Find the radius of the circle circumscribed around an equilateral triangle, if the radius of the circle inscribed into this triangle is 10 cm.

Answer:

-x² -2x -5 -12/(x-2)

Step-by-step explanation:

The attachment shows the synthetic division. You can find the remainder by evaluating the dividend for x=2:

-2³ -2 -2 = -12 . . . . matches the above answer, not [A] or [C] shown

_____

You can always multiply out your answer to see if it matches the problem.

(-x^2 -2x +3)(x -2) +3 = -x^3 +7x -3 . . . . not the dividend you started with

Answer:

Step-by-step explanation:

It is x=24

Answer:

(C) [tex]x=12[/tex]

Step-by-step explanation:

Given: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36.

To find: The value of x.

Solution: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36, thus using the proportionality theorem, we get

[tex]\frac{ON}{OM}=\frac{PQ}{PM}[/tex]

Substituting the given values, we have

[tex]\frac{7}{7+21}=\frac{x}{x+36}[/tex]

Upon solving the above equation, we get

[tex]\frac{7}{28}=\frac{x}{x+36}[/tex]

[tex]\frac{1}{4}=\frac{x}{x+36}[/tex]

[tex]x+36=4x[/tex]

[tex]x=12[/tex]

Hence, the value of x is 12 and option C is correct.

Answer:

• lateral area: 36√3 square units

• total surface area: (36 +36√3) square units

Step-by-step explanation:

The area of an equilateral triangle of side length s is given by ...

A = (√3)/4·s^2

Your pyramid has four (4) such faces of side length 6 units, so the total (lateral) area of the triangular faces is ...

LA = √3·(6 units)^2 = 36√3 square units

___

Of course the area of the square base is simply the square of its edge length, so is ...

A = (6 units)^2 = 36 square units

That means the total surface area, the lateral area plus the base area, is ...

(36 +36√3) square units

Answer:

1. QM≅RM

2. reflexive property of congruence

3. ΔPQM≅ΔPRM

4. SSS congruence postulate

5. CPCTC

Step-by-step explanation:

1. As M is the midpoint of line QR, dividing it in two equal parts that are QM and MR. Hence

                            QM≅RM

2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case,

                            PM≅PM

3. ΔPQM is congruent to ΔPRM because all the three sides PQ, QM and PM of ΔPQM are congruent to all the three sides PR, RM and PM of ΔPRM repectively.

4. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case, the three sides

PQ≅PR

QM≅RM

PM≅PM

hence ΔPQM ≅ΔPRM

5. CPCTC stands for congruent parts of congruent triangles are congruent. In given case as proven in part 4 that ΔPQM ≅ΔPRM so their corresponding angles will also be congruent. Hence

                           ∠Q≅∠R

!

Answer:

  C  34ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

In this geometry, the height of the tree is the side Opposite the angle of elevation, with the Adjacent side being the one that is the 25 ft distance from Joey to the tree. The angles of elevation and depression are equal.

Hence ...

  tan(53°51') = height/(25 ft)

  height = (25 ft)·tan(53°51') ≈ 34.22 ft ≈ 34 ft.

The answer to the problem is Undefined slope .

Answer:

Step-by-step explanation:

21 inches

Answer:

75 yd

Step-by-step explanation:

Given in the question a right angle triangle.

Base of right angle triangle = x

Height of right angle triangle = 40yd

To find x we will use trigonometry identity

here Ф = 62°

opposite = base

adjacent = height

Plug values in the formula to find x

Tan(62) = x / 40

   x        = (40)(Tan(62))

             = 75.229 yd

             ≈ 75 yd

The value of x is:

              x=75.2 yard.

We are given a right triangle with base 40 yard.

