Charles opened a door hinged at O by an angle of 45 degrees. The width of the door was 80 centimeters. Find the area swept by the door. Leave your answer in terms of pie

Answer:

  4(x - 2)^2 + 3x – 2 + 1 = 0

Step-by-step explanation:

The equation that has a highest x-power (degree) of 2 is quadratic.

The degrees of the answer choices are ...

So, only the first answer choice is a quadratic.

Answer:

10x8 + 7x4 + 1 = 0, or C

Step-by-step explanation:

got it right on edge

Hope this helps :)

Answer:           Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

Step-by-step explanation :   For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number ! Again, hoped this helped. If you do used, don't word for copy. Make it into your own words.

Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

Answer:

D:step 4

Step-by-step explanation:

Answer:

an = a1 + d(n - 1)

a88 = 4 + (-5)(88 - 1)

a88 = 4 + (-5)(87)

a88 = 4 - 435

a88 = -431

So, the 88th term of the arithmetic sequence is -431.

The 88th term of the given arithmetic sequence is equal to -431.

Given the following data:

To calculate the 88th term of the given arithmetic sequence:

Mathematically, the nth term of an arithmetic sequence is given by the formula:

[tex]a_n = a_1 + d(n - 1)[/tex]   ...equation 1.

Where:

First of all, we would determine the common difference as follows:

[tex]d = a_2 - a_1\\\\d=-1-4[/tex]

d = -5

Substituting the values into eqn. 1, we have:

[tex]a_{88} = 4 + [-5](88 - 1)\\\\a_{88} = 4 -5(87)\\\\a_{88} = 4 -435\\\\a_{88} = -431[/tex]

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Answer:

option 1

Step-by-step explanation:

The shaded area is area of circle - area of 2 congruent triangles

area of circle = πr²

Note that the base and height of both triangles is the radius

Area o triangle = [tex]\frac{1}{2}[/tex] ×  r × r = [tex]\frac{1}{2}[/tex]r²

area of 2 triangles = 2 × [tex]\frac{1}{2}[/tex] × r² = r²

area of shaded region = πr² - r² = r²(π - 1) → (1)

To represent the area of the shaded region in the figure, use the expression "r² (π+1)" as it closely approximates the calculation for the shaded area.

In the figure described, ABO and GOF are right triangles, and there's a shaded region within these triangles. To represent the area of the shaded region, we can consider the difference between the areas of the larger triangles ABO and GOF and the smaller semicircles centered at O within each triangle.

The area of a triangle is given by (1/2) × base × height, and the area of a circle is πr², where "r" is the radius.

Calculate the area of ABO: (1/2) × AB × AO

Calculate the area of GOF: (1/2) × GO × GF

Calculate the area of one semicircle: (1/2) × πr²

Now, to find the area of the shaded region, subtract the sum of the areas of the two semicircles from the sum of the areas of the two triangles:

Shaded Area = (ABO - πr²) + (GOF - πr²)

So, the representation for the area of the shaded region is:

Shaded Area = (1/2) × AB × AO + (1/2) × GO × GF - πr²

Therefore, option 2, "r² (π+1)," is the closest representation of the area of the shaded region.

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Answer:

7*(2a-1)

Step-by-step explanation:

Answer:

7*(2a+1) / 2*(7a+1)

Step-by-step explanation:

Answer:

3,854

Step-by-step explanation:

There’s 82 kids each learned 47 lines you would multiply

The children learned a total of 3854 lines of the song. This is found by multiplying the number of children by the number of lines in the song.

This problem involves simple multiplication. Since each child needs to learn one line of the song, and the fun song has 47 lines, to find the total number of lines the children learned altogether, you simply multiply the number of children by the number of lines in the song. Therefore, 82 (number of children) x 47 (number of lines in the song) equals 3854. So, the children learned 3854 lines in total.

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We have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2

Solution:

Given that,

For a game, Tony has a rectangle drawn on a piece of paper that has an area of 18 in.^2

In order to have a similar rectangle that's area is only 2 in.^2

Thus, we need to find the scale factor

Let "c" be the scale factor

Let "x" be the area of original rectangle

Let "y" be the area of dilated rectangle

Therefore,

[tex]c = \frac{y}{x}\\\\c = \frac{2}{18}\\\\c = \frac{1}{9}[/tex]

Therefore, we have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2

Answer:

Divide them by three.

