To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.

Answer:

[tex](6x-5)(x^2+2)[/tex]

Step-by-step explanation:

[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]

Answer:

e)as we know in this current century many modern country is polluting air pollution that may lead to impact our health

Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:

b. 45.

The order of the pieces is not important, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:

[tex]C_{10,2} = \frac{10!}{2!8!} = 45[/tex]

Which means that option b is correct.

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Answer:

35 hrs

Step-by-step explanation:

Hope this helps! Have a great day!!

Answer:

you will only pay one dollar I did this question before, and it was easy Please mark me brainiest please

Step-by-step explanation:

Based on the information shown through the bar graph, a misrepresentation of the data is that: B. the categories along the horizontal axis are missing one of the days.

A bar graph can be defined as a type of chart that is used for the graphical represent of data (information), especially through rectangular bars or vertical columns.

Based on the information shown through the bar graph in the image attached below, we can logically deduce that a misrepresentation of the data is that the categories along the horizontal axis are missing one of the days (Friday).

In conclusion, this bar graph misrepresented the data because Friday is missing from the categories along the horizontal axis.

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Answer:

C

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{RS}{FG}[/tex] = [tex]\frac{ST}{GH}[/tex] ( substitute values )

[tex]\frac{RS}{21}[/tex] = [tex]\frac{4}{12}[/tex] ( cross- multiply )

12 RS = 84 ( divide both sides by 12 )

RS = 7 cm

Answer:

Answer is in pictures

Step-by-step explanation:

36=6x6 90=9x10

256+7=263 104=98+6-2

678=678 81+9=90

Answer:

10

Step-by-step explanation:

no. of students in each group=164/18=9.111111...=10 (nearest 10)

Answer:

8

Step-by-step explanation:

When rounding to the nearest 10:

Therefore:

164 rounded to the nearest 10 = 160

18 rounded to the nearest 10 = 20

To approximate the number of students in each year group, divide the rounded number of students by the rounded number of groups:

⇒ 160 ÷ 20 = 8

Based on the difference in the observed means given, we can infer that energy drink does indeed have an effect on performance.

First find the observed mean difference:

= 11.6 - 10.8

= 0.8 seconds

When the exercise is done only once, we see that on average, those who took the energy drink were faster and so finished earlier than those who didn't.

We can therefore infer that the energy drink has an effect on performance.

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The recorded angle measurements of ∠BAC and ∠CAD could be 110° and 70°, vice versa.

Supplementary angles are a pair of angles that always sum up to 180°. These angles can either;

Adjacent supplementary are angles with a common vertex and arm.

Non- adjacent supplementary angles are angles without a common vertex or arm.

∠BAC and ∠CAD are adjacent supplementary angles because they have a common vertex, A, and a common arm AC.

They add up to 180°.

∠ BAC = 110° and ∠CAD = 70°

Hence, the angles could be 110° and 70°.

Note, this is an overview as the question is not complete.

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Answer: When the two angles are supplementary, m∠BAC = m∠CAD = 90° and m∠DAB = 180°.

Step-by-step explanation: Edmentum Answer

Answer: COSINE

Step-by-step explanation:

I PROMISE

Answer:

See below

Step-by-step explanation:

For a right triangle, with the information given,   tangent function is most appropo

tan 41 = 4/x re-arrange to

      x = 4 / tan(41)             then x = 4.60

Answer:

A.2x^2 + 12x

Step-by-step explanation:

Here,
f(x) = 1/2 x^2 + 3x
Now,
4.f(x) = 4(1/2 x^2 + 3x) = 4/2 x^2 + 12x = 2x^2 + 12x

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

Explanation:

A full circle of radius r = 14 cm has a circumference of...

C = 2pi*r

C = 2*3.14*14

C = 87.92

This is the approximate distance around the circle, aka the perimeter.

Half of this is 87.92/2 = 43.96 which is the curved distance of this semicircle.

The straight line portion is 14+14 = 28 cm long.

The total perimeter of the semicircle shown is 43.96+28 = 71.96 cm

Answer:

the third option

Step-by-step explanation:

because the numbers down there are the coefficients of the top equations

The expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

The points are given as:

(-3, 4) and (6, -2)

The distance between two points is calculated using:

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

This gives

[tex]d = \sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

Hence, the expression that gives the distance is [tex]\sqrt{(-3 - 6)^2 + (4 + 2)^2}[/tex]

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From the calculation below, the actual difference, if Robert had read the numbers correctly, is 168.

Let X represents the number from which subtrahend is subtracted.

Therefore, we can calculate X as follows:

X – 17 = 222

X = 222 + 17 = 239

If the subtrahend is read correctly as 71 and then subtracted from 239, we have:

Actual difference = 239 – 71

Actual difference = 168

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Angle B is the largest angle. , Option D is the correct answer.

A triangle that has two sides equal is called an Isosceles Triangle.

It is given in the question a triangle ABC

With BA =BC

therefore angle A is equal to angle C

In a triangle the angle opposite to the longest side is the biggest angle

Therefore angle B is the largest angle.

Option D is the correct answer.

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The value of the angle P and Q are equal which is equal to 36.86°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From Δ it is obtained that;

[tex]\rm cos P = \frac{B}H} \\\\ \rm cos P = \frac{16}{20} \\\\ P=cos^{-1}\frac{16}{20} \\\\ P= 36.86 ^0[/tex]

[tex]\rm sin \ Q = \frac{12}{20} \\\\ Q= sin^{-1}(0.6) \\\\ Q= 36.86^0[/tex]

sin P= sin Q

Hence, the value of the angle P and Q are equal which is equal to 36.86°.

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Answer:

True

Step-by-step explanation:

Answer:

a= 2x-3 b= 2x+5

ab= (2x-3)(2x+5)

= 2x*2x+ 2x*5- 3*2x- 3*5

= 4x+ 10x- 6x- 15

= 14x- 6x- 15

= 8x -15

x= 2

= 8(2)- 15

= 16-15

= 1

Answer:

Volume

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, [tex]\pi[/tex] = 3.14
V = radius^2 x height x [tex]\pi[/tex]
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3

Surface Area

Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.

if we take 30 to be the 100%, what is 27 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]

Answer:

A

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{120}{360}[/tex]

     = 2π × 8 × [tex]\frac{1}{3}[/tex]

    = 16π × [tex]\frac{1}{3}[/tex] = [tex]\frac{16\pi }{3}[/tex] m

Answer:

Answer:

the sequence begins as {4, 7, ... }

Step-by-step explanation:

a(n) = 3n + 1

The first term is a(1) = 3(1) + 1 = 4, and

the second term is a(s) = 3(2) + 1 = 7

So the sequence begins as {4, 7, ... }

Answer:

Step-by-step explanation:

→ The lines TN and FL intersect each other  

at the point R forming the opposite angles ∠TRF and ∠NRL

then

∠TRF and ∠NRL are verticals angles.

………………………………………………………………………

→ The lines LF and AE intersect each other  

at the point R forming the opposite angles ∠LRE and ∠FRA

then

∠LRE and ∠FRA are verticals angles.