What is the factored form of 2x3 + 4x2 - 30x? A. 2x(x + 5)(x + 3) B. (x2 + 5)(2x - 6) C. (2% + 10)(2x - 6) D. 2x(x + 5)(x + 3)​

AAA ( Angle - Angle - Angle) congruence rule is one of congruence postulate but not preferable, for showing the similarity in two triangles

Two triangles are said to be congruent if one can be superimposed on the other exactly by rigid body motion, and the congruence theorem gives the conditions under which this occurs.

AAA Congruence rule:

It is stands for angle-angle-angle Congruence rule. When all three angles of one triangle is equals to the corresponding angles of another triangle. but it is possible if and only if the corresponding sides of both triangles are equal and when all three sides of two triangles are equal to each other then we use SSS Congruence rule. So, it not considered as preferable congruence rule . For example, In ∆ABC and ∆PQR

all three angles of ∆ABC is equal to corresponding angles of ∆PQR. So,∆ABC and ∆PQR are congruent.

To learn more about AAA (angle-angle-angle) Congruence rule, refer:

https://brainly.com/question/29792706

#SPJ4

Answer:start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.

Step-by-step explanation:

gg

The complete question is,

Use the drawing tool(s) to form the correct answers on the provided graph.

Graph the system of equations given below on the provided graph.

2x– 3y = –18

3x + y = -5

A graph can be described as a pictorial representation or a diagram that methodically describes data or values.

In math, a graph can be described as a pictorial representation or a diagram that methodically describes data or values. The points on the graph often characterize the connection between two or more things.

2x– 3y = –18

3x + y = -5

Transforming the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

For plotting the graph, the online graphing calculator  can be utilized.

The points can be estimated by putting negative and positive values of x in both equations.

The graph exists attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it stands for the solution of the provided system of linear equations.

To learn more about Graph refer to:

https://brainly.com/question/12600212

#SPJ2

Answer: A

Step-by-step explanation:

The correct option is A.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given is that a graph,

So, from the graph we can concluded that it is an exponential and positive function,

Therefore, as x increases y also increases.

We know that the exponential function is given by =

y = abˣ

So, when x = 0, y = 100,

100 = a × b⁰

a = 100

When x = 4, y = 150,

150 = 100 × b⁴

b⁴ = 1.5

b = 1.11

y = 100(1.11)ˣ

Change = 110-100 / 100 × 100% = 10%

Therefore, we can say the value of a $100 stock grows in value by 10% each year.

Hence the correct option is A.

Learn more about exponential function click;

https://brainly.com/question/29287497

#SPJ2

Answer:

2.2

Step-by-step explanation:

5.6-9.4=15.0

so you subtract 12.8 from 15.0 which gives you the answer 2.2 so your answer is 2.2

Answer:

- 13 + 13 = 0

Step-by-step explanation:

The average throughput for this connection up through time = 5 RTT can be calculated using the formula: (N * MSS) / (5 * RTT).

To calculate the average throughput for this connection up through time = 5 RTT (round-trip time), you will need to follow these steps:

1. Determine the MSS (maximum segment size) and RTT for the connection. Since these values are not provided, I will use placeholders: MSS = X and RTT = Y.

2. Calculate the total time taken for the connection up through time = 5 RTT. In this case, the total time is 5 * Y, where Y is the RTT.

3. Determine the total amount of data transferred during this time. This would require information about the connection and the number of segments transmitted. Let's assume the connection transferred N segments during the 5 RTT period.

4. Calculate the total data transferred in terms of MSS. This is done by multiplying the number of segments (N) by the MSS (X): Total data = N * X.

5. Finally, calculate the average throughput by dividing the total data transferred by the total time taken: Average Throughput = (N * X) / (5 * Y).

In summary, the average throughput for this connection up through time = 5 RTT can be calculated using the formula: (N * MSS) / (5 * RTT).

Learn more about average throughput:

https://brainly.com/question/30745255

#SPJ11

Answer:

21.25

Step-by-step explanation:

If 2in is 5ft, then 1 inch is 2.5 ft

Then we can say that the height of the original house is:

8.5 * 2.5 = 21.25 inches

Hope this helps!

