Which of the following best describes the expression 7(x + 9)? (1 point)

a
The product of a constant factor 7 and a 2-term factor x + 9

b
The sum of a constant factor 7 and a 2-term factor x + 9

c
The sum of constant factors 7 and x + 9

d
The product of constant factors 7 and x + 9

[tex]\qquad \qquad \textit{Inverse Trigonometric Identities} \\\\ \begin{array}{cccl} Function&Domain&Range\\[-0.5em] \hrulefill&\hrulefill&\hrulefill\\ y=cos^{-1}(\theta)&-1 ~\le~ \theta ~\le~ 1& 0 ~\le~ y ~\le~ \pi \\\\ y=tan^{-1}(\theta)&-\infty ~\le~ \theta ~\le~ +\infty &-\frac{\pi}{2} ~\le~ y ~\le~ \frac{\pi}{2} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \theta \hspace{5em}\stackrel{\textit{so we can say}}{cos(\theta )=-\cfrac{\sqrt{2}}{2}} \\\\\\ \theta =cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \stackrel{ \textit{on the II Quadrant} }{\theta =\cfrac{3\pi }{4}} \\\\[-0.35em] ~\dotfill\\\\ sin\left[ cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right) \right]\implies sin\left( \cfrac{3\pi }{4} \right)\implies \boxed{\cfrac{\sqrt{2}}{2}}[/tex]

now let's find the angle for the inverse tangent

[tex]sin\left( \cfrac{\pi }{2} \right)\implies 1\hspace{5em}\stackrel{\textit{so we can say}}{tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]}\implies tan^{-1}(1) \stackrel{ \textit{on the I Quadrant} }{\implies\boxed{\cfrac{\pi }{4}}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left[ cos^{-1}\left( -\frac{\sqrt{2}}{2} \right) \right]~~ + ~~tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]\implies \cfrac{\sqrt{2}}{2}~~ + ~~\cfrac{\pi }{4} \implies \boxed{\cfrac{2\sqrt{2}+\pi }{4}}[/tex]

for the sine function we end up in the II Quadrant because the inverse cosine function range is constrained to the I and II Quadrants only, so our angle comes from that range.

Likewise, our angle from the inverse tangent comes from the I Quadrant, because inverse tangent range is only I and IV Quadrants.

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

To learn more about sum, click here:

brainly.com/question/29034036

#SPJ4

The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

Learn more about geometric sequence

brainly.com/question/30491267

#SPJ11

Note that the angles above are marked to  be similar hence, one half of the base has a length of 16 units.

To solve this problem, we can use the fact that the line bisecting the angle at the top of a triangle also bisects the base. This means that the two halves of the base are equal in length.

Let's call the length of one half of the base "z". Then, the length of the other half of the base is also "z". The total length of the base is 32 units, so we can set up an equation:

z + z = 32

Simplifying this equation, we get:

2z = 32

Dividing both sides by 2, we get:

z = 16

So one half of the base has a length of 16 units.

Learn more about angles at:

https://brainly.com/question/28451077

#SPJ1

Answer:

45.6%

Step-by-step explanation:

166.50 minus 45.6% equals 90 dollars

As a result, during its flight, the football will strike the ground twice: once when it is kicked off and once more 3 seconds later.

A mathematical equation, including such 6 x 4 = 12 x 2, states that two quantities and values are equivalent. a meaningful noun. Equations are employed when two or more variables need to be added up and the results need to be computed in order to comprehend or explain the entire issue. As a result, the football will hit the ground twice during its flight: once after the game has kicked off and again three seconds later.

h =

0 = -16x² + 48x

0 = 16x(3 - x)

Either 16x or (3 - x) equals 0, which makes this equation equal to zero.

Hence, the answers to x are:

x = 0, when 16x = 0

when 3 - x = 0, x equals 3.

The football will therefore strike the ground twice during its flight—once when it is kicked off and once more 3 seconds later.

To know more about equation visit:

brainly.com/question/29538993

#SPJ1

The circle at -6 is closed because the inequality does not include the possibility of y being equal to -6.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

by the question.

the solution set of the inequality 1/2y < -3

Graph the solution set of the inequality 1/2y &lt; -3 - 1

To solve the inequality 1/2y < -3, we can begin by isolating the variable y on one side of the inequality:

1/2y < -3

Multiplying both sides by 2 yields:

y < -6

So, the solution set of the inequality is all real numbers y that are less than -6.

To graph the solution set on a number line, we can draw a closed circle at -6 and shade to the left of it, indicating that all values to the left of -6 are solutions to the inequality. The graph would look like this:

<=======o----------------------

To learn more about number:

https://brainly.com/question/13465215

#SPJ

Answer: -2g^7h^8

Step-by-step explanation:

Therefore, the value of a for triangle 2 is 44 degrees.

