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3 years ago

Solve the simultaneous equations 2x – 3y = 12 3x + 4y = 1

Mathematics

2 answers:

Drupady [299]3 years ago

8 0

Answer:

x=3 and y=−2

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 3.

4(2x−3y=12)

3(3x+4y=1)

Becomes:

8x−12y=48

9x+12y=3

Add these equations to eliminate y:

17x=51

Then solve17x=51for x:

17x=51

17x

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=12

Substitute3forxin2x−3y=12:

(2)(3)−3y=12

−3y+6=12(Simplify both sides of the equation)

−3y+6+−6=12+−6(Add -6 to both sides)

−3y=6

−3y

−3

(Divide both sides by -3)

y=−2

levacccp [35]3 years ago

4 0

Answer:

$(3,-2)$

Step-by-step explanation:

$2x-3y=12$

$2(3)-3(-2)=12$

$6--6=12$ Two negative signs together makes a addition

$3x+4y=1$

$3(3)+4(-2)=1$

$9-8=1$

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HELP MATH ONE MORE AFTER THIS

Lady_Fox [76]

Answer:

58 units squared

Step-by-step explanation:

We want to find the area of the square. To do so, we need to find the hypotenuse of the right triangle because this coincides with the side length of the square.

We use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a^2 + b^2 = c^2

Here, a = 7 and b = 3, so:

7^2 + 3^2 = c^2

c^2 = 49 + 9 = 58

Now, the area of a square is: A = s^2, where s is the side length. Well, c is the side length, and we've already found what c^2 is (it's 58), so that means the area of the square is 58 units squared.

Thus, the answer is 58 units squared.

5 0

4 years ago

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Which amount is greater:50% of 40 or 40% of 50?

Rina8888 [55]

50% of 40 is 20, and 40% of 50 is 20, neither one is greater, they're equal

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4 years ago

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A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye

Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we select appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{x}=n\mu$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{x}=\sqrt{n}\sigma$

The information provided is:

μ = $970

σ = $129

n = 102

Since the sample size is quite large, i.e. n = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

$\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)$