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Artemon [7]
4 years ago
6

Solve system by elimination y=x^2 y=x+2 SHOW YOUR WORK

Mathematics
1 answer:
Dimas [21]4 years ago
3 0
We have that
y=x²----> equation 1<span>
y=x+2-----> equation 2

multiply equation 1 by -1
-y=-x</span>²

add equation 1 and equation 2
-y=-x²
 y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²-x)=2
<span>Complete the square. Remember to balance the equation by adding the same constants to each side
</span>(x²-x+0.5²)=2+0.5²

Rewrite as perfect squares

(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1

for x=2
y=x²----> y=2²----> y=4
the point is (2,4)

for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)

the answer is
the solution of the system are the points
(2,4) and (-1,1)


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mel-nik [20]

Answer:

x=26

Step-by-step explanation:

we know that  

m∠KOL+m∠LOM+256°=360° -----> by complete circle

substitute the given values and solve for x

(x+3x)\°+256\°=360\°\\4x=360-256\\4x=104\\x=26

5 0
3 years ago
The same type of television is being sold at two different stores. Store A is selling the television for $ 800, which is $ 120 m
erma4kov [3.2K]

Answer: $340

Step-by-step explanation:

$800 - $120 = $680

1/2 of $680 is $340

Hope this helps!

7 0
4 years ago
What is the Greatest Common Factor of x4 and x5? <br> x − x4 <br> x3 <br> x2 <br> x
const2013 [10]

Answer: x^4

Step-by-step explanation:

Here, the given expressions are,

x^4

x^5

The factors of x^4 = x × x × x × x

While, the factors of x^5 = x × x × x × x × x

Hence, the common factors = x × x × x × x = x^4  

So, the greatest common factor of the given expression is x^4          

5 0
3 years ago
Which is the best estimate of 5 5/6 - (1 1/4 + 3 7/8)​
pantera1 [17]

Answer:

Step-by-step explanation:

"Best estimate' doesn't happen automaticallly, because you have to define "best" in this context.  We could merely round all numbers and work with the results:  

For example, starting with the work inside parentheses, we have:

5 5/6 - (1 + 4) = 5 5/6 - 5.  We must round 5 5/6 up to 6.  Then the "best estimate' is 6 - 5, or just 1.

3 0
3 years ago
Rewrite the function by completing the square. f(x)= 2x^{2}+3x-2f(x)=2x 2 +3x−2
Elena L [17]

Answer:

2\Bigl[(x+\frac{3}{4} )^2-\frac{25}{16} \Bigr]

Step-by-step explanation:

Step 1

We factor out 2 so that the coefficient of the quadratic term is 1.

f(x)=2x^2+3x-2\\f(x)=2\bigl(x^2+\frac{3}{2} -1\bigr)

Step 2

In this step we add and subtract  the square of the coefficient of the x term, this term is  \Bigl(\frac{1}{2} \bigl(\frac{3}{2}\bigr)\Bigr)^2. This is the step where we complete the square.

f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-(\tfrac{3}{4})^2 -1 \Bigr]\\f(x)=2\Bigl[x^2+\frac{3}{2}x+(\frac{3}{4})^2-\frac{25}{16} \Bigr]

Step 3

In this step we factor out the perfect square tri-nomial formed by the first 3 terms in last line of step 2.  This calculation is shown below,

f(x)=2\Bigl[\bigl(x+\frac{3}{4} \bigr)^2-\frac{25}{16} \Bigr]

6 0
3 years ago
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