Check whether the two expressions 2x+3y2x+3y and 2y+3x2y+3x equivalent.
The first expression is the sum of 2x2x 's and 3y3y 's whereas the second one is the sum of 3x3x 's and 2y2y 's.
Let us evaluate the expressions for some values of xx and yy . Take x=0x=0 and y=1y=1 .
2(0)+3(1)=0+3=32(1)+3(0)=2+0=22(0)+3(1)=0+3=32(1)+3(0)=2+0=2
So, there is at least one pair of values of the variables for which the two expressions are not the same.
Answer: Yes, Yukio is correct.
Step-by-step explanation:
Assuming that Triangle DEF and ABC have the same angles (they do because they are right-angled), we can take the length from the larger triangle (DEF) and divide it by the length of the smaller triangle (ABC).
Length of DEF = 6cm
Length of ABC = 2cm
= 6/2
= 3
Proves that scale of DEF to ABC is 3:1
Answer:
x=0,-1 and x=
x=\frac{2+\sqrt{10}}{3},\frac{2-\sqrt{10}}{3}x=
3
Step-by-step explanation:
1 Cancel 2 on both sides.
3{x}^{2}+3x=03x
2
+3x=0
2 Factor out the common term 3x3x.
3x(x+1)=03x(x+1)=0
3 Solve for xx.
x=0,-1x=0,−1
1 Move all terms to one side.
3{x}^{2}-3x-1-x-1=03x
2
−3x−1−x−1=0
2 Simplify 3{x}^{2}-3x-1-x-13x
2
−3x−1−x−1 to 3{x}^{2}-4x-23x
2
−4x−2.
3{x}^{2}-4x-2=03x
2
−4x−2=0
3 Use the Quadratic Formula.
x=\frac{4+2\sqrt{10}}{6},\frac{4-2\sqrt{10}}{6}x=
6
4+2√
10
,
6
4−2√
10
4 Simplify solutions.
x=\frac{2+\sqrt{10}}{3},\frac{2-\sqrt{10}}{3}x=
3
2+√
10
,
3
2−√
10
