Answer:
Step-by-step explanation:
(3,0),(4,1) ⇒ (x₁,y₁),(x₂,y₂)
to find the equation of the line
y-y₁= {(y₂-y₁)/(x₂-x₁)}(x-x₁)
y-0= [(1-0)/(4-3)] (x-3)
y-0 = 1/1(x-3)
y-0 = x-3
y= x-3+0
y=x-3
compare to y=mx+c, where m is the gradient and c is the intercept on y-axis
m=1, c=-3
∴the y-intercept of the line is -3
Answer:
<u>3</u><u>z</u><u>^2 + 3z - 6 </u>=0
3
3 (z^2 + z -2) = 0
3(z+2)(z - 1) = 0
z + 2-2 = 0 - 2
z = -2
z - 1 + 1 = 0 + 1
z = 1
Step-by-step explanation:
- factor out the GCF (3) and divide everything by it, and then set it equal to zero.
- since you have a degree of 2, factor it into two binomials that start with the square root of the first term and end with the square root of the second term.
- 3=0 is extraneous solution so we leave it, then we set each binomial equal to zero to solve for z.
note: your solutions is based on the degree or the exponent of the polynomial or the function.
x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.
Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.
So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.
They need at least $510 to purchase the new gaming station.
Therefore,
12x + 9y ≥ 510
Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.
Therefore,
y ≤ 2x
Also, Fabio will walk at least 25 dogs.
Therefore,
y ≥ 25
Hence, the constraints are:
12x + 9y ≥ 510
y ≤ 2x
y ≥ 25
Let red marbles be x.
Blue : 2x
Red : x
Yellow : x+8
2x + x + x + 8 = 56
4x = 48
x = 12
Red marbles: 12
Blue : 24
Yellow: 20
