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3 years ago

Determine whether the lines are parallel or perpendicular or neither. 2x=y−10 and y=−2x

Mathematics

1 answer:

MrRa [10]3 years ago

7 0

Put the first equation in slope-intercept form, or y = mx + b. Start by subtracting y from both sides.

2x - y = -10, subtract 2x from both sides.

-y = -10 - 2x

Divide both sides by negative one.

y = 10 + 2x

To find the slope when the equations are in slope-intercept form you look at the coefficient of x. The first equation has the slope of 2 (which we just found), and the second equation has the slope of -2.

Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.

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Find the distance between xequals[Start 2 By 1 Matrix 1st Row 1st Column 8 2nd Row 1st Column negative 5 EndMatrix ]and yequals[

kherson [118]

Answer:

Distance =√(x₁ - y₁)²+ (x₂ - y₂)² = √97 = 9.85

Step-by-step explanation:

The Matrix X and Y could also be referred to as vectors in Rⁿ dimensions.

if Vector X = ( x₁ , x₂) and Vector Y = (y₁ , y₂)

then, Distance (X-Y) = ||X-Y|| = √(x₁ - y₁)²+ (x₂ - y₂)²

where, x₁ = 8, x₂ = -5 and y₁ = -1 , y₂ = -9

Distance = √(8 - (-1))²+ (-5 - (-9))² = √9² + 4² =√97 = 9.85

4 0

3 years ago

The price of an item has been reduced by 85% the original price was $95 what is the price of the item

Yanka [14]

Answer:

14.25

Step-by-step explanation:

95 x 0.85 = 80.75

95-80.75 = 14.25

3 0

3 years ago

How do you solve for X?<br> BD= 5x+3 AE= 4x+18

Kaylis [27]

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6 0

3 years ago

Consider the rational expression (IMAGE ATTACHED)

Keith_Richards [23]

Answer:

3x² is a term in the numerator
x + 1 is a common factor
The denominator has 3 terms

Step-by-step explanation:

You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.

When you factor the expression, you get ...

$\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}$

This reveals a common factor of x+1.

So, the above three observations are true of this rational expression.

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4 years ago

A manufacturing company produces 3 different products A, B, and C. Three types of components, i.e., X, Y, and Z, are used in the

Murljashka [212]

Answer:

Step-by-step explanation:

Using the Excel Formula:

Decision Variable Constraint Constraint

A 65 65 100

B 80 80 80

C 90 90 90

14100 300 300

= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90

Now, we have:

Suppose A, B, C represent the number of units for production A, B, C which is being manufactured

A B C Unit price

Need of X 2 1 1 $20

Need of Y 2 3 2 $30

Need of Z 2 2 3 $25

Price of

manufac - $200 $240 $220

turing

Now, for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.

Thus, the cost or unit of manufacturing of A is:

$20 (2) + $30(2) + $25(2)

$(40 + 60 + 50)

= $150

Also, the market price of A = $200

So, profit = $200 - $150 = $50/ unit of A

Again;

For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.

So, total cost of manufacturing a unit of B is:

= $20(1) + $30(3) + $25(2)

= $(20 + 90+50)

= $160

And the market price of B = $240

Thus, profit = $240- $160

profit = $80

For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:

SO, the total cost of manufacturing a unit of C is:

= $20 (1) + $30(2) + $25(3)

= $20 + $60 + $25

= $155

This, the profit = $220 - $155 = $65

However; In manufacturing A units of product A, B unit of product B & C units of product C.

Profit --> 50A + 80B + 65C

This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40

The current demand is:

100 - A

80 - B

90 - C respectively

So, the total penalty

${(100 - A) + (80 - B) +(90 - C) } + \$40$

This should be subtracted from profit.

So, we have to maximize the profit

$Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};$

Subject to constraints;

we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity

Then;

$2A + B +C \le 300$ due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.

Next; demand for A, B, C will not exceed 100, 80, 90 units.

Hence;

$A \le 100$

$B \le 80$

$C \le 90$

and $A, B, C \ge 0$ because they are positive quantities

The objective is:

$\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}$

A, B, C $\to$ Decision Varaibles;

Constraint are:

$A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0$

6 0

3 years ago