A regular hexagon is inscribed in a circle of radius 1 inch. what is the area of the shaded region?

[tex] {x}^{2} - 7x - 34 = 10 \\ = > {x }^{2} - 7x - 34 - 10 = 0 \\ = > {x}^{2} - 7x - 44 = 0 \\ = > {x}^{2} - 11x + 4x - 44 = 0 \\ = > x(x - 11) + 4(x - 11) = 0 \\ = > (x + 4)(x - 11) = 0 \\ = > x = - 4 \: \: and \: \: 11[/tex]

Answer:

x = -4 and 11

Hope you could understand.

If you have any query, feel free to ask.

Step-by-step explanation:

x² - 7x - 34 = 10

x² - 7x - 44 = 0

factorization by completing the square.

we know that (x + c)² = x² + 2cx + c²

so, what do we have ?

x² done

2cx = -7x

2c = -7

c = -7/2 done

but that means we should have (-7/2)² = 49/4 at the end. and we have -44 instead.

-44 = -176/4 (-44×4/4)

the difference between 49/4 and -176/4 is -225/4.

so, the equation with the completed square is transformed

(x - 7/2)² - 225/4 = 0

or

(x - 7/2)² = 225/4

and now we can solve based on this by creating the square root.

x - 7/2 = 15/2 or -15/2

x1 = 15/2 + 7/2 = 22/2 = 11

x2 = -15/2 + 7/2 = -8/2 = -4

The value of x from the diagram is 29 degrees.

From the given figure, we have the following parameters:

Sin x = opposite/hypotenuse

Sin x = 12/25

Sin x = 0.48

x = arcsin(0.48)

x = 28.685

x = 29 degrees

Hence the value of x from the diagram is 29 degrees.

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Answer:

Step-by-step explanation:

Use the law of cosines:

Here

Apply law of cosines

[tex]\ \ \sf\longmapsto cosB=\dfrac{a^2+b^2+c^2}{2ac}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{22^2+21^2+16^2}{2(22)(16)}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{484+441+256}{704}[/tex]

[tex]\ \ \sf\longmapsto cosB=\dfrac{1181}{704}[/tex]

[tex]\ \ \sf\longmapsto cosB=0.42[/tex]

[tex]\ \ \sf\longmapsto B=cos^{-1}(0.42)[/tex]

[tex]\ \ \sf\longmapsto B=64.8°[/tex]

Answer:

5(x+2)

Step-by-step explanation:

to factor it we need to find a common term(5) and then we take it out(divide) resulting in the answer abover

Answer:

65%

Step-by-step explanation:

if there are 20 squares assume that 20 is equivalent to a 100% as a whole and only 11 squares are shaded therefore if 20 = 100% then

Let x be the percentage

Divide both sides by 20

Equation: 20x/20 = 100/20

----> x = 5

Each Number is equivalent to 5 percent.

therefore 11 = 65%

Answer:

1/15

Step-by-step explanation:

The angle of rotation is 180°.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

Given that the quadrilateral in Quadrant II is the image of the quadrilateral in Quadrant IV after a counterclockwise rotation about the origin.

We have two quadrilaterals here.

Coordinates of original quadrilateral in quadrant 4 is,

(5, -3), (3, -7), (11, -7) and (9, -3).

Coordinates of the image of the quadrilateral in quadrant 2 is,

(-5, 3), (-3, 7), (-11, 7) and (-9, 3).

Transformation of the point (x, y) is in the form (-x, -y).

This is the result of the rotation of 180° counterclockwise about the origin.

Hence the quadrilateral is rotated 180° counterclockwise about the origin.

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Answer:

C

Step-by-step explanation:

Answer:

I'll answer this tomorrow. I'm busy.

Step-by-step explanation:

Answer:

We do this by first finding the greatest common factor of 63 and 24, which is 3. Then, we divide both 63 and 24 by the greatest common factor to get the following simplified fraction: 21/8 Therefore, this equation is true

Hey there!

24.638

2: tens

4: ones

.
6: tenths

3: hundredths

8: thousandths

• When you’re putting it in word form:

twenty-four and six hundred thirty-eight thousandths

Therefore, your answer is: hundredths

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

im sorry too other people

maybe i didn't have that book

on the math

Disclaimer: The shapes were missing. I have provided the required diagram.

The area of the given shape is 46.26cm².

Area of a triangle = (1/2)*base*height.

For a right-angled triangle, the base and height are the two sides making the right angle, that is, the base and the perpendicular.

∴ Area of a right-angled triangle = (1/2)*base*perpendicular.

We know the formula for the area of a circle is πr².

A semi-circle is half of the circle, so the area will also be its half.

∴ Area of a semi-circle = (πr²)/2

According to the Pythagoras theorem, the square of the hypotenuse is the sum of the squares of the other two sides. If we say the hypotenuse is 'c' and the other two sides are 'a' and 'b', then by the theorem:

a² + b² = c².

The given shape consists of one right-angled triangle and a semi-circle. To calculate its area, we first find the area of the right-angled triangle and the semi-circle individually and then add them to calculate the area of the shape.

Area of a right-angled triangle = (1/2)*base*perpendicular,

or, Area of a right-angled triangle = (1/2)*6*6 = 18cm².

We find AC using the Pythagoras theorem,

AC² = AB² + BC² = 6² + 6² = 72.

or, AC = √72 = √(36*2) = 6√2cm

The radius of the semi-circle (r)= (1/2)*diameter = (1/2)*6√2 = 3√2cm.

Area of a semi-circle = (πr²)/2,

or, Area of the semi-circle = (π*(3√2)²)/2 = 18π/2 = 9π.

Now, we can find the total area, by adding the two areas.

