Expand and simplify (3x - 1)(9x² + 3x + 1)​

Answer:

Step-by-step explanation:

xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc

First, we need to find the value of g(pi/2):

g(pi/2) = cos(pi/2) = 0

Now we can substitute this value into f(x):

f(g(pi/2)) = f(0) = sin(0) = 0

Therefore, f(g(pi/2)) = 0.

The factοred fοrm οf a pοlynοmial is

1. 30b³- 54b² = 6b²(5b−9)

2. 3y⁵ - 48y³ = 3y³(y  −4)(y + 4)

3. x³ + 8 = (x + 2) (x² – 2x + 2²)

4. y³ - 64 = (y - 4) (y² – 4y + 4²)

5.  8c³ + 343(2c + 7)(4c² − 14c + 49)

The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.

One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.

We will use the formula

a³ + b³ = (a + b) (a² – ab + b²)

And

a³ - b³ = (a - b) (a² – ab + b²)

1. [tex]30b^3-\ 54b^2[/tex]

⇒ 6b²(5b−9)

2. 3y⁵ - 48y³

⇒ 3y³(  y² - 16y)

⇒ 3y³(  y² - 4 + 4 - 16y)

⇒ 3y³(y  −4)(y + 4)

3. x³ + 8

⇒ x³ + 2³

Using a³ + b³ = (a + b) (a² – ab + b²)

⇒ x³ + 2³

⇒ (x + 2) (x² – 2x + 2²)

4. y³ - 64

⇒ y³ -  4³

Using a³ - b³ = (a - b) (a² – ab + b²)

⇒ y³ -  4³

⇒ (y - 4) (y² – 4y + 4²)

5. 8c³ + 343

Using a³ + b³ = (a + b) (a² – ab + b²)

2c + 7

(2c + 7)(4c² − 14c + 49)

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Therefore, when the equation  x = 72 - 3x, the value of 2 - 3x is -52.

An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.

Here,

When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:

x + 3x = 72

Combining like terms, we get:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now that we know x = 18, we can substitute this value into the expression 2 - 3x:

2 - 3x = 2 - 3(18)

2 - 3x = 2 - 54

2 - 3x = -52

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Answer:

the maximum height is 2 meters

Answer:

Cost price (CP) = Rs20

% Profit = 10%

Selling price (SP) = y

By formula:

% Profit = (Profit/CP) x 100%

But Profit= SP - CP

Therefore;

% Profit = [(SP-CP)/C.P)] x 100%

Substituting, we have:

10% = [(y-20)/20] x 100%

10/100 = (y-20)/20

1/10 = (y-20)/20

1 = (y-20)/2

Cross multiply

y - 20 = 2

y = 2 + 20

y = 22

Therefore, the Sale price is Rs 22

Answer:1st one

Step-by-step explanation:

Based on the information in the diagram of circle P, the magnitude of the missing angle are as follows;

m∠BPC = 80 degrees.

m∠ADC = 205 degrees.

In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.

Based on the information provided about circle P, the central angle of circle P is represented by m∠BPC and the measure of arc BC is equals to 80 degrees. Therefore, the magnitude of angle BPC is given by:

m∠BPC = 80 degrees.

Since m∠A is an inscribed angle, its magnitude can be calculated as follows;

m∠A = 1/2(m∠BPC)

m∠A = 1/2(80)

m∠A = 40 degrees.

For the magnitude of m∠ADC, we have:

m∠ADC = 360 - (80 + 75)

m∠ADC = 360 - 155

m∠ADC = 205 degrees.

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The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.

A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.

Here,

To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.

Triangle 1 has angles 41°, 30°, and 109°.

Triangle 2 has angles 30°, 41°, and 109°.

We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.

Note that the order of the angles does not matter when comparing triangles for similarity.

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Answer:

the test does not provide convincing evidence that the proportion is greater than 90%

84500 reams of paper are the total amount the two companies sell in the past five years.

65500 is the amount that Company B performed better than company A.

A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.

The Amount that is made by company A is

[tex]7.5 \times 10000[/tex]

[tex]=75000[/tex]

The amount of paper manufactured by company B is

[tex]= 9.5 \times 1000[/tex]

[tex]= 9500[/tex]

A) The total that is made by both companies in 5 years will be

[tex]= \text{Company A + Company B}[/tex]

[tex]= 75000 + 95000[/tex]

[tex]= 84500[/tex]

B) Company B made better products as compared to Company A

[tex]= \text{Company B - Company A}[/tex]

[tex]=75000 - 9500[/tex]

[tex]=65500[/tex]

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Answer:

Step-by-step explanation:

You want the sum and difference of 7.5×10^4 and 9.5×10^3.

Numbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...

  9.5×10^3 = 0.95×10^4

  total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500

  difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500

__

Additional comment

You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.

The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y

Let's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,

Let S represent the total cost of purchasing a pool membership from the Swimming Hole.

