All Answers 358147 Answers

You're very new to math too, as if the answer is negative and lower than -1 then it will be less than 1. so the answer then, is obviously (-1, 1]

You're very new to math, in this case, if you include -1 in the denominator, the answer is undefined, so you're WRONG. The answer is $(-\infty, -1)U(-1, 1)$

3x^2  + 12x  -  k  =  0

Sum of roots  =  -12/ 3  = -4

So

x + 1/x=  -4

x^2 + 4x + 1 =  0

x^2 + 4x  =  -1          complete the square on x

x^2 + 4x  + 4 =  -1 + 4

(x + 2)^2  = 3        take  both roots

x + 2 =  sqrt (3)             x + 2 = -sqrt (3)

x = sqrt (3) - 2              x =  -sqrt (3) - 2

Product of the roots  =   -k /3

So

(sqrt (3) - 2) (-sqrt (3)  -2)  =  -k/3

- (sqrt (3) - 2) (sqrt (3) + 2)  = -k/3

(sqrt (3) -2) ( sqrt (3) + 2)  = k /3

3 -4  =  k/3

-1  = k/3

k = -3

$\displaystyle \frac{3-z}{z+1} \geq{1}$

This can guide you: https://web2.0calc.com/questions/in-solving-the-system-of-equations-y-7-and-x-2-y

Multiply both sides by z + 1: 3 - z >= z + 1

Then 2z <= 2, so z <= 1.

Solution: (-inf,1].

Note that if the roots are reciprocals of each other, they will multiply to 1, meaning \(c \over a \) will equal 1, according to Vieta's. 

This means \({-c \over 3} = 1\), meaning \(\color{brown}\boxed{k = -3}\)

x^2  + (7)^2  =  100

x^2 + 49 = 100

x^2    =  51             take both roots

x = sqrt (51)          x  = -sqrt (51)

Sum  of x soutions  =   0 

There are 26 choices for each letter, 5 even digits and 26 letters, that make for \(26^3 \times 5^2 \times 26^2 = \color{brown} \boxed{297,034,400}\) choices. 

The answer is 25.  See https://web2.0calc.com/questions/if-a-and-b-must-be-positive-integers-what-is-the-largest-integer-n-such-that-13a-13b-n-has-no-solutions

Here :  https://web2.0calc.com/questions/quadratic_28591

floor  [  2pi + 4sqrt (7)  - 5/3 ]  =   15  whole numbers

The question is basically asking how many times the line crosses the y value of -1. 

Can you take it from here?

A + 2  = B -2   →  B = A + 4

A + 2 = C + 2 →  A = C

A + 2 = D - 2 →   D = A + 4

So

A + B + C + D = 36

A + (A + 4)  + A  + (A + 4) =  36

4A  + 8 =  36

4A = 28

A = 7   C  = 7    B =  11     D =   11

ABCD =  7^2 * 11^2  =    5929

Howard's salary =  (10/7) (3500)  =  $5000

If Howard's is decreased by 15%  he makes 85% of what he was making  =   5000 (.85)  =  $4250

Fiona  now makes   4250 (7/10)  =   $2975

We could get an algebraic solution, but a graph seems easier :

The toal length of the drive  ≈  73.54  miles

You are within the transmission range for  ≈ 31.5 miles

So

31.5 /  73.54 ≈ .428  =   42.8%  of the time    (assuming a constant speed)

-5t^2 + 20t + 3 =  13              subtract 13 from  both sides

-5t^2  + 20t  - 10  =  0            divide through by -5

t^2  - 4t + 2  =  0                   

Using the quadratic formula

t =   4 ±   sqrt [ 4^2 - 4 (1) (2) ]                4 ±  sqrt [ 8]       4 ± 2sqrt (2)

       _____________________  =        ___________  =  __________  =

                     2 * 1                                           2                     2

2 ± sqrt (2) =      about .59 sec   and   about 3.4 sec 

Let's solve this!

\(k^2-7k+12.25>0\)

\(\left(k-3.5\right)^2>0\)

\(k-3.5<0\quad \mathrm{or}\quad \:k-3.5>0\)

\(\begin{bmatrix}\mathrm{Solution:}\:&\:k<3.5\quad \mathrm{or}\quad \:k>3.5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:3.5\right)\cup \left(3.5,\:\infty \:\right)\end{bmatrix}\)

Hope this helps!

It should be 114. That was a typo

My bad

Multiplying 19 and 6 together gives us 144   

There's a typo in the above.  Actually, 19 • 6 = 114  

_.

You can make a system of linear equations, and then solve for x and y.
\({x-y=13}\)
\({x+y=25} \)

Next you can add these two equations together.

\({2x=38}\)

\({x=19} \)

Substituting in our first equation will then give us \({y=6}\)

Multiplying 19 and 6 together gives us 144