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sertanlavr [38]

3 years ago

12

How to draw a point: w and z

1 answer:

trapecia [35]3 years ago

4 0

Please provide the proper image.

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A house was valued at $540,000 last year. The house has now appreciated and increased in

Zigmanuir [339]

Answer:

The house worth now: $540,000*(1+4%)= $561,600

Step-by-step explanation:

4 0

3 years ago

Show work and explain with formulas.

vova2212 [387]

Answer:

$\large\boxed{4.\ S_{13}=260}$

$\large\boxed{5.\ \sum\limits_{k=1}^7(2k+5)=91}$

$\large\boxed{6.\ a_1=17,\ a_2=26,\ a_3=35}$

Step-by-step explanation:

4.

We have:

$a_6=18,\ a_{13}=32$

These are the terms of the arithmetic sequence.

We know:

$a_n=a_1+(n-1)d$

Therefore

$a_6=a_1+(6-1)d\ \text{and}\ a_{13}=a_1+(13-1)d\\\\a_6=a_1+5d\ \text{and}\ a_{13}=a_1+12d\\\\a_{13}-a_6=(a_1+12d)-(a_1+5d)\\\\a_{13}-a_6=a_1+12d-a_1-5d\\\\a_{13}-a_6=7d$

Substitute a₆ = 18 and a₁₃ = 32:

$7d=32-18$

$7d=14$ <em>divide both sides by 7</em>

$d=2$

$a_6=a_1+5d$

$18=a_1+5(2)$

$18=a_1+10$ <em>subtract 10 from both sides</em>

$8=a_1\to a_1=8$

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{a_1+n_1}{2}\cdot n$

Substitute a₁ = 8, a₁₃ = 32 and n = 13:

$S_{13}=\dfrac{8+32}{2}\cdot13=\dfrac{40}{2}\cdot13=20\cdot13=260$

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

5.

We have

$\sum\limits_{k=3}^7(2k+5)\to a_k=2k+5$

Calculate $a_{k+1}$

$a_{k+1}=2(k+1)+5=2k+2+5=2k+7$

Calculate the difference:

$a_{k+1}-a_k=(2k+7)-(2k+5)=2k+7-2k-5=2$

It's the arithmetic sequence with first term

$a_1=2(1)+5=2+5=7$

and common difference d = 2.

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute n = 7, a₁ = 7 and d = 2:

$S_7=\dfrac{2(7)+(7-1)(2)}{2}\cdot7=\dfrac{14+(6)(2)}{2}\cdot7=\dfrac{14+12}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)\\\\S_7=91$

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

6.

We have:

$a_1=17,\ a_n=197,\ S_n=2247$

The formula for the n-th term of an arithmetic sequence:

$a_n=a_1+(n-1)d$

The formula of the sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute:

$(1)\qquad 197=17+(n-1)d\\\\(2)\qquad2247=\dfrac{(2)(17)+(n-1)d}{2}\cdot n$

Convert the first equation:

$197=17+(n-1)d$ <em>subtract 17 from both sides</em>

$180=(n-1)d$ Substitute it to the second equation:

$2247=\dfrac{34+180}{2}\cdot n\\\\2247=\dfrac{214}{2}\cdot n$

$2247=107n$ <em>divde both sides by 107</em>

$21=n\to n=21$

Put the value of n to the equation (n - 1)d = 180:

$(21-1)d=180$

$20d=180$ <em>divide both sides by 20</em>

$d=9$

Therefore we have the explicit formula for the nth term of an arithmetic sequence:

$a_n=17+(n-1)(9)\\\\a_n=17+9n-9\\\\a_n=9n+8$

Put n = 1, n = 2 and n = 3:

$a_1=9(1)+8=9+8=17\qquad\text{CORRECT :)}\\\\a_2=9(2)+8=18+8=26\\\\a_3=9(3)+8=27+8=35$

4 0

3 years ago

The squirrel could store 48 nuts in a hiding place. If there were 768 nuts to hide, how

Dmitrij [34]

Answer:

16 hiding places

Step-by-step explanation:

768/48

=16

nuts hided/storing the nuts

7 0

3 years ago

Read 2 more answers

Given: 2x + 3y = 1470 Convert to slope intercept form to find the slope and y-intercept.

kirza4 [7]

Answer:

Slope = 2/3 and y-intercept = 490

Step-by-step explanation:

2x + 3y = 1470

3y = -2x + 1470

y = 2/3 x + 490 <----------Slope intercept form

Slope = 2/3 and y-intercept = 490

7 0

3 years ago

What is the value of the expression below? -28÷-4

Damm [24]

Answer: +7

Step-by-step explanation: Since a negative divided

by a negative always equals a positive, (-28) ÷ (-4) = +7

7 0

3 years ago

Read 2 more answers