Can someone help me with this plss

Answer:

Proved

Step-by-step explanation:

Given

[tex]a_n = 2n[/tex]

Required

Prove that [tex]S_n = n(n+1)[/tex]

The given sequence is an arithmetic sequence.

The Sn of this sequence is:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

Calculate a1

[tex]a_n =2n[/tex]

[tex]a_1 =2*1[/tex]

[tex]a_1 =2[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]

Factor out 2

[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]

[tex]S_n = n(1 + n)[/tex]

[tex]S_n = n(n + 1)[/tex] --- Proved

Answer:

the first graph

Step-by-step explanation:

the one with (0,-1) (-3,1) (3,-3)

Answer:

[tex]r \le 10[/tex]

[tex]s > -1[/tex]

[tex]t \ne 5[/tex]

[tex]x \le -3[/tex]

[tex]y \ne 1[/tex]

Step-by-step explanation:

Required

Translate to mathematical statements

a) r is less than or equal to ten.

less than or equal means [tex]\le[/tex]

So, the expression is:

[tex]r \le 10[/tex]

b) s is more than negative one

More than means >

So, the expression is:

[tex]s > -1[/tex]

c) t isn't the same as negative  five.

isn't the same means not equal to ([tex]\neq[/tex])

So, the expression is:

[tex]t \ne 5[/tex]

d) x is at most negative three.

At most means [tex]\le[/tex]

So, the expression is:

[tex]x \le -3[/tex]

e) y is never one.

is never means not equal to ([tex]\neq[/tex])

So, the expression is:

[tex]y \ne 1[/tex]

Answer:

B 2:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x=18°

Step-by-step explanation:

5x-18=4x

subtract 4x from both sides

x-18=0

add 18 to both sides

x=18°

answer 41x

Step-by-step

Answer:

31/2 d nada xdddddddddddddddddddddddddddd

Answer:

0.1709 in words-

Point one seven zero nine

Answer:

33-11

48-26

Alice’s age (a) = Martha’s age (m) + 22

Step-by-step explanation:

In order to find the blank spots you would need to find the difference in the filled spots. We are trying to figure out the difference which is subtraction.

28 - 6 = 22

To make sure we are correct we would do another problem.

37 - 15 = 22

So in order to find Martha's age when Alice was 33, we would subract 22.

33 - 22 = 11

Same when Alice was 48.

48 - 22 = 26

And the last equation is asking the difference between them, which would be 22.

Answer: 11 and 26

Step-by-step explanation:

hope this helps :)

Step-by-step explanation:

1

9

2

5

5

8

6

7

−

1

9

8

9

7

6

6

6

7

+

4

4

5

Answer:

Step-by-step explanation:

Answer:

Slope: 5/3

Step-by-step explanation:

Linear equation:

y = mx + b

m is the slope

so if,

y = 5/3x - 4

5/3 is the slope.

Hope this helps :)

Let me know if there are any mistakes!!

Answer:

2,540 miles

Step-by-step explanation:

The computation of the fewer miles is given below;

For Space explorer B

= 15,000 miles ÷ 5 hours

= 3,000 miles per hour

For space explorer A

y = 4,600 x

That means in one hour it covered 460 miles

So, the fewer miles would be

= 3,000 - 460

= 2,540 miles

Answer:

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Length times width. 3 is length and width is 5

Answer:

suree.

Step-by-step explanation:

The correct reason for the statement ∠1 ≅ ∠2 will be;

⇒ Definition of Vertical Angles.

Option D is true.

What is Vertical angles?

When the two lines are crosses to each other at a point then the vertical angles are formed.

Given that;

∠1 and ∠2 are formed between two lines which crosses at a point.

Now,

The two lines are vertical lines which passes through a point and ∠1 and ∠2 are formed between them.

So, By definition of Vertical Angles;

∠1 ≅ ∠2

Therefore,

The correct reason for the statement ∠1 ≅ ∠2 will be;

⇒ Definition of Vertical Angles.

Learn more about the vertical angles visit:

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Answer:

y=-2/7x+1/7

Step-by-step explanation:

Find the slope first

-1-1/4+3

-2/7

m=-2/7

y=-2/7x+b

1=-2/7(-3)+b

b=1/7

Answer:

a)

Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.

Proof by Contrapositive:

Assumed statement: Suppose that integers x and y do not have opposite parity.

Proven Statement: x and y are not a pair of consecutive integers.

Proof -

x = 2u₁ , y = 2u₂

Then

(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)

If y = 2u₁ + 1

Not possible

⇒x and y are not a pair of consecutive integers.

