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monitta
2 years ago
5

The first term in this sequence is -1. Write the function that represents the sequence

Mathematics
1 answer:
sattari [20]2 years ago
3 0

Answer:

a_{n} = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

a_{n} = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

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What's the solution of the equation 4[x+2(3x-7)]=22x-65
padilas [110]

Answer:

x = -3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+2(3x−7))=22x−65

Step 1: Simplify both sides of the equation.

4(x+2(3x−7))=22x−65

(4)(x)+(4)(2(3x−7))=22x+−65(Distribute)

4x+24x+−56=22x+−65

(4x+24x)+(−56)=22x−65(Combine Like Terms)

28x+−56=22x−65

28x−56=22x−65

Step 2: Subtract 22x from both sides.

28x−56−22x=22x−65−22x

6x−56=−65

Step 3: Add 56 to both sides.

6x−56+56=−65+56

6x=−9

Step 4: Divide both sides by 6.

6x = -9

6       6

x =  -3/2

8 0
2 years ago
Which of the following is the correct graph of the solution to the inequality −18 > −5x + 2 ≥ −48?
monitta

Answer:

Option D. A number line with an open circle on 4 with shading to the right and a closed circle on 10 with shading to the left

Step-by-step explanation:

we have

-18 > -5x+2 \geq -48

Divide the compound inequality into two inequalities

-5x+2 \geq -48 -----> inequality A

-5x \geq -48-2

-5x \geq -50

Multiply by -1 both sides

5x \leq 50

Divide by 5 both sides

x \leq 10

The solution of inequality A is the interval ----> (-∞,10]

All real numbers less than or equal to 10

-18 > -5x+2 -----> inequality B

-18-2 > -5x

-20 > -5x

Multiply by -1 both sides

20 < 5x

Divide by 5 both sides

4 < x

Rewrite

x > 4

The solution of the inequality B is the interval ----> (4,∞)

All real numbers greater than 4

The solution of the compound inequality is

(-∞,10] ∩ (4,∞)= (4,10]

All real numbers greater than 4 and less than or equal to 10

A number line with an open circle on 4 with shading to the right and a closed circle on 10 with shading to the left

8 0
3 years ago
Read 2 more answers
How to Convert 3x^2+3y^2=10 to polar form
JulsSmile [24]

Answer:

18

Step-by-step explanation:

you times it

6 0
3 years ago
A pineapple is 7 times as heavy as an orange. the pineapple also weighs 870 grams more than the orange. what is the total weight
san4es73 [151]
Let's translate each sentence into "Math".

Pineapple = p

Orange = x

is means equal

 

Pineapple is 7 times as heavy as an orange:  p = 7x

Pineapple weighs 870 grams more than orange. p = 870 + x

 

Substitute  p = 7x  into the second equation:

7x = 870 + x

Subtract  x from both sides

6x = 870

divide by 6

x = 145

 

The orange weighs 145 grams.

The pineapple weights 7 times the orange = 7(145) = 1015 grams.

4 0
3 years ago
Find the simple interest accrued on a $500 investment made for 2 years at an interest rate of 8% per year.
Artemon [7]

Answer:

3,125 i think sorry if this is incorrect....

Step-by-step explanation:

Answer:

P = $ 3,125.00

Equation:

P = I / rt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 8%/100 = 0.08 per year,

then, solving our equation

P = 500 / ( 0.08 × 2 ) = 3125

P = $ 3,125.00

The principal required to

accumulate interest of $ 500.00

on a rate of 8% per year for 2 years is $ 3,125.00.

3 0
2 years ago
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