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defon
3 years ago
14

Show that the statement is true. If GH has endpoints G(−2, 1) and H(4, −1), then the midpoint M of GH lies on the line y = −x +

1.
The midpoint M is ( , ). The midpoint does not lie or lies on the line y = −x + 1 since its coordinates satisfy or do not satisfy the equation.
Mathematics
1 answer:
Alex777 [14]3 years ago
7 0
Midpoint = (x1 + x2) / 2, (y1 + y2)/2
(-2,1)....x1 = -2 and y1 = 1
(4,-1)...x2 = 4 and y2 = -1
time to sub
m = (-2 + 4) / 2 , (1 + (-1) / 2
m = (2/2), (0/2)
m = (1,0) <==

y = -x + 1.....(1,0)...x = 1 and y = 0
0 = -1 + 1
0 = 0 (correct)

so the midpoint  M (1,0) lies on the line since its coordinates satisfy the equation <===
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(3n^2+13n^3+5n)-(7n+4n^3)
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F=-GMn/D^2 solve for M
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Jovita divides $12,000 into three investments: a savings account paying 4% annual interest, a bond paying 6%, and a money market
xenn [34]

Answer:

$2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

Step-by-step explanation:

Let a, b, and c be the fractions of the $12,000 that is invested in the savings, bond, & money fund respectively.

Let S1, S2, S3 be the total monies from the savings, bond, & money fund after the year with interest respectively.

We know that a+b+c=1

and

S1+S2+S3 = 12000 + 860

S1+S2+S3 = 12860

From, the question, we know that b = 2a, and c = 1 - 3a based on the condition of 2 times more in the bond account that the savings account.

Thus;

S1 = a(12000)(1.04) = 12480a

S2 = 2a(12000)(1.06) = 25,440a

S3 = (1 - 3a)(12000)(1.09) = 13080 - 39240a

We already know that;

S1+S2+S3 = 12860

Thus, Adding the 3 equations gives;

12480a + 25,440a + 13080 - 39240a = 12860

Thus, simplifying gives;

13080 - 12860 = 39240a - 12480a - 25,440a

220 = 1320a

a = 220/1320

a = 0.1667

So,b = 2 x 0.1667 = 0.3334

c = 1 - (3 x 0.1667)

c = 1 - 0.5

c = 0.5

Thus,

S1 = 12480a = 12480 x 0.1667 ≈ $2080

S2 = 25,440a = 25440 x 0.1667 ≈ $4241

S3 = 13080 - 39240(0.1667) ≈ 6539

So, $2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

3 0
3 years ago
Read 2 more answers
Solve 6 2/3 -1 1/2+4 1/6​
Tju [1.3M]

Answer:

9 1/3

Step-by-step explanation:

Make 2/3 , 1/2 , & 1/6 have the same denominator. 6 is the least common multiple for all 3 fractions.

2/3 gets multiplied by 2/2

1/2 gets multiplied by 3/3

1/6 stays the same

2/3 becomes 4/6

1/2 becomes 3/6

1/6 stays 1/6

Follow the order of operations from the original equation.

4/6 - 3/6 = 1/6 then 1/6 + 1/6 = 2/6

6 - 1 = 5 then 5 + 4 = 9

Simplify 2/6 to 1/3

Remember to add 1/3 back to 9 making it 9 1/3

8 0
2 years ago
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