15 cm
10 cm
o
10 cm
Diagram NOT accurately drawn
The diagram shows a sector of a circle, centre 0, radius 10 cm.
The arc length of the sector is 15 cm.
Calculate the area of the sector.

The process of how to construct a square with a compass and straightedge is explained

To construct a square using a compass and straightedge, follow these steps:

1. Start with a line segment AB. This will be one side of the square.

2. Use a compass to mark off four equal distances along the line segment AB. These points will be the vertices of the square.

Let's call these points C, D, E, and F.

3. With the compass centered at point C, draw an arc that intersects line segment AB at two points. Label these points G and H.

4. With the compass centered at point D, draw an arc with the same radius as in step 3. This arc should intersect line segment AB at two points. Label these points I and J.

5. Use a straightedge to draw lines through points G and H and extend them until they intersect. Label this intersection point K.

6. Similarly, use a straightedge to draw lines through points I and J and extend them until they intersect. Label this intersection point L.

7. Finally, use a straightedge to draw lines through points K and L, as well as points C and D. These lines will intersect at point M, which will be the fourth vertex of the square.

Now constructed a square with sides equal to the length of line segment AB using only a compass and straightedge.

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After the taxes and rent, the remaining amount in his gross pay is $5,700

The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.

Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.

And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.

Therefore, the remaining amount in his hand is calculated as,

=> $38000 - [35% of income + 50% of income]

Here the 35% of income is

=> 38000 x 35/100

=> 380 x 35

=> 13300

Similarly, the 50 percent of the income is

=> 38000 x 50/100

=> 380 x 50

=> 19000

Then the remaining amount is calculated by apply the values on it, then we get,

=> $38000 - [$13300 + $19000]

=> $3800 - $32300

=> $5700

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The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

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

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

60

Step-by-step explanation:

57 times 100 divided by 95

Answer:

The original price is $60

Step-by-step explanation:

So we can make an equation

We know the sale is 5 percent

So 5 percent off technically means we‘re just paying 95 percent of the product

The new sale price is 57

So an equation could be

We just don’t know what the orignal price is, that could be the variable X

0.95x=57

You multiply the original price by 0.95 becuase your paying 95 percent for the object so its easier, its a simple 1 step, you can of course do a 2 step (below) but I prefer 1.

Now solve the equation normally

57/0.95=60

So 60 is the original price

You can check by just multiplying 60 by 0.95 becuase you pay 95 percent of object, you’d get 57

OR you can check by just multiplying 60 by 5 percent or 0.05 and you’d get 3. 60-3=57

Answer:

10

Step-by-step explanation:

Answer:

good morning i hope your day is going well so far

Step-by-step explanation:

the answer to your question is 10

i hope this helps!!!

If 2 angles are complementary, then they add up to 90 degrees. Therefore, you can find the measure of the complementary angle by subtracting 12 from 90, which is 78 degrees.

The measure of ∠4, given that angles 3 and 4 are complementary and ∠3 = 27 degrees, is 63 degrees. Complementary angles add up to 90 degrees, so by subtracting the given angle from 90, we find that ∠4 is 63 degrees.

Complementary angles are two angles that add up to 90 degrees. Since ∠3 and ∠4 are complementary, we can set up the equation ∠3 + ∠4 = 90. Substituting the given value of ∠3 as 27, we have 27 + ∠4 = 90. To solve for ∠4, we subtract 27 from both sides of the equation: ∠4 = 90 - 27 = 63.

Therefore, the measure of ∠4 is 63 degrees.

In conclusion, when two angles are complementary and one of the angles is given as 27 degrees, the measure of the other angle (∠4) is determined by subtracting the given angle from 90 degrees, resulting in a measure of 63 degrees.

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Answer: 12:16

Step-by-step explanation: If you simply the ratio by dividing each side by 4 you are left with 3:4

Answer: 12:16,6:8

Step-by-step explanation:

simplify

12:16=3:4

6:8=3:4

De Morgan's laws are two rules in formal logic that involve negating statements. The first law states that the negation of a conjunction (an "and" statement) is equivalent to the disjunction (an "or" statement) of the negations of the individual components.

The second law states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual components.

Therefore, the negation of the original statement is "She does not make the bed, and I make the bed." This means that both she does not make the bed and I make the bed must be true in order for the negation to be true.

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Answer:

The simplified expression is 498,400÷7. The value is 71,200.

Step-by-step explanation:

712×25×14×2= 498,400.

498,400÷7 becomes our expression. And that answer is 71,200. I hope this helps

Answer:

Step-by-step explanation:

substitute

a + 2p = 4

x − 2y = 6

Answer:

22 degrees

Step-by-step explanation:

90-68=22

Answer:

7+2/8+5

Step-by-step explanation:

The degree of the polynomial h(x) is 2.

The degree of a polynomial is determined by the highest power of the variable present in the polynomial.

