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3 years ago

What is the 7th term in the geometric sequence described by this explicit formula?

Mathematics

2 answers:

elixir [45]3 years ago

8 0

A7=2*5^n-1
2*5^(7-1)
2*5^6
2*15625
31250= a7

Natasha_Volkova [10]3 years ago

5 0

The answer to this question is d

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Explain why 1/2 ab sin(theta) gives the area of a triangle with sides a and ???? and included angle theta.

Jet001 [13]

Answer:

Please find the attachment.

Step-by-step explanation:

We are asked to explain why $\frac{1}{2}ab\cdot \text{sin}(\theta)$ gives the area of a triangle with sides a and b and included angle theta.

We know that area of a triangle is equal to half the product of base and height of the triangle.

$\text{Area of triangle}=\frac{1}{2}\cdot bh$

Upon looking at our given triangle, we can see that the base of the triangle is equal to 'a'.

The height of the triangle can be determined using sin(theta) as sine relates opposite side of right triangle with its hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(\theta)=\frac{h}{b}$

$h=b\cdot \text{sin}(\theta)$

Upon substituting our given values in area formula, we will get:

$\text{Area of triangle}=ab\cdot \text{sin}(\theta)$

Hence, proved.

8 0

3 years ago

The length of a rectangle is 1 ft less than twice the width, the area of the rectangle is 21 ft squared. What’s the length

guapka [62]

Answer:

The length of the rectangle is 6 feet

Step-by-step explanation:

Given as :

The length of rectangle is 1 feet less than twice the width

So, let The width of rectangle = w feet

The length of rectangle = ( 2 w - 1 ) feet

The area of the rectangle = 21 feet²

Now,

∵ The area of the rectangle = length × width

Or, 21 feet² = ( 2 w - 1 ) feet × w feet

or, 21 = 2 w² - w

or, 2 w² - w - 21 = 0

or, 2 w² + 6 w - 7 w - 21 = 0

or , 2 w ( w + 3 ) - 7 ( w + 3 ) = 0

or, ( w + 3 ) ( 2 w - 7 ) = 0

So, w = - 3 feet , $\frac{7}{2}$ feet

here we consider only positive value of w i.e $\frac{7}{2}$ feet

∴ The length of rectangle = ( 2 w - 1 ) feet

or, The length of rectangle = 2 × $\frac{7}{2}$ - 1

Or, The length of rectangle = 7 - 1 = 6 feet

Hence The length of the rectangle is 6 feet , Answer

3 0

3 years ago

Five pens and four pencils cost $2.55. But four pens and five pencils cost $2.40. How

Trava [24]

1*5=12.75

2*4=9.6

so nine pens cost 3.15

one pen will be 0.35$

so one pencil will be .20$

8 0

3 years ago

Read 2 more answers

The table shows a relation between x and y.<br><br> is the relation a function, and why?

notsponge [240]

<h2>Function Definition</h2>

A function is a relation in which there is only one y-value for every x-value.

If we given an input of 3 for x, for example, we would only get one output for y, like 1, for example.

<h2>Answer</h2>

If we look at the table, we can see that the x-value of 3 gives us two outputs: 7 and 9.

Therefore, this relation is not a function.

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2 years ago

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Harrizon [31]

Awnser:

Explanation:

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3 years ago