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4 years ago

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

1 answer:

3 0

We have that
y=x²----> equation 1
y=x+2-----> equation 2

multiply equation 1 by -1
-y=-x²

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
Complete the square. Remember to balance the equation by adding the same constants to each side
(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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Line

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? x − x4 x3 x2 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