Select the correct answer from each drop-down menu.Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of each sideof the square pleces of paper must be approximately equal to 3.46 v Inches. If each side were exactly this length, the area of eachsquare would bev square Inches.1. 11.97162. 12.04093. 16

a)

In order to find the list of all potential rational roots, let's find the factors of the division between the constant term and the leading term.

Since the constant term is zero, so the only potential rational root in the list is 0.

b)

Since the constant term is zero, so 0 is a root of the polynomial. Then, let's factor it to find the remaining roots:

Solving this quadratic equation using the quadratic formula, we have:

Therefore the actual roots of P(x) are:

0 (multiplicity 1) and -5 (multiplicity 2).

The answer is, Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number.

Three times the sum of twice a number and one is equal to twelve less than the product of three and the same number.

It has a wide spread throughout the Mathematics. It is referred to as the integer part of a division, or as the fraction, or as a ratio. It is used when indicating the presence or the degree of a characteristic in something or by someone. Quotient is the result of a division. It is obtained when we divide one number by another. Quotient means how many times. And it is derived from the Latin.

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Step 1

Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?

Step 2

Thus;

Answer;

Explanation:

The graph shows a ine crossing the parabola. The solution of the systems is the point where both system of equations intersect.

The line crosses the parabola at two point:

At x = 2, y = 2

This point is applicable to both. Since both have same values at this point, (2, 2) is one of the solution

At x = -2, y = -6

Both graphs have this point . This shows point (-2, -6) is also a solution

Hence, the solutions of the systems are (2, 2) and (-2, -6)

a. Solve for F(5).

To solve for F(5), substitute x = 5 to the given function, and evaluate accordingly to the operation

b. Solve for F(x+b)

Again we substitute the paremeters by x+b to the given function, and we get

c. Solve for F(-3)

Substitute x = -3

Given function is:

Now put f(x)=0

so the first point is (6,0) now for another points:

So the points are (-4,0) and (2,0) and(6,0)

Hence the correct options are 1,2 and 4.

Answer:

Lily drank 5 cartons of juice in February.

Explanation:

From the question, we're told that in January, Lily drank 2 1/2 cartons of juice and drank twice of that amount in February, so all we need to do is multiply the amount she drank in January by 2 to get the amount she drank in February.

Solving this, we'll have;

Therefore, Lily drank 5 cartons of juice in February.

The prime factorization of 54 is

54 = 2 × 3 × 3 ×3

Using the exponential form of the prime factorization that is

54 = 2 × 3³

In order to find the exponential regression we are going to select some values of the given data.

An special value is when x=0.

On the table we can see that when x=0 then y=9

Replacing x by 0 in the given choices, we have that:

Observing the results we have that the two choices with closer results to 9 are A (with 8.04) and C (with 6.61)

Now, we are going to select two additional values from the table in order to find which is the best answer: A or C.

Let's take x=1.

When x = 1, then y=10.

Replacing on the equation A we have:

and for the equation C:

For x=1, the nearest result is from the equation C.

Let's verify what happens when x=2.

When x=2 then y=16. Replacing on the equation A we have:

and for the equation C:

Again, for x=2, the nearest result is from the equation C.

Then, we can conclude that the best candidate is equation C.

We could try other values of x to double check:

We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;

Let x represent the number times she mows a lawn;

Let y represent the number of times she walks a dog;

The inequality can be modelled thus;

The triangles that are similar is A and B

Answer:

The length EI is;

The measure of angle IFE is;

Explanation:

Given the rectangle in the attached image.

Given;

Recall that the length of the diagonals of a rectangle are equal so;

solving for x, we have;

Since we have the value of x, let us substitute to get the length of diagonal EG;

Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;

Therefore, the length EI is;

To get the measure of angle IFE;

Reason: base angles of an isosceles triangle are equal.

So;

Reason: Complementary angles.

Substituting the value of angle IFG;

Therefore, the measure of angle IFE is;

To find:

The derivative of function f(x) using the first principle.

Solution:

By the first principle, the derivative of the function f(x) is given by:

So, the derivative of the given function can be obtained as follows:

Thus, the derivative of the given function is:

Okay, here we have this:

Let's take the packages as (x), so we obtain:

Melissa Starts with: 4x+8 ballons (1)

Her brother gave her: 3x+20 ballons (2)

And as she now has twice the number of balloons she started with. This mean that:

2(4x+8)=(3x+20)+(4x+8)

Let's clear x in this equation:

8x+16=3x+20+4x+8

8x+16=7x+28

8x-7x=28-16

x=12

Finally we obtain that in a package are 12 ballons, now let's calculate How many balloons did Melisa start with?:

Remember that Melissa Starts with: 4x+8 ballons, so replacing x with 12, we obtain that Melissa Starts with: 4(12)+8=48+8=56.

