use basic trigonometric identities to simplify the expression: sin^3 (x) + cos^2 (x) sin (x)

Answer: [tex]9x-4[/tex]

Step-by-step explanation:

Reflecting across the y-axis means [tex]f(x) \longrightarrow f(-x)[/tex].

[tex]g(x)=-9(-x)-4=9x-4[/tex]

(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined area of the two rooms.

the given dimensions of the living room are given as follows,

length =12

width/breadth =10

thus the area of the living room will be,

length x breadth, i.e.

=12 x 10

=120 sq. feet

the given dimensions of the dining room are given as follows,

length= x

width/breadth=10

thus the area of the dining room can be calculated as

length x breadth

=10x sq. feet

Now, to calculate the combined area of both the rooms, we have to add the area of the dining room and the area of the living room,

that is,

(120 + 10x) sq. feet

What is area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

to learn more about area visit:

https://brainly.com/question/25292087

#SPJ9

The bananas will last 2 days at the zoo (found by division).

According to the question,

We have the following information:

The elephants at the zoo eat [tex]3\frac{1}{6}[/tex] buckets of bananas each day. The zookeeper bought [tex]6\frac{1}{3}[/tex] buckets of bananas.

Now, first we will find the number of days taken in eating 1 bucket of bananas.

[tex]3\frac{1}{6}[/tex] buckets = 1 day

Now, we will convert this mixed fraction into simple fraction.

19/6 buckets = 1 day

1 bucket = 1/(19/6) days

1 bucket = 6/19 days

Now, we have the total number of buckets as [tex]6\frac{1}{3}[/tex].

Now, after converting this mixed fraction, we have:

19/3 buckets

1 bucket =  6/19 days

19/3 buckets = (6/19)*(19/3)

19/3 buckets = 2 days

2 is a whole number.

Hence, the given buckets of bananas will last 2 days.

To know more about division here

https://brainly.com/question/18089147

#SPJ1

ANSWER

EXPLANATION

We want to solve the given linear equation:

To do this, divide both sides of the equation by -6 to isolate u and simplify:

That is the solution to the linear equation.

Given:

Slope = 1/3

Contain the point = ( -3,-1 )

Find-:

The equation of a line.

Explanation-:

The general equation of a line is:

Where,

Given the slope is 1/3, then the equation of the line become.

The value of y-intercept is:

The point (-3,-1) contains the line so its satisfied the equation.

So equation of line become:

The final equation of line is:

Answer:

3x - 4

Step-by-step explanation:

"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.

"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.

"the difference of ___ and ___" means to subtract those two things.

So we get 3x - 4

The equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

The equation of the line in slope intercept form is written as

y = mx + c ,

where m is the slope of the line , and c is the y intercept .

In the question ,

the equation of the line is given

equation of line is given as 4x-20y = -160

to convert the equation in slope intercept form , we rewrite it as

20y = 4x+160

dividing both sides by 20 ,

we get

20y/20 = 4x/20 + 160/20

y = x/5 + 8

hence ,the slope intercept form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .

Therefore , the equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

Learn more about Lines here

https://brainly.com/question/21206550

#SPJ1

To answer this question, we will use the next table (obtained from the Question Tab):

City -------- Number of restaurants

Carlsbad 489

Potter Valley 261

Little Heath 282

Edgbaston 216

Barrow 317

If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:

From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow.

We can check this as follows:

In summary, we can say that there are 172 more restaurants in Carlsbad than in Barrow.

The sectorial area of the circle is equal 31.3cm^2

The formula for the b of the sector of a circle is /360o (r2) where r is the radius of the circle and  is the angle of the sector.

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.

Data;

The area of the sector can be calculated using the formula given

[tex]A = \frac{\theta }{360} * \pi r^2[/tex]

Substituting the values into the formula;

[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]

The area is equal 31.3cm^2

Translation:

The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.

Learn more on area of a sector here;

https://brainly.com/question/22761976

#SPJ1

Answer:
The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit

Hi i hope this helps you out

We need to count the number of zeros in a number multiplied by a power of 10. Which is shown below:

The power of 10 will add a certain number of zeros, which is equal to the expoent of the power, in this case it's 7, but there is one more zero which is present in the "40", therefore the total number of zeros will be 8.

To answer this question, we will use the following diagram as reference:

To determine the tangent of θ, we have to find the value of x.

