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3 years ago

Solve the system of equations. 3x-4y=8 18x-5y=10

Mathematics

1 answer:

ipn [44]3 years ago

7 0

Answer:

y = -2 x = 0

Step-by-step explanation:

1. 3x-4y = 8

2. 18-5y = 10

Multiply equation 1 by 6

3. 18x-24y = 48

Subtract equation 2 from equation 3

4. -19y = 38

y = 38/-19

y = -2

Sub y = -2 back into equation 1

3x-4(-2) = 8

3x + 8 = 8

3x = 0

x = 0/3

x = 0

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How many eights are there in 6 1/2

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8*6.5 = 52 eighths in 6 1/2

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3 years ago

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Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 weeks, but a river that can

Romashka [77]

Answer:

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it $R_{empty}$ empties the lake in 10 weeks and a river (with rate $R_{river}$ can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

$R_{empty}=\frac{1\ lake}{10\ weeks}$ which implies that this rate empties 0.1 of the lake per week, thus, $R_{empty}=0.1/week$ .

Using the same idea, we can obtain that the filling rate of the river is:

$R_{river}=\frac{1\ lake}{20\ weeks} = 0.05 /week$

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

$R_{total}=R_{empty}+R_{river}\\R_{total}= -0.1 + 0.05=-0.05/week$ , which means that the lake is being empty at a rate of -0.05 week and using the rule of three:

$\frac{0.05}{1} = \frac{1}{total\ of\ weeks} \\total\ of\ weeks = \frac{1}{0.05}=\frac{1}{\frac{1}{20} }\\ total\ of\ weeks = 20$

Thus, It takes 20 weeks to empty the lake.

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3 years ago

If the degree measure of an angle is 40° less than 3 times the degree measure of its supplementary angle, what is the degree mea

pishuonlain [190]

Let the measure of the unknown angle is x °
Supplementary angles sum up to 180°. So the supplementary angle of x° will be (180 - x)°

According to the given data, measure of x is 40° less than 3 times the measure of its supplementary angle (180 - x). So we can set up the equation for this scenario as:

$x = 3(180 - x ) - 40 \\ \\ 
x = 540 - 3x - 40 \\ \\ 
x + 3x = 500 \\ \\ 
4x = 500 \\ \\ 
x = 125$

So the degree measure of the required angle is 125°.

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3 years ago

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Please please i need help i will mark u brill

sergij07 [2.7K]

Answer:

Step-by-step explanation:

65 ÷ b + 8 x 4 = 20

Putting value of b = 5 in the equation

65 ÷ 5 + 8 x 4 = 20

13 + 8 x 4 = 20

13 + 32 = 20