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3 years ago

Solve the following system of equations by graphing.

Mathematics

1 answer:

MrMuchimi3 years ago

8 0

Answer:

<h2>Graph b</h2>

Step-by-step explanation:

The equation of a linear function in slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The graph of linear function is a straight line therefore we need only two points to the plotting the graph.

$-4x+3y=-12\qquad\text{add 4x to both sides}\\\\3y=4x-12\qquad\text{divide both sides by 3}\\\\y=\dfrac{4}{3}x-4\\\\for\ x=0\to y=\dfrac{4}{3}(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=3\to y=\dfrac{4}{3}(3)-4=4-4=0\to(3,\ 0)$

$-2x+3y=-18\qquad\text{add 2x to both sides}\\\\3y=2x-18\qquad\text{divide both sides by 3}\\\\y=\dfrac{2}{3}x-6\\\\for\ x=0\to y=\dfrac{2}{3}(0)-6=0-6=-6\to(0,\ -6)\\\\for\ x=3\to y=\dfrac{2}{3}(3)-6=2-6=-4\to(3,\ -4)$

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Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplifi

Gnom [1K]

I think there is a mistake in this problem

7 0

4 years ago

Goal

morpeh [17]

The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:

50% for necessities (housing, food, transportation, utilities) $740

30% for luxuries, savings, vacations, entertainment, etc. $461

20% for Emergency Funds and Retirement $335

<h3>What is a personal budget?</h3>

A personal budget is the household budget for a single person for a period.

The personal budget shows an estimate of the person's revenue and expenses over the period.

<h3>Data and Calculations:</h3>

Hourly rate of earnings = $12

Working hours per week = 40 hours

Working hours per month = 160 hours (40 x 4 weeks)

Total monthly earnings = $1,920 ($12 x 160)

Assumed tax rate = 20%

After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)

<h3>Monthly Necessities:</h3>

Rent of apartment = $300

Heating = $40

Water cost = $20

Sewage bill = $10

Food = $300

Transportation = $50

Other costs = $20

Total cost for necessities = $740

Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.

Learn more about personal budgets at brainly.com/question/1943261

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6 0

2 years ago

Make g the subject of the formula w = 7 - √g

mrs_skeptik [129]

Isolate the g

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides

w (-7) = -√g + 7 (-7)

w - 7 = -√g

multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g
-1w + 7 = √g

to get rid of the square root, you must square both sides
Note: -1w is the same as -w
Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²
g = (-w + 7)²
g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or g = (-w + 7)² )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²
(-w)(7) = -7w
(7)(-w) = -7w
(7)(7) = 49

g = w² - 7w - 7w + 49

simplify (combine all like terms)

g =w² - 7w - 7w + 49

g = w² - 14w + 49

g = w² - 14w + 49 is your answer

hope this helps

5 0

3 years ago

What is the answer to 8/15 * 5/8

LiRa [457]

Answer:

1/3

Step-by-step explanation:

8/15*5/8=40/120=1/3

6 0

4 years ago

Read 2 more answers

HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:

hichkok12 [17]

Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:

a) 900,000.

b) 78,125.

c) 10,000.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is: