Marcia has a balance of $1700 on her credit card, which she plans to pay off by making a payment of the same amount each month.

Utilize the details to create inequalities that reflect each limitation or requirement.

2) Label the variables. 

c: count of color copies
b: count of black-and-white copies

3) Define each constraint:

i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>

3c + b ≤ 12
<span />

4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)

5) Here’s how to illustrate that:

i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.

ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.

iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.

iv) The concluding area is the overlap of the previously mentioned shaded regions.

v) The graph can be viewed in the attached figure.

Answer:

a. i) Please refer to the attached graph representing the equation $10·x + $12·y = $300

ii) The intercepts indicate the maximum number of short-sleeve (at the x-intercept) and long-sleeve shirts (at the y-intercept) that can be ordered.

Step-by-step explanation:

The details provided are as follows:

Cost of each short-sleeve shirt = $10

Cost of each long-sleeve shirt = $12

Total budget available = $300

The equation for total spending is given by $10·x + $12·y = $300

Where;

x = Number of short-sleeved shirts

y = Number of long-sleeved shirts

Rearranging the equation into slope-intercept form, we have:

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Attached is the graph produced using Microsoft Excel

The coordinates that can be used for graph plotting are as follows:

x, y

(0, 25)

(5, 20.83)

(10, 16.67)

(15, 12.5)

(20, 8.33)

(25, 4.17)

(30, 0)

The x-intercept denotes the quantity of short-sleeve shirts purchasable with a $300 budget, while the y-intercept signifies the quantity of long-sleeve shirts achievable under the same budget.

Answer:

The rate of surface coating is = 74 inch²/min

Step-by-step explanation:

The cylinder has a diameter of 6.5 inches and a height of 7.75 inches, with a filling rate or dv/dt of 120 inch/min.

<pthe differential="" of="" an="" equation="" represents="" the="" rate="" change="" in="" relation="" to="" another="" variable.=""><pradius d="" inches="" ds="" can="" also="" be="" viewed="" as="" the="" rate="" at="" which="" interior="" surface="" area="" of="" paint="" is="" being="" coated.=""><pthe formula="" for="" the="" surface="" area="" of="" a="" cylinder="" is="" given="" by="" which="" represented="" as="" equation=""><pthe formula="" for="" volume="" the="" cylinder="" is="" v="πr²h.&lt;/p">

dv/dt = πr² x dh/dt, where r remains constant.

120 = π x (3.25)² x dh/dt.

Now, dh/dt = 120/π x (3.25)².

Next, differentiate equation 1 for the surface area.

ds/dt = 2 x π x r dh/dt + 0, where r remains constant.

Substituting the value of dh/dt in the ds/dt equation yields:

ds/dt = 2 x π x 3.25 x (120/π x (3.25)²).

Thus, ds/dt = 73.846 ≅ 74 inch²/min.

</pthe></pthe></pradius></pthe>

Given that x y is parallel to z w and x z serves as a transversal that crosses both x y and z w, it follows that ∠ x z w equals ∠ z x y, which are alternate interior angles because x y is parallel to z w. Also, v is where x z intersects y w, therefore ∠ x v y is congruent to ∠ z v w due to vertically opposite angles. Consequently, this yields triangle Δ x y v being similar to triangle Δ z w v based on the angle-angle similarity.

X^3-7x^2-5x+35

= x^2(x-7) - 5 (x-7) using definitions

=(x^2-5)(x-7)

I hope this is helpful.