A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
Answer:
The Fullers can reach the national park
Step-by-step explanation:
<u><em>The complete question is</em></u>
The Fuller family wants to drive to a national park. Some information about their trip is given in the table below.
Distance to national park 515 miles
Car’s gas tank capacity 20 gallons
Average gas mileage for car 26 miles per gallon
The family wants to determine if they can drive to the national park using just one tank of gas in their car. Determine whether the Fullers can reach the national park. Show your work or explain your answer.
we know that
The Average gas mileage for the car is 26 miles per gallon
That means
With 1 gallon the car runs 26 miles
so
using a proportion
Find out how many miles the car runs with 20 gallons (one tank of gas)
Compare with the distance to the national park
therefore
The Fullers can reach the national park
Answer:
0.162
Step-by-step explanation:
(12+13)/154
25/154
0.162
Answer: y=2x+4 for parallel and y=-1/2x+1 1/2
Step-by-step explanation: you need to do an equation using the slope which you can find by using y2-y1/x2-x1
from there you have to use y-y1=m(x-x1)
Answer: .625 (yes he did leave enough
Step-by-step explanation: First you need to divde the fractions( or solve them) ,so 7 divided by 8 and so on Then you take subtract the paint ivan used, if it is less than half than ivan didn't leave enough for his poor sister
but there are other ways if this one is to hard
