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Xelga [282]
3 years ago
13

How many solutions does the system have? y=−2x+1 y=−2x^2+1

Mathematics
1 answer:
balu736 [363]3 years ago
8 0

Answer:

The system has two distinct solutions.

Step-by-step explanation:

The given system of equations are:


y=-2x+1--(1)

and

y=-2x^2+1---(2)


In order to determine the number of solutions the two equations have, we need to equate the two equations to obtain,



-2x^2+1=-2x+1


We now group all terms on the left hand side and equate everything to zero.

-2x^2+2x=0

x^2-x=0


This is now a quadratic equation in x^2 with a=1,b=-1,c=0.

At this stage we check the number of solutions using the discriminant.

D=b^2-4ac


\Rightarrow D=(-1)^2-4(1)(0)=1


Since the discriminant is greater than zero, the equation will have two distinct roots.

Therefore the system of equations has exactly two distinct solutions.


If you wish to see these solutions, you can continue as follows;

We factor x to obtain,

x(x-1)=0


\Rightarrow x=0,x-1=0



\Rightarrow x=0,x=1


When x=0,y=-2(0)+1


Then we have,

x=0,y=1


When x=1,y=-2(1)+1


Then we have,

x=0,y=-1


See graph






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Answer:

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Step-by-step explanation:

7(-7)= -49

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Answer:

a) 4 people ordered streak dinner

b) 3 people ordered chicken dinner

Step-by-step explanation:

Let the number of people that ordered steak dinner be x

and the number of people that ordered chicken dinner be y

From the question,

There are 7 people in your family

Hence, we can write that

x + y = 7 ...... (1)

Also from the question

Some order the chicken dinner for $13 and some order the steak dinner for $18 and the total bill was $111.

We can then write that

13y + 18x = 111 ...... (2)

From equation (1)

x + y = 7

Then,

x = 7 - y ...... (3)

Put this into equation (2)

13y + 18x = 111

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13y + 126 - 18y = 111

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5y = 15

y = 15 / 5

y = 3

Put the value of y into equation (3) to get x

x = 7 - y

Then

x = 7 - 3

x = 4

Hence, 4 people ordered streak dinner

and 3 people ordered chicken dinner

a) 4 people ordered streak dinner

b) 3 people ordered chicken dinner

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Martha earned $180 during the summer doing chores. She bought 3 books worth $14 each using her chore money. How much money was l
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Answer:

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We can first turn the words into a mathematical equation by substituting words with the information we have:

Total earning - ( Price of three books)

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Finally, after we have created the mathematical equation, we solve it!

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The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and
NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120

Let's find h with the quadratic formula:

\fbox {Quadratic formula:}  \frac{-b\pm\sqrt{b^2-4ac}}{2a}

h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}

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But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

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\fbox {Pythagorean equation:} <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

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H = 17

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So, the hypotenuse decreases H - H' \approx 17 - 14.3 = 2.7

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