Answer:
The slope of the line passing through the points (−3, −5) and (−1, −6) is 
(-0.5)
Step-by-step explanation:
Equation of a straight line:
y = mx + b where m is the slope and b is the y-intercept
(x1, x2) and (y1, y2) : (−3, −5) and (−1, −6)
Calculating Slope (m).
m = 
m = 
m = 
m =
we can take this a step further by finding the equation:
Now putting value of m in equation (i)
y = -0.5x + b
Calculating Y-intercept (b).
Lets choose the first point, (-3,-5) for calculating y-intercept:
y = mx + b
-5 = -0.5(-3) + b
-5 = 1.5 + b
-6.5 = b
b = -6.5
Now putting value of b in equation
y = -0.5x + -6.5
Answer:
384 cm²
Step-by-step explanation:
Since it is a square pyramid, the total surface area of the pyramid is the area of its square base plus the area of its 4 triangular faces.
Area of a triangular face
= ½ ×12 ×10
= 60 cm²
Base area of pyramid
= 12 ×12
= 144 cm²
∴ Surface area of pyramid
= 4(60) +144
= 240 +144
= 384 cm²
Answer:
f(x) = 12x³ - 19x² + 17x - 17
Step-by-step explanation:
We can the numerator by multiplying the denominator by the quotient, and then adding the remainder.
We're given a denominator of 4x - 5
a quotient of 3x² - x + 3
and a remainder of -2
so the original numerator is:
(4x - 5)(3x² - x + 3) - 2
= 12x³ - 4x² + 12x - 15x² + 5x - 15 - 2
= 12x³ - 19x² + 17x - 17
Let's test that by dividing it by 4x -5 with long division:
That matches, so we know our answer's right, and:
f(x) = 12x³ - 19x² + 17x - 17
Answer:
Ticket Taker Tony collects more tickets per minute.
Step-by-step explanation:
In order to find out which ticket taker collects more tickets per minute, you need to solve for how many tickets each Ticket Taker collects per minute to compare. Since 90:5 and 128:8 are different ratios, you need to find the unit rate, or how many tickets each collects per minute. To find unit rate, you divide the numerator by the denominator:
Ticket Taker Tony: 
= 
Ticket Taker Tina: 
= 
Every minute, Tony collects 18 tickets, while Tina only collects 16, so Ticket Taker Tony collects more.
