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3 years ago

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Mathematics

1 answer:

Vesnalui [34]3 years ago

6 0

I think it’s the 1st one i tried let me know if it’s right

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Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and 2/5x+1/6y=3/10

natka813 [3]

ANSWER

$( \frac{2}{3} , \frac{1}{5} )$

EXPLANATION

The first equation is

$\frac{1}{2} x - \frac{3}{4} y = \frac{11}{60} ...(1)$

The second equation is

$\frac{2}{5} x + \frac{1}{6} y = \frac{3}{10} ...(2)$

We want to eliminate y, so we multiply the first equation by

$\frac{4}{5}$

$\frac{4}{5} \times \frac{1}{2} x - \frac{4}{5} \times \frac{3}{4} y = \frac{11}{60} \times \frac{4}{5}$

$\frac{2}{5} x - \frac{3}{5} y = \frac{11}{75} ...(3)$

We now subtract equation (3) from (2)

$(\frac{2}{3} x - \frac{2}{3} x )+ ( \frac{1}{6} y - - \frac{3}{5}y ) =( \frac{3}{10} - \frac{11}{75} )$

$\frac{1}{6} y + \frac{3}{5}y =\frac{3}{10} - \frac{11}{75}$

$\frac{23}{30}y = \frac{23}{150}$

Multiply both sides by

$\frac{30}{23}$

$\implies \: \frac{30}{23} \times \frac{23}{30}y= \frac{23}{150} \times \frac{30}{23}$

$\implies \: y = \frac{1}{5}$

Substitute into the first equation to solve for x .

$\frac{1}{2} x - \frac{3}{4} \times \frac{1}{5} = \frac{11}{60}$

Multiply to obtain

$\frac{1}{2} x - \frac{3}{20} = \frac{11}{60}$

$\frac{1}{2} x = \frac{11}{60} + \frac{3}{20}$

$\frac{1}{2} x = \frac{1}{3}$

Multiply both sides by 2.

$2 \times \frac{1}{2} x =2 \times \frac{1}{3}$

$x = \frac{2}{3}$

The solution is

$( \frac{2}{3} , \frac{1}{5} )$

5 0

3 years ago

Read 2 more answers

A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select ano

IgorC [24]

Answer:

Step-by-step explanation:

Total fruits T= 5+7 = 12

No. Of apple n(A) = 5

No. Of peaches n(P) = 7

P(A) 1st = n(A)/T = 5/12

P(P) 2nd = n(p)/(T-1) = 7/11

: P(A and P) = 5/12 × 7/11

= 35/132

4 0

3 years ago

How do I solve this and what answers are correct?

DanielleElmas [232]

It would be the first one and the third one then the last

8 0

3 years ago

Phyllis invested $10,500 a portion earning a simple interest rate of 9(1/5)% per year and the rest earning a rate of 9% per year

Alenkinab [10]

Total investment = $10,500

Let x = amount of first investment, and y the amount of the second investment.

First investment:
Interest rate = 9 (1/5)% = 0.092
Earned interest = 0.092x

Second investment:
Interest rate = 9% = 0.09
Earned interest = 0.09y

Total interest after one year is $957.00, therefore
0.092x + 0.09y = 957
or
1.0222x + y = 10633.33 (1)

Also,
x + y = 10500 (2)

Subtract (2) from (1).
0.0222x = 133.33
x = 6000
y = 10500 - x = 4500

Answer:
The first investment is $6,000 at 9 (1/5)% rate;
The second investment is $4,500 at 9% rate.

7 0

3 years ago

If a fair coin is tossed 9 times, in how many different ways can the sequence of heads and tails appear

Ilya [14]

10 different sequences
all tails, 1 head 8 tails,2 heads 7 tails,3 heads 6 tails,4 heads 5 tails,5 heads 4 tails,6 heads 3 tails,7 heads 2 tails,8 heads 1 tail and All heads.

3 0

3 years ago