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2 years ago

What is the function for the arithmetic sequence 2,7,12,17,22

2 answers:

4 0

Hey there,

Your question states:
<span>
What is the function for the arithmetic sequence
(2,7,12,17,22)

By using the formula </span> $[tex] a_{n} \ a_{1} + d(n-1) \ to \ get \ the \ sequence$
<span>
The </span> $mean$ of the <span>arithmetic sequence would be </span> $\boxed{12}$

And by identifying the sequence by using the formula, it would be . . .

$\boxed{a_{n} =5n-3}$

Hope this helps.
~Jurgen

Deffense [45]2 years ago

3 0

The common difference, d, is 5 and the starting value, a, is 2.
Filling this in the form of $x_n=a+d(n-1)$

<span>you get

</span> $x_n = 2+5(n-1)$

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Write an equation for the line that passes through (1, -1) and (0, -4).

Lynna [10]

The solution to the question

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2 years ago

One of the vertices of an equilateral triangle is on the vertex of a square and two other vertices are on the not adjacent sides

Elina [12.6K]

<h2>Answer:</h2>

<em> The side of the triangle is either 38.63ft or 10.35ft</em>

<h2>Step-by-step explanation:</h2>

This problem can be translated as an image as shown in the Figure below. We know that:

The side of the square is 10 ft.
One of the vertices of an equilateral triangle is on the vertex of a square.
Two other vertices are on the not adjacent sides of the same square.

Let's call:

Since the given triangle is equilateral, each side measures the same length. So:

x: The side of the equilateral triangle (Triangle 1)

y: A side of another triangle called Triangle 2.

That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:

$\mathbf{(1)} \ x^2=100+y^2$

We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:

$y+(10-y)=10$

Therefore, for Triangle 3, we have that by Pythagorean theorem:

$(10-y)^2+(10-y)^2=x^2 \\ \\ 2(10-y)^2=x^2 \\ \\ \\ \mathbf{(2)} \ x^2=2(10-y)^2$

Matching equations (1) and (2):

$2(10-y)^2=100+y^2 \\ \\ 2(100-20y+y^2)=100+y^2 \\ \\ 200-40y+2y^2=100+y^2 \\ \\ (2y^2-y^2)-40y+(200-100)=0 \\ \\ y^2-40y+100=0$

Using quadratic formula:

$y_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ y_{1,2}=\frac{-(-40) \pm \sqrt{(-40)^2-4(1)(100)}}{2(1)} \\ \\ \\ y_{1}=37.32 \\ \\ y_{2}=2.68$

Finding x from (1):

$x^2=100+y^2 \\ \\ x_{1}=\sqrt{100+37.32^2} \\ \\ x_{1}=38.63ft \\ \\ \\ x_{2}=\sqrt{100+2.68^2} \\ \\ x_{2}=10.35ft$

<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>

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2 years ago

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The answer is 44%
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2 years ago

Find the word or phrases that best complete the sentence intersecting planes ___ intersect in exactly one point

mars1129 [50]

Answer:

never

Step-by-step explanation:

Intersecting planes are planes that intersect along a given line.

To explain this better, consider the following definitions:

i. A point: This is denoted by a dot and it is a location marked on a space or a plane.

ii. A line: This is the distance between two points. It is one-dimensional.

iii. A plane: This is a two-dimensional, flat surface with no thickness formed by points and extends infinitely.

Therefore, since intersecting planes intersect along a line, it is not possible that they intersect in exactly one point given that a line is the distance between points.

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2 years ago

Will mark as brainliest

STALIN [3.7K]

Answer:

Step-by-step explanation:

When planes intersect, it means they'll cross over each other at some point, so A is the only right answer.

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3 years ago