If the measure of each interior angle of a polygon is 150°, how many sides does it have?

[tex]\bf{1) \ x^4-61x^2+900=0 }[/tex]

Applying the factorization method, for example:

      [tex]\bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}[/tex]

               [tex]\bf{\\ &=(x+6)(x-6)(x+5)(x-5); }[/tex]

              [tex]\bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5 }[/tex]

[tex]\bf{2) \ x^4-25x^2+144=0 }[/tex]

Applying the factorization method:

          [tex]\bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }[/tex]

             [tex]\bf{ =(x-4)(x+4)(x-3)(x+3); }[/tex]

            [tex]\bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3 }[/tex]

[tex]2ay + 3az = 2dx + 3dy[/tex]

[tex]2ay - 3dy = 2dx - 3az[/tex]

[tex]y(2a - 3d) = 2dx - 3az[/tex]

[tex]y = \frac{2dx - 3az}{2a - 3d} \\ [/tex]

Answer:

The angles are 24.6° and 155.4°

Step-by-step explanation:

Supplementary angles add up to 180°

Let the measure of the supplementary angle = x

So, the angle is 130.8 more than 'x'

     The angle = x + 130.8

The angles are supplementary.

x + (x + 130.8) = 180

x + x + 130.8 = 180

  2x + 130.8  = 180

                2x = 180 - 130.8

                 2x = 49.2

                   x = 49.2/2

                   x = 24.6

x + 130.8 = 24.6 + 130.8

                =  155.4

The angles are 24.6° and 155.4°

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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

An angle measures 130.8º more than its supplementary angle. What is the measure of each angle?

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

Supplementary angles add up to 180º.

In order to find the unknown angles, we should first let the angle be x.

Set up an equation:-

(remember, there are 2 angles, x and x+130.8):-

x+x+130.8=180

Add the x's:-

2x+130.8=180

Subtract 130.8 from both sides:-

2x=49.2

Divide by 2 on both sides:-

x=24.6º

To find the other angle, add 130.8º:-

24.6+130.8=155.4º

Second angle=155.4º

Now, we need to make sure our solution is correct.

We can easily check it by adding both angles together and seeing whether or not we end up with 180:-

155.4+24.6=180

180=180

Since the left-hand side equals the right-hand side, our solution is indeed correct.

The angles are 24.6º and 155.4º

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Since the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.

The equation which have a degree of one will be called as the linear equation the graph of the equation will be always a straight line.

Here we have the equation:

x-5=-5+x

or

x-5=x-5

Here we can see that the ratios are same:

[tex]\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}\\\\\\\\\dfrac{1}{-5}=\dfrac{1}{-5}[/tex]

So the equations will be coincident to each other or line one will coincide with line 2. Hence the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.

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Answer:

Radiation is the emission and propagation of energy in the form of waves, rays or particles

Step-by-step explanation:

If the discount is 75% so the new price of the product will be 0.25P.

Discount is the reduced amount on the MRP of any product. So we will give the less amount then the MRP of the product.

Here the discount on P is given as 75% so the price of the product now becomes P-0.75P;

The expression will be calculated as:

P-0.75P=0.25P

Hence If the discount is 75% so the new price of the product will be 0.25P.

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Step-by-step explanation:

hope u understand......

Answer:

1 over 4,989,600 That's the answer yw btw

The rectangle maximum area will be A=9 square units with the length=3 and the width=3.

Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.

It is given that the perimeter of rectangle is P=12

So from the formula of perimeter of rectangle

2(L+W)=12

L+W=6

L=6-W

Now the area of rectangle will be

A=LxW

A=(6-W)W

Now for maximum area we will find the derivative and equate to zero.

[tex]A=(6W-W^2})[/tex]

[tex]A'=6-2W=0[/tex]

[tex]W=3[/tex]

[tex]L=6-W=6-3=3[/tex]

So the area will be

[tex]A=3\times 3=9 \ square \ units[/tex]

Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.

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Answer: 24

Step-by-step explanation:

¼ of Andy's sweets = 5 + 1 with Dan

¼ of Andy's sweet is 6

Andy has 6×4 sweet

Answer:

0.6063

Step-by-step explanation:

Just substitute in the binomial probability formula from 4 successes until 6 successes.

Answer:

it is 65 byeeeeeeeeeeeeeeeeee

Answer:

well total surface area of this prism is sum of area all sides of prism.

therefore 170 + 170 + 160 + 120 + 120 = 740m²

Therefore total surface area is 740m² i didn't give explanation since you said you don't need it.

By : Modern Einstein

[tex]~~~~~x(x+1)(x-2)^2 =0\\\\\implies x = 0~~ \text{or}~~ x +1 = 0~~ \text{or}~~ (x-2)^2 = 0\\\\\implies x = 0, ~ x = -1 , ~x=2\\\\\text{Hence the roots are}~0,-1 ,~2[/tex]

The given function 9.1% of 80 is the closest to the number which is approximate 7.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We have to find that 9.1% of 80 is the closest to which number.

[tex]\dfrac{9.1}{100} \times 80\\\\= 0.91 \times 8\\\\\= 7.28[/tex]

Hence, The given function 9.1% of 80 is the closest to the number which is approximate 7.

