05               2

2(0.05)           3

3(0.05)           4

4(0.05)            5

5(0.05)            6

6(0.05)            7

The accumulated value of this cash flow is:

(0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653

So Susan accumulated values is:

X = 7 + 1.1653

X = 8.1653

Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.

The cashflow of Lori interest payments are;

Payments    0     0.025     2(0.025)       3(0.025)    .........   13(0.025)

Time             1        2              3                    4            ..........  14

The accumulated value of cash flow is:

(0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719

Now, Lori's accumulated value is:

Y = 14 + 2.5719

Y = 16.5719

Since; Susan value X = 8.1653

Lori's value Y = 16.5719

∴

\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}

= 2.02955

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