How do you evaluate a geometric series?

A dodecagon is a twelve-sided polygon that's equally spaced around a circle and with all sides, the same length.

Answer:

Step-by-step explanation:

Answer:

They are similar because triangle AMY has sides double the size of CED. If you divide AMY's triangle sides by 2, you will have a triangle that is the exact size of CED. :)

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Answer:

The triangles are similar

Step-by-step explanation:

To tell whether the triangles are similar or not we can compare their side lengths

if the triangle are similar then their side lengths' will be proportional:

MY/CD = AY/ED

10/5 = 8/4 cross multiply expressions

40 = 40 as we can see from this result, the side lengths are proportional so we can say these triangles are similar

Answer:

Exact area = 272 - 28.125pi  square cm

Approximate area = 183.6875 square cm  (when using pi = 3.14)

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

Explanation:

The trapezium has the parallel sides of 12+13 = 25 cm and 15 cm. Those vertical sides average to (25+15)/2 = 40/2 = 20. Multiply this with the height of the trapezium to get 20*24 = 480 sq cm as the area.

You could also use this trapezium area formula

A = h*(b1+b2)/2

A = 24*(25+15)/2

A = 480

Whichever method you use, the trapezium has an area of exactly 480 square cm.

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

The paralellogram has base of 13 and height of 16, so its area is base*height = 13*16 = 208 sq cm

The semicircle has area of 0.5*pi*r^2 = 0.5*pi*7.5^2 = 28.125pi square cm. Notice that I used r = 7.5 which is half of the diameter 15 cm.

The parallelogram and semicircle areas add to 208+28.125pi

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

Subtract this from the area of the trapezium to wrap things up

480 - (208+28.125pi)

480 - 208 - 28.125pi

272 - 28.125pi

This is the exact area of the blue shaded region in terms of pi

To get the approximate area, replace pi with something like 3.14 and compute.

So 272 - 28.125pi = 272 - 28.125(3.14) =  183.6875 is the approximate area when pi = 3.14

Use more decimal digits of pi to get a more accurate value.

Answer:

107⁰

Step-by-step explanation:

The m<g =107⁰

I hope it helped you

The measure of the angle ∠PGL will be equal to 107 degrees.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔPGL and ΔNHE,

PG  = NH (given)

GL = HE (given)

If the angle ∠PGL and ∠NHE become congruent, the triangle ΔPGL and ΔNHE will be congruent to each other.

∠PGL = ∠NHE

∠PGL = 107°

The measure of the angle ∠PGL will be equal to 107 degrees.

More about the triangle link is given below.

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Given,

[tex] \: [/tex]

To Find,

[tex] \: [/tex]

Solution :

First of all, we'll find the circumference of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\[/tex]

Now, we'll substitute the required values in the formula :

[tex]\\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 3.14 \times 3.5}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 3.14 \times 7}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \pmb{ \: Circumference_{(circle)} = 21.98}}}} \: \: \\ \\[/tex]

Therefore,

[tex] \: [/tex]

Now, we'll find the area of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Area_{(circle)} = \pi r^2}}}}}} \: \: \bigstar \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times (3.5)}^{2} }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times 3.5 \times 3.5 }}}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times 12 .25 }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{\pmb { \sf{ \: \: Area_{(circle)} = 38.465 }}}}}} \: \: \\ \\[/tex]

Therefore,

The hypotenuse is the longer of the 3 sides:

answer: b.26

Answer:

[tex]\huge\boxed{\bf\: b. \: 26 \rightarrow hypotenuse }[/tex]

Step-by-step explanation:

Consider a right angled triangle with sides as 10, 26 & 24 units.

Here, we need to find the hypotenuse of the triangle.

The hyptenuse is the side which is opposite to the right angle (90°) & is also the longest side of the triangle.

Then, among the given values, we can clearly say that 26 > 10, 24.

