Combine Like Terms

7x^4 - 5x^4=

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The number of ducks in a farm are 20 and the number of pigs in a farm are 8.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, in a farm there are 28 animals and combined they have 72 legs.

Let the number of pigs be p and let the number of ducks be d.

Here, p+d=28 ------(i)

4p+2d=72 -------(ii)

From equation (i), p=28-d

Substitute p=28-d in equation (ii), we get

4(28-d)+2d=72

112-4d+2d=72

112-72=2d

d=20

Substitute d=20 in equation(i), we get

p+20=28

p=8

Therefore, the number of ducks in a farm are 20 and the number of pigs in a farm are 8.

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Answer:

\(x = \frac{1}{2} \)

The step by step explanation is attached to the answer.

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Answer:75%

Step-by-step explanation:

Answer:

75% voted

Step-by-step explanation:

9 out of 12 is 75%

Answer:

$4 per foot

Step-by-step explanation:

What we know:

    - 50 feet of fencing

    - $200 spent in total

What we want to know:

    - How much to spend per foot

How to execute:

    - We must divide

Step (1 of 1) Divide:

200 ÷ 50 = 4

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The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

1.97 day; 1 day.

Step-by-step explanation:

0.07*100 = 7

31.91x - 7 = 70

70 - 7 = 63

31.91x = 63

63 / 31.91 = 1.97

Hudson can afford to drive the car for 2 days and stay under his budget.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We know that it costs $0.07 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:

31.91x + 0.07(100) ≤ 70

31.91x + 7 ≤ 70

Rearranging the inequality so we have the variable isolated on one side, we get:

31.91x ≤ 63

Divide both sides by 31.91 to get x alone.

x ≤ 1.97430

x ≤ 2

From obtaining the solution, Hudson can afford to drive the car for 2 days and stay under his budget.

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The question seems incomplete, the complete question would be as:

A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing that:

• He plans to drive 100 miles.

• He has at most $70 to spend.

Which inequality can be used to determine, the maximum number of days Hudson can afford to rent for while staying within his budget?

Answer:

area = 572.3 m²

Step-by-step explanation:

area = PiR²

r = 27/2

area = (3.14)(13.5²)

area = 572.3 m²

Answer:

A =  6  +  B /x −  4 /x

B  =  Ax  +  4  −  6 x

x = b-4/a-6

Step-by-step explanation:

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The values of A and B that will result in an equation with infinite solutions are 6 and 4

For an equation to have infinite number of solutions, the equations on both sides must be the same,

Given the equation

Ax + 4 = 6x + B

If the equation has infinite number of solution, then

Ax = 6x

A= 6

Similarly

4 = B

B = 4

Hence the values of A and B that will result in an equation with infinite solutions are 6 and 4

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The quadrilaterals have the following congruent angles: ∠ A ≅ ∠ W, ∠ B ≅ ∠ X, ∠ C ≅ ∠ Y, ∠ D ≅ ∠ Z.

Herein we find the case of two similar quadrilaterals, that is, two quadrilaterals that have four pairs of congruent angles and four pairs of proportional sides.

Thus, by direct observation, we have the following conclusions on congruence of angles and proportionality of sides:

Angles

∠ A ≅ ∠ W

∠ B ≅ ∠ X

∠ C ≅ ∠ Y

∠ D ≅ ∠ Z

Sides

AB / XW = BC / XY = CD / YZ = AD / WZ

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Answer:

2000 metres

Step-by-step explanation:

1000 metres = 1 km

therefore, (1000×2) metres = 2 km

2000 metres = 2km

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer: 13/24

Step-by-step explanation: M A T H W A Y Calculator

Answer:

0.54166666666 or 13/24

Step-by-step explanation:

Answer:

9 meters every second

Step-by-step explanation:

45/5=9

5/5=1

9:1

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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The gallons of gas that each vehicle would consume for the different amounts of driving are as follows:

a) For 300 mi of city driving plus 100 mi of highway driving, car A will consume 12.825 gallons of gas, while car B will consume 14.05 gallons of gas.

b) For 100 mi of city driving plus 300 mi of highway driving, car A will consume 13.475 gallons of gas, while car B will consume 12.52 gallons of gas.

                                           City Driving     Highway Driving

Car A                                     32 mi/gal            29 mi/gal

Car B                                     27 mi/gal            34 mi/gal

                   City Driving     Highway Driving

a)                       300 mi              100 mi

b)                       100 mi              300 mi

                   City Driving               Highway Driving              Total

a)              9.375 gal.(300/32)         3.45 gal. (100/29)        12.825 gal.

b)              3.125 gal.(100/32)         10.35 gal    (300/29)     13.475 gal.

                   City Driving               Highway Driving             Total

a)                11.11 gal. (300/27)         2.94 gal. (100/34)         14.05 gal.

b)              3.70 gal. (100/27)          8.82 gal. (300/34)        12.52 gal.

Thus, different driving ratings (miles per gallon) show the differences in gas consumption by vehicles in city driving and highway driving.

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The probability that no one in a family of five will be hospitalized in a year 0.2373 .

Let P(E) denote the probability of being hospitalized during a year and P'(E) the probability of not being hospitalized during a year

Then , using equation (1) , we get

          \(0.25+P'(E)=1\\P'(E)=1-0.25\\P'(E)=0.75\)

The probability that no one in a family of five will be hospitalized in a year is equal to \((P'(E))^n\) where n is the number of member .