Then we can write the following system of inequalities:

A = 75 + 20x (total cost of Aquatics Club membership)

S = 15 + 65x (total cost of Swimming Hole membership)

Alfonso has no more than y dollars to spend

So, we have

75 + 20x ≤ y

15 + 65x ≤ y

Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y

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Answer:

i think 16 im not sure

Step-by-step explanation:

The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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So, the right response is that, in order to more accurately fit the scatterplot that depicts a curve in the data, you need add a quadratic component while performing regression.

As ax² +bx + c, a quadratic equation can be expressed. In a quadratic equation, the largest exponent is 2, which limits the number of terms to a maximum of 3. These terms are exponent 2 (ax²) and exponent 1 (bx) fixed term.

Regression can be improved by including a quadratic component to better match scatterplots of data that display curves. This is so that the independent and dependent variables can have a nonlinear connection, which is made possible by a quadratic term. A quadratic component can assist capture inherent curvature of a data and enhance the fit of a regression model in cases where the connection between both the variables isn't really strictly linear.

A quadratic term may not be appropriate or required, though. A quadratic factor would not increase the model's fit if the variables' relationships are strictly linear and might even result in overfitting. In addition, if the scatterplot contains too many anomalies or the data is not consistent, adding a quadratic factor might not be beneficial.

In order to properly fit a scatter plot graph that depicts a curve in the data, the correct response is you would like to add a quadratic term while performing regression.

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He bought 4.29 Kilos of fruit.

4+0.29=4.29

Luke bought 4.29 kilograms of fruit in all

Step-by-step explanation:

Simple addition will be used to find the total fruit Luke bought.

Given

Amount of apples he bought  = 4 kilograms

Amount of oranges he bought = 0.29 kilograms

so the total fruit will be:

[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]

[tex]=4+0.29[/tex]

[tex]=4.29[/tex]

So,

Luke bought 4.29 kilograms of fruit in all

Keywords: Measurement, addition

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A hexagon with two lines

hope helped you please make me brainalist and keep smiling dude

I hope you are form India

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]

Based on the information, the pollster's conclusion makes sense.

To know if the pollster is right with his conclusion we must perform the following operation.

In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.

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Using trigonometric functions, the value of the side AC = 2.85 units.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.

The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of  f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.

Now in the given figure,

The angle is a right-angled triangle.

Now as per the trigonometric functions,

Sin 35° = AC/AB

⇒ 0.57 = x/5

⇒ x = 0.57 × 5

= 2.85.

The length of the opposite side AC is 2.85 units.

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Answer:

6 5/6 cups

Step-by-step explanation:

Add.

4 2/3 = 4 4/6

4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.

Hope this helps!

Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

I inserted in an image below to help you with the rule.

The 1st point  is (6,1) . This becomes (1,-6).

The 2nd point is (-5,-6). This becomes (-6, 5)

The magnitude and direction of the net force are found by adding the two forces together as resultant force vectors.

a) 11.82 N

b) 74.07°

To find the net force, we add the two force vectors F_1 and F_2:

Fnet = F_1 + F_2

Fnet = (1.31 + 4.6j) N + (3.2i + 6.8j) N

Fnet = 3.2i + (1.31 + 4.6j + 6.8j) N

Fnet = 3.2i + (1.31 + 11.4j) N

To find the magnitude of the net force, we use the Pythagorean theorem:

|Fnet| = sqrt[(3.2)^2 + (1.31 + 11.4)^2] N

|Fnet| ≈ 11.6 N

To find the direction of the net force, we use the inverse tangent function:

θ = tan^(-1)(y/x)

θ = tan^(-1)(11.4/3.2)

θ ≈ 73.8 degrees

Since the net force is in the first quadrant, the direction counterclockwise from the +x-axis is simply θ:

Direction = 73.8 degrees counterclockwise from the +x-axis

Therefore, the net force is Fnet = 3.2i + (1.31 + 11.4j) N, with a magnitude of approximately 11.6 N and a direction of approximately 73.8 degrees counterclockwise from the +x-axis.

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The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.

According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.

Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.

Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.

Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

So the answer is 120.

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Answer:

Step-by-step explanation:

a. The mean of X is 1.7549 and the standard deviation is 0.3536.

b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.

c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.

d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.

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Answer: 1500000

Step-by-step explanation:

use a calculator

Answer:

1,500,000

Step-by-step explanation:

Breaking it up into an easier problem:

20x50 = 1,000

30x50=1,500

1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.

Thus, the answer is 1,500,000

The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"

The correct answer choice is option B.

Type of Sandwich Number of Customers

Vegetarian 30

Turkey 20

Ham 35

Chicken 15

Total number of customers = 30 + 20 + 35 + 15

= 100

Percentage of each sandwich:

Vegetarian = 30/100 × 100

= 30%

Turkey = 20/100 × 100

= 20%

Ham = 35/100 × 100

= 35%

Chicken = 15/100 × 100

= 15%

Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.

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Answer: y is equal to 8

Step-by-step explanation:

by substituting the x for its vale of three we can add the two values to get 8 or y=8