A child has 12 blocks, of which 6 are black, 4 are red, 1 is white and 1 is blue. All blocks of the same color are identical. If the child puts the blocks in a line, how many arrangements are possible?

[tex]\bold{\huge{\blue{\underline{Solution}}}}[/tex]

Let's start ,

From the figure, we can assume the beam forms as AD, BC, EF , GH and so on.

Therefore,

[tex]\sf{ ABCD , AEFD, AGHD.. so \:on similar\: to \:each \:other }[/tex]

So,

[tex]\sf{ Angle\:BAD = Angle\:EBC = Angle\:GEF}[/tex]

Or,

[tex]\sf{ Angle\: ADC = Angle\:BCF = Angle\: EFH }[/tex]

Now, By using similarity theorem we can determine their sizes, braces and angles that is,

[tex]\sf{\red{ AD/BC = AB/AE = CD/CF = BC/EF}}[/tex]

[tex]\bold{\huge{\blue{\underline{Answers :- }}}}[/tex]

Answer 1 :-

For answering the above questions we use knowledge and practices regarding the questions we can do the activity by making figures of unknown sides by assuming it in the form of x, y.so that we can find the known values.

Answer 2 :-

The best way of solving the above questions is that it is already given in the question that the beam is symmetrical so, here we can use similarity theorem.

Answer 3 :-

It necessary to learn about trapezoid and it's properties because if we don't know the properties and what is trapezoid then we will not be able to answer the given question.

Some properties of trapezoid

Answer 4 :-

Well, The answer is very easy that if we don't know anything regarding the trapezoid then we will not be able to any question based on it and if we have incomplete knowledge about it then we will able to solve it but we always got incorrect answers most probably.

Answer:

B = (3, -5)

D = (0, -1)

C = (3, 5)

Step-by-step explanation:

We want to find the coordinates of B, C, and D given that AB = 5 and BC = 10.

Because AB = 5 and BC = 10, we can find the slope of the line using the slope formula:
[tex]\displaystyle \begin{aligned} m & = \frac{\Delta y}{\Delta x} \\ \\ & = \frac{(10)}{(5)} \\ \\ & = 2 \end{aligned}[/tex]

Point A(-2,-5) is on the line. Hence, the equation of the line is:
[tex]\displaystyle \begin{aligned} y-y_1 &= m(x-x_1) \\ \\& = y-(-5) = 2(x-(-2)) \\ \\ y + 5 & = 2x+4 \\ \\ y & = 2x-1 \end{aligned}[/tex]

Because AB is 5, B is simply A shifted rightwards five units. Hence:

[tex]\displaystyle B = (-2+5, -5) = (3, -5)[/tex]

At Point D, x = 0. Hence:
[tex]\displaystyle y = 2(0) -1 = -1[/tex]

Thus, D is at (0, -1).

B and C are collinear. Hence, the x value of C is 3:

[tex]\displaystyle y = 3(2) - 1 = 5[/tex]

Therefore, C is at (3, 5).

you are wrong, the correct answer is x^2 - 16

Answer:

Step-by-step explanation:

We can let d represent the number of hours that Dylan volunteered. Then Tadeo volunteered for 6d hours, and their total hours were ...

  d +6d = 14

  7d = 14 . . . . . . collect terms

  d = 2 . . . . . . . divide by the coefficient of d

  6d = 6(2) = 12

Tadeo volunteered 12 hours; Dylan volunteered 2 hours.

1/4 is the gradient.

gradient => (2-3)/(4-8)

gradient => -1/(-4)

gradient => 1/4

Answer:

each song would be 67 cents (0.67)

Step-by-step explanation:

9.38/14=0.67

Answer:

12 times

Step-by-step explanation:

There are 3 blue marbles and 9 marbles total. The probability of selecting a blue marble is 3/9, reduced it is 1/3.

Multiply the probability by 36

[tex]\frac{1}{3}[/tex] × [tex]\frac{36}{1}[/tex]

[tex]\frac{36}{3}[/tex]

12

Answer:

629r2

Step-by-step explanation:

Hope this helped!