   \((P'(E))^n=(0.75)^5\\(P'(E))^n=0.2373\)

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9514 1404 393

Answer:

  d  4x +y = 17

Step-by-step explanation:

The only equation satisfied by the given point is also in standard form:

  4x +y = 17

__

Trying the given point in the different equations, we have ...

a) 4x -y = 4(5) -(-3) = 23

b) 4x +y = 4(5) +(-3) = 17

c) -4x +y = -4(5) +(-3) = -23

d) 4x +y = 4(5) +(-3) = 17 . . . . equation D matches the point

Solving for y, we have ...

  y = -4x +17  . . . .  a slope of -4 . . . . equation D matches the slope

Answer:

Let karly's age be x

mona is four years older

mona = 4+x

Alexis it twice as old as mona

alexis= 2(4+x)

alexis= 8+2x

the sum of their ages is 48

x + 4+x + 8+2x= 48

4x+12=48

4x=48-12

4x=36

x=9

katly is nine years old

mona = 4+x

mona = 4+9

mona = 13

mona is 13 years old

alexis = 8+ 2x

alexis = 8+ 2(9)

alexis = 8+18

alexis = 26

alexis is 26 years old

Answer:

400 litres

Step-by-step explanation:

Answer:

y =3x + 5

Step-by-step explanation:

The slope intercept form of an equation is expressed as;

y = mx+c

m is the slope

c is the intercept

Get the intercept

Substitute m = 3 and (-2,-1) into y = mx+c

-1 = 3(-2)+c

-1 = -6 + c

c = -1+6

c = 5

Get the equation.

Recall that y = mx+c

y =3x + 5

This gives the required equation

The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:

Branch of Santosh & Co. Chennai

For the year ended December 31, 2018

Sales revenue            $40,300

Cost of goods sold         4,200

Gross profit                 $36,100

Expenses:

Office expenses $36,000

Salaries                    3,600

Total expenses         $39,600

Loss                             $3,500

An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.

The profit or loss is the difference between the total revenue and the total expenses for the accounting period.

Credit sales at branch 40,000

Office expenses by Head office 36,000

Cash remittance to branch for petty cash 9,000

Goods sent to Branch 7,200

Salaries paid by head office 3,600

Debtors 31.12.2018 30,000

Petty cash on 31.12.2018 16,200

Cash sales at branch 300

Stock of 31.12.2018 3,000

Sales revenue   $40,300 ($40,000 + $300)

Cost of goods sold $4,200 ($7,200 - $3,000)

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The compound interest is solved and the amount in her account in 2047 is given by A = $ 1315.46

Given data ,

To determine how much money Carly has in her account after 37 years, we need to substitute the value of t as 37 into the equation:

P = 600(1.0375)^t

P = 600(1.0375)^37

P ≈ 600(1.0375)^37 ≈ 600(2.19243) ≈ $ 1315.46

Therefore , Carly has approximately $1315.46 in her account after 37 years.

To calculate the growth rate, we need to find the rate of change between the initial and final amounts over the given time period.

Regarding how long it takes for Carly's account to reach $750, we'll assume you mean when the account reaches or exceeds $750. Let's set up the equation and solve for t:

750 = 600(1.0375)^t

Dividing both sides by 600, we get:

1.25 = 1.0375^t

Taking the logarithm of both sides (base 1.0375):

log(1.25) = t * log(1.0375)

t ≈ log(1.25) / log(1.0375) ≈ 8.5 years

Hence , it takes approximately 8.5 years for Carly's account to reach or exceed $750

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Answer:

Step-by-step explanation:

The price of the box of cereal for each week remains the same:

Week 1: $2.55

Week 2: $2.50

In the first week, the price of a box of oat cereal at the grocery store was $2.55.

In the next week, the store decided to put the cereal on sale.

The price for that week was reduced to $2.50.

If the digit in the thousandth decimal place is 5 or greater, we round up; otherwise, we round down.

In this case, both prices already have the digit in the hundredth decimal place specified, so no rounding is needed.

Therefore, the price of the box of cereal for each week, rounded to the nearest tenth of a dollar, remains the same:

Week 1: $2.55

Week 2: $2.50

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Answer:

It would be answer choice D

Answer:

27

Step-by-step explanation:

Given expression :  

    1 + 24 + ( + 3) = 1

Bring the number 1 to the left side of the equal sign. The positive 1 becomes negative 1 when brought towards the left side of the equal sign.

1 + 24 + ( + 3) - 1 = 0

Now, opening the bracket, we get

1 + 24  + 3 - 1 = 0

Negative 1 and positive 1 will get cancel

24  + 3  = 0

or 27

Therefore, the value of the numerical expression  1 + 24 + ( + 3) = 1 is 27.

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Answer:

y = 3x + 3 :D

Step-by-step explanation:

Equation of line: y = mx + b :)

b: Y intercept

m: Slope

Now lets solve :)

Lets find M first :)

We need 2 points so lets use (0,3) and (1,6) :)

We fist need to subtract :)

6 - 3 = 3

1 - 0 = 1

Now we divide :)

3/1 = 3

Lets put that into our equation :)

y = 3x + b

Now lets find B :)

To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!

The y intercept will be 3 :)

The final equation will be y = 3x + 3 :)

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