Put these steps in order to solve this equation

The line representing a proportional relationship always goes through the point (0,0). If x is zero, multiplying x by the consta

Sidana [21]

Answer:

B (2, 4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the constant of proportionality k is given and is equal to

$k=2$

so

The linear equation is given by

$y=2x$

That means ----> the y-coordinate is two times the x-coordinate

therefore

The other point is B(2.4)

Because

For x=2, y=4

the y-coordinate is two times the x-coordinate

$4=2(2)\\4=4$

3 0

3 years ago

4,7,10,13,16,19,22 Write down the number of matches of the n term

LiRa [457]

Answer:

tn=a+(n-1)*d

=4+(n-1)*3

5 0

3 years ago

Find the lateral surface area of a regular triangular prism with base edges 7cm and height of 11cm

Flauer [41]

This is a tricky question to answer without diagrams and there are useful videos online. A regular triangular prism has an equilateral triangle as its base with edge length 7cm, forming a prism with a total height of 11cm. We wish to calculate the area of the 3 equal triangular faces.

The formula for area of a triangle is 0.5 x base x height. We have the base (7cm) but the problem is we do not have the height (or slant length) of the lateral faces, we only have the height of the entire prism. We must first calculate the slant length by building a triangle inside the prism which goes from the centroid of the base (the inradius) to the centre of an edge. As the base is an equilateral triangle finding the inradius is much more difficult than for a square pyramid.

inradius = 1/6 x (SQRT of 3) x length
inradius = 1/6 x (SQRT of 3) x 7cm = 2cm

We now have a right angle triangle with base = inradius, height = height of prism, and hypotenuse = slant length we need.

Use pythag to calculate hypotenuse a^2 + b^2 = c^2
2^2 + 11^2 = c^2
4 + 121 = c^2
c= SQRT(125) = 11.18cm

We now have the missing slant length or height of the lateral triangles of the prism. We can find the area of one face and multiply it by 3 to get the total surface area of the lateral faces of the pyramid.

base = 7cm
height = 11.18cm
area of triangle = 0.5 x 7 x 11.18 = 39.13cm^2
Multiply this area by 3 to get the sum of all 3 lateral triangle surface areas, total area = 117.39cm^2

7 0

3 years ago

Write a recursive rule and an explicit rule for the sequence 3,7,11,15

m_a_m_a [10]

Answer:

The Recursive formula for the sequence is:

aₙ = aₙ₋₁ + d

The Explicit formula for the sequence is:

$a_n=4n-1$

Step-by-step explanation:

Given the sequence

3,7,11,15

Here:

a₁ = 3

computing the differences of all the adjacent terms

7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4

The difference between all the adjacent terms is the same and equal to

d = 4

We know that a recursive formula basically defines each term of a sequence using the previous term(s).

The recursive formula of the Arithmetic sequence always involves the first term.

a₁ = 3

We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.

so

The recursive formula of the sequence is:

aₙ = aₙ₋₁ + d

substitute n = 2 to find the 2nd term

a₂ = a₂₋₁ + d

a₂ = a₁+ d

substitute a₁ = 3 and d = 4

a₂ = 3 + 4

a₂ = 7

Thus, the recursive formula for the sequence 3,7,11,15 is:

aₙ = aₙ₋₁ + d

An explicit rule for the sequence

Given the sequence

3,7,11,15

We already know that

a₁ = 3

d = 4

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

substituting a₁ = 3 and d = 4

$a_n=4\left(n-1\right)+3$

$a_n=4n-4+3$

$a_n=4n-1$

Therefore, an explicit rule for the sequence

$a_n=4n-1$

6 0

3 years ago

Please help me with question 3

alexira [117]

There's no picture I wish I could help

5 0

4 years ago