Using proportions, it is found that 8 more seventh graders are involved in the yearbook.

A proportion is a fraction of a total amount.

Researching the problem on the internet, it is found that 10% of the 6th graders and 18% of the 7th graders are on the yearbook, hence:

0.1 x 280 = 28 6th graders.

0.18 x 200 = 36 7th graders.

36 - 28 = 8

8 more seventh graders are involved in the yearbook.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

See the attached table.

Step-by-step explanation:

Each row, column, and diagonal all add up to six.

[tex]\left[\begin{array}{cccc}9&-5&-4&6\\-2&4&3&1\\2&0&-1&-5\\-3&7&8&-6\end{array}\right][/tex]

Hope that helps!

Answer:

*

Step-by-step explanation:

9  -5  -4   6

-2   4   3    1

2   0  -1   5

-3    7   8  -6

Hey there!

ORIGINAL EQUATION

|5x - 4| = 11

~~~~~~~~~~~~~~~~~~~~
Possible EQUATION #1

5x - 4 = 11

ADD 4 to BOTH SIDES

5x - 4 + 4 = 11 + 4

CANCEL out: -4 + 4 because it gives you 0

KEEP: 11 + 4 because it help solve for the x-value

NEW EQUATION: 5x = 11 + 4

SIMPLIFY IT!

5x = 15

DIVIDE 5 to BOTH SIDES

5x/5 = 15/5

CANCEL out: 5/5 because it gives you 1

KEEP: 15/5 because it help solve for the x-value

NEW EQUATION: x = 15/5

SIMPLIFY IT!

x = 3

~~~~~~~~~~~~~~~~~~~~
Possible EQUATION #2

5x - 4 = -11

ADD 4 to BOTH SIDES

5x - 4 + 4 = -11 + 4

CANCEL out: -4 + 4 because it gives you 0

KEEP. -11 + 4 because it help solve for the x-value

NEW EQUATION: 5x = -11 + 4

SIMPLIFY IT!

5x = -7

DIVIDE 5 to BOTH SIDES

5x/5 = -7/5

CANCEL out: 5/5 because it gives you 1

KEEP: -7/5 because it help solve for the x-value

NEW EQUATION: x = -7/5

SIMPLIFY IT!