Answer:

BC is 25 units

Step-by-step explanation:

AB = AC

4x + 4 = 6x - 14

4x + 4 - 4x + 14 = 6x - 14 - 4x + 14

18 / 2 = 2x / 2

9 = x

2(9) + 7

18 + 7

25

Answer:  BC is 25 units

Answer:

Slope=4.25

Step-by-step explanation:

Formula for slope is y2-y1/x2-x1

Y1=51,y2=17,x1=12,x2=4

Input this values into the above formula

17-51/4-12

Slope=-34/-8

Divide both numerator and denominator by -2

Slope=17/4

Slope=4.25

Answer:

10[tex]\leq[/tex]D+R

D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)

Step-by-step explanation:

Say that D = Decaf and R = Regular

10[tex]\leq[/tex]D+R

D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)

Answer:

284.6 square yards

284.6 yd^2

Step-by-step explanation:

Base: 7 × 13 = 91

Rectangle Sides: 6.1 × 13 = 79.3 (x2 = 158.6)

Triangle Sides: 5 × 7 = 35 (÷2 ×2 = 35)

Add: 91 + 158.6 + 35 = 284.6

Here is the graph for the equation

Given function to be graphed is,

f(x) = (x - 2)(x - 6)

We will convert the equation of the function into the vertex form,

(x - 2)(x - 6) = x(x - 6) - 2(x - 6)

                  = x² - 6x - 2x + 12

                  = x² - 8x + 12

                  = x² - 2(4x) + 16 - 4

            f(x) = (x - 4)²- 4

By comparing this equation with the vertex form of the equation of a parabola,

g(x) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola.

Therefore, vertex of the function 'f' will be (4, 4).

Now we will find the x-intercepts and y-intercept of the function.

For x-intercept, put f(x) = 0

0 = (x - 4)²- 4

(x - 4) = ±2

x = 4 ± 2

x = 2, 6

Therefore, x-intercepts of the function are (2, 0) and (6, 0).

For y-intercept, put x = 0

f(0) = (0 - 2)(0 - 6)

f(0) = 12

Therefore, y-intercept of the function is (0, 12).

By plotting these ordered pairs and joining them by a curve we can get the graph of the parabola.

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Answer:

Step-by-step explanation:

A supplementary angle is equal to 180 degrees. So subtract 96.7 degrees from 180. 180-96.7= 83.3 degrees

Your answer is 83.3 degrees.

Answer: 83.7 is supplimentary

Step-by-step explanation: 180 - 96.7 = 83.7

Answer: 1) 1 1/2, 2 1/4, and 4

Step-by-step explanation: 1) We know that the equation would be the cups of flour being multiplied by the batches. Like, 5 times 3/4 would equal 15/4 which would simplify to 3 3/4.

                 So, to find the first missing number, we do 2 x 3/4, which equals 6/4( 1 1/2).

                The next missing number would be 3, because we're going in order-- like 1, 2, 3, 4. So we do 3 x 3/4.

               We then don't have a number for batches this time. So we still do, 3/4 x 3 but this time we cross out both the 3 on the top and we're left with 4, our answer.

                The equation for this is 3/4 x b. (Did this help..?)

Answer: 5>14x

Step-by-step explanation: 5 is more than the product which means multiplaction is 14 and x is the number so its 14x.

please give bainliest

Answer: Lydia

Step-by-step explanation:

Convert all distances to the smallest measure in which all distances can be in the same distance type, so that you can see what is the farthest. Note: inches won't be necessary because that's an unreasonable way to measure distance if you walk very far.

Rowan travelled 450 feet

Janelle travelled 429 feet 8 inches

Domingo travelled 392 feet

Lydia travelled 460 feet

Answer: Lydia

Step-by-step explanation:

Convert all distances to the smallest measure in which all distances can be in the same distance type, so that you can see what is the farthest. Note: inches won't be necessary because that's an unreasonable way to measure distance if you walk very far.

Rowan travelled 450 feet

Janelle travelled 429 feet 8 inches

Domingo travelled 392 feet

Lydia travelled 460 feet

Answer:

682,500 people

Step-by-step explanation:

so just find how many people per year it grows by then add that number 15 times to 300,000

so 8.5% of 300,000 is 25,500 people

now multiply that by 15 to get 382,500

add that to 300,000

Final answer:

Using the exponential growth formula, the population of a city with an initial population of 300,000 and an annual growth rate of 8.5% will be approximately 962,100 after 15 years.

Explanation:

To calculate the future population of a city with an initial population of 300,000 people and an annual growth rate of 8.5% over 15 years, we use the formula for exponential growth:

P = P_0 (1 + r)[tex]^{t}[/tex]

where:

P is the future population,

P_0 is the initial population (300,000),

r is the annual growth rate (expressed as a decimal, so 8.5% becomes 0.085), and

t is the number of years (15).

Substituting the values we get:

P = 300,000 (1 + 0.085)¹⁵

Calculating this, we find:

P = 300,000 (1.085)¹⁵

P = 300,000 (3.207)

P ≈ 962,100

Therefore, after 15 years, the population is expected to be approximately 962,100, rounding to the nearest whole number.

The two teachers have 16 and 64 homework papers to return, totalling in 80.

They also have 14 and 60 quizzes to return, totalling in 74.

The ratio of homework papers to quizzes that need to be returned is 80:74

In total, there are 80 homework papers and 74 quizzes to be returned. The ratio for the total would be 80 : 74 (or 80/74), and 40 : 37 (or 40/37) simplified.

For Ms. G alone, the ratio would be 16 : 14 (or 16/14), and 8 : 7 (or 8/7) simplified.

