1.Consider the system of equations. x-5y=2
3x-10y=11
(a) Jamar rewrote the first equation as –2x + 10y = –4. What justification did he have for doing this?
(b)Jamar combined the equation in Part (a) with the second equation in the system to get x = 7. Explain Jamar’s reasoning.
(c) What is the solution of the system? (d) How do you know, without graphing, that the graph of 4x – 15y = 13 passes through the point whose coordinates are the solution of the system?
Answer:
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.
3. Using the above relationship, ...
short-side/hypotenuse = 8/y = y/(8+23)
y^2 = 8·31
y = 2√62
__
long-side/hypotenuse = z/(8+23) = 23/z
z^2 = 23·31
z = √713
__
short-side/long-side = 8/x = x/23
x^2 = 8·23
x = 2√46
_____
4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,
y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)
z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)
x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)
Given:
A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.
Pilot's speed in still air is 315 miles per hour.
To find:
The speed of the wind.
Solution:
Let the speed of wind be x miles per hour.
Speed with wind = 315+x miles per hour
Speed against wind = 315-x miles per hour
We know that,
According to the question,
Divide both sides by 90.
By cross multiplication, we get
Divide both sides by 9.
Therefore, the speed of wind is 35 miles per hour.
Steps:
Use the divisor and find x :
x - 1 = 0 **add 1
x= 1
Now we will use the 1 in dividing:
take the coefficients from in front of all terms
** make sure you include 0's for x^2 and x since you have to have all terms
set it up with a 1 in a box:
1| 1 0 0 1 **bring the first number down
____________
1 **multiply the boxed number by the first number and add it to the second number
1| 1 0 0 1
____+1_____ **repeat with the rest of the terms
1 1
1| 1 0 0 1
___+1_+1_+1
1 1 1 2
**when you're done, use the new numbers to write an equation starting with a term with a degree one less than the previous equation.
**since there is a remainder, rewrite it divided by the original divisor
final answer:
x^2 + x + 1 + (2/ x -1)
