Answer:
y = 9x/5 + 50
Step-by-step explanation:
We are represent the information as coordinate (x,y)
If the cost for an order of 100 kilograms of steel bars is $230, this is expressed as (100, 230)
Also if the cost for an order of 150 kilograms of steel bars is $320, this is expressed as;
(150, 320)
Find the equation of a line passing through the points. The standard form of the equation is expressed as y = mx+c
m is the slope
c is the intercept
Get the slope;
m = y2-y1/x2-x1
m = 320-230/150-100
m = 90/50
m = 9/5
Get the y-intercept by substituting m = 9/5 and any point say (100, 230) into the expression y = mx+c
230 = 9/5(100)+c
230 = 9(20)+c
230 = 180 + c
c = 230-180
c = 50
Get the required equation
y = mx+c
y = 9/5 x + 50
Hence an equation for the cost of an order of steel bars (y) in terms of the weight of steel bars ordered (x) is y = 9x/5 + 50
Answer: 16 inches
Step-by-step explanation:
The area of a triangle = bh/2
where b = base = unknown
h = height = 5 3/4 inches
Area = 46 inches²
Therefore, 46 = base × 5 3/4 / 2
Cross multiply
46 × 2 = base × 5 3/4
92 = base × 5 3/4
Base = 92 ÷ 5 3/4
Base = 92 ÷ 23/4
Base = 92 × 4/23
Base = 4 × 4
Base = 16 inches
The correct slope is -5/2.
The formula for slope is
m = (y₂-y₁)/(x₂-x₁)
The y-coordinate of the second point is 0, and the y-coordinate of the first point is 2. The x-coordinate of the second point is 0.8 and the x-coordinate of the first point is 0:
m = (0-2)/(0.8-0) = -2/0.8 = -2 ÷ 8/10 = -2 × 10/8 = -2/1 × 10/8 = -20/8 = -5/2
Answer:
p(x)
Step-by-step explanation:
Substitute x = 3 into each function and calculate the value.
p(3) = 2(3)² + 4(3) + 11 = 2(9) + 12 + 11 = 18 + 12 + 11 = 41
h(3) = 4(3) = 12
s(3) = 10(3) = 30
Thus p(x) = 41 is the largest value when x = 3
To factor both numerator and denominator in this rational expression we are going to substitute
with
; so
and
. This way we can rewrite the expression as follows:
Now we have two much easier to factor expressions of the form
. For the numerator we need to find two numbers whose product is
(30) and its sum
(-11); those numbers are -5 and -6.
and
.
Similarly, for the denominator those numbers are -2 and -5.
and
. Now we can factor both numerator and denominator:
Notice that we have
in both numerator and denominator, so we can cancel those out:
But remember than
, so lets replace that to get back to our original variable:
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is
