each month for 7 months, samuel mows 3 lawns. how many more lawns does he need to mow before he has mowed 29 lawns?

Answer:

The correct option is D.

Step-by-step explanation:

The given quadratic equation is

[tex]p^2+13p-30=0[/tex]

First find two numbers whose sum is 13 and whose product is -30.

The two numbers are 15 and -2.

[tex]p^2+(15-2)p-30=0[/tex]

[tex]p^2+15p-2p-30=0[/tex]

[tex]p(p+15)-2(p+15)=0[/tex]

[tex](p+15)(p-2)=0[/tex]

By using zero product property, equate each factor equal to 0.

[tex]p+15=0[/tex]

[tex]p=-15[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Therefore the values of p are -15 and 2. Option D is correct.

The original cost of the mink coats was $6,000. This is determined by dividing the markup amount of $3,000 by the markup percentage, which is 50% or 0.50 in decimal form.

A 50% markup on cost means that the extra amount added to the cost price of the coats is 50% of that original cost price. Since the markup on the mink coats is given as $3,000, we can set up the equation as follows to find the original cost price (C):

Markup = 50% of Cost
3000 = 0.50  imes C

To find the cost (C), we divide the markup by the percentage, which in decimal form is 0.50:

C = $3,000 / 0.50
C = $6,000

Hence, the original cost of the mink coats was $6,000.

The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

It is true that (x -a) is a factor of the polynomial.

Let the polynomial function be f(x)

When divided by x -a, we have:

f(x)/(x - a) = Some polynomial remainder 0

The above can be represented as

f(a) = 0

This means that it is true that (x -a) is a factor of the polynomial.

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Answer:

1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Step-by-step explanation:

To find : What is 1626 divided by 12 as a mixed number ?

Solution :

Writing 1626 divided by 12 in a fraction from,

[tex]\frac{1626}{12}[/tex]

Writing fraction in simpler form by reducing with common factors,

[tex]\frac{1626}{12}=\frac{2\times 3\times 271}{2\times 2\times 3}[/tex]

[tex]\frac{1626}{12}=\frac{271}{2}[/tex]

Writing [tex]\frac{271}{2}[/tex] in mixed fraction by dividing 271 by 2,

[tex]271=135\times 2+1[/tex]

i.e. [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Therefore, 1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Answer:

The determinant of an identity matrix is always 1.

Step-by-step explanation:

Given : An identity matrix.

We have to find the determinant of an identity matrix.

Consider an identity matrix,

Identity matrix is a matrix having entry one in its diagonal and  rest all entries are zero.

Let us consider a 2 × 2 identity matrix,

[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

We know determinant of a  2 × 2 matrix

[tex]I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

is given by

D = ad - bc

Thus, here a = 1 , b = 0 , c= 0 d= 1

Thus, D = 1 - 0 = 1

Thus, The determinant of an identity matrix is always 1.

The function rule representing a worker's earnings e as a function of hours n worked at a rate of $8.75 per hour is e(n) = 8.75 × n. This formula is used to calculate the worker's pay based on their hours worked.

To represent a worker's earnings e as a function of the number of hours n worked at a rate of $8.75 per hour, you would write the function rule as:

e(n) = 8.75 × n

Here, n represents the number of hours worked and e(n) represents the earnings for those hours.

For example, if a worker puts in 8 hours of work, their earnings would be calculated as:

e(8) = 8.75 × 8

      = $70

This means the worker would earn $70 for an 8-hour workday.

The first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are: -10, -15, -20, -25, -30.

To generate the first five terms in the sequence using the explicit formula [tex]y_n[/tex]  = -5n - 5,

we substitute the values of n from 1 to 5 into the formula.

For n = 1:

[tex]y_1[/tex]= -5(1) - 5 = -10

For n = 2:

[tex]y_2[/tex] = -5(2) - 5 = -15

For n = 3:

[tex]y_3[/tex] = -5(3) - 5 = -20

For n = 4:

[tex]y_4[/tex] = -5(4) - 5 = -25

For n = 5:

[tex]y_5[/tex] = -5(5) - 5 = -30

Therefore, the first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are:

-10, -15, -20, -25, -30.

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Answer:16( 3+2)

Step-by-step explanation:

Another way of expressing 48 + 32 are:

32 + 48 and 80.

Addition is a basic mathematical operation that combines two numbers to give a total or sum.

