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NikAS [45]
2 years ago
7

Alex draws a diagonal in a rectangle that is 4 inches long and 3 inches wide. What is the area of one of two triangles that are

formed?
Mathematics
1 answer:
sukhopar [10]2 years ago
8 0

Answer:

3.975 square inches

Step-by-step explanation:

Step 1

We find the length of the triangle

We solve using Pythagoras Theorem

Diagonal² = Length² + Width²

Diagonal = 4 inches

Width = 3 inches

Length² = Diagonal² - Width²

Length = √Diagonal² - Width²

Length = √4² - 3²

Length = √16 - 9

Length = √(7)

Length = 2.6457513111 inches

Length = 2.65 inches

Step 2

Area of Triangle = 1/2 × Base × Height

Base = Length = 2.65 inches

Height = Width = 3 inches

=1/2 × 2.65 inches × 3 inches

= 3.975 square inches

Therefore, the area of one of the triangles that are formed is 3.975 square inches

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leonid [27]

Answer:

  • The value of a = 5.8
  • The value of b = 4.4

Step-by-step explanation:

Given

7.2, a, b, 3 are in A.P

2a = 7.2+b

b = 2a - 7.2

as

a, b, 3 are also in A.P

2b\:=\:a\:+\:3

Putting b = 2a - 7.2

2\left(2a-7.2\right)=a+3

4a-14.4=a+3

\mathrm{Add\:}14.4\mathrm{\:to\:both\:sides}

4a-14.4+14.4=a+3+14.4

4a=a+17.4

4a-a=a+17.4-a

3a=17.4

\mathrm{Divide\:both\:sides\:by\:}3

\frac{3a}{3}=\frac{17.4}{3}

a=5.8

Now, plugging a=5.8 in b = 2a - 7.2

b=2\left(5.8\right)-7.2

b=2\cdot \:5.8-7.2

b=11.6-7.2

b=4.4

Therefore,

  • The value of a = 5.8
  • The value of b = 4.4
4 0
3 years ago
Can someone explain what geometric sequences are?
Fed [463]

Explanation:

A sequence is a list of numbers.

A <em>geometric</em> sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.

<u>Examples</u>

  • 1, 2, 4, 8, ... common ratio is 2
  • 27, 9, 3, 1, ... common ratio is 1/3
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<u>General Term</u>

Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...

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where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...

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You can see that these formulas are exponential in nature.

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<u>Sum of Terms</u>

Another useful formula for geometric sequences is the formula for the sum of n terms.

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3 years ago
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faltersainse [42]

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x = \frac{1}{3}

Substitute x = \frac{1}{3} into (1) for corresponding value of y

y = 9 × \frac{1}{3} = 3

Solution is ( \frac{1}{3}, 3 )

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