Note that the 2nd equation can be re-written as y=8x-10.
According to the second equation, y=x^2+12x+30.
Equate these two equations to eliminate y:

8x-10 = x^2+12x+30

Group all terms together on the right side. To do this, add -8x+10 to both sides. Then 0 = x^2 +4x +40. You must now solve this quadratic equation for x, if possible. I found that this equation has NO REAL SOLUTIONS, so we must conclude that the given system of equations has NO REAL SOLUTIONS.

If you have a graphing calculator, please graph 8x-10 and x^2+12x+30 on the same screen. You will see two separate graphs that do NOT intersect. This is another way in which to see / conclude that there is NO REAL SOLUTION to this system of equations.

6 0

3 years ago

The points ????(0,0), ????(−4,1), ????(−3,5), and ????(1,4) are the vertices of parallelogram OABC Is this parallelogram a

gavmur [86]

Answer:

Yes, parallelogram OABC is a rectangle.

Step-by-step explanation:

The vertices of a parallelogram are O(0,0), A(-4,1), B(-3,5) and C(1,4).

A parallelogram is a rectangle if its any two adjacent sides are perpendicular to each other.

product of slopes of two perpendicular lines is -1.

Formula for slope is

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Using the formula we get

$m_{OA}=\dfrac{1-0}{-4-0}=-\dfrac{1}{4}$

$m_{AB}=\dfrac{5-1}{-3-(-4)}=-\dfrac{4}{1}=4$

$m_{OA}\times m_{AB}=-\dfrac{1}{4}\times 4=-1$

It means OA is perpendicular to AB.

Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.

6 0

3 years ago

I dont understand what to do and what the answer is

hodyreva [135]

Answer:

-1

Step-by-step explanation:

slope=(y2-y1)/(x2-x1)=(2-4)/(0+2)=-2/2=-1

3 0

2 years ago

Read 2 more answers

1- the diameter of a CD is 24 cm nearest to cm .find its upper and lower bound.

Tanya [424]

Answer:

1) Lower bound = 23.5 cm

Upper bound = 24.5 cm

2) I disagree

3) 7.88

4) 2.32

5) Ahmed = 60 kg

Jasim = 20 kg

Dalal = 100 kg

Step-by-step explanation:

1) diameter = 24 cm was rounded up to the nearest cm.

Now, usually, we round up 0.5 to the next whole number. This means that, the actual diameter is;

23.5 ≤ D < 24.5

Thus;

Lower bound = 23.5 cm

Upper bound = 24.5 cm

2) If you weigh 57g,converting to kg is 0.57 kg.

Now, this does not fall in between 56.5kg and 57.5kg given.

Thus, I disagree that your weight could be anything between 56.5kg and 57.5kg .

3) 7.875 approximated to the nearest two decimal place = 7.88

4) 2.3242900000 to the nearest 2 decimal place = 2.32

5) 180 kd shared between ahmed ,jasim and Dalal in the ratio of 3:1:5.

Total part of ratio = 3 + 1 + 5 = 9

Their respective shares are;

Ahmed = 3/9 × 180 = 60 kg

Jasim = 1/9 × 180 = 20 kg

Dalal = 5/9 × 180 = 100 kg

4 0

2 years ago