Simplify: 3^2 * 3^4

The sum of the first three terms of a sequence is 6 and the fourth term is 16

Sati [7]

Answer:

a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence: $\boxed{\bold{a_n=7n-12}}$

Step-by-step explanation:

a₁ + a₂ + a₃ = 6

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2 ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7 ⇒ a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

$a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}$

6 0

2 years ago

1) solve for y.

stepladder [879]

As a variable in algebra, but variables can be any letter. An expression ... Evaluate each expression if x. 2, y. 7, and z. 4. 1. x y z. 2. (z x) y. 3. 2x z. 4. 4y. 3z. 5. 4(x y) z. 6. ... The order in which numbers are multiplied does not the sum. ..... Find the quotient of 110 and 11. Solve each equation. 11. t. 72 6. 12. 84 6 p. 13. 40 (8) f.[PDF]

7 0

2 years ago

The probability of drawing two red candies without replacement is 1335 , and the probability of drawing one red candy is 25 . Wh

professor190 [17]

The probability would be 50 because 25+25=50

3 0

2 years ago

Find the domain and range pls!

skad [1K]

Domain should be, (-♾️,♾️)
And range should be, (-♾️, 2)

If you ment something other then this please message me so I can help!

4 0

2 years ago

Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)

Tom [10]

$\bold{\huge{\underline{ Solution }}}$

<h3>Given :-</h3>

We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

We have to calculate the length of the sides of given triangle and also we have to determine whether it is right angled triangle or not

<h3>Let's Begin :-</h3>

Here, we have 

Coordinates of P =( x1 = -4 , y1 = 6)
Coordinates of Q = ( x2 = 6 , y2 = 1 )
Coordinates of R = ( x3 = 2 , y3 = 9 )

By using distance formula 

$\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

Subsitute the required values in the above formula :-

Length of side PQ

$\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}$

$\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ 100 + 25 }}$

$\sf{ = }{\sf\sqrt{ 125 }}$

$\sf{ = 5 }{\sf\sqrt{ 5 }}$

Length of QR

$\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}$

$\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}$

$\sf{ = }{\sf\sqrt{16 + 64 }}$

$\sf{ = }{\sf\sqrt{80 }}$

$\sf{ = 4 }{\sf\sqrt{5 }}$

Length of RP

$\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}$

$\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}$

$\sf{ = }{\sf\sqrt{ 36 + 9 }}$

$\sf{ = }{\sf\sqrt{ 45 }}$

$\sf{ = 3}{\sf\sqrt{ 5 }}$

We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

By using Pythagoras theorem :-

Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

That is,

$\bold{ PQ^{2} + QR^{2} = PR^{2}}$

Subsitute the required values,

$\bold{ 125 + 80 = 45 }$

$\bold{ 205 = 45 }$

From above we can conclude that,

The triangle PQR is not a right angled triangle because 205 ≠ 45 .

6 0

2 years ago