Answer:

y = -3x + 2

Step-by-step explanation:

The linear equation is in the form

y = mx + b

where m is the slope and b is the y-intercept

the slope can be calculated using two points

Let us have; (-2,8) and (0,2)

The equation of the slope is ;

m = (y2-y1)/(x2-x1) = (2-8)/(0+2) = -6/2 = -3

So for the y-intercept, we select any of the points to substitute

Let us have (0,2)

Substitute this into;

y = -3x + b

2 = -3(0) + b

b = 2

So the equation is;

y = -3x + 2

Answer:

cause it is

Step-by-step explanation:

it just is, sorry i can't help. maybe bc there are more positive functions then negative ones?

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

To learn more about trigonometric function click the below link

https://brainly.com/question/25618616

#SPJ11

There is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

To find the probability that a group of 10 persons will exceed the load limit of the elevator, we need to calculate the probability that the total weight of the group exceeds 2000 lb.

Since the weights of the people are normally distributed with a mean of 185 lb and a standard deviation of 22 lb, we can use the properties of the normal distribution to solve this problem.

First, we need to calculate the mean and standard deviation of the total weight of the group. The mean of the total weight is simply the mean weight of a person multiplied by the number of persons, which is 185 lb * 10 = 1850 lb.

The standard deviation of the total weight is calculated by taking the square root of the sum of the variances of each person's weight. Since the weights are independent, the variance of the total weight is equal to the sum of the variances of each person's weight. So, the standard deviation of the total weight is sqrt(10) * 22 lb ≈ 69.296 lb.

Next, we can use the normal distribution to calculate the probability that the total weight exceeds 2000 lb. We standardize the value using the formula z = (x - mean) / standard deviation, where x is the threshold value of 2000 lb.

Calculating the z-score: z = (2000 - 1850) / 69.296 ≈ 1.81

Finally, we look up the probability corresponding to this z-score in the standard normal distribution table or use a calculator to find the area under the curve to the right of the z-score. The probability that the group of 10 persons will exceed the load limit of the elevator is approximately 0.0351, or 3.51%.

Therefore, there is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

To know more about probability, visit:

https://brainly.com/question/23743305

#SPJ11

The margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

To calculate the margin of error for a 99% confidence interval estimate, we can use the formula:

Margin of Error = Z * sqrt(p_hat * (1 - p_hat) / n)

Where:

Z is the z-value corresponding to the desired confidence level (99% confidence level corresponds to a z-value of approximately 2.576).

p_hat is the sample proportion (percentage of apples with bruises), which is calculated as the number of apples with bruises divided by the total sample size.

n is the sample size.

Given:

Sample size (n) = 100

Number of apples with bruises = 12

Calculating the sample proportion:

p_hat = 12 / 100 = 0.12

Using the z-value for a 99% confidence level (z = 2.576), we can calculate the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * (1 - 0.12) / 100)

Calculating the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * 0.88 / 100)

Margin of Error = 2.576 * sqrt(0.1056 / 100)

Margin of Error = 2.576 * sqrt(0.001056)

Margin of Error ≈ 2.576 * 0.0325

Margin of Error ≈ 0.0838

Therefore, the margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

for such more question on confidence interval

https://brainly.com/question/14771284

#SPJ11

The area of the cottonwood leaf. height 4in, base is 5in is 10 inches².

Based on the information given, it should be noted that the leaf is in the shape of a triangle.

It is important to note that the area of a triangle will be:

= 1/2 × base × height

Base = 5 inches

Height = 4 inches..

Area = 1/2 × base × height

= 1/2 × 5 × 4

= 10 inches²

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer: 2000KM

Step-by-step explanation: I just took the quiz

Answer:

2k

Step-by-step explanation:

The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

To learn more about sine function click here;

brainly.com/question/32247762

#SPJ11

Answer:

16%

Step-by-step explanation:

Let's assume the original price of the item was Rs. 100.

After the price increased by 45%, the new price became:

New price = Original price + (45% of Original price)

New price = 100 + (0.45 x 100)

New price = Rs. 145

Now, the price dropped by 20% from the increased price of Rs. 145:

Final price = New price - (20% of New price)

Final price = 145 - (0.2 x 145)

Final price = Rs. 116

We can calculate the overall change in price by finding the difference between the final price and the original price:

Overall change in price = Final price - Original price

Overall change in price = 116 - 100

Overall change in price = 16

So, the price increased by Rs. 16. To find the percentage increase, we can use the formula:

Percentage increase = (Overall change in price / Original price) x 100%

Plugging in the values, we get:

Percentage increase = (16 / 100) x 100%

Percentage increase = 16%

Therefore, the price of the item increased by 16%.

