Which equation can be used to find the value of x?

Which statement best explains a negative impact that zebra mussels can have on an ecosystem?

Oduvanchick [21]

The correct answer is D

8 0

2 years ago

Work out and simplify where possible a) 2/5+1/3 b) 5/9-1/2

Vlad1618 [11]

The answer is
a) 11/15
b) 1/18

5 0

3 years ago

Find sin 2x, cos 2x, and tan 2x from the given information. cscx=4,tanx<0.

lutik1710 [3]

Answer:

Step-by-step explanation:

Given the expression cosec (x) = 4 and tan(x)< 0

since cosec x = 1/sinx

1/sinx = 4

sinx = 1/4

From SOH, CAH TOA

sinθ = opposite/hypotenuse

from sinx = 1/4

opposite = 1 and hypotenuse = 4

to get the adjacent, we will use the Pythagoras theorem

adj² = 4²-1²

adj² = 16-1

adj ²= 15

adj = √15

cosx = adj/hyp = √15/4

tanx = opposite/adjacent = 1/√15

since tan < 0, then tanx = -1/√15

From double angle formula;

sin2x = 2sinxcosx

sin2x = 2(1/4)(√15/4)

sin2x = 2√15/16

sin2x = √15/8

for cos2x;

cos2x = 1-2sin²x

cos2x = 1-2(1/4)²

cos2x = 1-2(1/16)

cos2x= 1-1/8

cos2x = 7/8

for tan2x;

tan2x = tanx + tanx/1-tan²x

tan2x = 2tanx/1-tan²x

tan2x = 2(-1/√15)/1-(-1/√15)²

tan2x = (-2/√15)/(1-1/15)

tan2x = (-2/√15)/(14/15)

tan2x = -2/√15 * 15/14

tan2x = -30/14√15

tan2x = -30/7√15

rationalize

tan2x = -30/7√15 * √15/√15

tan2x = -30√15/7*15

tan2x = -2√15/7

5 0

3 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

2 years ago

The temperature dropped from 12° to 8° this was drop of how many degrees

lapo4ka [179]

Answer:

4°

Step-by-step explanation:

12-8=4

therefore the answer would be 4 degrees

6 0

3 years ago