In the following diagram, a circle is inscribed in a square. How can you find the area of the shaded region?

Notice that the shaded region of the figure is composed of four identical pieces. However, each piece has a curved side, which makes it very difficult to find its area using a direct method. In this type of diagram, the easiest way to find the area uses an indirect method. Look at the diagram using a different perspective. The shaded region is composed of four identical pieces. OR, the shaded region is the area of the square minus the area of the circle. Since you know how to find the area of both a square and a circle, this is a much easier method for solving!
Area of square: s2 = (6 cm)2 = 36 cm2
Area of circle: r2 ≈ (3.14)(3 cm)2 ≈(3.14)(9 cm2) ≈ 28.26 cm2
Area of shaded region: 36 cm2 - 28.26 cm2 = 7.74 cm2
The area of the shaded region is approximately 7.74 square centimeters.
Answer the questions based on the following diagram. Note: The two triangles meet at the center of the circle.


What is the approximate area of the circle? Use 3.14 in your calculation.

What is the area of one of the triangles?

What is the approximate area of the shaded region of the diagram?

Answer:

The solutions are

[tex]x=-8\\x=-1[/tex]

Step-by-step explanation:

We must solve the equation:

[tex]x^2+9x+8=0[/tex]

To solve the equation we can use the factoring method.

To factor the expression, look for two numbers that when you add them, get the result 9 and when multiply them, get the result 8.

You can verify that the numbers that meet this requirement are: 8 and 1.

Then the polynomial factors are:

[tex](x + 8) (x + 1)[/tex]

So

[tex]x^2+9x+8=(x + 8) (x + 1) = 0[/tex]

Then

[tex]x+8= 0[/tex]   or  [tex]x+1 =0[/tex]

[tex]x=-8[/tex] or  [tex]x= -1[/tex]

Answer:

x = -1 or x = -8

Step-by-step explanation:

It is given the function

x² + 9x + 8 = 0

To find the solution of given function

x² + 9x + 8 = 0

By using splitting method we can write,

x² + x + 8x + 8 = 0

x(x + 1) + 8 (x + 1) = 0

(x + 1)(x + 8) = 0

x+ 1 = 0   or x + 8 = 0

x = -1 or x = -8

It's the second one because each means one or single and a singular subject has a singular verb...

Answer:8 inches

Step-by-step explanation:304/38 = 8 inches

Answer:

2x² - 2x + 7

Step-by-step explanation:

Given

(8x² + 9) - (6x² + 2x + 2) ← distribute by - 1

= 8x² + 9 - 6x² - 2x - 2 ← collect like terms

= (8x² - 6x²) - 2x + (9 - 2)

= 2x² - 2x + 7

Answer:

2x² - 2x + 7

Step-by-step explanation:

Ape-x

Check the picture below.

so we have 3 rectangles and 1 semicircle.

let's recall that the area of a circle = A = πr², so then the area of a semi-circle is πr²/2.

let's get the area of all figures, sum them up, and that's the area of the composite.

[tex]\bf \stackrel{\textit{top rectangle}}{(2\cdot 5)}+\stackrel{\textit{middle rectangle}}{(4\cdot 11)}+\stackrel{\textit{bottom rectangle}}{(9\cdot 2)}+\stackrel{\textit{semicircle}}{\cfrac{25\pi }{2}} \\\\\\ 10+44+18+12.5\pi \implies 72+12.5\pi \qquad \approx\qquad 111.27[/tex]

20.00 + 4.00 + 00.50 + 00.08

To write expanded from take each number from left to right and turn all the numbers that are after it into zeros (if there is a decimal then turn the numbers  before it into zeros as well)

2 has 4 numbers after it so it gets 4 zeros: 20.00

4  has 2 numbers after it so it gets 2 zeros: 4.00

5 is a decimal that has two numbers before it and one after, so before the decimal there are two zeros, then after the decimal comes the five, then there is one number after the 5 so one zero after the five.

8 is a decimal that has three numbers before it , so before the decimal there are two zeros, then after the decimal is a number that becomes zero then the 8

Hopefully that made sense to you and was helpful! Let me know!