To find x, we use the Pythagorean theorem and get:

Therefore:

Therefore:

Answer:

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

The price that Misu can pay for a comforter based on the markup percentage is $103.57.

From the information, the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40 percent markup on selling price.

Let the selling price be represented as x. Based on the information given, this will be illustrated as:

x + (40% × x) = 145

x + 0.4x = 145

1.4x = 145

Divide

x = 145/1.4.

x = 103.57

The selling price will be $103.57.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.

However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.

When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:

Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:

Now, we group the like-terms and add them:

For yhe other one, Let's do each term and then make the substraction:

So:

Answer:

Part A: C(x) = 0.068x+0.8

Part B: 1.28

Part C: 9.76

Explanation:

Part A:

The cost C equals

cost = revenue - profit

which is

Part B:

The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives

Hence, the cost of producing 7 items is 1,28 million dollars.

Part C:

To break even, the cost must equal the revenue

or

subtracting 0.068 from both sides gives

dividing both sides by 0.082 gives

which is the break-even point

The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

Given,

The equation of the line: x - 4y = 20

The points which the line passes through, (x₁, y₁) = (8, 0)

We have to find the equation of the line parallel to the given line.

The formula for the slope intercept form:

(y - y₁) = m(x - x₁)

m is the slope of the line.

Lets find the slope of the line given.

x - 4y = 20

x = 20 + 4y

x - 20 = 4y

y = (x - 20) / 4

y = 1/4x - 5

Here, slope of the line is 1/4

Now, substitute the slope of the line and (x₁, y₁) in the slope intercept formula to get the equation of line parallel to the given line

(y - y₁) = m(x - x₁)

(y - 0) = 1/4(x - 8)

y = 1/4x - 8/4

y = 1/4x - 2

1/4x - y = 2

Therefore,

The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

Learn more about equation of the line here:

https://brainly.com/question/19699006

#SPJ1

Answer:

72.7% to nearest 10th percent would be 73%!

Step-by-step explanation:

Hope it helps! =D

Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

The product of  (7) (-16)(-7) (-1) is - 784 by using simple multiplication.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).

7 × -16 = -112

-112 × -7 = 784

784 × -1 = -784

To know more about multiplication click here:

https://brainly.com/question/26583342

#SPJ13

A.

[tex]3n =19 - 1 \\ 3n = 18 \\ \frac{3n}{3} = \frac{18}{3} \\ n = 6[/tex]

B.

[tex]21 + 5 = - 2p \\ 2p = - 26 \\ \frac{2p}{2} = \frac{26}{2} \\ p = 13[/tex]

HOPE THIS HELPS.

The ordered pair that describes the location of N is (2,6)

Given:

N's coordinates are: (-2,-6)

Point N ′ is produced by reflecting point N over the y-axis.

By reflecting point N' over the x-axis, the final point N" is produced.

x , y = -x , y

N(-2 -6) = N'(2 6)

To locate the ordered pair describing where N" is located.

Point N's coordinates are (-2,-6). Point N ′ is produced by reflecting point N over the y-axis.

x , y = -x , y

N(-2 -6) = N'(2 6)

The resultant point N" is created by reflecting point N' over the x-axis.

The ordered pair for point N" is therefore (2,6) gives its location.

Learn more about ordered pairs at

https://brainly.com/question/22312665

#SPJ9

The formula for the volume of a cone is a third of the product of pi, its height h and the square of its radius r. Then, it is:

Answer: C

Answer:

it would be 600

Question 16

[tex](f(x), g(x))=x^2, (x-9)[/tex]

Question 17

[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]

The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).

in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.

Learn more about Composite functions at:

brainly.com/question/17749205

#SPJ1

We are given the following equation:

In the first step we will use the distributive property on the left side:

In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:

Solving the operations we get:

In step 3 we will add 34x to both sides, this is the inverse additive inverse:

Solving the operations:

In step 4, we divide both sides by 17, this is the division property of equality:

Solving the operations:

Given the two sides measurement,

• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :

• We can find the value of side h by using Pythagorean theorem:

• Subsequently, we will find angle angle , as shown in the diagram above as follows:

• Since we have angle ,= 56.3 °, ,we can find, angle :

• + + 90° = 180 °,....(angles in a triangle adds up to 180°)

∴ = 180° -90° -56.3°

=33.7°