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the equation of the line a is given as y = -3/4 x -2. Suppose the line a is parallel to line b and lime t is perpendicular to li

Orlov [11]

Answer:

equation 'b': y = -3/4x + 5

equation 't': y = 4/3x - 2

Step-by-step explanation:

parallel lines must have the same slope

the slope of perpendicular lines must be opposite and reciprocal

7 0

3 years ago

The Toy Company sells two types of kids' basketball hoops, Jordan size and Shaq size.

Hoochie [10]

Answer:

Maximum Profit = 13050

when

The Toy company sells Jordan Size hoops = 7

The Toy company sells Shaq Size hoops = 3

Step-by-step explanation:

Given - The Toy Company sells two types of kids' basketball hoops, Jordan size and Shaq size. A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together. The Company requires the neighborhood to order at least 2 Jordan sizes and at least 3 Shaq sizes. The Toy Company makes a profit of $1,350 on the Jordan size and $1,200 on the Shaq size.

To find - What is the maximum profit they can make given the constraints above?

Proof -

Let us assume that,

The Toy company sells Jordan Size hoops = x

The Toy company sells Shaq Size hoops = y

Now,

Given that, A neighborhood needs no more than 10 Jordan sizes and Shaq sizes all together.

⇒x + y ≤ 10

Now,

Given that, The Company requires the neighborhood to order at least 2 Jordan sizes and at least 3 Shaq sizes.

⇒ x ≥ 2

y ≥ 3

Now,

Given that,

The Toy Company makes a profit of $1,350 on the Jordan size and $1,200 on the Shaq size.

So,

The objective function becomes

Z = 1350x + 1200 y

So,

The Linear Programming Problem (LPP) becomes

Maximize Z = 1350x + 1200 y

Subject to

x + y ≤ 10

x ≥ 2

y ≥ 3

x, y ≥ 0

We will Solve the LPP by Graphical method.

The graph is as follows :

The points on the Boundary are -

A(2, 8)

B(2, 3)

C(7, 3)

So,

Points (x,y) Objective function value ( Z = 1350x + 1200y)

B(2,3) 1350(2) + 1200(3) = 6300

C(7,3) 1350(7) + 1200(3) = 13050

A(2,8) 1350(2) + 1200(8) = 12300

So,

Maximum value = 13050 at point C(7,3)

∴ we get

Maximum Profit = 13050

when

The Toy company sells Jordan Size hoops = x = 7

The Toy company sells Shaq Size hoops = y = 3

6 0

3 years ago

Picture picture picture

cluponka [151]

Soo what do you need help with? It seems pretty easy. I can help you if you want.

6 0

3 years ago

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What is 5/7 of 14.7 kg plz helppp

eimsori [14]

Answer: i'm pretty sure the answer is 10.5

Step-by-step explanation: <em>i multiplied 5/7 by 14.7 </em>

I'm sorry if this is wrong but if it's right i need brainliest to rank up so please mark me brainliest:)

5 0

3 years ago

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Factor completely: 2x4 − 32.

vazorg [7]

Answer:

Option b) is correct.

The completed factor of given expression is $2(x-2)(x+2)(x^2+4)$

Step-by-step explanation:

Given expression is $2x^4-32$

To find the completed factor for the given expression:

$2x^4-32$ :

Taking the common number "2" outside to the above expression we get

$2x^4-32=2(x^4-16)$

Now rewritting the above expression as below

$=2(x^4-2^4)$ (since 16 can be written as the number 2 to the power of 4)

$=2((x^2)^2-(2^2)^2)$

The above expression is of the form $a^2-b^2=(a+b)(a-b)$

Here $a=x^2$ and $b=2^2$

Therefore it becomes

$=2(x^2+2^2)(x^2-2^2)$

$=2(x^2+4)(x^2-2^2)$

The above expression is of the form $a^2-b^2=(a+b)(a-b)$

Here $a=x$ and $b=2$

Therefore it becomes

$=2(x^2+4)(x+2)(x-2)$

$=2(x+2)(x-2)(x^2+4)$

Therefore $=2(x+2)(x-2)(x^2+4)$

$2x^4-32=2(x-2)(x+2)(x^2+4)$

Option b) is correct.

The completed factor of given expression is $2(x-2)(x+2)(x^2+4)$

3 0

3 years ago

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