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andreyandreev [35.5K]
2 years ago
14

This math my graduation depends on it

Mathematics
1 answer:
In-s [12.5K]2 years ago
7 0

In an arithmetic sequence, consecutive terms have a fixed distance d between them. If a₁ is the first term, then

2nd term = a₂ = a₁ + d

3rd term = a₃ = a₂ + d = a₁ + 2d

4th term = a₄ = a₃ + d = a₁ + 3d

and so on, up to

nth term = a_n = a_{n-1} + d = a_{n-2} + 2d = a_{n-3} + 3d = \cdots = a_1 + (n-1)d

so that every term in the sequence can be expressed in terms of a₁ and d.

6. It's kind of hard to tell, but it looks like you're given a₁₃ = -53 and a₃₅ = -163.

We have

a₁₃ = a₁ + 12d = -53

a₃₅ = a₁ + 34d = -163

Solve for a₁ and d. Eliminating a₁ and solving for d gives

(a₁ + 12d) - (a₁ + 34d) = -53 - (-163)

-22d = 110

d = -5

and solving for a₁, we get

a₁ + 12•(-5) = -53

a₁ - 60 = -53

a₁ = 7

Then the nth term is recursively given by

a_n = a_{n-1}-5

and explicitly by

a_n = 7 + (n-1)(-5) = 12 - 5n

7. We do the same thing here. Use the known terms to find a₁ and d :

a₁₉ = a₁ + 18d = 15

a₃₈ = a₁ + 37d = 72

⇒   (a₁ + 18d) - (a₁ + 37d) = 15 - 72

⇒   -19d = -57

⇒   d = 3

⇒   a₁ + 18•3 = 15

⇒   a₁ = -39

Then the nth term is recursively obtained by

a_n = a_{n-1}+3

and explicitly by

a_n = -39 + (n-1)\cdot3 = 3n-42

8. I won't both reproducing the info I included in my answer to your other question about geometric sequences.

We're given that the 1st term is 3 and the 2nd term is 12, so the ratio is r = 12/3 = 4.

Then the next three terms in the sequence are

192 • 4 = 768

768 • 4 = 3072

3072 • 4 = 12,288

The recursive rule with a₁ = 3 and r = 4 is

a_n = 4a_{n-1}

and the explicit rule would be

a_n = 3\cdot4^{n-1}

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What degree of rotation about the origin will cause the triangle below to map onto itslef
drek231 [11]

Answer:

360^o

Step-by-step explanation:

Given

The attached plot

Required

Which degree maps the triangle onto itself

The degrees that can map a point, line, or shape onto itself are:

\theta=360,720,1080,1440, 1800, 2160, 2520, 2880, 3240, 3600

i.e. multiples of 360

Looking at the given options

(a)\ 360^o is correct because it can be found in the listed multiples

In other words, it will map point (x,y) to point (x,y)

5 0
2 years ago
christian has $425.82 in his checking account . How much does he have in his account after he makes a deposit if 120.75 and with
Oksanka [162]
A deposit adds to the amount of a checking account.
So a deposit of $120.75 is + 120.75.
A withdraw subtracts from the amount of a checking account.
So a withdraw of $185.90 is - 185.90.

If the original amount is $425.82, you would simply add the amount of the deposit then subtract the amount of the withdraw.

425.82 + 120.75 - 185.90 = 360.67

So the amount in Christian's checking account after <span>a deposit if $120.75 and withdrawal of $185.90 is $360.67.

Answer:
$360.67

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5 0
3 years ago
Need help with this pls <br> (Show work pls!!)
Aleksandr-060686 [28]
This is my first time on this app but this question doesn’t look to hard i’m ok at math but not that good at showing my work

Isosceles triangles have to equal sides

and each side is 5 cm greater than the base

you know the perimeter is 46

i would use basic algebra

x = base

46 = 2(x +5) + x

the 2(x +5) is the equal sides

46 = 2(x+5) + x

using distributive property

46 = 2x + 10 + x

add the common variable

46 = 3x + 10

now it’s easy

3x = 46 - 10

3x = 36

x = 36 / 3

x = 12

now that we got x (base)

we know that the equal sides are 5 cm longer than the base

12 + 5 = 17

since there are 2 sides and they are equal they are both 17

so each side of the triangle would be
1. 17 cm
2. 17 cm
3. 12 cm


to check you should be able to add them all together and get 46

17 + 17 + 12 = 46


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3 years ago
Solving Linear Equations<br> 10 = 4m + 28
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Answer:

m = -4.5

Step-by-step explanation:

10 = 4m + 28

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m = -4.5

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