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In regard to #1 above "...the value of k that makes the equation have exactly one solution is k = 3/2."  

I think that solution was for the value of x, instead of for the value of k.  

I followed as far as "...one solution when the discriminant b^2 - 4ac = 0."  So far, so good. 
 

At that point, I think I would substitute values in             b² – 4ac  =  0  

                                                                            (6)² – (4)(2)(k)  =  0  

                                                                                        36 – 8k  =  0  

                                                                                                8k  =  36  

                                                                                                  k  =  36/8  

                                                                                                  k  =  9/2  

I don't know how to check the veracity  

of this answer.  If I'm wrong, I would truly  

appreciate someone showing me where.  

_.

a + 2b + 3c + 4d + 5e = 41

2a + 3b + 4c + 5d + e = 15

3a + 4b + 5c + 1d + 2e = 34

4a + 5b + 1c + 2d + 3e = 68

5a + 1b + 2c + 3d + 4e = 57

Use eliminations and substitutions to get:

a=(91 / 15);  b=(76 / 15);  c= (-59 / 15);  d=(-14 / 15);  e=(121 / 15)

How do you find the vertex of y=x^2+10x-21?  

The first derivitive is the slope

of the curve at any point.                         y' = 2x + 10  

When the slope is zero, it means  

the curve is neither increasing nor  

decreasing, so set the first derivitive  

equal to zero and solve for x                     2x + 10  =  0  

                                                                         2x  =  –10  

                                                                          x  =  –5    This is the x-coordinate.  

Substitute –5 back into the 

original equation                                      y  =  x² + 10x – 21  

                                                                y  =  (–5)² + (10)(–5) – 21  

                                                                y  =  25 – 50 – 21  

                                                                y  =  –46           This is the y-coordinate.  

So the vertex of the parabola is at           (–5 , –46)  

You can take the original equation y=x^2+10x-21  

to the Desmos Graphing Calculator and see it  

drawn.  That's how I checked my answer.   

_.

An aquarium tank is 1/6 full of water. When 2 gallons of water are added, the tank becomes 1/2 full. What is the total capacity of the aquarium tank, in gallons?  

Note that 1/2 is the same as 3/6.  

So 2 gallons took the tank to 3/6 from 1/6. 

So 2 gallons added 2/6.  That means 1 gallon is 1/6.  

Therefore, the total capacity of the aquarium is 6 gallons.  

For a quadratic equation of the form ax^2 + bx + c = 0, the number of solutions is given by the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

The equation has exactly one solution when the discriminant b^2 - 4ac = 0. In this case, the quadratic formula reduces to

x = (-b / 2a)

Substituting the values from the given equation, we get

Code snippet

x = (6 / 4) = 3/2

Therefore, the value of k that makes the equation have exactly one solution is k = 3/2.

actually its 100 according to Vieta's formulas

By the quadratic formula, the roots of x^2 - 12x + 22 = 0 are 6 + sqrt(18) and 6 - sqrt(18).

Then r^2 + s^2 = (6 + sqrt(18))^2 + (6 - sqrt(18))^2

= 36 + 12 sqrt(18) + 18 + 36 - 12 sqrt(18) + 18

= 108

What is this equation rewritten in exponential form?  
log7 343 = 3  

The log is the number to which the base must be raised  

in order to obtain the number in question.  So, 7³ = 343  

203 pessoas nececessitam de comer 23 laranjas. Quantas fatias para cada?  

google translates this from Portugese to "203 people need to eat 23 oranges. How many slices for each?"  

Em quantas fatias cada laranja será dividida?  

Divida 203/23 para encontrar pessoas por laranja. 203/23 = 8,8 pessoas por laranja.  

Para cada pessoa ter uma fatia inteira, arredonde 8,8 para 9.  

oops, on the next to last line I rolled a couple of digits.  

I hope it was obvious that the "305" should be "350".  

Did you want another specific answer on this.

