Answer:
1
+ 
p - 8
Step-by-step explanation:
The sum of one-half of d and one-third of p, minus 8;
i.e
1 + p - 8
Putting it into improper fraction becomes:
d + 
p - 8
Answer:
I won't stop the line for a half hour break.
Step-by-step explanation:
<u>Proportions</u>
One quantity A is said to be proportional to other B if A can always be obtained by multiplying or dividing B by any constant number. Numbers {4,8,12} are proportional to {2,4,6} because they can be computed as twice their value
.
There is a situation described in the problem where we need to know if there will be enough time to produce the 900 toasters (the goal for the day) when the assembly line is stopped by half an hour.
Actual time: 2:00 pm
Final time: 5:00 pm
Rate of production: 2 toasters/minute
Actual production: 560 toasters
Updated goal: 900-560 = 340 toasters
Those 340 toasters must be produced in the remaining 3 hours (180 minutes) of work. If the assembly line stops for half an hour (30 minutes), there will be only 150 minutes to finish the goal production. At a rate of 2 toasters/minute, there will be 2*150 = 300 toasters produced. But we need to produce 340 more toasters, so that break cannot be granted or we'll be 40 toasters under goal.
It the line keeps producing for 180 minutes, it would produce 2*180 = 360 toasters, 20 more than the goal.
Note: The maximum break time that can be granted is 20/2 = 10 minutes
Answer:
Step-by-step explanation:
Step 1: Add 4n to both sides.
n+4n=−4n−1+4n
5n=−1
Step 2: Divide both sides by 5.
5n
5
=
−1
5
n=
−1
5
Answer:
y = - 3x - 2
Step-by-step explanation:
The function is linear and can be expressed in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (- 1, 1) ← 2 ordered pairs from the table
m = 
= 
= 
= - 3 , then
y = - 3x + c
To find c substitute any ordered pair into the equation
using (0, - 2 ) , then
- 2 = - 3(0) + c = 0 + c ⇒ c = - 2
y = - 3x - 2 ← function rule
Answer:
Zero
Step-by-step explanation:
The distance AB is ...
... √((5-1)²+(5-2)²) = √(16+9) = 5
The largest right triangle that can be constructed with AB as the hypotenuse is one with an altitude of 5/2 = 2.5 units. Its area will be ...
... (1/2)·5·2.5 = 6.25 . . . . square units
It is not possible to construct the triangle ABC described.
_____
In order to achieve the given area, ∠C would need to be 87.75° or smaller. It could not be 90°.