Area of the shape = Area of a right-angled triangle + Area of the semi-circle.

or, Area of the shape = 18 + 9π = 18 + 9*3.14 = 18 + 28.26 = 46.26cm²

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Answer:

This is an arithmetic sequence since there is a common difference between each term. In this case, adding 5 5 to the previous term in the sequence gives the next term. In other words, an = a1 +d(n−1) a n = a 1 + d ( n - 1). This is the formula of an arithmetic sequence. Substitute in the values of a1 = 7 a 1 = 7 and d = 5 d = 5.

Step-by-step explanation:

Answer: Check out the diagram below for the filled out table

Explanation:

Use square brackets to include the endpoint. A curved parenthesis is used to exclude the endpoint. This is to set up the interval notation.

So for example, writing [a,b] means [tex]a \le x \le b[/tex]

Another example: writing (a, b] means [tex]a < x \le b[/tex]

The set notation is practically identical to the inequality notation. All that's new is the use of surrounding curly braces, and the x | up front. In my opinion, the third column seems a bit redundant.

Answer:

Thom has $18.00 and Tyrone has $6.00

Step-by-step explanation:

let the amount Tyrone has be x , then Thom has 3x , so

x + 3x = 24

4x = 24 ( divide both sides by 4 )

x = 6

Then Tyrone has $6.00 and Thom = 3 × $6.00 = $18.00

Answer:

5^3 = 125 cm^3

Step-by-step explanation:

The Volume of a cube is expressed as: V = s^3 - where s is the side of the cube and V is volume. Since all sides are 5cm long then the volume of the cube is 125 cm^3 OR it could also be expressed as 125 mL (since 1 cm^3 = 1 mL).

Answer:

that looks hard sucks for you

Answer:

x=2 ; y=-5

Step-by-step explanation:

Answer:

9.6

Step-by-step explanation:

Hope this help : ) . Bye.

Answer:

[tex]m\angle Y =120 \degree [/tex]

[tex]m\angle Z =120 \degree [/tex]

Step-by-step explanation:

In quadrilateral TVZY.

TY = VZ (Given)

Therefore,

Quadrilateral TVZY is an isosceles trapezoid.

TV || YZ and VZ is transversal.

[tex]m\angle Z = 180 \degree - 60 \degree \\ (interior \: angles \: on \: same \: side \: \\ of \: transversal) \\ m\angle Z = 120 \degree \\ \\ m\angle Y = m\angle Z \: \\ (base \: angles \: of \: isosceles \: \\ trapezoid) \\ \implies \: m\angle Y =120 \degree [/tex]

Answer:

4

Step-by-step explanation:

60 minutes can be broken down into 4 quarters of time - 15 minutes

Step-by-step explanation:

An quarter of an hour is 15 mins. 60÷15 =4 so there are 4 quarters in an hour.

Answer:

-4

Step-by-step explanation:

to do this you use y2-y1/x2-x1

so this would be -4-8/1- - 2

-12/3 = -4

Answer:

6 ÷ 6 + 6 + 6 = 13 its a confusing problem

6 + 6 + 6 ÷ 6 = 13

i just used a cal-

Answers:

================================================

Explanation:

x = number of blue monsters

y = number of purple monsters

z = number of yellow polka-dotted monsters

x,y,z are positive whole numbers

Let's count the number of heads. We can say

x+y+z = 51

because there are 51 heads from all the monsters combined, and each monster has 1 head.

Now to the number of arms.

Gracie counted 173 arms in total, so,

5x+4y+2z = 173

Lastly, the number of feet

She counted 175 feet in total, giving us this third equation

4x+2y+3z = 175

---------------

We have this system of three equations and three unknowns.

[tex]\begin{cases}x+y+z = 51\\5x+4y+2z = 173\\4x+2y+3z = 175\end{cases}[/tex]

which honestly seems really tricky to solve.

There are a number of approaches we could take. I'll use substitution.

Let's solve for z in the first equation

[tex]x+y+z = 51\\z = 51-x-y\\[/tex]

which we can then plug into the other equations.

Plug it into the second equation to get

[tex]5x+4y+2z = 173\\5x+4y+2(51-x-y) = 173\\5x+4y+102-2x-2y = 173\\3x+2y+102 = 173\\3x+2y = 173-102\\3x+2y = 71\\[/tex]

Repeat for the third original equation mentioned

[tex]4x+2y+3z = 175\\4x+2y+3(51-x-y) = 175\\4x+2y+153-3x-3y = 175\\x-y+153 = 175\\x-y = 175-153\\x-y = 22\\[/tex]

---------------

We have this reduced system of equations with two unknowns and two equations this time

[tex]\begin{cases}3x+2y = 71\\x-y = 22\end{cases}[/tex]

We'll use the same idea as earlier: Solve for one variable, then plug it into the other equation.

Let's solve for x in this new equation 2

[tex]x-y = 22\\x = 22+y[/tex]

Then plug this into the first equation. Afterward, solve for y.

[tex]3x+2y = 71\\3(22+y)+2y = 71\\66+3y+2y = 71\\66+5y = 71\\5y = 71-66\\5y = 5\\y = 5/5\\y = 1\\[/tex]

Then we'll use this y value to find x

[tex]x = 22+y\\x = 22+1\\x = 23\\[/tex]

Lastly, we'll use those x and y values to find z

[tex]z = 51-x-y\\z = 51-23-1\\z = 27\\[/tex]

---------------

To summarize, we found

This means there are

There's probably a (much) faster way to solve this, but it's not coming to mind at the moment.

The expression which is an equivalent form of the expression (n)-³ is; 1/n³.

According.to the question;

In essence, the variable n is raised to a power of -3.

On this note, using the law of indices regarding negative power; we can conclude that;

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