Divide. State the quotient in simplest form.
4x5/ 12x²/
x2_3x-4 3x+3, x ≠ − 1, 4

The surface region of the cylinder will be 301.44 square inches.

Let r be the radius and h be the altitude of the cylinder. Then the surface region of the cylinder will be given as,

SA = 2πrh + 2πr² square units

The radius of the cylinder is 4 inches and the height of the cylinder is 8 inches.

Then the surface area of the cylinder is calculated as,

SA = 2πrh + 2πr²

SA = 2 x 3.14 x 4 x 8 + 2 x 3.14 x 4²

SA = 200.96 + 100.48

SA = 301.44 square inches

The surface region of the cylinder will be 301.44 square inches.

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The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

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Answer:

-12.13

Step-by-step explanation:

To add two negative numbers, drop the negative signs and add the two positive numbers. Then make the answer negative.

-9.24 + (-2.89) =

We are adding two negative numbers, -9.24 and -2.89.

Step 1: ignore the negative signs and add the number 9.24 + 2.89

9.24 + 2.89 = 12.13

Step 2: the answer is negative, so add a negative sign to the sum above.

-9.24 + (-2.89) = -12.13

Answer:

175 degrees.

Step-by-step explanation:

Supplementary angles add up to 180 degrees

Therefore the answer is:

180 - 5

= 175 degrees.

Hi Student!

The first step to almost any problem is that we must concentrate the important information that is given to us in the problem.  This problem gives us information including that the measure of an angle is 5 degrees and that this angle is part of a supplementary pair.  Let's define what a supplementary pair or angles are.

Now that we have our definitions and important information, we can move onto the next part which is actually finding the other angle.  This step is simple now that we know that supplementary angles add up to 180.  We can just create an equation that will help us determine our solution.

\(angle_1\ +\ angle_2 = 180\ degrees\)

\(5\ degrees\ +\ angle_2 = 180\ degrees\)

\(5\ degrees-5\ degrees\ +\ angle_2 = 180\ degrees-5\ degrees\)

\(angle_2 = 175\ degrees\)

Therefore, our final solution to the supplementary angle of 5 degrees is 175 degrees which can be found by subtracting the given angle from 180.

² = QR² - QT²

= 13² - 5²

= 169 - 25

= 144

TR = √144

TR = 12 cm

Menentukan panjang PR

PR = 2 × TR

= 2 × 12 cm

PR = 24 cm

Answer: 1.25

Step-by-step explanation:

The explicit formula for the sequence is \(a_{n}=10(0.5)^{n-1}\)

Substituting in n=4,

\(a_{4}=10(0.5)^{4-1}=\boxed{1.25}\)

Answer:

3(3px + 4y)(3px - 4y)

Step-by-step Explanation:

This is the answer because:

1) We can factor using the difference of squares formula.

2) a^2 − b^2 = (a + b) (a − b) where a = 3px and b = 4y .

Hope this helps!

Roman Rounds normally charges $18 for a large pizza.

What is the equation in one variable?

An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.

Let's use p to represent the normal price of each large pizza charged by Roman Rounds.

Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:

12(p - 2) = $192

We can simplify this equation by first distributing the 12 on the left side:

12p - 24 = $192

Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:

12p = $216

Finally, we can solve for p by dividing both sides by 12:

p = $18

Therefore, Roman Rounds normally charges $18 for a large pizza.

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The equation of the axis of symmetry of the parabola is x = 7.

We have,

The axis of symmetry of a parabola is a vertical line that passes through the vertex.

Now,

The equation of the axis of symmetry is the vertical line passing through the x-coordinate of the vertex.

And,

The x-coordinate of the vertex is 7.

Now,

So the equation of the axis of symmetry is x = 7.

Thus,

The equation of the axis of symmetry of the parabola is x = 7.

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Answer:

-8/15

Step-by-step explanation:

Divide the fraction

Answer:

8/15

Step-by-step explanation:

The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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The correct answer is,

(a) Very unlikely. It will almost certainly never happen.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The winning number in a Pick 4 lottery was 1234 two days in a row.

Now,

Since, there is a 1 in 10,000 chance of drawing any particular four-digit number in a single drawing, there is very little chance that the same number will be picked twice in a row in a Pick 4 lottery.

Even less likely, at one in 100,000,000,000, is the same number being selected three times in a row.

So, (a) Very unlikely is the correct response. It's almost probably never going to happen.

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The number of miles of the trip was 24

The given parameters are

Flat rate = $5

Rate = $1.50 per mile

The total charge is calculated as:

y = Flat rate +Rate * x

This gives

y = 5 + 1.5x

When the charge is 41, we have:

5 + 1.5x = 41

Evaluate the like terms

1.5x= 36

Divide by x

x = 24

Hence, the number of miles of the trip was 24

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If the parent function is $y = 2x$, then the function of the graph is also $y = 2x$.

