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3 years ago

Point M is the midpoint of CD. What is the value of a in the figure?

Mathematics

1 answer:

liq [111]3 years ago

8 0

Answer:

a=3

Step-by-step explanation:

Given points (a, b) and (c,d), the midpoint of the points will be at

((a+c)/2, ((b+d)/2)

Therefore, given (9, 2) and (a,2a), our midpoint is at

((9+a)/2, (2+2a)/2) = (6,4)

Matching the x values to their corresponding x values and doing the same with the y values, we get

(9+a)/2 = 6

(2+2a)/2 = 4

First, we have

(9+a)/2 = 6

multiply both sides by 2 to remove the denominator

9+a = 12

subtract 9 from both sides to isolate a

a = 3

2a = 2 * a = 6

Confirming this, we have

(2+2a)/2 = 4

(2+6)/2 = 4

8/2=4

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What is the step by step equation to solve 5 (y + 2/5) = -13

Temka [501]

5( y + 2/5) = -13

Distribute the 5 by multiplying the 5 by each term inside the set of parentheses:

5y + 2 = -13

Subtract 2 from both sides:

5y = -15

Divide both sides by 5:

Y = 3

The answer is y = 3

4 0

3 years ago

A shopkeeper sold a dressing table for 7512.75 at a profit of 19*1/4% What was the cost price.

Katarina [22]

Cp=7512.75×[100÷(100+77÷4)]
=7512.75×(100÷119.25)
=6300
c.p=6300

4 0

3 years ago

Enos took out a 25-year loan for $135,000 at an APR of 6.0%, compounded monthly, and he is making monthly payments of $869.81. W

Alborosie

Present value = 135000
Monthly interest, i = 0.06/12 = 0.005
Monthly payment, A= 869.81

Future value of loan after 16 years
$F=P(1+i)^n$ [compound interest formula]
$=135000(1+.005)^{16*12}$
$=351736.652$

Future value of payments after 16 years
$\frac{A((1+i)^n-1)}{i}$
$=\frac{869.81((1+0.005)^{16*12}-1)}{0.005}$
$=279287.456$

Balance = future value of loan - future value of payments
=351736.652-279288.456
= $ 72448.20

Note: the exact monthly payment for a 25-year mortgage is
$A=\frac{P(i*(1+i)^n)}{(1+i)^n-1}$
$=\frac{135000(0.005*(1+0.005)^{25*12}}{(1+0.005)^{25*12}-1}$
$=869.806892$

Repeating the previous calculation with this "exact" monthly payment gives
Balance = 72448.197, very close to one of the choices.

So we conclude that the exact value obtained above differs from the answer choices is due to the precision (or lack of it) of the provided data.

The closest choice is therefore <span>$72,449.19</span>

6 0

3 years ago

Read 2 more answers

A table is 3.5 meters long how many centimeters long is the table

Rom4ik [11]

Maybe 70 iam not sure.

8 0

3 years ago

Read 2 more answers

The animal department wants to estimate baboon population. So they paint 50 baboons with a mark. These baboons were then release

Svet_ta [14]

Answer:

600 baboons

Step-by-step explanation:

Half the number of marked baboons showed up in the sample, so we expect the sample size to be about half of the total population. 300 is half of 600.

___

Many assumptions are involved in such an experiment and analysis. Not the least of which are the assumptions that the marked baboons end up evenly distributed through the population, and that the sample is a fair sample of the entire population.

3 0

3 years ago