The quadratic function y = ax ^ 2 + BX + C (a) is known

The quadratic function y = ax ^ 2 + BX + C (a) is known

When x = - 1, Y0
The symmetry axis of parabola is a straight line x = 1, that is - B / 2A = 1, that is a = - B / 2
Therefore, from A-B + C0
So 2C

Is there only one solution for a system of linear equations of two variables
ditto

There are three cases of binary linear equations
1. There is only one set of solutions, such as x + y = 1, 2x-y = 8
2. No solution. For example, x + y = 10,2x + 2Y = 1,
3. Innumerable solutions, such as x + y = 10,2x + 2Y = 20,

As shown in the figure, R2 = 60 Ω, R is a sliding rheostat with a maximum resistance of 20 Ω, and the power supply voltage U is constant (1) When switch S is closed and P is set at a end, the indication of ammeter A is 0.5 A, and that of A1 is 0.3 A. calculate the value of power supply u and the resistance value of R1. (2) when switch S is open and the slide of sliding rheostat moves from a end to B end, calculate the indication change range of ammeter A and voltmeter v

(1) It can be seen from the circuit diagram that when s is closed and P is placed at the a end, the resistors R1 and R2 are connected at both ends of the power supply. Ammeter a measures the main circuit current, and ammeter A1 measures the branch current of R1. The current through resistor R2 is I2 = ia-ia1 = 0.5a-0.3a = 0.2A, the power supply voltage is u = U2 = i2r2 = 0.2A × 60 Ω = 12V; ∵ I = ur, ∵ resistor R1 = u1i1 = uia1 = 12v0.3a = 40 Ω; (2) it can be seen from the circuit diagram that when switch S is open, the resistor R2 is closed In series with sliding rheostat, when the slide is at the a end, the total resistance of the circuit is the minimum, the circuit current is the maximum, the indication number of ammeter A is IMAX = UR2 = 12v60 Ω = 0.2A, the voltage indication number Umax = u = 12V; when the slide is at the B end, the circuit resistance is the maximum, the circuit current is the minimum, IMAX = UR2 + Rmax = 12v60 Ω + 20 Ω 0.15A, the voltage indication number Umax = IMAX, R2 = 0.15A × 60 Ω = 9V; then the current indication number changes Range: 0.15A ~ 0.2A, voltage indication range: 9V ~ 12V; answer: (1) power supply voltage is 12V, R1 resistance value is 40 Ω. (2) current indication range: 0.15A ~ 0.2A, voltage indication range: 9V ~ 12V

Factorization (a + b) (a + B-4) + 4

(a+b)(a+b-4)+4
=(a+b)²-4(a+b)+4
=(a+b-2)²

In May 2012, my mother deposited 4000 yuan in a bank for three years, with an annual interest rate of 5%. When it was due, how much interest did my mother get?

Interest = 4000 × 3 × 0.05 = 600 yuan

Find the probability, take the formula, will advance,
To awesome university students' innovative ability, only three teams a, B, C, and 1 are awarded to the finals. (1) the probability of obtaining the first two positions of the two teams in the first and second teams? (2)

The first question, a total of 6 cases, a and B in the first two, a one, or B one. So the probability is 1 / 3
Second, there are still six cases, a and B are not adjacent or two, a and C and B, or B, C and a, so the adjacent probability is still 1-1 / 3 = 2 / 3

Mathematical problems formula calculation
I have 10000 yuan, and the annual increment interest rate is 5%. After 80 years, how much money do I have? How should I make a formula?

One year later, you have: 10000 * (1 + 5%) (yuan)
Two years later, you have: 10000 * (1 + 5%) (1 + 5%) (yuan)
Three years later, you have: 10000 * (1 + 5%) (1 + 5%) (1 + 5%) (yuan)
80 years later, you have: 10000 * [(1 + 5%) ^ 80] = 495614.41 (yuan)

What is the difference between frequency and frequency in mathematics
rt.

Generally, the number of data in different groups is the frequency of the group

6.3 divided by (four and one seventh minus 0.07 divided by one fiftieth) multiplied by one and two seventh

Original formula = 6.3 / [4 + 1 / 7-0.07 / (1 / 50)] × (1 + 2 / 7)
=(6.3+1.8)/[4+1/7-3.5]
=8.1/(1/2+1/7)
=8.1/(9/14)
=0.9×14
=12.6

For a certain work, it takes 10 days for Party A and Party B to cooperate and 18 days for Party B to do it alone. After 5 days of cooperation, Party A leaves for business and Party B does it alone
We can finish the work in a few days
The equation of first degree with one variable is used

Set X days to finish the work
5/10+x/18=1
x/18=1-5/10=1/2
x=18*1/2=9
A: we can finish the work in 9 days