Also, the perpendicular length of the triangle corresponding to angle 62° is: x

Now we find the value of x using the trignometric formula as:

[tex]\tan 62\degree=\dfrac{x}{40}[/tex]

We know that the value of tan 62°=1.88073

Hence, we have:

[tex]1.88073=\dfrac{x}{40}\\\\\\x=40\times 1.88073\\\\\\x=75.2292[/tex]

         Hence, we have: x=75.2 yard

Answer:

(-5,1)

(-2,4)

Step-by-step explanation:

y = x + 6

y = x^2 + 8x + 16

Since both equations are equal to y, we can set them equal to each other

x + 6  = x^2 + 8x + 16

Subtract x from each side

x -x + 6

= x^2 + 8x-x + 16

6 = x^2 +7x +16

Subtract 6 from each side

6-6 = x^2 +7x +16-6

0 = x^2 +7x +10

Factor

What 2 numbers multiply together to give us 10 and add together to give us 7?

5*2 = 10

5+2 =7

0 = (x+5) (x+2)

Using the zero product property

x+5 = 0  x+2 = 0

x = -5   x=-2

Now we need to find the y's that go with the x's

x=-5

y= x+6

y =-5+6

y=-1

(-5,1)

x=-2

y = -2+6

y=4

(-2,4)

For this case we must find the difference of the following expressions:

[tex]0.00067\\2.3 * 10 ^ {- 5}[/tex]

For the second expression we must run the decimal 5 times to the left, because the exponent is negative, that is:

[tex]0.000023[/tex]

We subtract:

[tex]0.00067-0.000023 = 0.000647[/tex]

Represented in scientific notation we have:

[tex]6.47 * 10 ^ {- 4}[/tex]

Answer:

Option A

Answer:

6.47 x 10^(-4)

Step-by-step explanation:

already did it mate

Answer:

10option a 10

11option d √58

12option b 16

13option d 68  

14option a 16

Step-by-step explanation:

To solve all these questions we will use trigonometry identity which says that

TanФ = opp / adj

Tan (b) = 2/11

 b = tan^-1(2/11)

b =  10.30

   ≈ 10

Bc² = 3² + 7²

BC = √3²+7²

BC =√58

sin(30) = opp/ hypo

sin(30) = 8 / pq

pq = 16

tanB = opp / adj

B = tan^-1(17/7)

B = 67.7 ≈ 68°  

sin(7) = opp / hyp

sin(7) = 2/x

x =  2/sin(7)

x = 16 miles

The answer is:

The radius of the circle is 29.21 units.

To solve the problem, we need to remember that the radius of a circle is the distance from its center to any point of the circle.

We can use the following equation to calculate the distance between the center and the given point:

[tex]distance=radius=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]

So, we are given the information:

[tex]Center(12,5)\\Point(-6,-18)[/tex]

Where,

[tex]x_1=12\\y_1=5\\x_2=-6\\y_2=-18[/tex]

Now, substituting and calculating, we have:

[tex]radius=\sqrt{((-6)-(12))^{2}+((-18)-(5)^{2}}\\\\radius=\sqrt{(-18)^{2}+(-23)^{2}}=\sqrt{324+529}=\sqrt{853}=29.21units[/tex]

Hence, we have that the radius of the circle is 29.21 units.

Have a nice day!

Answer:

AB =  29.23

Step-by-step explanation:

Points to remember

Distance formula

Distance between two points (x₁, y₁) and (x₂, y₂) is given by

Distance = √[(x₂- x₁)² + (y₂ - y₁)²]

To find the radius

Center = (12, 5) and point on the circle = (-6, -18)

Radius = √[(x₂- x₁)² + (y₂ - y₁)²]

  =  √[(12 - - 6)² + (5 -  -18)²]

  = √[(12 + 6)² + (5 +18)²]

  =√[18² + 23²] = √[324 +529 ]  =  29.23

Answer:

  2∠180° . . . or . . . 2(cos(180°) +i·sin(180°))

Step-by-step explanation:

-2 is 2 units along the negative real axis. The direction of that from the origin is at an angle of 180° measured from the positive real axis. So, the magnitude is 2 units and the angle is 180°.

