Which number forms a Pythagorean triple with 8 and 10? Is it 6 or 15?

Heather, Eric, and Chang sent a total of 116 text messages over their cell phones during the weekend. Chang sent 3 times as many

notka56 [123]

Answer:

Step-by-step explanation:

Declaration

Let Heather's number of messages = x

Let Eric's number of messages = x + 9

Let Chang's number of messages = 3(x +9)

Equation

x + x + 9 + 3(x + 9) = 116

Solution

x + x + 9 + 3(x + 9) = 116 Remove the brackets

x + x + 9 + 3x + 27 = 116 Combine like terms

x + x + 3x + 9 + 27 = 116

5x + 36 = 116 Subtract 36 from both sides

5x + 36 - 36 = 116 - 36 Combine

5x = 80 Divide both sides by 5

5x/5 = 80/5

x = 16

Answer

Heather = 16

Eric = 16 + 9 = 25

Chang = 3*25 = 75

5 0

1 year ago

A playground is shaped like a quaderaleteral with all sides 27 feet long, with two angles measures of 65 degrees and two angles

Ksivusya [100]

Answer:

Rhombus

Step-by-step explanation:

Shape of a playground is a quadrilateral

It is given that all sides of a quadrilateral are= 27 feet

Since all the sides of a quadrilateral are equal that it can be either a rhombus or it can be a square

Two angle are 65° each

And other two angers are 115° each

65°+ 115°= 180°

It forms a co-interior angle

Hence the quadrilateral is a parallelogram

Since all the four sides of parallelogram are equal, than the given figure must be rhombus

Hence, geomatric shape best describes the shape of the playground is Rhombus.

7 0

3 years ago

What is the binomial expansion of (x 2y)7? 2x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5 14xy6 2y7 x7 14x6y 42x5y2 70x4y3 70x3y4 42x2y5

AysviL [449]

You can take x = a, 2y = b and then can apply the binomial theorem.

The expansion of given expression is given by:

Option D: $x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$ is

<h3>What is binomial theorem?</h3>

It provides algebraic expansion of exponentiated(integer) binomial.

According to binomial theorem,

$(a+b)^n = \sum_{i=0}^n ^nC_i a^ib^{n-i}$

<h3>How to use binomial theorem for given expression?</h3>

Taking a = x, and b =2y, we have n = 7, thus:

$(x+2y)^7 = \: ^7C_0x^0(2y)^7 + \: ^7C_1x^1(2y)^6 + \: ^7C_2x^2(2y)^5 + \: ^7C_3x^3(2y)^4 + \:^7C_4x^4(2y)^3 + \:^7C_5x^5(2y)^2 + \:^7C_6x^6y^1 + \: ^7C_0x^7y^0\\\\
(x+2y)^7 = 128y^7 + 448xy^6 + 672x^2y^5 + 560x^3y^4 + 280x^4y^3 + 84x^5y^2 + 14x^6y + x^7\\\\
(x+2y)^7 = x^7 + 14x^6y + 84x^5y^2 + 280x^4y^3 + 560x^3y^4 + 672x^2y^5 + 448xy^6 + 128y^7$