Please help asap! Due tonight!

Type the correct answer in each box. Use numerals instead of words.

lubasha [3.4K]

Answer:

System A has 4 real solutions.

System B has 0 real solutions.

System C has 2 real solutions

Step-by-step explanation:

System A:

x^2 + y^2 = 17 eq(1)

y = -1/2x eq(2)

Putting value of y in eq(1)

x^2 +(-1/2x)^2 = 17

x^2 + 1/4x^2 = 17

5x^2/4 -17 =0

Using quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 5/4, b =0 and c = -17

$x=\frac{-(0)\pm\sqrt{(0)^2-4(5/4)(-17)}}{2(5/4)}\\x=\frac{0\pm\sqrt{85}}{5/2}\\x=\frac{\pm\sqrt{85}}{5/2}\\x=\frac{\pm2\sqrt{85}}{5}$

Finding value of y:

y = -1/2x

$y=-1/2(\frac{\pm2\sqrt{85}}{5})$

$y=\frac{\pm\sqrt{85}}{5}$

System A has 4 real solutions.

System B

y = x^2 -7x + 10 eq(1)

y = -6x + 5 eq(2)

Putting value of y of eq(2) in eq(1)

-6x + 5 = x^2 -7x + 10

=> x^2 -7x +6x +10 -5 = 0

x^2 -x +5 = 0

Using quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a= 1, b =-1 and c =5

$x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(5)}}{2(1)}\\x=\frac{1\pm\sqrt{1-20}}{2}\\x=\frac{1\pm\sqrt{-19}}{2}\\x=\frac{1\pm\sqrt{19}i}{2}$

Finding value of y:

y = -6x + 5

y = -6(\frac{1\pm\sqrt{19}i}{2})+5

Since terms containing i are complex numbers, so System B has no real solutions.

System B has 0 real solutions.

System C

y = -2x^2 + 9 eq(1)

8x - y = -17 eq(2)

Putting value of y in eq(2)

8x - (-2x^2+9) = -17

8x +2x^2-9 +17 = 0

2x^2 + 8x + 8 = 0

2x^2 +4x + 4x + 8 = 0

2x (x+2) +4 (x+2) = 0

(x+2)(2x+4) =0

x+2 = 0 and 2x + 4 =0

x = -2 and 2x = -4

x =-2 and x = -2

So, x = -2

Now, finding value of y:

8x - y = -17

8(-2) - y = -17

-16 -y = -17

-y = -17 + 16

-y = -1

y = 1

So, x= -2 and y = 1

System C has 2 real solutions

4 0

3 years ago

Read 2 more answers

What is the image of point (4, 5) after a counterclockwise rotation of 270º about the origin?

andriy [413]

A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin.

Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

A clockwise rotation of 90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, a counterclockwise rotation of 270º about the origin which is equivalent to a clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)

Therefore, a counterclockwise rotation of 270º about the origin of the point (4, 5) will result in an image with the coordinate of (5, -4) (option C)

3 0

3 years ago

Savannah earns $247.00. How many hours did she work?

vivado [14]

Answer:

1. 8.25

2. Savannah

3.

Earnings of Savannah: $190

Earnings of Greg: $180

Earnings of Kevin: $165

4. 26 Hours

5. 55.55 hours (or 56 hours)

Step-by-step explanation:

Full Question Shown in the Image Attached.

1.

Constant of Proportionality is the constant value (k) of two proportional quantities.

Here, it is hours vs. wage.

It is usually y divided by x.

In this problem, hours worked is "x" and wage is "y". We can take the first row of Kevin's wages from table and find the constant of proportionality.

$\frac{Wage}{Hour}=\frac{16.5}{2}=8.25$

Thus, the constant of proportionality is 8.25

2.

We can find the highest hourly wage by first finding the unit rate, or the hourly wage for each person. Then we will compare between the 3 person.

For Savannah:

We divide the total wage (Earned Column) divided by Hours.

$\frac{19}{2}=9.5$

Hourly wage is 9.5

For Greg:

We do the similar division shown below:

$\frac{27}{3}=9$

Hourly wage is 9

For Kevin:

Again, doing the same process, we get:

$\frac{16.5}{2}=8.25$

Hourly wage is 8.25

By comparing the hourly wages of 3 people, we see that the highest hourly wage is that of Savannah's.

3.

We know hourly wage for each person. To know how much each one makes if they work 20 hours, we have to multiply 20 with their respective hourly wages.

Earnings of Savannah: 20 * 9.5= $190

Earnings of Greg: 20 * 9 = $180

Earnings of Kevin: 20 * 8.25 = $165

4.

Since she earn's $247 and her hourly wage is 9.5, we can find the hours she worked by dividing her earnings (247) by the hourly wage (9.5). Hence,

$\frac{247}{9.5}=26$

Thus, Savannah worked 26 hours

5.

For Greg to earn 500 dollars, we need to divide his earnings (500) by his hourly wage, which is $9 per hour. Thus we have:

$\frac{500}{9}=55.55$

So, Greg needs to work 55.55 hours to earn $500. If fractional hours are not possible, then Greg needs to work 56 hours.

7 0

3 years ago

When two events are mutually exclusive, why is P(A and B) 0? Explain.

Oliga [24]

probably because they dont happen at the same time so you cant't happen at the same time/.

8 0

3 years ago

Can someone help Me please?

Sindrei [870]

9514 1404 393

Answer:

minimum: 2 at x=0
maximum: 10 at x=10

Step-by-step explanation:

When looking for extremes, one must consider both the turning points and the ends of the interval. Here, there is a relative minimum at x=7, and a relative maximum at x=3. However, the values at the ends of the interval are more extreme than these.

The absolute minimum on the interval is 2 at x=0.

The absolute maximum on the interval is 10 at x=10.

8 0

2 years ago