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4 years ago

Which ordered pair is a solution to the system of linear equations?

Mathematics

2 answers:

enyata [817]4 years ago

5 0

2x + 3y = 6.....multiply by 3
-3x + 5y = 10...multiply by 2
-----------------
6x + 9y = 18 (result of multiplying by 3)
-6x + 10y = 20 (result of multiplying by 2)
-----------------add
19y = 38
y = 38/19
y = 2

2x + 3y = 6
2x + 3(2) = 6
2x + 6 = 6
2x = 6 - 6
2x = 0
x = 0

solution is : (0,2)

LiRa [457]4 years ago

4 0

Answer is (0,2). I have the picture above as my work. I am very sure it's right.

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Is it possible to solve a quadratic equation that is not factorable over the set of integers? Explain.

zvonat [6]

Answer:

Yes

Step-by-step explanation:

Yes it is possible to solve a quadratic equation that is not factorable over the set of integers.

The solution may vary like Integers, rationals, irrationals or complex solutions.

To find two roots of the equation we can always use the formula given below to solve a quadratic equation,

For the quadratic equation,

$ax^2+bx+c=0$ , we have,

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3 years ago

A train travels at a constant speed of 35 miles per hour how long does it take the train to travel 490 miles

charle [14.2K]

We have to write a proportion. We put 35 over 60 to show that 35 miles can go in every 60 minutes. Next to it we write another fraction and put 490 over x because we are trying to find how many MINUTES first. we multiply 490 by 60 which is 29400. Now we divide that by 35. we get 840 minutes. Now we convert this into hours by dividing it by 60 because there are 60 minutes in an hour. 840 divided by 60 is 14 hours. The answer is 14 hours.

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3 years ago

Solve each quadratic equation by completing the square. Give exact answers--no decimals.

Sholpan [36]

Answer:

$x_1 = -2 + 2i\\\\x_2 = -2 -2i$

Step-by-step explanation:

In this problem we have the equation of the following quadratic equation and we want to solve it using the method of square completion:

$7x ^ 2 + 28x +56 = 0$

The steps are shown below:

For any equation of the form: $ax ^ 2 + bx + c = 0$

1. If the coefficient a is different from 1, then take a as a common factor.

In this case $a = 7$ . Then:

$7(x ^ 2 + 4x) = -56$

2. Take the coefficient b that accompanies the variable x. In this case the coefficient is 4. Then, divide by 2 and the result squared it.

We have:

$\frac{4}{2} = 2\\\\(\frac{4}{2})^2 = 4$

3. Add the term obtained in the previous step on both sides of equality, remember to multiply by the common factor $a = 7$ :

$7(x ^ 2 + 4x + 4) = -56 + 7(4)$

4. Factor the resulting expression, and you will get:

$7(x + 2) ^ 2 = -28$

Now solve the equation:

Note that the term $7(x + 2) ^ 2$ is always $> 0$ therefore it can not be equal to -28.

The equation has no solution in real numbers.

In the same way we can find the complex roots:

$7(x+2)^2 = -28\\\\(x+2)^2 = -\frac{28}{7}\\\\x+2 = \sqrt{-\frac{28}{7}}\\\\x = -2 + \sqrt{-4}\\\\x = -2 + 2\sqrt{-1}\\\\x_1 = -2 + 2i\\\\x_2 = -2 -2i$

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4 years ago

Read 2 more answers

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Lynna [10]

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It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.

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3 years ago

if 5 billion pennies are minted each year, how long would it take to mint the pennies needed to stack to the sun? plsss show all

dimulka [17.4K]

98 years.
the sun is 432,690 away and a penny is 1.52 mm in thickness
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2 years ago