All categories

2 years ago

The first term of an arithmetic sequence is 4 and the tenth term is 67.

Mathematics

1 answer:

Dmitry [639]2 years ago

6 0

Answer:

Step-by-step explanation:

Formula

tn = a1 + (n-1)* d

Givens

tn = 67 (it is the last term or the nth term

n = 10

a1 = 4

find d

Solution

67 = 4 + (10 - 1)*d

67 = 4 + 9*d Subtract 4 from both sides

67 - 4 = 9d

63 = 9d Divide by 9

63/9 = 9d/9

7 = d

Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.

You might be interested in

04.01 mc y-2x=-1 and 2y-x=4 choose the correct graph of the given systems of equations

ira [324]

Answer:

1st one m=0

y= 0.49875311x / cm

No horizonal asymptotes

x= 1/2 + 2.005 mcy

2nd one is

slope 1/2

y intercept (0,2)

x y

-4 0

0 2

Step-by-step explanation:

for 2

starting point ay y 2 make a point

then rise over run

go up 1 and to the right 2 and point , then up 1 and to the right 2 and point

there is your graph

6 0

3 years ago

Solve the proportion of 2/v = 4/6

dsp73

$\dfrac{2}{v} = \dfrac{4}{6}$

Cross multiply:
$4v = 12$

Divide both sides by 4:
$v = 3$

3 0

3 years ago

What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE

maks197457 [2]

Given:

The equation of a line is:

$2y+3x=10$

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

$2y+3x=10$

For $x=0$ ,

$2y+3(0)=10$

$2y+0=10$

$y=\dfrac{10}{2}$

$y=5$

For $x=2$ ,

$2y+3(2)=10$

$2y+6=10$

$2y=10-6$

$2y=4$

Divide both sides by 2.

$y=\dfrac{4}{2}$

$y=2$

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(0,5)\to A'(3(0),3(5))$

$A(0,5)\to A'(0,15)$

Similarly,

$B(2,2)\to B'(3(2),3(2))$

$B(2,2)\to B'(6,6)$

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\dfrac{6-15}{6-0}(x-0)$

$y-15=\dfrac{-9}{6}(x)$

$y-15=\dfrac{-3}{2}x$

Multiply both sides by 2.

$2(y-15)=-3x$

$2y-30=-3x$

$2y+3x=30$

Therefore, the equation of the line after the dilation is $2y+3x=30$ .

3 0

3 years ago

Write an equation for a line that has a slope of negative 3 over 4 and y intercept of negative 5

oee [108]

F(x) = 3/4x - 5 would be your equation

5 0

3 years ago

Also need help with this on I especially don’t get this one

Artyom0805 [142]

4) 60

5) 1 cup of yellow and 1.75 cups blue

7 0

4 years ago