Answer:

25 ft

Step-by-step explanation:

a² + b² = c²

7² + 24² = c²

49 + 576 = c²

c² = 625

c = √625

c= 25

Answer:

D. 25 ft.

Step-by-step explanation:

To find the missing length of any right triangle, you can use the Pythagorean Theorem (A^2+B^2=C^2) to solve. A and B represent the legs (which we do have) and C represents the hypotenuse (which we are trying to find). Insert our known values into the theorem, and we will get 24^2+7^2=C^2. Now we just do the basic math for the numbers that we have (24^2 is 576; 7^2 is 49), and that added up would equal to 625. Now, since C is being squared on the other side, we now have to root both sides. On the side where C is, the radical and the square will cancel out each other, leaving us with just C. But, on the side where 625 is, it should root to 25. Since C is by itself now, the number on the other side (25) will be our answer. Therefore, the missing side is 25 feet long.

Answer:

x=13

Step-by-step explanation:

x+2x=3x

-6+9+-19=-16

3x-16=23

+16     +16

3x=39

divide by 3 on both sides.

x=13

Answer:

[tex]\large\boxed{a=\dfrac{58}{25},\ b=0}[/tex]

Step-by-step explanation:

[tex]\dfrac{3\sqrt3+\sqrt2}{3\sqrt3-\sqrt2}+\dfrac{3\sqrt3-\sqrt2}{3\sqrt3+\sqrt2}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{(3\sqrt3+\sqrt2)(3\sqrt3+\sqrt2)}{(3\sqrt3-\sqrt2)(3\sqrt3+\sqrt2)}+\dfrac{(3\sqrt3-\sqrt2)(3\sqrt3-\sqrt2)}{(3\sqrt3+\sqrt2)(3\sqrt3-\sqrt2)}\\\\=\dfrac{(3\sqrt3+\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}+\dfrac{(3\sqrt3-\sqrt2)^2}{(3\sqrt3)^2-(\sqrt2)^2}\qquad\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]=\dfrac{(3\sqrt3)^2+2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}+\dfrac{(3\sqrt3)^2-2(3\sqrt3)(\sqrt2)+(\sqrt2)^2}{3^2(\sqrt3)^2-2}\\\\=\dfrac{3^2(\sqrt3)^2+6\sqrt6+2}{9\cdot3-2}+\dfrac{3^2(\sqrt3)^2-6\sqrt6+2}{9\cdot3-2}\\\\=\dfrac{9\cdot3+6\sqrt6+2}{27-2}+\dfrac{9\cdot3-6\sqrt6+2}{27-2}\\\\=\dfrac{27+6\sqrt6+2}{25}+\dfrac{27-6\sqrt6+2}{25}\\\\=\dfrac{29+6\sqrt6}{25}+\dfrac{29-6\sqrt6}{25}\\\\=\dfrac{29+6\sqrt6+29-6\sqrt6}{25}\\\\=\dfrac{58}{25}[/tex]

Slope equation: y2-y1/x2-x1

7-9/-12-(-10)

-2/-2 = 1

Answer:

Slope = 1

Step-by-step explanation:

(y2 - y1) ÷ (x2 - x1) = (7 - 9) ÷ (-12 - [-10]) = -2 ÷ (-2) = 1

Answer:

5/6

Step-by-step explanation:

The ratio is:

45 / 54

Or, reduced:

5 / 6

The ratio of boys to girls in the senior class of the school is 45:54.

The question is asking to find the ratio of boys to girls in a senior class. Since the class has 45 boys and 54 girls, the ratio is typically written in the simplest form as 'boys: girls'. The given figures are in simplest form because they do not have a common factor other than 1. Therefore, the ratio of boys to girls in the senior class is 45:54.

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Answer:

False

Step-by-step explanation:

If both lines are linear, they can only have 0, 1 or infinite solutions. If one was a quadratic function, they would intercept twice.

Answer:

A. 0.7

Explanation:

B is irrational

I have no idea was c and d so that leads to A because it’s terminated

Answer:0.7

Step-by-step explanation:

A pex quiz

Answer:

Exponential function.

[tex]y = - 6( {3}^{x - 1} ) = - 2( {3}^{x} )[/tex]

As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.

The answer is B.

For an expression to be a polynomial term, any variables in the expression must have whole number powers.

-3/x isn’t a polynomial term because the variable is in the denominator.

Answer:

D

Step-by-step explanation:

it only consists of one term.