The given expression is:

48 + 32

The commutative property is:

A+B  = B+A

Since Addition always holds the commutative property

Therefore, we can write the given expression as,

32 + 48

We can also express it by direct sum,

   3 2

+  4 8

_______

   8 0

_______

So, the sum of 32 and 48 is 80.

Hence,

We can express the given expression as 32 + 48 and 80.

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Final answer:

To solve a quadratic equation using the quadratic formula, put the equation in ax² + bx + c = 0 form, identify a, b, and c, plug them into the formula x = (-b ± √(b² - 4ac)) / (2a), calculate the discriminant, and find the two possible values for x.

Explanation:

To solve a quadratic equation by using the quadratic formula, you should follow these steps:

For example, if we have the equation t² + 10t - 200 = 0, by identifying a=1, b=10, and c=-200, and plugging them into the quadratic formula, we can solve for t.

The method of pay that results in the most earnings is the second method of pay

In order to determine which method of pay would result in the most earnings ,  the value of each method would be determined

Value of the first option

6% commission on all sales = 6% x  $73,620.

0.06 x  $73,620. = $4,417.20

Value of the second option

Monthly salary of $3,000 plus 2% commission on all sales =  $3,000 + (2% x  $73,620)

$3,000 + (0.02% x  $73,620)

= $3000 + $1472.40

= $4472.40

Value of the third option

Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that.

= (4% x $50,000) + (9% x $23,620)

= $2000 + $2125.80

= $4125.80

Value of the fourth option

Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.

= (5% x$35,000) + (7% x $38,620)

= $1750 + $2703.40

= $4,453.40

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Answer:

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

Step-by-step explanation:

Given that x and y are the lengths of the sides adjacent and opposite θ, then they are related by:

tan θ = y/x

Differentiating respect to t, we get:

sec^2 θ * dθ/dt = (dy/dt * x - y * dx/dt)/(x^2)

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

The slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area is -2.

To find the slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area, we need to set up an integral to find the area under the parabola. The equation of the line will be in the form y = mx, where m is the slope we need to find. Setting up the integral, we get:

Solve the integral to find:

Substituting the limits of integration and solving, we get:

Therefore, the slope of the line that divides the region into two equal areas is -2.

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Answer:

Option 4). Machine with $8 per hour operating cost, producing 14 pounds of candy per hour.

Step-by-step explanation:

We have to find the most profitable investment for a candy shop that earns $1 per pound of candy.

We will take up each option one by one.

Option 1).

Producing eight pounds of candy per hours means profit = $1×8 = $8

But workers take $10 per hours so expenditure = $8 - $10 = -$2

There is a loss of $2 in this investment.

Option 2).

Production of 16 pounds candy per hour will make the profit = $1 × 16 = $16

But workers take $12 per hour so profit earned = 16 - 12 = $4

Option 3).

Machine produces 10 pound of candy per hour so profit will be = $1 ×10 = $10

Operating cost of the machine = $5 per hour

So profit generated = profit - Operating cost of machine

                                 = 10 - 5 = $5

Option 4).

Profit earned by production of 14 pounds of candy per hour = $1 × 14 = $14

Operating cost of the machine = $8 per hour

Therefore, Total profit per hour = 14 - 8 = $6

Finally we can say that the maximum profit will be generated in option 4.

Therefore, Option 4) will be the best option to invest.

Final answer:

The most profitable investment for a candy shop is the machine with an $8 per hour operating cost, producing 14 pounds of candy per hour, yielding a net profit of $6 per hour.

Explanation:

The task is to determine the most profitable investment for a candy shop that makes $1 profit per pound of candy. To calculate the profitability of each option, we need to figure out the net profit per hour for each.

Worker at $10 per hour, producing eight pounds of candy per hour:

Profit = 8 pounds * $1 profit per pound - $10 wage per hour = $8 - $10 = -$2 per hour.

Worker at $12 per hour, producing 16 pounds of candy per hour:

Profit = 16 pounds * $1 profit per pound - $12 wage per hour = $16 - $12 = $4 per hour.

Machine with $5 per hour operating cost, producing 10 pounds of candy per hour:

Profit = 10 pounds * $1 profit per pound - $5 operating cost per hour = $10 - $5 = $5 per hour.

Machine with $8 per hour operating cost, producing 14 pounds of candy per hour:

Profit = 14 pounds * $1 profit per pound - $8 operating cost per hour = $14 - $8 = $6 per hour.

Comparing the net profit per hour for each option, the Machine with $8 per hour operating cost, producing 14 pounds of candy per hour, is the most profitable investment.