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zvonat [6]
3 years ago
8

A relay with n laps was run by 4 people. The 1st runner ran half the laps. The 2nd runner ran half the number of laps the 1st ru

nner ran. The 3rd runner ran half the number of laps the 2nd runner ran. The remaining laps were completed by the 4th runner. How many laps did the 4th runner complete?
Mathematics
1 answer:
castortr0y [4]3 years ago
6 0

Answer:

n/16

Step-by-step explanation:

I am pretty sure.

please mark me brainliest!

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If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

4 0
3 years ago
Which system of equations can be used to find the roots of the equation4x^5-12x^4+6x=5x^3-2x?
goblinko [34]

Answer:

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

Step-by-step explanation:

The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

We simply formulate two equations by splitting the left and the right hand sides of the given equation.

The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.

The roots of the given equation will be given by the points where these two equations will intersect.

The graph of these two equations is as shown in the attachment below;

The roots are thus;

x = 0 and x = 0.813

5 0
3 years ago
I can't figure it out​
kap26 [50]

Answer:

the first one

Step-by-step explanation:

this picture has the workings

8 0
3 years ago
What is the value of A when we rewrite... (PLZ HELP QUICK)
Marina86 [1]

Answer:

<h2>\frac{133}{8}</h2>

Step-by-step explanation:

Given,

{( \frac{5}{2} )}^{x}  +  {( \frac{5}{2} )}^{x + 3}

=  {( \frac{5}{2}) }^{x}  +  {( \frac{5}{2}) }^{x}  \times  {( \frac{5}{2} )}^{3}

= ( \frac{5}{2} ) ^{x} (1 +  {( \frac{5}{2} )}^{3}

=  {( \frac{5}{2} )}^{x} (1 +  \frac{125}{8} )

=  {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )

=  {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )

{( \frac{5}{2} )}^{x} ( \frac{133}{8} )

Comparing with A • {( \frac{5}{2}) }^{x}

A = \frac{133}{8}

Hope this helps...

Good luck on your assignment...

7 0
3 years ago
If a point on the pre-image has coordinates (3, -4), and the coordinates of its image are (12, -16), what scale factor was used
just olya [345]
A scale factor of 4. This is a simple dilation problem. 
8 0
3 years ago
Read 2 more answers
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