BRAINLIEST PLEASE

The percentage by which the price increased is; 16%

Percentage Increase

Let the price of an item be denoted as x

Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x

Now, the price after inflation decreased by 20% or 0.2. Thus;

Final price is now; 1.45x(1 - 0.2)

⇒ 0.8(1.45x)

⇒ 1.16 x

Since the original price is x, then;

Difference in price = 1.16x - x

Difference in price = 0.16x

In percentage, this difference in price represents a 16% increase.

The complete question is;

Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?

Read more about percentage increase at; brainly.com/question/2085058

The four steps to solve a radical equation are: Isolate the radical, square both sides, solve the resulting equation, and check for extraneous solutions.

To solve a radical equation, follow these four steps:

1. Isolate the radical: Move any terms that don't contain the radical to the other side of the equation. This step ensures that the radical term is alone on one side of the equation.

2. Square both sides: Raise both sides of the equation to the power that eliminates the radical. If you have a square root, square both sides. If you have a cube root, cube both sides, and so on. This step helps eliminate the radical.

3. Solve the resulting equation: Once you've eliminated the radical, solve the resulting equation for the variable. At this stage, you should have an equation without any radicals.

4. Check for extraneous solutions: After finding a potential solution, substitute it back into the original equation and verify if it satisfies the equation. Sometimes, in the process of eliminating the radical, you may introduce extraneous solutions that don't actually satisfy the original equation. If the substituted solution doesn't satisfy the equation, discard it as an extraneous solution.

By following these four steps, you can solve radical equations systematically and ensure that you find all valid solutions.

To know more about radical equation, refer here:

https://brainly.com/question/12794073

#SPJ4

The total volume of air inside six of Jake's basketballs is 2140.9074 in³.

volume of sphere = \(\dfrac{4}{3} \times\pi\times radius^3\)

properly inflated basketball measures = 8.8 inches across

so, the diameter of each basketball, d = 8.8 inches,

Also, the radius of each basketball, r = 4.4 inches,

Assumption has given, that the wall of each ball is infinitely thin.

As we know a basketball is a sphere in shape, thus,

\(\begin{aligned}Volume &= \dfrac{4}{3} \times\pi\times radius^3\\&= \dfrac{4}{3} \times\pi\times 4.4^3\\&= 356.8179\ in^3\\\end{aligned}\)

A Total volume of air inside six of Jake's basketballs =volume of 1 basketball x 6

\(\begin{aligned}Volume\ of\ six\ basketball &= 356.81790\times6\\&=2,140.9074\ in^3\end{aligned}\)

Hence, the total volume of air inside six of Jake's basketballs is 2140.9074 in³.

To know more visit:

https://brainly.com/question/364206

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

Learn more about structures on

https://brainly.com/question/20848481

#SPJ1

Answer:9

Step-by-step explanation:

Given the net of a figure:

As shown the number of faces = 7 faces

The number of bases = 2 bases

As the base has 7 sides it will be a heptagon

The height of the prism = the length of one side of the base

The surface area of the prism = area of the bases + area of the faces

= area of 2 heptagons + area of 7 squares

Answer:

Step-by-step explanation:

y = 5x - 4

y = 6x $\Rightarrow$ x = y/6

y = 5*y/6 - 4

y = 5y/6 - 4

6y = 5y - 24

y = -24.

So, x = -4

Answer:

there are 16 inches of bases

2

Step-by-step explanation:

\(12 x + 4x = 32 \)

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

Learn more about Polynomials here:

https://brainly.com/question/11536910

#SPJ1

Complete question:

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



learn more about geometric series here here

https://brainly.com/question/30264021



#SPJ11

Answer:

x = - 3

Step-by-step explanation:

y = 3x + 2 → (1)

y = x - 4 → (2)

Subtract (2) from (1) term by term

y - y = 3x - x + 2 - (- 4)

0 = 2x + 2 + 4

0 = 2x + 6 ( subtract 6 from both sides )

- 6 = 2x ( divide both sides by 2 )

- 3 = x