If [tex]z=1-i[/tex], then [tex]|z|=\sqrt{1^2+(-1)^2}=\sqrt2[/tex] and [tex]\arg z=-\dfrac\pi4[/tex] because [tex]z[/tex] lies in the fourth quadrant.

By DeMoivre's theorem,

[tex]z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i[/tex]

so the answer is B.

Answer:

B

Step-by-step explanation:

edge 2020

By the recursive definition,

[tex]a_3=2a_2-a_1=2\cdot9-4=14[/tex]

[tex]a_4=2a_3-a_2=2\cdot14-9=19[/tex]

[tex]a_5=2a_4-a_3=2\cdot19-14=24[/tex]

[tex]a_6=2a_5-a_4=2\cdot24-19=29[/tex]

Answer:

  a3=14, a4=19, a5=24

Step-by-step explanation:

Put the numbers where the symbols are and do the arithmetic.

  a3 = 2(a2) -(a1) = 2(9) -4 = 14

  a4 = 2(a3) -(a2) = 2(14) -9 = 19

  a5 = 2(a4) -(a3) = 2(19) -14 = 24

  a6 = 2(a5) -(a4) = 2(24) -19 = 29

_____

With a little work, you can show that this is an arithmetic sequence with a common difference of a2-a1 = 5.

Let d = a[2] -a[1]

Of course, the second term is that difference added to the first:

  a[2] = a[1] + (a[2] -a[1]) = a[1] +d

The third term is ...

  a[3] = 2a[2] -a[1] = a[2] +(a[2] -a[1]) = a[2] +d

  a[4] = 2a[3] -a[2] = a[3] +(a[3] -a[2]) = a[3] -(a[2] +d) -a[2] = a[3] +d

Answer:

3/b^4

Step-by-step explanation:

b^0 = 1

3b^(-4) / b^0 = 3b^(-4) / 1 = 3b^-4

Since you are instructed to write only positive exponents, the answer is 3/b^4

Answer:

  (7+Z)²

Step-by-step explanation:

A less ambiguous way to describe the quantity might be "the square of the quantity seven plus Z".

As it is, we rely on the presence of the comma to tell us that the quantity to be squared is (7+Z). If the comma were not present, we would assume you want to add 7 to the square of Z: 7+Z².

  the quantity 7 plus Z: (7+Z)

  that quantity squared: (7+Z)²

Answer:

see the attachment for a graph

Step-by-step explanation:

When asked to graph an equation like this, you can first recognize that the equation you are given is in "slope-intercept" form:

y = mx + b . . . . . m is the slope; b is the y-intercept.

This immediately tells you one point on the graph: the y-intercept at (0, -4).

Another point on the graph can be found by making use of the slope to choose a point that is different from the y-intercept by the rise and run indicated by the slope.

Here, the slope is rise/run = -5/6, which means the line "rises" -5 units for each "run" of 6 units. Alternatively, it rises 5 units for a run of -6 units. That is the second point we have plotted on the graph below. Subtracting 6 from x=0 gives x=-6; adding 5 to y=-4 gives y=1, so our second point is (-6, 1).

[tex]17 \times 17 = 289 [/tex]

then you want to do 3.14 x 17×17 = .... then add them both and you got the area

Answer:

Step-by-step explanation:

9x0.1 would 0.9 because 9x1 = 9

9

x

0.1

_______

0.9

Answer:

Helloooo~ The answer is 0.9 :)

Step-by-step explanation:

You're multiplying 9 by 0.1

9 times 0.1 is 0.9.

D: Dead plants fall in swamp...

This is the answer because the plants must begin to accumulate in a location, then continue to build tall enough for the rest of the process to continue.

A is incorrect because the plants must die before piling up

B is incorrect because the plants must die and accumulate before compressing

C is incorrect because plants must die before being buried.

Coal is formed in a multi-step process over millions of years. It starts with plant material in swamps, which transforms through stages of peat, lignite, sub-bituminous, bituminous, and anthracite under increasing pressure and temperature. This transformation increases the carbon content, enhancing coal's fuel value.

