Answer:
a) a= (3/4)t
4a = 3t
b = (5/2)t
2b = 5t
b)See explanation below
c) It will take 30.075 hours for the whole business to make at least $500 profit
Step-by-step explanation:
a) First we would represent the information given in terms of amount of bracelet produced and time spent in production with variables in order to convert to linear equations
Let number of bracelet Darrelle makes = a
Number of bracelet Danica makes = b
Let the time spent in producing them in hours = t
Darrelle takes 4 hours to make 3 bracelets:
Rate of producing bracelet = (number of bracelet produced)/time
Rate = a/t = 3/4
4a = 3t
Linear equation form: y = mx + c
a= (3/4)t
The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 3/4
4a - 3t = 0 (equation in standard form )
Danica makes 5 bracelets every 2 hours:
Rate of producing bracelet = (number of bracelet produced)/time
Rate = b/t = 5/2
2b = 5t
Linear equation form: y = mx + c
b = (5/2)t
The above equation is in the slope-intercept form indicating the intercept = 0 and slope = 5/2
2b - 5t = 0 (equation in standard form)
b) The equations are linear equations, hence they can be graphed.
But as regards graphing using special functions, this answer can only be answered by you as I'm not aware of the special functions discussed in the course.
c) Darrelle makes $10.50 in profit per bracelet.
Danica makes $3.50 in profit per bracelet
Since Darrelle and Danica work the same amount of time, we have to find the relationship between their profit, the number of bracelets produced and the time.
Profit for Darrelle for 'a' number of bracelet product = $10.50 × a = $10.50a
Profit for Danica per 'b' number of bracelet product = $3.50 × b = $3.50b
Let P = total profit made by both
P = $10.50a + $3.50b
Relationship of profit in terms of time spent in production when they work same amount of time:
P = $10.50(3/4 ×t)+ $3.50(5/2 × t)
P = 16.625t
When P = $500, t = ?
500 = 10.50(3/4 ×t)+ 3.50(5/2 × t)
500 = 7.875t + 8.75t
500 = 16.625t
t = 30.075 hours
It will take 30.075 hours for the whole business to make at least $500 profit
Answer:
- The graph of y > 3x − 4 has shading above a dashed line.
- The graph of y < x + 1 has shading below a dashed line.
- The graphs of the inequalities will intersect.
Step-by-step explanation:
y > ... means the shading will be above the corresponding line.
y < ... means the shading will be below the corresponding line.
These lines have different slopes, so the solution spaces <em>must</em> overlap, hence <em>there must be solutions</em> to the system.
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<em>Comment on last choice</em>
It isn't clear exactly what is intended by the last offered statement. Both of the listed points are in the solution space of y > 3x-4. Neither point is in the solution space of y < x+1.
Together, the two graphs intersect the entire y-axis. Jointly, they only intersect the y-axis on the interval -4 < y < 1.
The y-intercepts of the two boundary lines are (0, 1) and (0, -4). Neither of these points is in the solution space of the system of inequalities.
4x+14x+84=174
18x=174-84
18x=90 divide both sides by 18
x=5
3b-8=168-5b
3b+5b=168+8
8b=176
8b/8=176/8
b=22