x = -7/5

~~~~~~~~~~~~~~~~~~~~~~~

ANSWER

x = 3 or x = -7/5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

The 2 factors of x^2 - 9x + 14 are (x - 7) and (x - 2) because -7 + -2 = -9 and -7 x -2 = 14.

The factors of the quadratic expression  x² – 9x +  14 is (x - 7)(x - 2) option (B) (x - 2) is correct.

Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

It is given that:

The quadratic expression is:

= x² – 9x +  14

Using factor method:

= x² – 7x - 2x +  14

= x(x - 7) - 2(x - 7)

= (x - 7)(x - 2)

The factors of the quadratic expression  x² – 9x +  14 is (x - 7)(x - 2)

Thus, the factors of the quadratic expression  x² – 9x +  14 is (x - 7)(x - 2) option (B) (x - 2) is correct.

Learn more about quadratic function here:

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#SPJ5

Answer:

13 units

Step-by-step explanation:

-25, -12

|-25| - |-12|

13 units

Hope it helps! :)

Answer:

perimeter of triangle=sum of all three sides

Step-by-step explanation:

[tex]( {2y}^{2} - {2x}^{2} ) + ( {y}^{2} - {x}^{2} + 11 ) \\ + ( {5x}^{2} - {2y}^{2} - 12)[/tex]

[tex] {2y}^{2} + {y}^{2} - {2y}^{2} + {5x}^{2} - {x}^{2} - {2x}^{2} + 11 - 12[/tex]

[tex] {y}^{2} + {2x}^{2} - 1[/tex]

Answer:

the answer is 406 L times H times W

Answer:

406 Sorry if wrong!

Step-by-step explanation:

Volume=length x width x height

Answer:

Equation: y = 2x + 25

Step-by-step explanation:

Here x determines the number of year. For the first year,we will see ( 2 * 1 ) = $2 increase. In the second year, ( 2 * 2 ) =$4 increase and like this goes on, whereas the $25 being constant. "y" determines the total cost for each year.

Therefore the equation can be made: y = 2x + 25

Equation in slope intercept form

Answer:

Step-by-step explanation:

There are 3 angles:

There is 1 missing angle:

Subtract 180°:

Missing angle found!

Missing angle:

Answer:

3x - 23 = 2828

Step-by-step explanation:

I'll assume the question is supposed to read "The sum of three times a number (x) and −23 is 2828."

"three times a number (x)" can be written as 3x

"sum of three times a number (x) and −23" means 3x - 23

"is 2828"  = 2828

Put them together:

3x - 23 = 2828

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

Not part of the question

If you want to solve for x:

3x = 2805

x = 935

Answer:

8(5x+3)

Step-by-step explanation:

Answer:

$468.582

Step-by-step explanation:

Hope this helps! Please mark me as brainliest so I can level up :)

Answer:

I believe it is 12 I can't remember fully but I know I've done this before

And if you can right now please give brainliest!

Answer:

6

Step-by-step explanation:

Once again I'm not going to explain in-depth as it is the same method as the other questions I explained!

Step 1:

16/8=2

Step 2:

12/2=6

Therefore the missing AC side should be 6 because the triangles use a factor of 2!

Answer:

Simplify them to the lowest.

What's the GCF( Greatest Common Factor). It's 8. So divide both sides by 8.

24/8 = 3

56/8 = 7

so it's

3 dogs to 7 cats

Step-by-step explanation:

Answer:

3 dogs to 7 cats

Step-by-step explanation:

Find the Greatest Common Factor of the two numbers- if you don't know what that means, it means to find the biggest number that both numbers can be divided by. Basically, it's like simplifying a fraction.

:) Hope this helps!

irrational number: cannot be expressed as a simple fraction

a. [tex]\tt 2-\sqrt{3}:irrational[/tex]

b. [tex]\tt \sqrt{2}\times \sqrt{3}=\sqrt{6}:irrational[/tex]

c. [tex]\tt \sqrt{27}\times \sqrt{3}=\sqrt{81}=9:rational[/tex]

d. [tex]\tt =0\sqrt{7}=0:rational[/tex]

Answer:

In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

Step-by-step explanation:

smarts.

hope this helps :))

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

Explanation

Part (a)

The smaller pyramid up top is the result of slicing at the halfway point.

This leads to the ratio 1:2 when comparing small side to larger side.

Cube both parts of that ratio to end up with 1:8 as the volume ratio.

This means if the smaller pyramid was say 1 cubic foot in volume, then the larger pyramid has a volume of 8 cubic feet.

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

Part (b)

Consider the case that,

The volume of the truncated base is 8-1 = 7 cubic feet.

The ratio of the smaller pyramid to the truncated base is 1:7

Answer:

30 cm

Step-by-step explanation:

30+60=90

30×2=60 so 30cm is the answer.

Step-by-step explanation:

If one price is 2 times the other one, that means it's equal to 2 of those parts. Let's decide our total wire by three to account for the larger part.

[tex]90 \div 3 = 30[/tex]

Now we know the shorter piece is 30 cm. To find the longer piece, multiply the shorter piece by 2.

[tex]30 \times 2 = 60[/tex]

Recap:

Shorter Piece: 30 cm

Longer Piece: 60 cm

That's all there is to it! hope this helps.

The systems of equations are known to be complex. We often use systems of equations in real-world scenario such as when calculating or thinking if one will make more money at one job than the other, here we look into variables such as wages, benefits and commissions, etc.

They  are used to calculate the amount of tax that is charge to people. They also help man to measure and understand the real- world situations and happenings.

The field or career that Equations are known to be widely used are the engineering profession. Chemical engineers, civil engineers, electrical engineers, etc. often uses it in construction of building, lighting a place, etc.

The Systems of equations are often applied in the real world by economists and entrepreneurs to known the time of equality of supply and demand.

Learn more about systems of equations from

https://brainly.com/question/14323743