Answer:

40

Step-by-step explanation:

The range is the difference between the largest value and the smallest value in the data set.

minimum value = 21 and maximum value = 61

range = 61 - 21 = 40

Answer: Range of the data set would be 40.

Step-by-step explanation:

Since we have given the data set as follows:

21,23,28,28,52,54,56,56,57,60,61,61.

We need to find the range of the data set.

As we know the formula for "Range":

Range = Highest number - Lowest number

Range = 61-21

Range = 40

Hence, range of the data set would be 40.

Step-by-step explanation:

the curves intersect at approcx=0.46

Answer:

Step-by-step explanation:

The given function is

[tex]log(6x+10)=log_{\frac{1}{2} }x[/tex]

If we graph this function, the result is like the image attached. There you can observe that the intersection point is at (0.464, 1.107).

If we round this points to the nearest hundred, they would be

x = 0.46 and y = 1.11.

Therefore, the right answer is

a. the curves intersect at approx. x=0.46

Answer:

[tex]y=-1,869.5x+27,995[/tex]

Step-by-step explanation:

Let

x-----> the time in years

y----> value of Zachary’s car in dollars

[tex]A(0,27,995), B(10,9,300)[/tex]

step 1

Calculate the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{9,300-27,995}{10-0}=-1,869.50[/tex]

step 2

Find the equation of the line

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=-1,869.50[/tex]

[tex]b=27,995[/tex]  -----> the y-intercept is the point A

substitute

[tex]y=-1,869.5x+27,995[/tex]

The linear equation to represent the value of Zachary's car after x years since its purchase is y = -1869.5x + 27995.

To write a linear equation to represent the value of Zachary's car after x years since its purchase, we need to determine the slope and y-intercept. The initial value of the car is $27,995, and after 10 years it depreciates to $9,300. The slope (m) can be calculated as (9300 - 27995) / (10 - 0) = -1869.5. The y-intercept (b) is the initial value, which is $27,995. Therefore, the linear equation that represents the value of Zachary's car is y = -1869.5x + 27995.

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Answer: Hope this helps, and hopefully this is what you needed!

1 7/16 = 23/16

11 5/9 = 104/9

30 5/9 = 275/9

10 10/13 = 140/13

24 3/5 = 123/5

129 1/2 = 259/2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The amount that David must have in the bank would be $783243.6

An annuity is a series of payments made at equal period of time.

We need to apply the formula for determining present annuity. It is expressed as

PV = R[1 - (1 + r)^- n]r

Where, PV represents the present value of the investment.

R represents the regular payments made(could be weekly, monthly)

r = represents interest rate/number of interval payments.

n is the total number of payments made.

From the information given;

r = 1.5/100 = 0.015

n = 30 years

R = $32,635.15

Therefore,

PV = 32635.15[1 - (1 + 0.015)^- 30]/0.015

PV = 32635.15[1 - (1.015)^- 30]/0.015

PV = 32635.15[1 - 0.64]/0.015

PV = 32635.15[0.36]/0.015

PV = 32635.15 × 24

PV = $783243.6

Learn more about annuity;

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Which would mean that 540 people died or left the town.

I hope that this helps! :D

Answer:

the answer is C.5

Step-by-step explanation:

ANSWER

[tex]{f}^{ - 1} (x) = 7x - 2[/tex]

EXPLANATION

The given function is:

[tex]f(x) = \frac{x + 2}{7} [/tex]

Let

[tex]y = \frac{x + 2}{7} [/tex]

Interchange x and y.

[tex]x= \frac{y + 2}{7} [/tex]

Solve for y by first multiplying through by 7.

[tex]7x = y + 2[/tex]

Add -2 to both sides of the equation.

[tex]7x - 2 = y[/tex]

Or

[tex]y = 7x - 2[/tex]

Hence the inverse function is:

[tex]{f}^{ - 1} (x) = 7x - 2[/tex]

Answer:

p(x) = 7x - 2

Answer:

5

Step-by-step explanation:

The expression 9 - z evaluates to 5 when z = 4. This is calculated simply by substituting 4 into the equation in place of z, and then performing the subtraction.

The question is asking you to evaluate the expression 9 - z when z = 4. The term 'evaluate' in mathematics means to calculate the numerical value of. So this is a straightforward substitution problem. You take the value of z (which is 4) and substitute it into the equation in place of z. So, the equation becomes 9 - 4, which equals 5.

