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inna [77]
3 years ago
8

What is a35 for the arithmetic sequence presented in the table below?

Mathematics
1 answer:
Kryger [21]3 years ago
7 0

Answer: choice B) a35 = -118

=====================================================

Explanation:

When n = 5, an = 32 as shown in the first column of the table. This means the fifth term is 32. Plug in those values to get

an = a1+d(n-1)

32 = a1+d(5-1)

32 = a1+4d

Solve for a1 by subtracting 4d from both sides

a1 = 32-4d

We'll plug this in later

Turn to the second column of the table. We have n = 10 and an = 7. Plug those values into the formula

an = a1+d(n-1)

7 = a1 + d(10-1)

7 = a1+9d

Now substitute in the equation in which we solved for a1

7 = a1+9d

7 = 32-4d+9d ... replace a1 with 32-4d

7 = 32+5d

5d = 7-32

5d = -25

d = -25/5

d = -5

This tells us that we subtract 5 from each term to get the next term.

Use this d value to find a1

a1 = 32-4d

a1 = 32-4*(-5)

a1 = 32+20

a1 = 52

The first term is 52

--------------

The nth term formula is therefore

an = 52 + (-5)(n-1)

which simplifies to

an = -5n + 57

To check this result, plug in n = 5 to find that a5 = 32. Similarly, you'll find that a10 = 7 after plugging in n = 10. I'll let you do these checks.

--------------

Replace n with 35 to find the 35th term

an = -5n + 57

a35 = -5(35) + 57

a35 = -175 + 57

a35 = -118

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How is (5^-3) written as repeated multiplication?
stich3 [128]

Answer:

To write repeated multiplication of the same number in exponential notation, first write the number being multiplied as the base. Then count how many times that number is used in the multiplication, and write that number as the exponent.

Step-by-step explanation:

5 0
2 years ago
A cuboid with a volume of 924cm^3 has dimensions
Leona [35]

The values of x are -22 and 10

The dimensions are 4 cm , 11 cm , 21 cm

Step-by-step explanation:

The given is:

  • A cuboid with a volume of 924 cm³
  • It has dimensions  4 cm , (x + 1) cm and (x + 11) cm

We want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions

The volume of a cuboid is the product of its three dimensions

∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)

∴ Its volume = 4(x + 1)(x + 11)

- Multiply the two brackets and then multiply the product by 4

∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)

∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms

∴ (x + 1)(x + 11) = x² + 12x + 11

∴ Its volume = 4(x² + 12x + 11)

∴ Its volume = 4x² + 48x + 44

∵ The volume of the cuboid = 924 cm³

- Equate the expression of the volume by 924

∴ 4x² + 48x + 44 = 924

- Subtract 924 from both sides

∴ 4x² + 48x - 880 = 0

- Simplify it by dividing all terms by 4

∴ x² + 12x - 220 = 0

Now let us factorize it into two factors

∵ x² = x × x

∵ 220 = 22 × 10

∵ 22(x) - 10(x) = 12x ⇒ the middle term

∴ x² + 12x - 220 = (x + 22)(x - 10)

∴ (x + 22)(x - 10) = 0

- Equate each factor by 0 to find x

∵ x + 22 = 0 ⇒ subtract 22 from both sides

∴ x = -22

∵ x - 10 = 0 ⇒ add 10 to both sides

∴ x = 10

∴ The values of x are -22 and 10

We can not use x = -22 because there is no negative dimensions, then we will use x = 10

∵ The dimensions are 4 , (x + 1) , (x + 11)

∵ x = 10

∴ The dimensions are 4 , (10 + 1) , (10 + 11)

∴ The dimensions are 4 cm , 11 cm , 21 cm

Learn more:

You can learn more about the factorization in brainly.com/question/7932185

#LearnwithBrainly

3 0
3 years ago
The disctance between -8 and 5 on the number line can be found by which expression??
Ilia_Sergeevich [38]
It's A.  First of all, one of the only 2 things in math that will NEVER be negative is distances/lengths and times.  You have a distance here, so because one of your 2 numbers is negative, you have to take the absolute value of the difference.  -8-5 = -11, but the absolute value of that is 11.  Put the numbers on a number line and count the units between -8 and +5 and there are 11 units between those 2 numbers.
5 0
3 years ago
Solve. Use models to help you.
oksian1 [2.3K]

Answer:

3.38

Step-by-step explanation:

x + y + z = 16.9

x = 2y

y = z

y=y

2y (x) + y(y) + y(z) = 16.0

5y = 16.9

y = 3.38

4 0
3 years ago
What’s the area of this figure
kvasek [131]

Answer:

743.25m^2

Step-by-step explanation:

Area of triangle = 1/2bh

= 1/2 x 30 x 26

= 390

Area of semi circle = 1/2 πr^2

= 1/ 2 x 3.14 x 15 x15

=353.25m^2

= 390 + 353.25

= 743.25m^2

8 0
3 years ago
Read 2 more answers
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