(2x+3y)⁴
1) let 2x = a and 3y = b
(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1
0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:
(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):
2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)
16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
Answer:
The number of deliveries that are predicted to be made to homes during a week with 50 deliveries to business is 87 deliveries
Step-by-step explanation:
The data categorization are;
The number of home deliveries = x
The number of delivery to businesses = y
The line of best fit is y = 0.555·x + 1.629
The number of deliveries that would be made to homes when 50 deliveries are made to businesses is found as follows;
We substitute y = 50 in the line of best fit to get;
50 = 0.555·x + 1.629 =
50 - 1.629 = 0.555·x
0.555·x = 48.371
x = 48.371/0.555= 87.155
Therefore, since we are dealing with deliveries, we approximate to the nearest whole number delivery which is 87 deliveries.
Answer:
Option B. 1990 - 1992
Step-by-step explanation:
If we have to calculate inflation rate in year 2000 from 1990, we use the formula
which means if consumer price index is increasing year by year the inflation rate will increase.
Now we analyse our options given with the help of graph given.
A. from 1994 - 2000
Consumer price index increased from year 1994 to 1998 but decreased between 1998 to 2000.
So this option doesn't show the continuous inflation.
B. Year 1990 - 1992
We find a continuous increase in C.P.I. therefore there will be a continuous increase in inflation.
So this option is correct.
C. Year 1992 - 1996
In this gap we see deflation from year 1992 to 1994 then inflation between 1994 - 1996.
So there is ups and downs in this period showing discontinuity in inflation.
D. 1992 - 1994
There is continuous decrease in C.P.I. so continuous deflation is reported between this period.
It's not the correct option.
Answer is Option B.
Answer:
option C. Angle BTZ Is-congruent-to Angle BUZ
Step-by-step explanation:
Point Z is equidistant from the vertices of triangle T U V
So, ZT = ZU = ZV
When ZT = ZU ∴ ΔZTU is an isosceles triangle ⇒ ∠TUZ=∠UTZ
When ZT = ZV ∴ ΔZTV is an isosceles triangle ⇒ ∠ZTV=∠ZVT
When ZU = ZV ∴ ΔZUV is an isosceles triangle ⇒ ∠ZUV=∠ZVU
From the figure ∠BTZ is the same as ∠UTZ
And ∠BUZ is the same as ∠TUZ
So, the statement that must be true is option C
C.Angle BTZ Is-congruent-to Angle BUZ