A triangle is a closed geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in many different areas of mathematics and science. The sum of the angles in a triangle is always 180 degrees, and there are many different types of triangles, including equilateral, isosceles, and scalene triangles, depending on the lengths of their sides and the sizes of their angles. Triangles are also commonly used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles.

Here,

The sum of the interior angles of a triangle is always 180 degrees. Therefore, for triangle 1, we have:

95 + 39 + x = 180

Simplifying the equation, we get:

134 + x = 180

x = 46

For triangle 2, we have:

90 + a + x = 180

Substituting the value of x from above, we get:

90 + a + 46 = 180

Simplifying the equation, we get:

a = 44

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

In a rectangle where the length is 3 times the width, and the perimeter is 3 times the width. The perimeter is 96 cm, the length is 36 cm and the width is 12 cm.

Given,

Length of a rectangle is 3 times the width.

Perimeter is 3 times the width.

Perimeter is 96 cm.

Let w be the width of the rectangle.

The length of the rectangle is 3 times the width, so the length l is 3w.

The perimeter of the rectangle is equal to the sum of all its sides, so:

2w + 2(3w) = 96

2w + 6w = 96

8w = 96

w = 12

Therefore, the length is 36 cm and the width is 12 cm.

To know more about Perimeter refer here:

https://brainly.com/question/6465134

#SPJ11

Answer:  Therefore, the maximum distance you can ride for $20 is 6 kilometers.

Step-by-step explanation:   The inequality to determine the distance in kilometers, d, you can ride for $20 is:

$5 + $2.50d ≤ $20

Simplifying the above inequality, we get:

$2.50d ≤ $15

Dividing both sides by $2.50, we get:

d ≤ 6

The factorised form of the given expression would be = (3x+2)(2x+y). That is option D.

Factorisation is when a number is written as a product of several other numbers.

The given expression is as follows:

6x² + 3xy + 4x + 2y

Insert bracket to simplify the above expression;

(6x² + 3xy) (4x + 2y)

Factorise the expressions one after the other;

3x(2x+y) +2( 2x+ y)

The factorised form = (3x+2)(2x+y). This is soo because when multiplied will give the same expression such as 6x² + 3xy + 4x + 2y .

Learn more about factorisation here:

https://brainly.com/question/28771141

#SPJ1

Answer:

D. (2x + y)(3x + 2)

Step-by-step explanation:

i took the test :)

The probability that the 15 cards contain exactly one queen given that they contain exactly two aces is approximately 0.060 or 6.0%.

We can use conditional probability. Let A be the event that the 15 cards contain exactly two aces, and B be the event that they contain exactly one queen. Then we want to find the conditional probability P(B|A).

First, let's find the probability of A. There are C(4,2) ways to choose the two aces out of four, and C(48,13) ways to choose the other 13 cards out of the remaining 48 cards. So the total number of ways to choose 15 cards with exactly two aces is:

C(4,2) × C(48,13) ≈ 4.57 × 10^12

Next, let's find the probability of both A and B. There are C(4,2) ways to choose the two aces out of four, C(4,1) ways to choose one queen out of four, and C(47,12) ways to choose the other 12 cards out of the remaining 47 cards. So the total number of ways to choose 15 cards with exactly one queen and exactly two aces is:

C(4,2) × C(4,1) × C(47,12) ≈ 2.76 × 10^11

Finally, we can use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

P(B|A) = (C(4,2) × C(4,1) × C(47,12)) / (C(4,2) × C(48,13))

P(B|A) ≈ 0.060

Therefore, the probability is approximately 0.060 or 6.0%.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

Hence, there's a 36.41 percent chance that a voicemail will be between 10 and 20 or 30 and 40 seconds in length.

It is based on the possibility that something will actually happen. The basis for theoretical probability is the justification for probability. For example, the theoretical probability of getting a head when flipping a coin is ½.

Calculating the area underneath the normal curve of distribution between the two iterations will allow us to determine the likelihood that a specific voicemail will last between 10 and 20 or 30 and 40 seconds.

The intervals must first be standardized by transforming it into z-scores using following formula:

z = (x - μ) / σ

Where x is the value, we want to convert, μ is the mean of the distribution, and σ is the standard deviation.

For the period of 10 to 20 seconds:

z1 = (10 - 40) / 10 = -3

z2 = (20 - 40) / 10 = -2

For the interval 30 to 40 seconds:

z3 = (30 - 40) / 10 = -1

z4 = (40 - 40) / 10 = 0

The region of the curve between such z-scores can now be calculated or found using a calculator and a standard normally distributed table. As an alternative, we can employ the normal distribution's CDF, or cumulative distribution function.

