Answer:
Step-by-step explanation:
Remark
You are going to use the Pythagorean Theorem. The trick is to find the length of the leg making up the base of the triangle.
That base is equal to the difference between the two bases.
Solution
The base of the triangle = 2x + 1 - (x + 3) Remove the brackets.
base = 2x + 1 - x - 3
base = x - 2
Now the height of the trapezoid is also the second leg of the triangle. Apply the Pythagorean Theorem.
c^2 = a^2 + b^2
a = x - 2
b = x + 4
c = 2x
4x^2 = (x - 2)^2 + (x + 4)^2 Expand the brackets
4x^2 = x^2 - 4x + 4 + x^2 + 8x + 16 Collect like terms
4x^2 = 2x^2 + 4x + 20 Subtract the right side from the left.
4x^2 - 2x^2 - 4x - 20 = 0
2x^2 - 4x - 20 = 0 Divide by 2
2x^2/2 - 4x/2 - 20/2 = 0
x^2 - 2x - 10 = 0
x = - b +/- sqrt(b^2 - 4*a*c)/ 2a
a = 1
b = - 2
c = - 10
x = (- -2 + / - sqrt((-2)^2 - 4*(1)*(-10) ) / 2
x = (2 + / - sqrt(4 + 40 ))/2 Only the plus root has any meaning.
x = ( 2 + sqrt(44 ) )/2
x = ( 2 + 2*sqrt(11) ) / 2
x = 1 + sqrt(11)
sqrt(11) = 3.3166
x = 1 + 3.3166
x = 4.3166
Answer: 1y=-2-3x
4x+3(-2-3x) =24----4x-6-6x=24---4x-6x=24+6---;-2x=30----x=30/-2---x=-15
Answer:
Erica has 6 more text then Tim and 2 more calls then Tim.
Step-by-step explanation:
What i did was 18-12 because those are both text and that was 6 so Erica has 6 more
Then i did 6-4 =2 and those where both of the calls so Erica has 2 more calls then Tim.
Answer:
3.5 miles
Step-by-step explanation:
Lydia:
3 gallons of gas = 114 miles
We want to know how many miles a friend can travel on one gallon of gas, so we divide both sides by 3
1 gallon of gas = 114/3 miles = 38 miles
Lucy:
One point is
10x corresponds to 415y
10 gallons = 415 miles
divide both sides by 10 to get one gallon on a side
1 gallon = 41.5 miles
Lydia:
38 miles = 1 gallon
Lucy:
41.5 miles = 1 gallon
For 1 gallon, the difference is 3.5 miles, with Lydia having 3.5 miles less than Lucy.
Answer:
67 times
Step-by-step explanation:
Spinner's sample space = (1, 2, 3, 4, 5, 6)
Number less than 5 = (1, 2, 3, 4)
Total possible outcomes = 6
Required outcome = 4
P(number less than 5) = required outcome / Total possible outcomes
P(number less than 5) = 4 /6 = 2/3
Number of spins = 100
Predicted Number of times a number less than less than 5 is spurn in 100 spins :
100 * 2/3
= 66.666
= 67 times
