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S_A_V [24]
3 years ago
12

An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16

cups of apples and 15 cups of flour. When you sell these at the Farmer’s Market you make $3.00 profit per apple pie and $2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize your profit. I'm stuck on the "Write any non-negativity constraints on x and y." part I know the inequality to show constraint for apples is 4x+2y<= and the flour equation is 3x+3y<=15
Mathematics
1 answer:
vova2212 [387]3 years ago
5 0
Both the x and y have to be greater than zero so you need to add two inequalities, x>0, y>0
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Prove that sin^4x + cos^4x= sinxcosx
yKpoI14uk [10]

Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

sin^4(x) + cos^4(x)

We can rewrite this as:

(sin^2(x))^2 + (cos^2(x))^2

Now we can add and subtract cos^2(x)*sin^2(x) to get:

(sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)

We can complete squares to get:

(cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2

and we know that:

cos^2(x) + sin^2(x) = 1

then:

1 - 2*sin(x)^2*cos(x)^2

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

1 - \frac{sin^2(2*x)}{2}

Then the simplification is:

cos^4(x) + sin^4(x)  = 1 - \frac{sin^2(2*x)}{2}

7 0
3 years ago
Which is the ratio 12 to 27 expressed as a fraction in lowest terms
raketka [301]

Answer:

4/9

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Multiplication Property of Equality---- If 6x divided by 8 = 40, then______
NNADVOKAT [17]

Answer:

Option C.) 6x=320

Step-by-step explanation:

we know that

The <u>Multiplication Property of Equality</u> states that if you multiply both sides of an equation by the same number, the sides remain equal

we have

\frac{6x}{8}=40

Apply the multiplication property of equality

Multiply by 8 both sides

\frac{6x}{8}(8)=40(8)

6x=320

therefore

The answer is the Option C

6 0
3 years ago
Read 2 more answers
5. 3x + 5y + 5z =1<br> x - 2y = 5<br> 2x + 4y = 11
lilavasa [31]

Answer:

see explanation

Step-by-step explanation:

Given the 3 equations

3x + 5y + 5z = 1 → (1)

x - 2y = 5 → (2)

2x + 4y = 11 → (3)

Use (2) and (3) to solve for x and y

Multiply (2) by 2

2x - 4y = 10 → (4)

Add (3) and (4) term by term

4x = 21 ( divide both sides by 4 )

x = \frac{21}{4\\}

Substitute this value of x into (3)

2 × \frac{21}{4\\} + 4y = 11

\frac{21}{2\\} + 4y = 11 ( subtract \frac{21}{2\\} from both sides )

4y = \frac{1}{2} ( divide both sides by 4 )

y = \frac{1}{8\\}

Substitute the values of x and y into (1) and solve for z

3 × \frac{21}{4\\} + 5 × \frac{1}{8\\} + 5z = 1

\frac{63}{4} + \frac{5}{8} + 5z = 1

\frac{131}{8} + 5z = 1 ( subtract \frac{131}{8} from both sides )

5z = - \frac{123}{8} ( divide both sides by 5 )

z = - \frac{123}{40}

Solution is

x = \frac{21}{4\\}, y = \frac{1}{8\\}, z = - \frac{123}{40}

3 0
3 years ago
Which number line shows the solution for
Brums [2.3K]

Answer:

It's the last choice.

Step-by-step explanation:

| n | ≤ 2  represents the distance between n and 0 that is less than or equal to 2.  The dots on the 2 and -2 are black because the equal sign is part of the inequality.

Note the vertical lines about the n mean the absolute value of n - the positive distance between  n and 0, which has a maximum of 2 either side of the 0.

6 0
3 years ago
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