(x+(x+2)+(x+4)+(x+6))=4x+12=212
x+x+x+x(2+4+6)=4x+12=212
4x (2+4+6)=4x+12=212
4x(6+6)=4x+12=212
12+4x=4x+12=212
<u>-12 -12 -12</u>
4x=4x=200
<u>/4 /4 /4</u>
<u>x=x=50</u>
<u>x=50</u>
Step 1. Convert 3 1/3 to improper fraction.
- 3 * 3 + 1/3 ÷ 9
Step 2. Simplify 3 * 3 to 9
-9 + 1/3 ÷ 9
Step 3. Simplify 9 + 1 to 10
-10/3 ÷ 9
Step 4. Use this rule: a ÷ b/c = a * c/b
-10/3 * 1/9
Step 5. Use this rule: a/b * c/d = ac/bd
-10 * 1/3 * 9
Step 6. Simplify 10 * 1 to 10
-10/3 * 9
Step 7. Simplify 3 * 9 to 27
-10/27
Answer:
By exterior angle theorem, we have;
∠DBE = ∠H + ∠HEB = ∠ECD = ∠H + ∠HDC
∴ ∠H + ∠HEB = ∠H + ∠HDC
By addition property of equality, we have
∠HEB = ∠HDC
∠H = ∠H by reflexive property
∴ ΔHCD ~ ΔHEB by Angle Angle AA similarity postulate
∴ HE/HD = EB/DC, by the definition of similarity
Therefore, by cross multiplication, we have;
HE × DC = EB × HD
Therefore, by commutative property of multiplication, we have;
HE × DC = HD × EB
Step-by-step explanation:
Direct variation is of the form y=kx. We are given the point (8, -4) so we can solve for k, the constant of variation...
-4=8k, divide both sides by 8
-4/8=k
k=-0.5, so our equation is:
y=-0.5x,
Answer: the two trains will meet in 2.8 hours
Step-by-step explanation:
Step 1
Speed of train A = 90mph
Speed of train B = 110 mph
Since both trains are travelling towards each other
, their effective speed will be= 90 mph + 110mph= 200mph
Step 2
we know that Speed = distance / time
therefore Time = Distance / speed
Distance = 560 miles
Speed = 200 mph
Time = 560miles / 200mph
2.8 hours