Finally we obtain that Melissa Starts with 56 ballons.

Given the inequality:

• You can solve it as follows:

1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:

2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):

• In order to graph the solution on the Number Line, you can follow these steps:

1. Since the symbol is:

You need to draw an open circle over the number -5.

2. Draw a line from the circle to the right.

Then, you get:

Hence, the answer is:

• Solution:

• Number Line:

We will have the following:

The expression that best describes the information is:

*When viewing the data for tolling a one, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.

EXPLANATION:

We are given the following coordinates for a figure on the coordinate plane;

To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;

Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.

Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.

Therefore, for the vertices given, the reflection across the x-axis would be;

ANSWER:

The coordinates of the reflection across the x-axis therefore will be;

The given situation is about the value of quarters and the number of quarters. If we think this through, we would deduct that the value of quarters depends on the number of quarters there are, for example, if there are 4 quarters, then the value is 1 dollar, and so on.

Hence,

The independent variable is the number of quarters.

The dependent variable is the value of the quarters.

The equation would be v = 0.25n.

If the input is 10, it means n = 10.

The output would be 2.5.

Answer: -32 is less than 15.

Step-by-step explanation: 15 is greater than zero therefore it is not a negative number. -32 is less than 0 therefore it is a negative number. Negatives will always be less than positives.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the proof are as follows:

Since

and

Then,

CPCTC means corresponding parts of congruent triangles are congruent

and

Thus,

VUTS is a parallelogram since diagonals of a parallelogram bisect each other

The answer is 92400

To solve this, we can count how many letters we have. There are 11 letters.

If those 11 letters were different from each other, the answer would be 11!

But we have letters that repeats:

3 P's

3 Y'2

3 G'2

2 U's

Since we want to know the quantity of distinct arrangements, we can divide by the repetition. This means:

We divide by 3! times 3! times 3! times 2!, because we have 3P's, 3Y's, 3G's and 2U's

Then on the calculator write the division and give us the answer 92400

Step-by-step explanation:

Given that f(x) is reflected across the y-axis to create the graph of function g.

i.e. f is reflected on the line x=0

Hence x will become -x in g.

When domain of f is x>=0 the domain of g can only be x less than or equal to 0.

Hence answer is option 3,The domain of f is x ≥ 0, while the domain of g is x ≤ 0

Answer:

The third one

Step-by-step explanation:

Probability that they are both raspberry = 5/33

From the question, we have

probability that they are both raspberry = 5/12*4/11

=5/33

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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Abraham, this is the solution of the polynomials division:

5x^3 - 3x^2 + 2x - 1/ x+1

Step 1:

5x² + (-8x² + 2x - 1)/(x + 1)

Step 2:

5x² - 8x + (10x - 1)/(x + 1)

Step 3:

5x² -8x + 10 + (-11/x + 1)

The four numbers below the line are: 5 -8 10 - 11

We need to find in which month we have that the total cost is the same, so we are going to do the equations of cost of the two companies

For the Tyson's Ethernet we have that the equation is

with m the month. And for the Darriana's DSL the equation is

We need to equalize the equations, so we have

Now to see the cost we replace in the two equations( wiith this we also verify), we have that

The answer is: after 10 months the total cost is the same, and this cost is $300.

EXPLANATION

Let's see the facts:

Bike Price: $99

Sold Price: $117

The percentage is given by the following relationship:

Replacing terms:

Answer: The markup was 18.18%

Answer:

B. (19/24)

Step-by-step explanation:

 1          1          5

------ + ------ + -------

 4         8         12

 1(6)     1(3)     5(2)

------ + ------ + -------

 4(6)   8(3)     12(2)

 6         3        10         19

------ + ------ + ------- = -------

 24      24       24        24

I hope this helps!

(Question 3)

Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that

Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,

We know that

We'll just have to plug in the value of x we calculated to find the lenght of AE

Therefore, AE = 36

(Question 4)

Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that

Therefore, RS = 5

The permutation formula is given as:

In this case n=27 and k=3; plugging the values in the formula we have:

Therefore, we have that P(27,3)=17550

Solution:

(a) Given the functions:

Then:

Similarly,

Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.

ANSWER: f and g are inverse of each other.

(b) Given:

Then:

Also,

ANSWER: f and g are not inverses of each other.