Hence proved.

Proof by Contradiction:

Assumed statement: Suppose x and y are not a pair of consecutive integers.

Proven Statement: Suppose x and y do not have opposite parity.

Proof -

If x and y are not a pair of consecutive integers.

⇒ either x and y are odd or even

If x and y are odd

⇒x and y have same parity

Contradiction

If x and y are even

⇒x and y have same parity

Contradiction

(b)

Proof by Contrapositive:

Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)

Proven Statement: n² is not odd (i.e n² is even)

Proof -

Let n is even

⇒n = 2m

⇒n² = (2m)² = 4m²

⇒n² is even

Hence proved.

Proof by Contradiction:

Assumed statement: Let n be an integer such that n² be odd.

Proven Statement:  suppose that n is not odd (i.e n is even)

Proof -

Let n² is odd

⇒n² is even

⇒n² = 2m

⇒2 | n²

⇒2 | n

⇒n = 2x

⇒ n is even

Contradiction

Answer:

$56.16

Step-by-step explanation:

74.88 times 0.75 =56.16

Answer:

$56.16

Step-by-step explanation:

To find the sale price, multiply the original price by 0.75:

74.88(0.75)

= 56.16

So, the sale price is $56.16

Answer:

375

Step-by-step explanation:

15 times 25 equals 375

Answer:186.66is answer

p=14000

r=8%

time=60days=2month/12=1/6year

Step-by-step explanation:

simple interest=ptr/100=14000×8×1/600=186.666

Answer:

-14. Aunque podría estar equivocado. Espero poder ayudar

Step-by-step explanation:

Answer:

72 square feet not covered

Step-by-step explanation:

100%-40% = 60%

60% of 120 = 0.6x120 = 72

Answer:

72

Step-by-step explanation:

because i know

Answer:

1065.1

Step-by-step explanation:

Part a:

1. Halloween's piecework pay = $148.20

2. Halloween's total hourly pay for the week = $364

3. Halloween's total pay for the week = $512.20

Part b:

Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.

Part c:

Halloween's hourly pay for 0 units production = $364

Salary is a compensation or fixed amount of money paid to an employee by an employer in return for work performed.

For the given situation,

Halloween's salary received per hour = $9.10

Halloween's piecework pay per unit = 15 cents

Total work per week = 40 hours

Total unit produced per week = 988 units.

Part a:

1. Halloween's piecework pay = [tex](988)(15)[/tex]

⇒ [tex]14820 cents[/tex]

we know that $1 = 100 cents

⇒ [tex]\$148.20[/tex]

2. Halloween's total hourly pay for the week = [tex](40)(9.10)[/tex]

⇒ [tex]\$364[/tex]

3. Halloween's total pay for the week = [tex]364+148.20[/tex]

⇒ [tex]\$512.20[/tex]

Part b:

Halloween's boss offered to pay her a straight $13 per hour and no piecework pay for the week.

Total amount received for the week = [tex](40)(13)[/tex]

⇒ [tex]\$520[/tex]

Difference in pay = [tex]520-512.20[/tex]

⇒ [tex]\$7.80[/tex]

Thus, she earns more when she get the straight salary on hourly basis.

Part c:

If her production is 0 units, then she might get her hourly pay only.

⇒ [tex](40)(9.10)[/tex]

Hence we can conclude that

Part a:

1. Halloween's piecework pay = $148.20

2. Halloween's total hourly pay for the week = $364

3. Halloween's total pay for the week = $512.20

Part b:

Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.

Part c:

Halloween's hourly pay for 0 units production = $364

Learn more about salary and wages here

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Answer:

You want to buy long pieces of paper at Dollar Tree for 66 cents. You have $12. How many long pieces of paper can you buy

Step-by-step explanation:

Answer:

93°

Step-by-step explanation:

In triangle ABC

one angle = 68°

Another angle = 19°

Let the third angle be X Then

x + 68° + 19° = 180° { being sum of angles of triangle }

x = 180° - 87°

x = 93°

The measure of the third Angle is 93°

Hope it will help :)

Answer:

the number of t-shirts sold to breakeven is 56 t-shirts

Step-by-step explanation:

The computation of the number of t-shirts sold to breakeven is shown below:

= Fixed cost ÷ (Selling price - cost price)

= $350 ÷ ($10 -  $3.75)

= $350 ÷ 6.25

=  56 t-shirts

Hence, the number of t-shirts sold to breakeven is 56 t-shirts