P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) = P(10 ≤ x ≤ 20) + P(30 ≤ x ≤ 40)

P(10 ≤ x ≤ 20) = P(-3 ≤ z ≤ -2) ≈ 0.0228

P(30 ≤ x ≤ 40) = P(-1 ≤ z ≤ 0) ≈ 0.3413

As a result, the likelihood that a voicemail will be between 10 and 20 or 30 and 40 seconds is:

P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) ≈ 0.0228 + 0.3413 ≈ 0.3641

A voicemail that is between 10 and 20 or 30 to 40 seconds in length has a 36.41% chance of being left.

To know more about probability visit:

brainly.com/question/30034780

#SPJ1

The equation for calculating the number of pairwise comparisons in a pairwise ranking matrix is: (n*(n-1))/2 where n is the number of items being compared in the matrix.

A pairwise ranking matrix is a tool that is used to rank items on the basis of pair-wise comparisons of the items. In order to find out the number of pairwise comparisons in such a matrix, one needs to use the following formula:(n*(n-1))/2where n is the number of items being compared in the matrix.

The formula works on the principle that every item in the matrix needs to be compared with every other item, but each comparison needs to be done only once. This is why the formula divides the total number of comparisons by two.

Therefore, the equation is: (n*(n-1))/2


To know more about matrix refer here:

https://brainly.com/question/28180105#

#SPJ11

Answer:33

Step-by-step explanation:45-12=33

The closest value to the standard deviation of the 100 times is (C) 20 seconds.

To determine the closest value to the standard deviation of the 100 times, we would need the actual histogram or the data points themselves.

In general, the standard deviation measures the spread or dispersion of a set of values. A higher standard deviation indicates a greater dispersion, while a lower standard deviation indicates a smaller dispersion.

Looking at the given options, (A) 2.5 seconds and (B) 10 seconds are relatively small values, which suggests a low dispersion among the times. On the other hand, options (D) 50 seconds and (E) 90 seconds are larger values, indicating a higher dispersion.

Option (C) 20 seconds falls in between the smaller and larger values. While it is difficult to determine the exact standard deviation without the data, option (C) of 20 seconds seems like a reasonable choice as it represents a moderate spread among the 100 times.

Therefore, the closest value to the standard deviation of the 100 times is (C) 20 seconds.

To know more about standard deviation follow

https://brainly.com/question/28738475

#SPJ12

15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.

Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:

15 divided by 289 is approximately equal to 0.0519 or 519/10000.

In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.

To know more about division problem click here:

brainly.com/question/28785787

#SPJ4

The accurate solution is that the probability of the proportion of nearsightedness of at least 0.09 is approximately 0.0324 or 3.24%.

There are a few steps to answer this question about probability with the proportion of nearsightedness:

1. Define the variable: Let p be the true proportion of children with nearsightedness.

2. Check the conditions for using the normal approximation to the binomial distribution: np = 356 × 0.09 = 32.04 and n(1 - p) = 356 × 0.91 = 323.96, both greater than or equal to 10.

3. Calculate the z-score using the formula: z = (x - np) / √(np(1 - p)), where x = 0.09 × 356 = 32.04.

4. Find the probability using a calculator.

The probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% is approximately 0.0324, or 3.24%.

To know more about probability refer here:

https://brainly.com/question/29110744#

#SPJ11

She needs 14 cups of fertiliser.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area = length * width

Find the area of the garden:

Area = 9 1/3 * 12

       = 28/3 * 12

       = 112  yards²

Find the amount of the fertiliser needed:

1   yards² = 1/8 cup

112  yards² = 1/8 * 112 = 14 cups

She needs 14 cups of fertiliser.

To learn more about the area from the given link

https://brainly.com/question/25292087

#SPJ1

The sum elements for the expected hidden state of a Kalman filter at time t1 given data at time t1 and a hidden state distribution at time t are the prior state distribution and the posterior state distribution.

The weights are the posterior probability, which is determined by the Kalman filter's prediction and measurement likelihood.

Learn more about probability

brainly.com/question/30034780

#SPJ11

Answer:

First figure:

Faces--5

Edges--8

Vertices--5

Type--pyramid

Second figure:

Faces--6

Edges--12

Vertices--8

Type--rectangular prism

As per the unitary method, the cost of one skirt is sh 20 and the cost of one blouse is sh 550.

Let us assume that the cost of one skirt is x and the cost of one blouse is y. We can now form two equations based on the given information.

Equation 1: 5x + 3y = 1750

This equation represents the cost of 5 skirts and 3 blouses together, which is given as sh 1750.

Equation 2: 3x + y = 850

This equation represents the cost of 3 skirts and 1 blouse, which is given as sh 850.

