Plane ABC and plane BCE ____ be the same plane.

A. must

B. may

C. cannot

Answer: The answer saying YES, is WRONG, the CORRECT ANSWER IS NO.

Answer:

The answer is no

0.45^2-4(-.005)(125)=2.7025

so no it do not exceed

Step-by-step explanation:

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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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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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:

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.

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:

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.

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)

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.

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 resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

To find the resulting acceleration of an object when a force is applied to it, you can use Newton's second law of motion, which states:

F = ma

Given that the force F = 7.1 Newtons and the mass m = 6.3 kg, we can rearrange the formula to solve for acceleration:

[tex]\[ a = \frac{F}{m} \]Substitute the given values:\[ a = \frac{7.1 \, \text{N}}{6.3 \, \text{kg}} \]Now, divide to find the acceleration:\[ a = \frac{7.1}{6.3} \, \text{m/s}^2 \]\[ a = 1.127 \, \text{m/s}^2 \][/tex]

So, the resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

Complete question:

An object with a mass of 6.3 kg has a force of 7.1 Newtons applied to it. What is the resulting acceleration of the object?​

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.

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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