Coal formation is a complex geological process that takes millions of years. The correct order of steps in the formation of coal is as follows:

Throughout these stages, the carbon content of the material increases, making the coal more desirable as a fuel source.

Answer:

A. (3, -5)

Step-by-step explanation:

Use the first equation to find an expression for x. (Add 3y.)

x = 18 + 3y

Now, use this where x is in the second equation.

2(18 +3y) +19 = -5y

55 +6y = -5y . . . . . . . eliminate parentheses

55 +11y = 0 . . . . . . . . .add 5y

5 +y = 0 . . . . . . . . . . .divide by the coefficient of y

y = -5 . . . . . . . . . . . . . add -5; corresponds to answer choice A

Using the expression for x, we can find its value:

x = 18 +3(-5) = 3

The solution is (x, y) = (3, -5). . . . . . matches choice A

Answer:

(3, –5)

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

-7 - 18 = -25

|-25| = 25

Answer:

25

Step-by-step explanation:

|x+y| when x=-7 and y= -18 is |-7 - 18| = 25

Answer:

degree

Step-by-step explanation:

The degree is the unit of measurement for angles; it is equal to 1/360th of a complete revolution.

Answer:

-13

Step-by-step explanation:

The absolute value of -13 is 13 so if you put a negative sign in front of it, it will make the 13 negative.

Answer:

-13

Step-by-step explanation:

it's absolute value, the absolute value of -13 is 13.  Then you have to use the other negative.

:))

Answer:

x = ±5

Step-by-step explanation:

x^2-25=0

Add 25 to each side

x^2-25+25=0+25

x^2 = 25

Take the square root of each side

sqrt(x^2) = sqrt(25)

x = ±5

Answer:

167.47 cubic feet

Step-by-step explanation:

Volume of the Cylinder

3.14×2^2×12=150.72

Volume of the Cone

3.14×2^2×4=50.24

50.24÷3=16.75

Total Volume

16.75+150.72=167.47

Volume is a three-dimensional scalar quantity. The total volume of the figure will be 167.552 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the figure is the sum of the volume of the cone and the volume of the cylinder.

The volume of the cone = (1/3)πr²h = (1/3)×π×2²×4 = 5.334π ft³

The volume of the cylinder = πr²h = π × 2² × 12 = 48π ft³

The total volume of the figure can be written as,

Total Volume = Volume of cone + Volume of cylinder

                       = 5.33π ft³ + 48π ft³

                       = 167.552 ft³

Hence, the total volume of the figure will be 167.552 ft³.

Learn more about Volume:

https://brainly.com/question/13338592

#SPJ2

Answer:

  see attached

Step-by-step explanation:

The function that tells you the number of dollars you spend on a given number of pounds creates graphs with the coordinates (pounds, dollars).

If you want 1 pound to correspond to G dollars, then a point on the graph will be ...

  (1, G)

Answer:

(1,g)

Step-by-step explanation:

hope this helps

Answer:

C.

Step-by-step explanation:

If we plot the vertex and the focus, since the parabola wraps itself around the focus, we can see that this is parabola that opens up to the right.  The distance between the vertex and the focus is 2 units.  The equation for this type of parabola is:

[tex]4p(x-h)=(y-k)^2[/tex]

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus.  We already know all of that info so we can jump right to filling in the equation:

[tex]4(2)(x+4)=(y+4)^2[/tex] which of course simplifies to your answer:

[tex]8(x+4)=(y+4)^2[/tex]

Answer:

C, the two rounded rectangles

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In A and B, you can see the figure has been transformed, while in C, it's the same shape and size, just a different color.

Answer:

C, the two rounded rectangles

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In A and B, you can see the figure has been transformed, while in C, it's the same shape and size, just a different color.

Read more on Brainly.com - https://brainly.com/question/12600222#readmore