Answer:
y = -5x/3 + 18
Step-by-step explanation:
The points can be written as;
(x,f(x))
where f(x) is same as y
So the points we have are;
(6,8) and (9,3)
We start by finding the slope or the line connecting the points
m = y2-y1/x2-x1 = (3-8)/(9-6) = -5/3
So now we have the general form of a linear equation as
y = mx + b
where m is slope and b is y intercept
We already have slope and we want to calculate y-intercept
Simply substitute one of the points
(9,3) in this case
9 for x and 3 for y
we have ;
y = -5x/3 + c
3 = -15 + c
c = 18
So the line equation is;
y = -5x/3 + 18
Answer:
8x(10)^9 - 2 x (10)^1
1x(10)^3 - 9 x (10)^2
Step-by-step explanation:
3.1 X (10)^4- 6.5 X (10)^2
= 31000- 650
= 30,350
For greater number
_x10^blank - _ x 10^_
8x(10)^9 - 2 x (10)^1 ( we use 9 as the power because greater number used as power gives the bigger number and the next smaller number 8 as base. Similarly we use smaller number for power to get a smaller for the greatest difference)
= 8,000,000,000 -20
= 7,999,999,980
For smaller number
_x10^blank - _ x 10^_
1x(10)^3 - 9 x (10)^2 ( we use 3 as the power because smaller number used as power gives the smaller number and the next smallest number 1 as base. Similarly we use next smaller number for power to get the next smaller for the smallest difference)
= 1000- 900
= 100
We fill in the blanks keeping in mind that we do not have to repeat the numbers from 1-9 and also the numbers should have such an arrangement that they show the smallest and largest possible differences.
1. 3t + 2b = 16....multiply by -3
5t + 3b = 25...multiply by 2
----------------
-9t - 6b = -48 (result of multiplying by -3)
10t + 6b = 50 (result of multiplying by 2)
---------------- add
t = 2
3t + 2b = 16
3(2) + 2b = 16
2b = 10
b = 5
so tacos (t) cost $ 2 and burritos (b) cost $ 5
===================
d + q = 75......d = 75 - q
0.10d + 0.25q = 10.95
0.10(75 - q) + 0.25q = 10.95
7.50 - 0.10q + 0.25q = 10.95
0.15q = 3.45
q = 23....so there are 23 quarters
=====================
x = 2 point shots, y = 3 point shots
x + y = 24.....multiply by -2
2x + 3y = 54
----------------
-2x - 2y = -48 (result of multiplying by -2)
2x + 3y = 54
----------------add
y = 6.......so there was 6 three point shots
x + y = 24
x + 6 = 24
x = 18......and 18 two point shots
======================
5.50g + 5 = 2.50g + 17
5.50g - 2.50g = 17 - 5
3g = 12
g = 4......they will cost the same with 4 game rentals
less then 4 rentals, use Fun Guys....more then 4, use Game Bank
=======================
(2,5)(4,9)
slope = (9 - 5) / (4 - 2) = 4/2 = 2
y = mx + b
slope(m) = 2
(2,5)...x = 2 and y = 5
now sub and find b, the y int
5 = 2(2) + b
5 = 4 + b
5 - 4 = b
1 = b
so ur equation is : y = 2x + 1 (line A)
(0,5)(3,8)
slope = (8 - 5) / (3 - 0) = 3/3 = 1
y = mx + b
slope(m) = 1
(0,5)...x = 0 and y = 5
now sub
5 = 1(0) + b
5 = b
so ur equation is : y = x + 5 (line B)
y = 2x + 1
y = x + 5
2x + 1 = x + 5
2x - x = 5 - 1
x = 4
y = 2x + 1
y = 2(4) + 1
y = 8 + 1
y = 9
so they will meet at (4,9)
=====================
sorry..not 100% sure about the bonus
Answer:
A & B
Step-by-step explanation:
Answer:
Step-by-step explanation:
The ratios are all 3 father steps to 5 son steps. Then ...
son-steps = 5/3·father steps
son-steps = 5/3·36 = 60
and
father-steps = 3/5·son-steps
father-steps = 3/5·30 = 18
___
As a <em>check</em>, you can realize that the numbers in the first blank, 36:60, are double those in the second blank, 18:30. The first of these, 36:60, is 3 times the row underneath it, 12:20.