Therefore, [tex]\boxed{\bf\: 26 \: units }[/tex] is the hypotenuse  of the triangle with side lengths as 10, 26, 24 units.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

this is a transformation of the function meaning f(x) is our base f(x+2) is a transformation of f(x) by 2

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

given f(x) then to find f(x + 2)

substitute x = x + 2 into f(x)

Answer:

A. 56 in3

Step-by-step explanation:

Formula for Volume; LWH

L * W * H = 4* 4 * 2

16 * 2 = 32(3)

(second half of the container)

LWH = 3 * 4 * 2

12 * 2 = 24(3)

32 + 24 = 56(3)

Break into two cuboids

In cuboid

Hence

#1

Volume:-

#2

Volume:-

Total:

Answer:

£177.92

Step-by-step explanation:

To increase something by 28% would be to multiply the original value by 1.28:

So to increase £139 by 28%, we do:

£139 × 1.28 = £177.92

So this is our final answer

Answer:

a) 240 grams

b) 360 grams

c) 2 packs

Step-by-step explanation:

a) 1 biscuit = 4 grams of flour

60 biscuits = 240 grams of flour

Conclusion, 240 grams of flour is needed for 60 biscuits.

b) 240×3÷2 = 360 grams of butter

c) 360÷250

= 1.44

≈ 2 packs

Hope this helps =)

Answer:graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Step-by-step explanation:

y

=

−

19

9

(

x

+

3

)

2

+

5

Explanation:

If an equation representing a parabola is in vertex form such as

y

=

a

(

x

−

k

)

2

+

h

then its vertex will be at

(

k

,

h

)

. Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form

y

=

a

(

x

+

3

)

2

+

5

If this parabola also passes through the point

(

0

,

−

14

)

then we can determine the

a

parameter.

−

14

=

a

(

0

+

3

)

2

+

5

9

a

=

−

19

a

=

−

19

9

So our equation in vertex form is

y

=

−

19

9

(

x

+

3

)

2

+

5

graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Answer:

c. 11

Step-by-step explanation:

Bottom row: 6 cubes

middle row: 4 cubes

top row: 1 cube

11 cubes total.

Answer:

[tex]=12\sqrt{15} -40\sqrt{5}\\[/tex]

Step-by-step explanation:

[tex](2\sqrt{10} )(3\sqrt{6} -5\sqrt{8} )=(2\sqrt{10} )(3\sqrt{6} )-(2\sqrt{10} )(5\sqrt{8} )[/tex]

[tex]=6\sqrt{60} -10\sqrt{80}[/tex]

[tex]=6\sqrt{4(15)} -10\sqrt{16(5)}[/tex]

[tex]=6(2)\sqrt{15} -10(4)\sqrt{5}[/tex]

[tex]=12\sqrt{15} -40\sqrt{5}[/tex]

Hope this helps

Answer: The unit rate is 1/3

Step-by-step explanation:

The slope of the line, which also represents the unit rate, is 1/3.

Answer:

No

Step-by-step explanation:

x + 1 is not a factor of the polynomial because the remainder is 2 and not 0

Answer:

D

Step-by-step explanation:

[tex]\frac{x+2}{3}[/tex] = [tex]\frac{2x-4}{2}[/tex] ( cross- multiply )

3(2x - 4) = 2(x + 2) ← distribute parenthesis on both sides

6x - 12 = 2x + 4 ( subtract 2x from both sides )

4x - 12 = 4 ( add 12 to both sides )

4x = 16 ( divide both sides by 4 )

x = 4

[tex] \longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

In this question we have to find the value of x .

[tex]\longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

So , by cross multiplying :

[tex] \longrightarrow \: 2(x + 2) = 3(2x - 4)[/tex]

Now , calculation left hand side as well as right hand side :

[tex]\longrightarrow \: 2x + 4 = 6x - 12[/tex]

Now , transposing 6x to left hand side and 4 to right hand side :

[tex]\longrightarrow \: 2x - 6x = - 12 - 4[/tex]

Now , solving left hand side and right hand side :

[tex]\longrightarrow \: - 4x = - 16[/tex]

As negative sign is present on both the side , so it will cancel out :

[tex]\longrightarrow \: \cancel - 4x = \cancel- 16[/tex]

Now we have :

[tex]\longrightarrow \: 4x = 16[/tex]

Now we are transposing 4 to right side and it will change into division from multiplication :

[tex]\longrightarrow \: x = \cancel \frac{16}{4} [/tex]

So we get :

[tex]\longrightarrow \: \green{ \boxed{ \bold x = 4}}[/tex]

We are verifying our answer by putting value of x in given question :

[tex]\longrightarrow \frac{4 + 2}{3} = \frac{2(4) - 4}{2} \: [/tex]

Solving ,

[tex]\longrightarrow \: \frac{6}{3} = \frac{8 - 4}{2} [/tex]

Now subtracting 8 and 4 :

[tex]\longrightarrow \: \frac{6}{3} = \frac{4}{2} [/tex]

Now , dividing 6 by 3 and 4 by 2 :

[tex]\longrightarrow \cancel{\frac{6}{3} } = \cancel{\frac{4}{2} }[/tex]

We get :

[tex]\longrightarrow \: \bold{2 = 2}[/tex]

That means ,

[tex]\longrightarrow L.H.S = R.H.S[/tex]

Answer:

36.