The parent function is the base function that represents the general form of a family of functions, and the function of a graph is the specific equation that describes the relationship between the variables in the graph. In this case, the parent function is $y = 2x$, which is a linear function that represents the general form of a family of linear functions. The function of the graph is also $y = 2x$, which is a specific linear function that describes the relationship between the variables in the graph. The graph of the function $y = 2x$ is a straight line that passes through the origin and has a slope of 2. The graph of this function represents the set of all points in the coordinate plane that satisfy the equation $y = 2x$.

For example, if $x = 1$, then $y = 2x = 2(1) = 2$, so the point (1, 2) is on the graph of the function. If $x = 2$, then $y = 2x = 2(2) = 4$, so the point (2, 4) is on the graph of the function.

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Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

We can write a proportion.

44:3 = 12:m

~Simplify

44m = 36

~Divide 44 to both sides

m = 36/44 or 9/11 minutes

Best of Luck!

Answer: 0.818 minutes

Step-by-step explanation:

You would normally divide 44/3 to see how many plates are washed per minute, but if you reverse it, 3/44 then you will know how much time is spent washing each plate which is 0.068181. Multiply that by 12 and there’s your answer

The equation of the new graph is:

f(x) = e^(x-6)

The graphs of the two functions f(x) = e^x and f(x) = e^(x-6) are shown below

From the question, we are to determine the equation of the new graph.

If the graph of the function f(x) = e^x is shifted 6 units to the right, the equation of the new graph can be found by replacing x with (x - 6) in the original equation.

This is because a horizontal shift of a function f(x) to the right by c units can be achieved by replacing x with (x - c) in the equation of the function. So, for the given function, a shift to the right by 6 units would be achieved by replacing x with (x - 6) in the original equation f(x) = e^x.

Therefore, the equation of the new graph is:

f(x) = e^(x-6)

This can also be written as:

f(x) = e^x / e^6

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The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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Answer: YES

Step-by-step explanation:

Answer:

the corrects answer is -3

Step-by-step explanation:

Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)

Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).

Answer: false

Step-by-step explanation:

false

Answer:

False

Step-by-step explanation:

Numbers dont add up

a) There are 2 students who study both Maths and Physics in the year group of 100 students at School A.

b) School B has more pupils studying both subjects.

Part A:

To solve this problem, we can use the principle of inclusion-exclusion. This states that the total number of students who study either Maths, Physics, or both can be calculated by adding the number of students who study Maths, the number of students who study Physics, and the number of students who study both, and then subtracting the number of students who study both.

In this case, the total number of students who study either Maths, Physics, or both is:

(73 students + 58 students) - (2 students) = 131 students - 2 students = 129 students

To find the number of students who study both Maths and Physics, we can subtract the number of students who study only one subject from the total number of students who study either Maths, Physics, or both:

129 students - (73 students - 2 students) - (58 students - 2 students) = 129 students - 71 students - 56 students = 2 students

Therefore, there are 2 students who study both Maths and Physics in the year group of 100 students at School A.

Part B:

To determine which school has more pupils studying both Maths and Physics, we need to calculate the number of students at each school who study both subjects.

At School A, we know that there are 2 students who study both Maths and Physics.

At School B, we know that 24% of the students study both Maths and Physics. To find the number of students at School B who study both subjects, we can multiply the total number of students by the percentage who study both:

(150 students) * (24%) = 36 students

Since 36 is greater than 2, there are more students at School B who study both Maths and Physics. Therefore, School B has more pupils studying both subjects.

Answer:

In School B there are more pupils stydying both maths and physics

To combine two fractions into one fraction if they are being added / subtracted from each other, make it so they share the same denominator.  To do this, one way is to make \(\frac{1}{3}\) have denominator \(3t\), so multiply the top and bottom of the fraction by \(t\):

\(\frac{t+2}{3t} - \frac{t}{3t}\)

and now you can just subtract the numerator.

\(= \frac{t+2 - t}{3t} = \frac{2}{3t}\)

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer: x> 4(y+7)/3

​

Step-by-step explanation:Simplify 4<3x/4-7 ad 7 to both sides multiply both sides by 4 regroup terms divide both sides by 3 and switch sides

.

Answer:

yes 6 lines are symmetry

Answer:

$6.50

Step-by-step explanation:

First start by adding the prices of the pairs of shoes combined.

19.95+23.55=43.50

subtract the total price of both pairs of shoes from her total

50-43.50 = 6.50