To apply the unitary method here, we can first find the value of one skirt by dividing equation 1 by 5, and then find the value of one blouse by subtracting 3 times the value of one skirt from equation 2.

Dividing equation 1 by 5, we get:

x + (3/5)y = 350

Subtracting 3 times the value of one skirt from equation 2, we get:

y = 850 - 3x

y = 850 - 3(350/5)

y = 550

So, we have found the value of y, which is the cost of one blouse. Now, we can substitute this value of y in equation 1 to find the value of x, which is the cost of one skirt.

5x + 3(550) = 1750

5x + 1650 = 1750

5x = 100

x = 20

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4

As per the concept of parallelogram, the area of the hexagons is 1237.9 cm², one isosceles trapezoid is 130 cm², one triangle is 60 cm², one circle is 78.5 cm².

Since we know the apothem is 10 cm, we can use the tangent function to find the length of the side:

tan(72) = side length / 10

Solving for the side length, we get:

side length = 10 * tan(72) ≈ 21.2 cm

Now that we know the side length, we can use the formula for the area of a regular polygon:

area of the hexagon = (5 x side length² x √(3)) / 2 ≈ 1237.9 cm²

Next, let's find the area of the isosceles trapezoid.

To find the area, we can use the formula:

area of the trapezoid = ((base1 + base2) / 2) x height

Substituting the given values, we get:

area of the trapezoid = ((12 + 14) / 2) x 10 = 130 cm²

Now, let's move on to the triangle. We are given the base (12 cm) and the height (10 cm). To find the area of a triangle, we can use the formula:

area of the triangle = (base x height) / 2

Substituting the given values, we get:

area of the triangle = (12 x 10) / 2 = 60 cm²

Next, let's find the area of the circle. We know that the diameter of the circle is equal to the height of the isosceles trapezoid (10 cm), so the radius is half of that:

radius = 10 / 2 = 5 cm

Using the formula for the area of a circle, we get:

area of the circle = π x radius² = π x 5² ≈ 78.5 cm²

To know more about parallelogram here

https://brainly.com/question/29147156

#SPJ4

Complete Question:

There are 3 regular hecagons, one isocrles trapezoid, one triangle, one circle and one parallelogram. Use the provded measurements to find the area. You will need to use trigonometry to find some measurements

base is 12 cm, length is 14 cm and height is 10 cm

Answer: 2.

Step-by-step explanation:

Mean = Population / Number of Integers.

Mean = 7.

Subtract the integers from the mean.

5 - 7 = -2

6 - 7 = -1

10 - 7 = 3.

Put differences in absolute value.

|-2| = 2

|-1| = 1

|3| = 3.

add the differences then divide by the population number.

2 + 1 + 3 = 6

6 / 3

2

Answer:Your answer is 67.

Step-by-step explanation:Your very welcome! :D

hope im right. Good luck acing your quiz!

The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.

The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.

Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.

So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

To learn more about cylinder please click on below link        

https://brainly.com/question/3216899

#SPJ1

The length of the long diagonal of the cube is 3sqrt(3) inches.

Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).

Using the given equation, we can write

a^3 + 3(12a) = 2(6a^2)

Simplifying this equation, we get

a^3 + 36a = 12a^2

a^3 - 12a^2 + 36a = 0

a(a^2 - 12a + 36) = 0

a(a - 6)^2 = 0

The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.

To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".

Using the Pythagorean theorem, we can write

d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2

d^2 = 3(6^2)/4

d = (sqrt(3)×6)/2

d = 3sqrt(3) inches

Learn more about cube here

brainly.com/question/27677658

#SPJ4

There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.

In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ4

When Trevor graduated high school, he put his pirating CDs behind him and got a job at a clothing store to save money for college. Saving money is an essential part of financing college.

A student can achieve their dream of attending college by following the steps below.

Step 1: Create a budget. Creating a budget is the first step in saving for college. The budget should include all expenses, such as tuition, room and board, books, and other fees.

Step 2: Find ways to save money. Save money by finding ways to reduce spending on non-essentials such as entertainment, dining out, and shopping. Every little bit counts, and the savings can be put toward college.

Step 3: Explore scholarships and financial aid. Apply for financial aid and scholarships to help pay for college. Grants, loans, and scholarships are available from federal, state, and private sources.

Step 4: Consider community college or online education. Consider community college or online education as an affordable way to earn college credit and save money.

Step 5: Work and save Continue working and saving money during college. A part-time job or paid internship can help cover expenses and reduce student loan debt.

These are the essential steps for saving money for college. A student can explore these options and make smart financial decisions to achieve their dream of attending college.

To learn more about “budget” refer to the https://brainly.com/question/8647699

#SPJ11