Answer:
3
Step-by-step explanation:
13, 16, 19, 22, 25,
16-13 = 3
19-16 =3
22-19 =3
the common difference is 3
Answer:
hope it helped brainliest pls
Answer:
a) 1
Step-by-step explanation:
3(x + 1) = -2(x - 1) +6
3x + 3 = -2x + 2 + 6
3x + 3 = -2x + 8
Subtract 3 from both sides
3x + 3 -3 = -2x + 8 -3
3x = - 2x + 5
Add 2x to both sides
3x + 2x = -2x + 5 +2x
5x = 5
Divide both sides by 5
5x/5 = 5/5
x = 1
Answer:
The required polynomial is f(x)=![2x^{3}-3x^{2}+3x+7](https://tex.z-dn.net/?f=2x%5E%7B3%7D-3x%5E%7B2%7D%2B3x%2B7)
Step-by-step explanation:
Given that polynomial is passing through points (-1,-1) (0,7) ( 1,9) and (2,17)
Let, The required polynomial be f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
For point (-1,-1)
f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
f(-1)=![a(-1)^{3}+b(-1)^{2}+c(-1)+d](https://tex.z-dn.net/?f=a%28-1%29%5E%7B3%7D%2Bb%28-1%29%5E%7B2%7D%2Bc%28-1%29%2Bd)
(-1)a+b-c+d=(-1) Equation 1
For point (0,7)
f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
f(0)=![a(0)^{3}+b(0)^{2}+c(0)+d](https://tex.z-dn.net/?f=a%280%29%5E%7B3%7D%2Bb%280%29%5E%7B2%7D%2Bc%280%29%2Bd)
d=7 Equation 2
For point ( 1,9)
f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
f(1)=![a(1)^{3}+b(1)^{2}+c(1)+d](https://tex.z-dn.net/?f=a%281%29%5E%7B3%7D%2Bb%281%29%5E%7B2%7D%2Bc%281%29%2Bd)
a+b+c+d=9 Equation 3
For point (2,17)
f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
f(2)=![a(2)^{3}+b(2)^{2}+c(2)+d](https://tex.z-dn.net/?f=a%282%29%5E%7B3%7D%2Bb%282%29%5E%7B2%7D%2Bc%282%29%2Bd)
8a+4b+2c+d=17 Equation 4
Replacing value of d of equation 2 in equation 1,3,4
For equation 1:
(-1)a+b-c+d=(-1)
(-1)a+b-c=(-8)
For equation 3:
a+b+c+d=9
a+b+c=2
For equation 4:
8a+4b+2c+d=17
8a+4b+2c=10
Now,
On adding equation 1 and 3
For equation 1: (-1)a+b-c=(-8)
For equation 3: a+b+c=2
((-1)a+b-c)+(a+b+c)=(-8)+2
2b=(-6)
b=(-3)
Replacing value of b in equation 1 and 4:
For equation 1: (-1)a+b-c=(-8)
(-1)a+(-3)-c=(-8)
(-1)a-c=(-5) Equation 4
For equation 4: 8a+4b+2c=10
8a+4b+2c=10
8a+4(-3)+2c=10
8a+2c=22 Equation 5
For value of a and c:
Equation 4 can be write as
(-1)a-c=(-5)
a+c=5
a=5-c
Replacing value of a in equation 5
8a+2c=22
8(5-c)+2c=22
40-8c+2c=22
-6c=-18
c=3
So,
a=5-c=5-3=2
a=2
Thus,
The value of
a=2, b=(-3), c=3 and d=7
The required polynomial is
f(x)=![ax^{3}+bx^{2}+cx+d](https://tex.z-dn.net/?f=ax%5E%7B3%7D%2Bbx%5E%7B2%7D%2Bcx%2Bd)
f(x)=![2x^{3}-3x^{2}+3x+7](https://tex.z-dn.net/?f=2x%5E%7B3%7D-3x%5E%7B2%7D%2B3x%2B7)
Answer:ED=9, DF=9sqrt3, and EF=18
Step-by-step explanation:30-60-90 triangle, a:short, asqrt3:longer, 2a:longest
m∠E=60°