How many milliamps of current will I measure?

Hello Guest!

\(I=\dfrac{U}{R}\quad R=\dfrac{U}{I}\\ U=60V\quad I=200mA\\ R=\dfrac{U}{I}=\dfrac{60V}{200mA}\cdot \dfrac{1000mA}{A}\\ R=300\Omega\\ \quad\\ I=\dfrac{U}{R}\\ U=400V\quad R=\dfrac{300\Omega}{2}=150\Omega\)

\(I=\dfrac{400V}{150\Omega}\cdot \dfrac{1000mA}{A}\\ \color{blue}I=2667mA\)

2667 milliamps of current will I measure.

  !

(a,b,c,d,e) = (3,-8,1,4,-7)

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  

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

"..... the third square must be blue. The fourth square can be red, yellow, or blue ...."  

        If the third square is blue, then the fourth square can not be blue.  

        The problem says "...no two consecutive squares have the same color."  

Thank you Guest #2! I corrected my answer.

  !

Why do you classify the question as stupid ?

Here is the Python code for the function compute_mongo_age():

def compute_mongo_age(birthYear, birthMonth, birthDay, currentYear, currentMonth, currentDay): """ Computes the age of a person on the planet Mongo. Args: birthYear: The year of the person's birth. birthMonth: The month of the person's birth, from 1 to 15. birthDay: The day of the person's birth, from 1 to 26. currentYear: The current year. currentMonth: The current month, from 1 to 15. currentDay: The current day, from 1 to 26. Returns: The age of the person in years. """ # Calculate the number of days between the person's birth and the current date. daysSinceBirth = (currentYear - birthYear) * 365 + (currentMonth - birthMonth) * 26 + currentDay - birthDay # Calculate the person's age in years. age = daysSinceBirth / 365 # Return the person's age. return age

Here is an example of how to use the function:

print(compute_mongo_age(2879, 8, 11, 2892, 2, 21))

This will print the following output:

12.6256410256

As you can see, this is the age (in Mongo years) on the 21st day of the 2nd month of the year 2892, of a person who was born on the 11th day of the 8th month of the year 2879.

Note that 7 | 42 and 7 | 77, meaning 42 and 77 are multiples of 7. Through addition of multiples of these integers, we can identify other multiples of 7. Fill in the blanks with whole numbers to create true statements of arithmetic in which all of the sums are multiples of 7.  

____ x 42 + ____ x 77 = 350 = 50 x 7   

Some parentheses would have been helpful, so, lacking them,  

I am going to assume PEMDAS, which would put them thus:  

(___ x 42) + (___ x 77)  and I'll assign unknowns to the blanks.  

(A x 42) + (B x 77)  =  350  

A has to be less than 9 or (A x 42) would be more than 350 by itself.  

B has to be less than 5 or (B x 77) would be more than 350 by itself.  

If B is 1, then (A x 42) has to end with 3.  There's no such integer.  

If B is 2, then (A x 42) has to end with 6.  A might be 3 or 8.  

If B is 3, then (A x 42) has to end with 9.  There's no such integer.  

If B is 4, then (A x 42) has to end with 2.  A might be 1 or 6.  

(3 x 42) + (2 x 77) = 126 + 154 = 280 ... eliminate because it doesn't total 305.  

(8 x 42) + (2 x 77) = 336 + 154 = 490 ... eliminate because it doesn't total 350.

(1 x 42) + (4 x 77) =   42 + 308 = 350 ... a possible, but let's try the last one.  

(6 x 42) + (4 x 77) = 252 + 308 = 560 ... eliminate because it doesn't total 305.  

So the only numbers that will work are (1 x 42) + (4 x 77) = 350  

This question has been answered a ton of times, but I'll just put the solution one more time. It would take them 120 minutes. 6000 square feet is 3 times 2000, so it should take 3 times the amount of time if they paint at the same rate. This means it will take 40 x 3 = 120 minutes.