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Montano1993 [528]
2 years ago
7

tell whether this has one solution, infinitely many solutions, or no solution. Explain your reasoning. y=2x+7, y=3x-1

Mathematics
1 answer:
hammer [34]2 years ago
8 0

Answer:

One solution

Step-by-step explanation:

They have isolated y for you in both equations so you can plug either one into the other.

y = 3x - 1

2x + 7 = 3x - 1

isolate the x

7 = x - 1

x = 8

Go back to the original and plug 8 into x to get y.

y = 2 (8) + 7

y = 16 + 7

y = 23

This means at (8, 23) y = 2x+7 is equal to y = 3x-1. In other words they share a point at (8, 23). This is the only solution because for any other x and y they'd not be equal.

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Which red triangle shows a 90° counterclockwise rotation of the blue triangle? Check all that apply. On a coordinate plane, a bl
Tcecarenko [31]

Question:

1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)

Red triangle points; (-4, -1), (-1, -1). and (-4, -5)

2) Blue triangle points (1, 1), (4, 5), (4, 1)

Red triangle points; (-1, 1), (-1, 4). and (-5, 4)

3) Blue triangle points (0, 1), (4, 4), (4, 1)

Red triangle points; (-4, 1), (-4, 4). and (0, 1)

4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)

Red triangle points; (1, 1), (4, 1). and (4, 5)

5) Blue triangle points (-2, 5), (4, 5), (4, 1)

Red triangle points; (-1, 4), (-5, 4). and (-5, -2)

Answer:

The correctly rotated red triangles are those of (1), (2), and (5)

Step-by-step explanation:

In a 90° counterclockwise rotation, every x and y points of the original triangle are switched while the y is turned negative, as shown in the following equation;

(x, y) to (-y, x)

Therefore, the triangles that undergo a 90° counterclockwise rotation are as follows;

1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)

Red triangle points; (-4, -1), (-1, -1). and (-4, -5)

(-1, 4) → (-4, -1)

(-5, 4) → (-4, -5)

(-1, 1) → (-1, -1)

Correctly rotated 90° counterclockwise

2) Blue triangle points (1, 1), (4, 5), (4, 1)

Red triangle points; (-1, 1), (-1, 4). and (-5, 4)

(1, 1) → (-1, 1)

(4, 5) → (-5, 4)

(4, 1) → (-1, 4)

Correctly rotated 90° counterclockwise

3) Blue triangle points (0, 1), (4, 4), (4, 1)

Red triangle points; (-4, 1), (-4, 4). and (0, 1)

(0, 1) → (0, 1) ≠ (-1, 0)

(4, 4) → (-4, 4)

(4, 1) → (-4, 1)

Not correctly rotated 90° counterclockwise

4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)

Red triangle points; (1, 1), (4, 1). and (4, 5)

(-5, 4) → (4, 5) ≠ (-4, -5)

(-1, 4) → (4, 1)

(-1, 1) → (1, 1)

Not correctly rotated 90° counterclockwise

5) Blue triangle points (-2, 5), (4, 5), (4, 1)

Red triangle points; (-1, 4), (-5, 4). and (-5, -2)

(-2, 5) → (-5, -2)

(4, 5) → (-5, 4)

(4, 1) → (-1, 4)

Correctly rotated 90° counterclockwise.

8 0
3 years ago
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What is the value of the rational expression 2x^2+5x+9/x^2+2x-1 when x=-2
Sergio039 [100]

Answer:

The value of the Rational expression when x=-2 is: -7

Step-by-step explanation:

For this exercise is important to remember:

  • When a negative number is raised to an even power, the result will be positive.
  • The multiplication of signs:

       (+)(+)=+\\(-)(-)=+\\(-)(+)=-

Then, given the following Rational expression:

\frac{2x^2+5x+9}{x^2+2x-1}

You need to follow these steps in order to find its value when x=-2:

1. Substitute the given value of "x" (x=2) into the expression:

 \frac{2(-2)^2+5(-2)+9}{(-2)^2+2(-2)-1}

2. Evaluate and simplify:

\frac{2(4)+5(-2)+9}{4+2(-2)-1}=\frac{8-10+9}{4-4-1}=\frac{7}{-1}=-7

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3 years ago
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The area of a square is 9 centimeters squared (cm^2) If the sides of the square are doubled in length, what is the new area, in
Mice21 [21]

Answer:

The question says area of a square = 9 cm squared.

And they said if the sides are doubled in length what is the new length

so new length = 9 cm^2 × 9 cm^2

which should give you 81cm^2

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2 years ago
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fiasKO [112]

Answer:

y = 14

Step-by-step explanation:

y = 5x + 4

When x = 2:

y = 5 \times 2 + 4

y = 14

That's it. :)

8 0
1 year ago
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