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Answer:

The answer in the procedure

Step-by-step explanation:

we have

[tex]\pi=3.14[/tex]

[tex]r=1\ units[/tex]

[tex]h=2\ units[/tex]

case a) If the expression is

[tex]\pi r^{2} h[/tex]

then

substitute

[tex](3.14)(1)^{2} (2)=6.28\ units^{3}[/tex]

Round to the nearest whole number

[tex]6.28=6\ units^{3}[/tex]

case b) If the expression is

[tex](1/3)\pi r^{2} h[/tex]

then

substitute

[tex](1/3)(3.14)(1)^{2} (2)=2.09\ units^{3}[/tex]

Round to the nearest whole number

[tex]2.09=2\ units^{3}[/tex]

Answer:

The mass of the cylinder is [tex]149\ g[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=7/2=3.5\ in[/tex] ----> the radius is half the diameter

[tex]h=1.5\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=(3.14)(3.5)^{2}(1.5)[/tex]

[tex]V=57.70\ in^{3}[/tex]

step 2

Find the mass

we know that

The density is equal to the mass divided by the volume

[tex]D=m/V[/tex]

Solve for the mass

[tex]m=D*V[/tex]

substitute the values

[tex]m=(2.58)*(57.70)=149\ g[/tex]

Answer:

2441 grams

Step-by-step explanation:

convert 7 and 1.5 inches into centimeters (2.54 centimeters per inch) so now you use half of 8.89 (7 * 2.54 = 2441) multiplied by 3.81

you find the area of the cylinder first by using [tex]\pi r^2*h[/tex] which should give you 945.97219

then plug it into the density formula, 2.58= mass/945.97219

that should give you mass=2440.61

and if you round it to the nearest gram, it's 2441

**THIS IS THE CORRECT ANSWER**

Answer:

4153. Read the explanation please. There is no point in just reading the answer because the same type of problem can come up in the RSM homework or in a test and you will have no idea how to solve it.

Step-by-step explanation:

Form an equation with the information you know.

1. Moving the last digit, 3, to the first position is the same as doing (x-3)/10 +3000, where x is the original 4-digit number.

    Why it works: This expression works because first, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there. To remove the zero, you divide by 10. Finally, to put the 3 at the first position, you add 3000.

2. Since you know that the number will decrease by 738, you can do the second part of forming the equation. Make the expression equal to x - 738, like so --> (x-3)/10 + 3000 = x - 738

Solve the equation.

3. (x-3)/10 + 3000 = x-73

   (x-3)/10 = x - 3738

   x-3 = 10x - 37380

   x = 10x - 37377

   -9x = -37377

   x = 4153

Well, I've got to get back to my RSM homework. I hope this helped!

P.S.- The next time you have a question, email your RSM teacher (I'm assuming you go to RSM) because he/she is much more qualified then me (I'm only 12) and you don't really know if you can trust people giving you answers on Brainly.com.

Answer:

Mean: 7.1, median: 7, mode: 4

Step-by-step explanation:

The mean, also known as the average, is equal to the sum of all the numbers divided by how many numbers there are.

4 + 8 + 11 + 6 + 4 + 5 + 9 + 10 + 10 + 4 = 71

10 numbers

71/10 = 7.1

The median is the number in the middle of the set.

4, 4, 4, 5, 6, 8, 9, 10 ,10 ,11

6 and 8 are in the middle, and the number between 6 and 8 is 7.

The mode of a set of numbers is the most common number. In this case, the number is 4 as it appears 3 times.

Answer:

Step-by-step explanation:

tan α=9÷(21/2)=18/21=6/7

α=arc tan(6/7)≈40.6°

ax - 5 = b

ax = b + 5

a = [tex]\frac{b+5}{x}[/tex]

Answer:

[tex]a=\frac{b+5}{x},x\ne0[/tex]

Step-by-step explanation:

The given equation is:

[tex]ax-5=b[/tex]

We want to solve this equation for a.

We add 5 to both sides of the equation to get:

[tex]ax=b+5[/tex]

We divide both sides by x to get:

[tex]a=\frac{b+5}{x},x\ne0[/tex]

We must restrict the domain because a is not defined for all values of x.