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soldi70 [24.7K]
3 years ago
9

A local store’s clearance rack is full of DVDs selling for $8 each and CDs selling for $6 each. Let x represent the number of DV

Ds, and let y represent the number of CDs. Which inequality can be used to find combinations of DVDs and CDs that can be bought with a $50 gift card?

Mathematics
2 answers:
azamat3 years ago
8 0

Answer:

8x+6y\leq 50

Step-by-step explanation:

Let

x------> the number of DVDs

y------> the number of CDs

we know that

8x+6y\leq 50 -------> inequality that represent the situation

The solution is the shaded area below the solid line between the positive values of x and y

The equation of the line is 8x+6y=50

The slope of the line is negative

The y-intercept of the line is the point (0,8.33)

The x-intercept of the line is the point (6.25,0)

The solution is the triangular area in the attached figure

kozerog [31]3 years ago
7 0
Let x represent the number of DVDs and y represents the number of CDs.
DVDs are sold for 8$ and CDs are sold for 6$.
If you have 50$ to buy gift cards then the following inequality should be satisfied:
8*x+6*y<50

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The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The
Bess [88]

Answer:

They would produce 14,400 packages of zetsy and the regular profit making would be $11,340.

Step-by-step explanation:

12-ounce

regular = 65%

mild = 35%

extra sharp zesty blend = 75%

extra sharp mild = 25%

8,100 mild for = $1.30

3,500 extra sharp = $1.50

cost blend and package = $0.30

regular sold = $1.8

zesty = $2.10

first we calculate the cost of each product

conversion Of  ounces to pounds:

1 pound = 16 ounces

regular cost:

12/16 pounds x 65% mild x $1.30

= 0.63375

12/16 pounds x 35% sharp x $1.50

= 0.39375‬

+ blend and package $0.30

total = $1.3275‬

contribution: $1.8 – $1.3275

= $0,4725‬

zesty cost:

12/16 pounds x 75% mild x $1.30

= 0.73125‬

12/16 pounds x 25% sharp x $1.50

= 0.28125‬

+ blend and package 0.30

total $1,3125‬

contribution: $2.10 – $1.3125

= $0,7875‬

to maximize profit:

profit = $0.4725Regular + $0.7875zetzy

adding the  constraint:

mild = Regular x $0.4775 + Zetzy x $0.5625 = 8,100

and

sharp = Regular x $0.2625 + Zetzy x $0.1875 = 3,100

contribution generated by each product/pound:

                                 Regular        Zesty

CM                          $ 0.47250 $ 0.47250

Constrain resource

( pounds of mild)         0.48750 0.56250

CM per constrain        $ 0.9692 $ 1.4000

Constrain resource

( pounds of sharp)         0.26250 0.18750

CM per constrain           $ 1.80      $ 4.20

As zesty is better we produce as much as we can:

8,100 pounts / 0.5625 per cheese spreads: 14,400

check for possibilities of other constraint:

14,400 zesty packages x 0.1875 pounds each = 2,700 pounds

because it’s possible we only produce zetsy

profit = $0.4725 (0) + $0.7875 (14,400)

profit =  $ 11,340

4 0
3 years ago
Please help me!!!!!​
Bas_tet [7]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity:     cos²A + sin²A = 1

<u>Proof LHS → RHS</u>

\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}

\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}

\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}

\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}

\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}

\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}

\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}

\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}

                               =  cos A

LHS = RHS:  cos A = cos A   \checkmark

4 0
3 years ago
IT WIFE<br> What is the measure of the missing angle?
Ilya [14]
Please add a picture
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3 years ago
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3)Find the Circumference of this circle.<br> 9 in
mr Goodwill [35]

Answer:

56.52 in

Step-by-step explanation:

  1. 2πr = C
  2. 2 × 3.14 × 9 = C
  3. 2 × 3.14 = 6.28
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I hope this helps!

4 0
3 years ago
Find the measure of b
amid [387]

Answer: 90°

Step-by-step explanation:

Angle b is vertical to the angle that has a measure of 90°

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