Let's analyze the given expression:\(f(g(x)) \times g(h(x)) \times h(f(x)).\)

Since f(x) has a degree of 6, g(x) has a degree of 3, and h(x) is a polynomial, we can determine the degree of h(x) by examining the degree of the resulting polynomial.

When we substitute g(x) into f(x), the resulting polynomial will have a degree of\(6 \times 3 = 18,\) since we are effectively raising the degree of f(x) to the power of 3.

Similarly, when we substitute h(x) into g(x), the resulting polynomial will have a degree of \(3 \times h,\) since we are effectively raising the degree of g(x) to the power of h.

Lastly, when we substitute f(x) into h(x), the resulting polynomial will have a degree of h \(\times\) 6 since we are effectively raising the degree of h(x) to the power of 6.

Since the overall polynomial expression has a degree of 36, we can set up the equation:

\(18 + 3 \times h + 6 \times h = 36\)  

Simplifying the equation, we get:

9h + 18 = 36

9h = 18

h = 2

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Answer:

Option C is correct.

Step-by-step explanation:

Here, boy knows his height and shadow length

And he know the length of tree shadow.

We need to find height of the tree.

And tree and it's shadow makes right angle at the point of intersection.

So, S A S rule works here.

Answer: -10, 2

Step-by-step explanation:

To find the next two numbers, we first need to determine the pattern. We can see that the next number is the result of the previous number divided by -5. This tells us we need to divide 50 by -5 and that solution by -5 also.

50÷(-5)=-10

-10÷(-5)=2

Now, we know the next two numbers are -10 and 2.

Answer:

-10 and 2

Step-by-step explanation:

To find the next two numbers, you have to find what operation is being applied to the given numbers. If we look at the numbers, we can see that the absolute value is getting smaller, which means they are decreasing. However, they are decreasing at an even rate, meaning that the numbers are being divided rather than subtracted. So, let's find what number 1250 was divided by to equal -250:

1250/x = -250

Multiply both sides by x to isolate it:

1250 = -250x

Divide both sides by -250 to isolate x:

-5 = x

Each number in the pattern is divided by -5 to find the next number in the pattern. Now that we know this, we can find the next two numbers:

50/-5 = -10

-10 is one of the numbers.

-10/-5 = 2

2 is the other number.

Hope this helps :)

Answer:

it is option D because it make supplementry or 180°

Answer:

A. -4

Step-by-step explanation:

−6 − (−2) = -6 + 2

              = -4

Hope this helped :)

Answer:

The answer should be C

Step-by-step explanation

I've had this problem before, and know it should most definitely be C.

Hope I helped!

The value of a in the given function is 4

To find the value of a in the equation f(g(x)) = (1 - x²)³, we need to substitute the function g(x) = a + x² into the function f(x) = (5 - x)³.

Replacing x in f(x) with g(x), we have:

f(g(x)) = (5 - g(x))³.

Substituting g(x) = a + x², we get:

f(g(x)) = (5 - (a + x²))³.

f(g(x)) = (5 - a - x²)³.

Comparing this expression with (1 - x²)³, we can equate the corresponding terms:

5 - a - x² = 1 - x².

5 - a = 1.

a = 5 - 1

a = 4

Therefore, the value of a is 4.

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We have to convert a sentence into an inequality. the sentence is the following

This tells us two things, that we subtract 5 from "w" and that this must be less than or equal to 16

In conclusion, the answer is:

The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

What is an area in math definition

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares

A slice is made parallel to the base of a right rectangular pyramid, as shown.

Then the area of the resulting two-dimensional cross-section will be

Area = 2 in × 2.5 in

Area = 5 in²

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Answer:

Below

Step-by-step explanation:

6.5 x 10^-9   is the same as  65 x 10^-10    now you can add them together (since the exponents are the same ) to get

69.6 x 10 ^-10  which is   6.96 x 10^-9

Answer:

There were 8 student who went on a trip.

Step-by-step explanation:

Let's call the original number of students "x". The total cost of the trip was $80, so the cost per student was $80/x.

When four more students decided to go, the new number of students became x + 4, and the cost per student was reduced by $1, to $80/x - $1.

We can set up an equation to solve for x:

$80/x = $80/(x + 4) - $1

Expanding the right side:

$80/x = $80/x + $80/4 - $1

Combining like terms:

$80/x = $80/4 + $80/x - $1

Solving for x:

$80/4 = $80/x - $1

$80/4 + $1 = $80/x

$20 + $1 = $80/x

$21 = $80/x

Finally, solving for x:

x = 80/$21 = 80/21 = 3.81 (rounded to nearest whole number)

So, there were 4 students on the original trip.

There were 4 students on the original trip and 4 more students joined, so in total, there were 4 + 4 = 8 students who went on the trip.

Answer: 8 student

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 500

2. 10

3. 25000

Answer: The answer is A.addition property of equality

Hope I helped

Pkease mark me as brainliest!

Step-by-step explanation:

We have x² + 9x + 18 = (x + 6)(x + 3).

Answer:

Step-by-step explanation:

x^2 + 9x + 18

(x + 6)(x + 3)