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(a) Exactly one real solution: when the two parabolas intersect at exactly one point. This happens when the parabolas are tangent, which means that their slopes are equal at the point of intersection. The slopes of the parabolas are 12x-9 and 10x, so they are equal when x=9/12=3/4. Substituting this value of x into either parabola, we get y=3/2. Therefore, the system has exactly one real solution when c=3/2.

(b) More than one real solution: when the two parabolas intersect at two points. This happens when the parabolas are not tangent, but they do intersect. This happens when the discriminant of the quadratic equation 6x^2-9x+c is non-negative. The discriminant is b^2-4ac=81-4(6)(c)=81-24c. This is non-negative when 81-24c>=0, or c<=3. Therefore, the system has more than one real solution when c<=3.

(c) No real solutions: when the two parabolas do not intersect. This happens when the parabolas are not tangent and they do not intersect. This happens when the discriminant of the quadratic equation 6x^2-9x+c is negative. The discriminant is b^2-4ac=81-4(6)(c)=81-24c. This is negative when 81-24c<0, or c>3. Therefore, the system has no real solutions when c>3.

In summary, the system has:

Exactly one real solution when c=3/2.

More than one real solution when c<=3.

No real solutions when c>3.

The original number of license plates is 534 = 60.

If both new letters are added to the same set, the number of additional license plates is 234 = 24.

If one new letter is added to each set, the number of additional license plates is 232 = 12.

The largest possible number of additional license plates is 24, so the answer is 24.

You need to find out how long one side is.

The the ends of the side are the intersection of  y=7  and  y = 2x^2 + 8x + 4

Solve simultaneously

\(7=2x^2+8x+4\\ 2x^2+8x-3=0\\ x=\frac{-8\pm\sqrt{64+24}}{4}\\ x=\frac{-8\pm\sqrt{88}}{4}\\ x=\frac{-8\pm2\sqrt{22}}{4}\\ x=\frac{-8\pm2\sqrt{22}}{4}\\ x=-2\pm\frac{\sqrt{22}}{2}\\ \text{Subtract the little from the big and you get the side length of }\;\;\\\ \frac{2\sqrt{22}}{2}=\sqrt{22}\\ \text{So area is 22 }units^2\)

In a store window, there was a box of berries having a total weight of 200 kg.  The berries were 99% water, by weight.  After two days in the sun, the water content of the berries was only 90%, by weight.  What was the total weight of the berries after two days, in kg?  

You start with 200 kg of berries, and 99% of that is water.  

Since they're 99% water, that means that there is 1% of solid stuff.  

1% of 200 kg means that there are 2 kg of solid stuff.   

The water evaporates in the sun, but the solid stuff doesn't.  

So there still remains 2 kg of solid stuff.  

Since the new water content is 90%, that means that now the solid stuff is 10%.  

So 2 kg (the solid stuff) is 10% of the total weight.  

That means the new total weight is 20 kg.  

_.

There are 8 pens to choose from for the dogs, 4 pens left to choose from for the cats, and 3 pens left to choose from for the roosters. This gives us a total of 8⋅4⋅3=96​ ways to make the allocation.  I hope this helps!

Line 1: The line must be made of a 2 and a 3 with either one first, so 2 orderings. There are 4 choices for the 2 and 3 choices for the 3 thus, 2x4x3 = 24 distinct lines.

Line 2: The line must be made of two 2's and a 3 and the 3 can be first, second, or third, so 3 orderings. Since we can't use the same words from the first line, there are 3x2 choices for the 2's and 2 choices for the 3, thus, 3x3x2x2 = 36 distinct lines.

Line 3: Like the first line, we must use a 2 and a 3 in some order, so 2 orderings. There is only 1 choice left for each of the 2 and the 3 thus, 2x1x1 = 2 distinct lines.

Putting all the options together, we get: 

24x36x2 = 1728

thanks

>>>>> and it was taken down <<<<<  

Are you certain?  Is it possible that so many new postings came in during those couple of days that your posting just got pushed down off the top page?  Maybe several pages down.  If you'd register an account, you could click your user name and get to a compilation of every thing you had posted under that username.     

_.

Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?  

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

The time on the clock is          2:00 pm + 54.29 min  =  2:54:17 pm 

(The :17 is because 0.29 minute is 17 seconds.)  

A bag contains yellow, green, blue, and white marbles.  The ratio of yellow, green, blue, and white marbles is 1:2:3:4.  If the bag contains 180 marbles, then how many blue marbles are there?  

Consider:  "The ratio of yellow, green, blue, and white marbles is 1:2:3:4."  

Call the number of yellow marbles X.  

So the number of green marbles is 2X. 

And the number of blue marbles is 3X.  

And the number of white marbles is 4X.  

Add up all the marbles and you have     10X  =  180  

Therefore                                                   X  =  18 yellow marbles  

                                                                 2X  =  36 green marbles  

                                                                 3X  =  54 blue marbles  

                                                                 4X  =  72 white marbles  

_.

Carissa's average speed during the entire round trip was 117.64 meters per hour.

To solve this problem, we can first calculate the total distance that Carissa traveled. We know that she walked from a café to a boba shop, and then took the same route in reverse. Let's assume that the distance from the café to the boba shop is 1000 meters. This means that Carissa traveled a total distance of 2000 meters.

Next, we need to calculate the time it took Carissa to complete the round trip. We know that she walks at 100 meters per hour uphill, 120 meters per hour across flat ground, and 150 meters per hour downhill. We can use this information to create a table of the time it took Carissa to travel each segment of the round trip:

SegmentDistanceSpeedTime

Uphill1000 meters100 meters per hour10 hours

Flat1000 meters120 meters per hour8.33 hours

Downhill1000 meters150 meters per hour6.67 hours

The total time it took Carissa to complete the round trip is 25 hours.

Finally, we can calculate Carissa's average speed by dividing the total distance by the total time. This gives us an average speed of 117.64 meters per hour.

Total distance = 2000 meters

Total time = 25 hours

Average speed = 2000 / 25 = 117.64 meters per hour

idk sorry i need this too

The answer is 60 cm.

This is equal to 2*sqrt(2).

First Method:

When the distance covered back and forth is the same, then:

Average speed = Harmonic mean

Harmonic Mean = 3 / [100^-1  +  120^-1  +  150^-1] =120 m/s - her average speed

Second Method:

Time travelled back and forth = 3 hours  + 1 hour  +  40 minutes  +  90 minutes =6 + 1/6 hours

Total distance travelled = 2 * [100 + 120 + 150] = 740 meters

Average speed = 740 / (6 1/6) =120 m/s - her average speed.

I agree, the answerer is impaired mentally.

That is incorrect.

Actually, I identify as NON BINARY. STOP ASSUMING MY GENDER.