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3 years ago

Two- step equation Solve each question

Mathematics

1 answer:

Mandarinka [93]3 years ago

5 0

To solve for a variable, isolate it! Get the variable alone on one side of the equation.

13) -15 = -4m + 5 ... -20 = -4m ... m = 5

14) 10 - 6v = -104 ... -6v = -114 ... v = 19

15) 8n + 7 = 31 ... 8n = 24 ... n = 3

16) -9x - 13 = -103 ... -9x = -93 ... x = 31/3

17) (n + 5) / -16 = -1 ... n + 5 = 16 ... n = 11

18) -10 = -10 + 7m ... 0 = 7m ... m = 0

19) -10 = -10(k - 9) ... 1 = k - 9 ... k = 10

20) (m / 9) - 1 = -2 ... m / 9 = -1 ... m = -9

21) 9 + 9n = 9 ... 9n = 0 ... n = 0

22) 7(9 + k) = 84 ... 9 + k = 12 ... k = 3

I cannot clearly read 23 and 24, but I hope you can see the principles I applied to produce these answers.

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Write an equation in slope-intercept form for the line with slope 1/4 and y intercept -4. Then graph the line

quester [9]

Answer:

Step-by-step explanation:

slope intercept form is y = mx + b

b is the y intercept ( crossing y axis value).... by inspection b = -4

m is the slope of the line, Slope = m = 1/4 note: the slope is positive

the slope equals the 'rise' over 'run'

if the line moves up the slope is positive, if the line moves down the slope is negative

the rise is how many y units does the line go 'up' or 'down'

the run is how many x units does the line go 'left' or 'right'

the rise = 1 Y unit

the run = 4 X units

y = mx + b m =1/4 b = -4

y = (1/4)x + (-4)

y = (1/4)x - 4

graph a line stating at y = -4 and going up (rising) to the right ONE Y Unit for every FOUR X units (the run)

3 0

3 years ago

Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. T

Kaylis [27]

Answer:

z (max) = 1250 $

x₁ = 25 x₂ = 0 x₃ = 25

Step-by-step explanation:

Profit $ mach. 1 mach. 2

Product 1 ( x₁ ) 30 0.5 1

Product 2 ( x₂ ) 50 2 1

Product 3 ( x₃ ) 20 0.75 0.5

Machinne 1 require 2 operators

Machine 2 require 1 operator

Amaximum of 100 hours of labor available

Then Objective Function:

z = 30*x₁ + 50*x₂ + 20*x₃ to maximize

Constraints:

1.-Machine 1 hours available 40

In machine 1 L-H we will need

0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40

2.-Machine 2 hours available 40

1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40

3.-Labor-hours available 100

Machine 1 2*( 0.5*x₁ + 2*x₂ + 0.75*x₃ )

Machine 2 x₁ + x₂ + 0.5*x₃

Total labor-hours :

2*x₁ + 5*x₂ + 2*x₃ ≤ 100

4.- Production requirement:

x₁ ≤ 0.5 *( x₁ + x₂ + x₃ ) or 0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0

5.-Production requirement:

x₃ ≥ 0,2 * ( x₁ + x₂ + x₃ ) or -0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0

General constraints:

x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers

The model is:

z = 30*x₁ + 50*x₂ + 20*x₃ to maximize

Subject to:

0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40

1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40

2*x₁ + 5*x₂ + 2*x₃ ≤ 100

0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0

-0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0

x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers

After 6 iterations with the help of the on-line solver AtomZmaths we find

z (max) = 1250 $

x₁ = 25 x₂ = 0 x₃ = 25

6 0

3 years ago

Jack took out a 6-year loan for $25,000 to purchase a boat at a 4.5% interest rate. If the interest is compounded monthly, what

Kruka [31]

Answer: $32,732.58

Step-by-step explanation:

To calculate the total loan payment over the course of the loan period, use the future value formula:

= Loan amount * (1 + rate) ^ number of years

As this loan is compounded monthly, you need to convert certain terms to monthly figures:

Number of periods = 6 * 12 months = 72 months

Interest = 4.5 / 12 = 0.375%

Total payment:

= 25,000 * ( 1 + 0.375%)⁷²

= $32,732.58

6 0

3 years ago

Jason is planning on retiring after 25 years of employment. For the last three years he

Flauer [41]

Jason's monthly pension is the product of the final three-year average salary is $32,625. Then the correct option is C.

<h3>What is a monthly pension?</h3>

Jason is planning on retiring after 25 years of employment.

For the last three years he has made $60,000; $56,000; and $58,000.

His employer offers a defined benefit plan in which the annual pension is calculated as the product of the final three-year average salary, the number of years of service, and a 2.25% multiplier.

Then Jason's monthly pension will be

$\rm Monthly \ pension = \dfrac{(60,000+56,000+58,000)}{12} \times 2.25\\\\Monthly \ pension = 14500 \times 2.25\\\\Monthly \ pension = \$ \ 32,625$

More about the monthly pension link is given below.

brainly.com/question/14271336

#SPJ1

5 0

3 years ago

Please help me on this question and explain how you got your answer

Vsevolod [243]

Answer:

Step-by-step explanation:

4 0

3 years ago