Step-by-step explanation:
the general line equation format is
y = ax + b
a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".
b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.
(i)
A (3, 5)
B (5, 9)
x changes by +2 (from 3 to 5).
y changes by +4 (from 5 to 9).
so, the slope (or gradient) is +4/+2 = 2
(ii)
the semi-finished equation is
y = 2x + b
let's use A to get b :
5 = 2×3 + b = 6 + b
b = -1
and the full equation is
y = 2x - 1
(iii)
for point (4, k) we get
k = 2×4 - 1 = 8 - 1 = 7
Bagels = x
sesame bagels = x/3 = 72
x/3=72
x=72x3
x=216
Answer:
68 chickens and 12 cows.
Step-by-step explanation:
Let x represents the number of chicken and y represents the number of cows in the barnyard,
Given,
Total heads = 80
⇒ x + y = 80 ------(1),
Also, total legs = 184,
Since, a chicken has two legs and cow has 4 legs,
⇒ 2x + 4y = 184 -----(2),
Equation (2) - 2 × equation (1),
We get,
4y - 2y = 184 - 160
2y = 24
y = 12
From equation (1),
x + 12 = 80 ⇒ x = 80 - 12 = 68
Hence, the number of chicken = 68,
And, the number of cows = 12
T's going to make a difference whether that 4 percent is compounded more
<span>than once a year. </span>
<span>We'll do the calculation assuming it's compounded only once a year, and if it </span>
<span>turns out to be compounded more often than that, then the calculation will </span>
<span>come out on the low side, and you'll wind up with a little bit more than $3,000. </span>
P<span> times (1.04)</span>3<span> = $3,000 </span>
P<span> = </span>3,000/<span>(1.04)3</span><span> = $2,666.980769 or </span><span>$2,667</span>