Step-by-step explanation:

100 - 40 = 60%  of heads.

60% = 0.60.

60 * 0.60 = 36.

The feasible region which is shown is the graph of is of the solution of  inequalities y<4,x>=0,x<4 and y>=1. which is option C.

An inequality is like an equation but is expressed in greater than ,less than, greater than or equal to, less than or equal to signs. It is equated to find the range of variables.

The given graph has three lines showing different inequality.

One which is parallel to x axis and present at y=4 is doted and because the region from this line is towards origin so the sign between y and 4 is of < sign and we don't use equal to sign as it is doted. The inequality will be y<4

Other line is also parallel to x axis at y=1 but it is not doted and the region shaded is away from the line and origin so we use > than sign and equal to sign. The inequality will be y>-1.

The solution lies in first quadrant so x>=0.

One line is parallel to y-axis at x=4 and because the solution is towards origin so we will use <=0 sign as it is not dotted also.

Hence the inequalities are y<4,x>=0<x<4, y>1.

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Answer:

Exact Form:

49/4

Decimal Form:

12.25

Mixed Number Form:

12 1/4

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

√x-2=√x-10

x-4√x+4=x-10

-4√x+4=-10

-4√x=-10-4

-4√x=-14

√x=7

-

2

x= 49

---

44

subtraction/algebraic subtraction

What you have looks right, the reason for step 7 should just be algebraic subtraction since there is a DG on both sides that can be simplified out of the equation

I’m not sure what exact answer your question will allow, but it’ll be something along the lines of subtraction

Answer:

C. 12 feet

Step-by-step explanation:

If a rectangle measures 1 foot by 5 feet, that means that one side is 1 foot and one side is 5 feet. Since a rectangle has two sets of parallel sides, the other sides of the rectangle will also measure 1 foot by 5 feet.

Adding all of the side lengths will give us the perimeter.

1 + 5 + 1 + 5 = 12

hope this helps :)

Answer:

125

Step-by-step explanation:

Assuming the lines are parallel :

n = 180-125

= 55

x = n

x = 55

z = 180-55

= 125

Answer:

Option A

Step-by-step explanation:

To simplify this fraction:

We subtract the powers:

[tex]\frac{6^{3} }{6^{6} } = 6^{3-6}[/tex]

[tex]6^{-3}[/tex] = [tex]\frac{1}{6^{3} }[/tex] = 1/216

These answers I wrote in the last line are options B,C and D.

Therefore Option A is not equivalent.

Answer:

acute

Step-by-step explanation:

Check using the Pythagorean Theorem:

A^2 + B^2 ≟ C^2

9^2 + 115 ≟ 11^2

196 > 121,

so this triangle is acute because the sum of each leg squared is longer than the length of the hypotenuse squared.

[tex]\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\\ [1-sin^2(x)]csc(x)~~ = ~~cos(x)cot(x) \\\\[-0.35em] ~\dotfill\\\\\ [1-sin^2(x)]csc(x)\implies cos^2(x)csc(x)\implies cos^2(x)\cdot \cfrac{1}{sin(x)} \\\\\\ cos(x)\cdot \cfrac{cos(x)}{sin(x)}\implies cos(x)cot(x)[/tex]

The function h(t)=6+3ln(t+1) is a logarithmic function

The height of the tree will exceed 18 feet after 53.6 years

The function is given as:

h(t)=6+3ln(t+1)

When the height is 18 feet, we have:

6+3ln(t+1) = 18

Subtract 6 from both sides

3ln(t+1) = 12

Divide both sides by 3

ln(t+1) = 4

Take the exponent of both sides

t + 1 = e^4

Evaluate the exponent

t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

Read more about logarithmic functions at:

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