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DedPeter [7]
3 years ago
13

Which system is equivalent to {y=-2x2 y=x-2}

Mathematics
1 answer:
kolezko [41]3 years ago
6 0

Answer:

OPTION C: y = -2y² - 8y - 8

                    x = y + 2

Step-by-step explanation:

The given equations are:

$ y = -2x^2 \hspace{20mm} \hdots (1) $

$ y = x - 2 \hspace{20mm} \hdots (2) $

From Equation (2), we get:

x = y + 2

Substituting this value of x in Equation (1), we get:

y = -2(y + 2)²

Expanding it in $ (a + b)^2  = a^2 + 2ab + b^2 $, we get:

y = -2{y² + 4y + 4}

⇒ y = - 2y² - 8y - 8

Therefore, OPTION C is the answer.

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Three ballet dancers are positioned on stage. Elizabeth is straight behind Hannah and directly left of Manuel. If Hannah and Eli
ki77a [65]

Answer: Elizabeth and Manuel have a distance of 4 meters between them.

Step-by-step explanation: Please refer to the picture attached.

From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.

We shall apply the pythagoras theorem in solving for the unknown side, EM.

The Pythagoras theorem states thus;

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the other two sides.

Substituting for the known values, we now have;

5² = 3² + EM²

25 = 9 + EM²

Subtract 9 from both sides of the equation

16 = EM²

Add the square root sign to both sides of the equation

√16 = √EM²

4 = EM

Therefore the distance between Elizabeth and Manuel is 4 meters

8 0
3 years ago
Question 14 (1 point)
valina [46]

Answer:

C(x) = 25 + 2x

Step-by-step explanation:

He already has 25 cards.

He is collecting 2 cards per month. In x months, he will have collected:

2 * x = 2x cards

That means that the number of cards he will have after x months will be the sum of the cards he already has and the cards he collects per month:

C(x) = 25 + 2x

8 0
3 years ago
Explain how to use absolute value to find the distance between (-2,-2) and (-2,5)
dem82 [27]
The absolute value of a number is its distance away from zero. Depending on how far away a number is, it has a less or greater absolute value. (-2,-2) have the same absolute value while (-2,5) have a different absolute value. Which has a greater absolute value? -25 or 6? The answer: -25, it is farther away from zero.
6 0
2 years ago
What is the answer to this problem (x+3)(x+5)
klasskru [66]
Easy, showing work,

using the method FOIL (First,Outer,Inner, Last)

Take, (x+3)(x+5) and multiply,

First,

x*x=x^{2}

Outer,

x*5=5x

Inner,

3*x=3x

Last,

3*5=15

Add the terms together,

x^{2}+8x+15   (x^{2}+5x+3x+15)

Thus, your answer.
4 0
3 years ago
Read 2 more answers
If you know that the exact volume of a cylinder is 500 π cm3, how can you find the approximate volume, without knowing the heigh
OLga [1]
The formula for the volume of a cylinder ( V<span>=πr2</span>h) is useable to find the missing height. Then, to find the radius, use the equation, <span>r = square root of (V / (pi x h)). Plug your numbers into the equation and solve.</span>
5 0
3 years ago
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