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Answer:

48 m^3

Step-by-step explanation:

along the length = 8 cubes = 8 m

breadth = 3 cubes = 3 m

height = 2 cubes = 2 m

volume = 48 m^3

Answer:

2

Step-by-step explanation:

We dont know how many spinner slots there are so I assume 8.

to get greater than 4 you need the cube which has 6 sides. Only 5 and 6 are > 4. So 2.

Sorry if this is incorrect...

Answer:

sin²x

Step-by-step explanation:

[tex]\frac{\tan \left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}[/tex]

[tex]=\frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)+\sin ^2\left(x\right)}[/tex]

Rewrite using trigonometric identities

[tex]=\sin ^2\left(x\right)[/tex]

Answer:

x=1/4

Step-by-step explanation:

4x - 1 = 0 /+1

4x = 1 /:4

x= 1/4

Answer:

3 [tex](\frac{5}{6}) ^{4}[/tex]

Step-by-step explanation:

each post is [tex]\frac{5}{6}[/tex] the height of the previous post

there are 4 poles between the tallest 3 ft and the smallest

this involves multiply the heights of previous poles by [tex]\frac{5}{6}[/tex] , 4 times

shortest pole = 3 × [tex](\frac{5}{6}) ^{4}[/tex]

Answer:

(A) Linear positive association

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

60.

Step-by-step explanation:

The second digit is 6, so we round up the first digit and add training zero. There is no need to add the '00' after the decimal point.

The remainder of the given expression will be 66.

Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic.

The given polynomlal x⁴+3x³-6x²-12x-8 will be divided by x-3 so we need to find the remainder:-

x-3) x⁴+3x³-6x²-12x-8 ( x³-6x²+12x+24

      x²-3x³

    _______________

            6x³-6x²-12x-8

            6x³-18x²

________________________

                   12x²-12x-8

                   -12x²-36x

  _____________________

                            24x-8

                            24x-72

_______________________

                                    66

Hence the remainder of the given expression will be 66.

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Answer:

{y| y is a real number}

Step-by-step explanation:

The range is all the y's that an equation can produce or all the y's on a graph of the function.

This graph has every and any real y (because it keeps going forever, even off the screen or paper) It's a little hard to see, bc we just see it going left and right mostly, but it is also slightly going up (to the left) and down (to the right)

Answer:

A. x-intercepts: prices at with profit is zero

    maximum: price at which profit is a maximum

    increasing: (-∞, 3); decreasing: (3, ∞) — profit increases with increasing pen price below $3, decreases with increasing pen price above $3

 B. -26 2/3; loss of profit for each dollar increase in pen price

Step-by-step explanation:

Part A:

The definition of the function tells you what points on the graph represent. The x-intercept at x=0 tells you the company's profit will be zero when the price of pens sold by the company is zero.

The x-intercept at x=6 tells you the company's profit will be zero when the price of pens sold is $6.

The maximum value of 120 at x=3 tells you the company's profit will be $120 when the price of pens sold is $3.

The graph goes "uphill" for x < 3, so the function is increasing for x < 3. The function goes "downhill", so is decreasing, for x > 3. This tells you profit increases with pen price when the price is below $3, and decreases with pen price above $3.

__

Part B:

The equation of the function describing the graph is ...

 f(x) = -120/9x(x -6)

so, at x=5, the value is ...

 f(5) = -120/9(5)(-1) = 600/9 = 66 2/3

Then the average rate of change from x=3 to x=5 is ...

 m = (f(5) -f(3))/(5 -3) = (66 2/3 -120)/2 = (-53 1/3)/2 = -26 2/3

This represents the average change in profit for each dollar increase in the price at which pens are sold.

Answer:

∠B=19°

Step-by-step explanation:

At the endpoints of a diameter, angle c meets the circle. It intercepts a 180-degree arc.We know that the measure of C is 90 degrees because the measure of an inscribed angle is half the measure of its intercepted arc. Angles of triangle of ABC must add up to 180.

m∠A+m∠B+m∠C= 180°

71°+m∠B+90°=180°

m∠B+161°=180°

m∠B=19°

Answer:

a)2975

b)3450

Step-by-step explanation:

Answer:

Perimeter: 26.43 m

Area: 27.99 sq m

Step-by-step explanation:

To find the perimeter we just add all the sides, 11.1+9.33+6 = 26.43

To find the area of a triangle, we use the formula we do (bh)/2

9.33 * 6 = 55.98

55.98 / 2 = 27.99

Hope this helped you! I would appreciate a Brainliest if this helped you a lot! Thank you, and have a good day!

Answer:

We first need to determine the perimeter of the triangle which is done by adding up all of the sides.  When combining [tex]11.1\ m[/tex], [tex]9.33\ m[/tex], and [tex]6\ m[/tex] we get a final answer of [tex]26.43\ m[/tex] as the perimeter of the triangle.

The second part that we need to determine is the area of the triangle which is done by using [tex]A=\frac{1}{2}*b*h[/tex].  In this example our base is [tex]6\ m[/tex] and our height is [tex]9.33\ m[/tex].  So when inputting those values into our area equation, we get [tex]A=27.99\ m^2[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

Step-by-step explanation:

Keep going I believe in you!