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3 years ago

The first term of an arithmetic sequence is -5, and the tenth term is 13.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

The common difference is 2

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1+d(n-1)

a1 = -5

a10 = 13

Substituting n=10 a10=13 and a1 =-5

13 = -5 +d (10-1)

13 = -5 +9d

Add 5 to each side

13+5 = -5+5 +9d

18 = 9d

Divide each side by 9

18/9 = 9d/9

2 =d

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Write the equation of the line in slope intercept form that passes through (10,21) and (15,36)

Tema [17]

Answer:

y = 3x - 9

Step-by-step explanation:

First, find the slope using rise/run (y2 - y1) / (x2 - x1)

Plug in the points:

(36 - 21) / (15 - 10)

15/5

= 3

Next, plug the slope and a point into the equation y = mx + b to find b (y-int)

y = mx + b

21 = 3(10) + b

21 = 30 + b

-9 = b

Then, plug this into the equation, as well as the slope:

y = 3x - 9

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3 years ago

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3 years ago

What is the distance between points A and B?

g100num [7]

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Step-by-step explanation:

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4 years ago

EL PERIMETRO DELCUADRADO X ES DOS TERCIOS DEL PERIMETRO DEL CUADRADO Y. EL UCADRADO Y ES DOS TERCIOS DEL PERIMETRO DEL CUADRADO

Keith_Richards [23]

the question in English is

THE SQUARE PERIMETER X IS TWO THIRDS OF THE SQUARE PERIMETER Y. THE PERIMETER OF THE SQUARE Y IS TWO THIRDS OF THE PERIMETER OF THE SQUARE Z. THE AREA OF THE SQUARE X IS 16 CM2 WHAT IS THE AREA OF THE SQUARE Z?

Let

Px--------> the perimeter of square x

Py--------> the perimeter of square y

Pz--------> the perimeter of square z

Ax--------> the area of square x

Az--------> the area of square z

Step 1

Find the length side of the square x

we know that

$Px=\frac{2}{3} Py$ -------> equation A

$Py=\frac{2}{3} Pz$ -------> equation B

$Ax=16\ cm^{2}$

$Ax=x^{2}$

$x^{2}=16$

$x=4\ cm$

Step 2

Find the perimeter of square x

$Px=4x$

substitute the value of x in the formula

$Px=4*4=16\ cm$

Step 3

Find the perimeter of square y

use the equation A

$Px=\frac{2}{3} Py$

solve for Py

$Py=\frac{3}{2} Px$

substitute the value of Px

$Py=\frac{3}{2}16=24\ cm$

Step 4

Find the perimeter of square z

use the equation B

$Py=\frac{2}{3} Pz$

solve for Pz

$Pz=\frac{3}{2} Py$

substitute the value of Py

$Pz=\frac{3}{2} 24=36\ cm$

Step 5

Find the area of square z

we know that

the area of the square z is equal to

$Az=z^{2}$

Find the length side of square z

$Pz=4z$

$Pz=36\ cm$

$4z=36$

$z=9\ cm$

substitute the value of z in the area's formula

$Az=9^{2}=81\ cm^{2}$

therefore

the answer is

the area of the square z is $81\ cm^{2}$

8 0

3 years ago