For Ms. M alone, the ratio would be 64 : 60 (or 64/60), and 16 : 15 (or 16/15) simplified.

Hope this helps!! :)

Answer:

Step-by-step explanation:

A. The regular cost is 55 per person. Using the given variable definitions, that cost can be expressed as ...

  y = 55x

__

B. The party special cost is 46 per person, with an added fee of 45. That cost can be expressed as ...

  y = 46x +45

_____

As you know, the cost of a purchase is the product of the cost of an item and the number of items. Here, the cost of entry is the cost of the item of interest, and the number of persons needing entry is the number of items. The party special has the addition item of a private room, so its cost is added to the total for the party special.

For the given set of equations, x = 0 and y = 3.

Step-by-step explanation:

Step 1:

From the question,

[tex]-x + 2y = 6[/tex], take this as equation 1,

[tex]6y =x+18, x - 6y = -18[/tex], take this as equation 2.

Step 2:

When we add equation 1 and equation 2, the x variable is canceled out and y can be calculated.

[tex]-4y = -12, y = \frac{-12}{-4}, y = 3.[/tex]

Step 3:

Substituting this value of y in any of the previous equations we will get x's value.

Here this value of y i.e y = 3 is substituted in equation 1.

[tex]-x + 6 = 6, -x = 6 -6, -x=0, x=0.[/tex]

So we have x = 0 and y = 3.

Maria had 2 yards of trim when she started.

Step-by-step explanation:

Step 1:

All of the sides of the triangle is 22 inches long each.

The total length of the sides of the triangle [tex]= 3(22) = 66.[/tex]

So the total length of the trim for the banner is 66 inches long.

If Maria still has [tex]\frac{1}{2}[/tex] a foot of trim left, she had 6 inches of the trim left.

The length of the trim when she started[tex]=66 +6 = 72[/tex] inches.

Step 2:

Now we need to convert the 72 inches into yards.

We have 1 inch = 0.0277778 yards.

So 72 inches [tex]= 0.0277778(72) = 2.[/tex]

So Maria had 2 yards of trim when she started.

Answer: 24

Step-by-step explanation:

Based on the inscribed angle theorem, the measure of angle CAB in circle (O) is: A. 24 degrees.

According to the inscribed angle theorem, the measure of an inscribed angle whose vertex lies on a circle is always half the measure of the intercepted arc that is subtended at a point on the circle.

Given the following data:

Based on the inscribed angle theorem, we have:

∠CAB = ∡CB/2

∠CAB = 48/2

∠CAB = 24 degrees.

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Surveys enable the collection of specific data points from a diverse population, allowing for a more accurate estimation of the percentage of citizens with children in school readiness support. This method ensures inclusivity and reliability in gathering information for decision-making purposes.

Conducting a survey would be the best method to gather information on the percentage of citizens in Los Angeles County who have children in school readiness support. Surveys allow for direct feedback from a representative sample of the population, providing a comprehensive understanding of the situation.

In the survey, a representative sample of citizens across different demographics can be asked whether they have children enrolled in school readiness support programs. By analyzing the responses, Los Angeles County can estimate the percentage of citizens with children in such programs.

Answer:

A, E

Step-by-step explanation:

Both of these numbers are 16 numbers away from 0.

The numbers for the absolute value of a number is 16 are;

a. 16

b. - 16

What is Modulus function?

The modulus function is the absolute value of a positive or negative number.

Given that;

The absolute value of a number is 16.

Now,

We know that;

The absolute value of number is always positive.

So, We get;

A. 16 = |16|

        = 16

E. - 16

= |- 16|

= 16

Thus, The numbers for the absolute value of a number is 16 are;

a. 16

b. - 16

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Answer:

4) J

5) D

Step-by-step explanation:

4) 416 = 2x² - 6x

2x² - 6x - 416 = 0

x² - 3x - 208 = 0

x² - 16x + 13x - 208 = 0

x(x - 16) + 13(x - 16) = 0

(x - 16)(x + 13) = 0

x = 16, -13(not possible)

So 16 rows

5) y = a(x - h)² + k

y = a(x - 3)² - 7

When x = 1, y = -10

-10 = a (1 - 3)² - 7

-10 = 4a - 7

4a = -3

a = -¾

y = -¾(x - 3)² - 7

Answer:

cube

Step-by-step explanation:

the four cubes in the middle make a square and the two other ones fill in the sides of the cube

Answer:

No

Step-by-step explanation:

Only products of variables is a monomial.

Quotient, sum or difference are not. This is a quotient

The question means in Portuguese: In a certain addition of three consecutive natural numbers, the smallest is 49. What should the sum be?

English: Since 49 is the smallest number, the next number up and the next number up give us the 3 consecutive numbers. So 49+50+51 is 150.

Portuguese: Como 49 é o menor número, o próximo número acima e o próximo número acima nos dão os 3 números consecutivos. Então 49 + 50 + 51 é 150.