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DIA [1.3K]
2 years ago
13

Solve the following system by any method.

Mathematics
1 answer:
Fed [463]2 years ago
8 0
answer is C. (3, 0)
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How much acid acid is in a 10 L container of acetic acid and water that is marked 80% acetic acid ​
Readme [11.4K]
8L because 80% —> 80/100 —> 8/10
8 0
3 years ago
How to factor <br> 49y^{2}-9x^{2}
lorasvet [3.4K]

Answer:

(7y + 3x)(7y - 3x)

Step-by-step explanation:

a² - b² = (a + b)(a - b)

49y² - 9x² = (7y)² - (3x)²                   {a = 7y ; b - 3x}

               = (7y + 3x)(7y - 3x)

7 0
2 years ago
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Darina [25.2K]

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

7 0
2 years ago
Which object has the same y-intercept as a function y=2/3x-3?
Licemer1 [7]

The 4th option.

The values with no x or y attached are the y intercept

6x - 7y = 21

Subtract 6x from both sides

6x - 7y - 6x = 21 - 6x

-7y = 21 - 6x

Divide both sides by - 7

-7y/-7 = 21/-7 - 6x/-7

Y = -3 +6x/7


The why intercept, -3 is the same as the one in the question


7 0
3 years ago
On a coordinate plane, triangle A B C has points (negative 3, negative 1), (negative 2, negative 3), (1, negative 1) and is refl
andreev551 [17]

Answer:

A' = (-3, 3)

Step-by-step explanation:

If the points are as follows:

A = (-3, -1)

B = (-2, -3)

C = (1, -1)

When reflecting across a y axis the x values remain the same.

When reflecting across y = 1 the y values will remain equal distant from y = 1.

A' = (-3, 3) y value = |-1 - 1| = 2 + 1 = 3

B' = (-2, 5) y value = |-3 - 1| = 4 + 1 = 5

C' = (1, 3) y value = |-1 - 1| = 2 + 1 = 3

7 0
2 years ago
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