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3 years ago

The first three terms of an arithmetic sequence are 2k+1, 5k, 7k+2. What is the value of k?

Mathematics

1 answer:

ki77a [65]3 years ago

4 0

Answer:

Step-by-step explanation:

In an arithmetic sequence, we keep adding/subtracting to get the next term in the sequence.

Therefore, we can make an equation that looks like this:

5k-(2k+1) = 7k+2-5k

We can subtract 2k+1 from 5k, and 5k from 7k+2, because from subtracting the difference would be the same. (common difference of sequence is what we would find)

Now, we just need to simplify.

5k-2k-1 = 2k+2

3k-1=2k+2

Now let's combine like terms, and we get:

k=3

Hope this helped!

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Put the following equation of a line into slope-intercept form, simplifying all

lilavasa [31]

Answer:

y = x -7

Step-by-step explanation:

2x - 2y = 14

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

Subtract 2x from each side

2x - 2y -2x = -2x+14

-2y = -2x+14

Divide each side by -2

-2y/-2 = -2x/-2 +14/-2

y = x -7

The slope is 1 and the y intercept is -7

8 0

4 years ago

Read 2 more answers

The sum of three consecutive numbers is equal to 4 times the largest number minus 29. What is the smallest of the three numbers?

gulaghasi [49]

The smallest of the three consecutive integers is 24.

<h3>How to solve algebraic word problems?</h3>

Let the 3 consecutive integers be;

x, y and z

Thus;

y = x + 1

z = x + 2

Now, we are told that their sum is equal to 4 times the largest number minus 29. Thus;

x + x + 1 + x + 2 = 4(x + 2) - 29

3x + 3 = 4x + 8 - 29

4x - 3x = 3 + 21

x = 24

Thus, we can conclude that the smallest of the three consecutive integers is 24.

Read more about algebra word problems at; brainly.com/question/13818690

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5 0

2 years ago

Total sales: $3546.95

Snezhnost [94]

Answer:

commission 446.9157$ or 446.92 $ and total pay 1646.92 $

Step-by-step explanation:

commission = 12.6% of 3546.95

= (12.6/100)×3546.95

= $446.9157

total pay = basic pay + commission

= 1200+446.92

= 1646.92 $

5 0

4 years ago

Write the equation of the line passing through (−1, 0) and (0, −3).

e-lub [12.9K]

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3)

m = $\frac{-3-0}{0+1}$ = - 3

note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - 3x - 3 ← in slope- intercept form

Add 3x to both sides

3x + y = - 3 ← in standard form → C

8 0

3 years ago

Read 2 more answers

What two numbers add up to 6 and multiply to 12?

GuDViN [60]

Erm

x+y=6
xy=12

x+y=6
y=6-x
sub back

xy=12
x(6-x)=12
6x-x^2=12
x^2-6x=-12
x^2-6x+12=0
quadratic formula
for
ax²+bx+c=0
$x= \frac{-b+/- \sqrt{b^2-4ac} }{2a}$

for
x²-6x+12=0
a=1
b=-6
c=12
and remember that √-1=i

$x= \frac{-(-6)+/- \sqrt{(-6)^2-4(1)(12)} }{2(1)}$
$x= \frac{6+/- \sqrt{36-48} }{2}$
$x= \frac{6+/- \sqrt{-12} }{2}$
$x= \frac{6+/- (\sqrt{-1})(\sqrt{12}) }{2}$
$x= \frac{6+/- (i)(2\sqrt{3}) }{2}$
$x= \frac{6+/- 2i\sqrt{3} }{2}$
x=3+/-i√3

the numbers are 3+i√3 and 3-i√3
no real numbers tho

7 0

4 years ago