The discriminant of the quadratic-equation -x^2 + 6x - 6 = 0 is 60.
The discriminant of a quadratic equation of the form ax^2 + bx + c = 0 is given by the expression Δ = b^2 - 4ac.
In the given quadratic equation -x^2 + 6x - 6 = 0, we can identify that a = -1, b = 6, and c = -6.
Substituting these values into the discriminant formula, we have:
Δ = (6)^2 - 4(-1)(-6)
The discriminant plays a crucial role in determining the nature of the solutions of a quadratic equation. If the discriminant is positive (Δ > 0), then the equation has two distinct real solutions. If the discriminant is zero (Δ = 0), then the equation has one real solution (also known as a double root). If the discriminant is negative (Δ < 0), then the equation has no real solutions, but it may have complex solutions involving imaginary numbers.
for more such questions on quadratic-equation
https://brainly.com/question/1214333
#SPJ8
PLEASE HELP! what direction will these electrostatic forces go?
Step-by-step explanation:
this is physics (not math per se).
the first moves to the left, because the distance to the positive charge on the left is shorter than the distance to the positive charge on the right.
the second moves to the right, because the positive charge is greater there and the distance to the positive charge is shorter too.
the third stays where it is. the -2 charge moves to the left until it hits the first +2 charge. there they neutralize each other, and nothing else is happening. also before -2 and +2 meet, they are neutralizing each other already for an outside observer (like the green ringed +2).
but - it depends how picky your teacher tries to be here.
because when you look at the very fine details, until -2 and the right +2 meet and really neutralize each other, there is a tiny little overhang of positive charges the green ringed +2 charge would "feel". simply because the +2 is a little bit closer than the -2.
and when we consider this, the green ringed +2 would move very little to the left (repelled by the other positive overhanging charge on the right) until -2 and +2 actually meet.
factor and solve if necessary
7x^2-14x+7
Hello!
7x² - 14x + 7
7(x² - 2x + 1)
= 7(x(x - 1) - 1(x - 1))
= 7((x - 1)(x - 1))
= 7(x - 1)²
Alexei finances her purchase of a $900 television. Her one-year loan has a fixed annual interest rate of 2.5%.
What is Alexei's monthly payment?
Alexei's monthly payment is approximately $18.56.
Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
For more such questions on payment
https://brainly.com/question/29475683
#SPJ8
Can someone help me please? ASAP
Answer:
triangle XYZ is similar to triangle RPQ
scale factor = 2/5
Step-by-step explanation:
Angles X and R are given as congruent.
Angles Z and Q are right angles, so they are congruent.
Then, angles Y and P must be congruent.
The similarity statement is
triangle XYZ is similar to triangle RPQ
To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.
10/25 = 2/5
The scale factor is 2/5.
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
Learn more about the present value at https://brainly.com/question/20813161.
#SPJ1
I need Help please!!!
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
Check this out-
https://brainly.com/question/29192128?referrer=searchResults
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.
Complete the table by classifying the polynomials by degree and number of terms.
quadratic
constant
exponential
Polynominal
(picture)
The names of the expressions are;
1) Monomial, quadratic
2) Monomial, constant
3) Binomial, Linear
4) Trinomial, quadratic
What are polynomials and trinomials?
An algebraic expression that has one or more terms, each of which is a variable raised to a non-negative integer exponent and multiplied by a coefficient, is referred to as a polynomial. The terms are mixed by adding or removing. A polynomial may include 0 terms or more.
A particular kind of polynomial known as a trinomial has exactly three terms. Trinomials are made up of three different pieces, which are frequently denoted by the formula "ax2 + bx + c," where "a," "b," and "c" are coefficients.
Learn more about polynomials:https://brainly.com/question/11536910
#SPJ1
Type the correct answer in each box.
Day Amount
1
$26
2
$23
3
$31
4
$26
5
534
The table shows the amount Bill spent on 5 days last week.
The mean of the amount he spent is $
The mean absolute deviation is $
Reset
Next
The mean absolute deviation is $106.6.
Given the table shows the amount Bill spent on 5 days last week.
DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.
Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,
the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:
Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406
The sum of all absolute deviations is:
10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.
For more question deviation
https://brainly.com/question/475676
#SPJ8