Find the tenth term in each sequence. -1,2/3,7/3,4,17/3

Answers

Answer 1

Answer:

It'a an arithmetic sequence:

$a_1=-1\n\na_2=-1+(5)/(3)=-(3)/(3)+(5)/(3)=(2)/(3)\n\na_3=(2)/(3)+(5)/(3)=(7)/(3)\n\na_4=(7)/(3)+(5)/(3)=(12)/(3)=4\n\na_5=4+(5)/(3)=(12)/(3)+(5)/(3)=(17)/(3)\n\vdots\n\n\text{The general formula for nth term of an arithmetic sequence}\n\na_n=a_1+(n-1)d\n\n\text{We have}\ a_1=-1\ \text{and}\ d=(5)/(3).\n\n\text{Substitute}\n\na_n=-1+(n-1)\left((5)/(3)\right)=-1+(5)/(3)n-(5)/(3)=(5)/(3)n-(3)/(3)-(5)/(3)$

$\boxed{a_n=(5)/(3)n-(8)/(3)}$

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Laticia randomly selected 25% of the seventh-grade students in her school an asked them their favorite season.Of the students surveyed,51 chose summer as their favorite season. Based on the data, what is the most reasonable prediction of the number of seventh-grade students in her school who would choose summer as their favorite season.

Answers

about 204 students would choose summer , I found this because 25% is one quarter of a whole and to get the whole you multiply by four so take 51 and multiply by four to get 204

Please help me asap i have other questions you can answer toosolutions to:
(3x+5)^2+5(3x+5)+6=0

Answers

Answer:

x = -8/3 = -2.667

x = -7/3 = -2.333

Step-by-step explanation:

Equation at the end of step 1 :

(((3x + 5)2) + 5 • (3x + 5)) + 6 = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 9x2+45x+56

The first term is, 9x2 its coefficient is 9 .

The middle term is, +45x its coefficient is 45 .

The last term, "the constant", is +56

Step-1 : Multiply the coefficient of the first term by the constant 9 • 56 = 504

Step-2 : Find two factors of 504 whose sum equals the coefficient of the middle term, which is 45 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 21 and 24

9x2 + 21x + 24x + 56

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (3x+7)

Add up the last 2 terms, pulling out common factors :

8 • (3x+7)

Step-5 : Add up the four terms of step 4 :

(3x+8) • (3x+7)

Which is the desired factorization

Solve : 3x+7 = 0

Subtract 7 from both sides of the equation :

3x = -7

Divide both sides of the equation by 3:

x = -7/3 = -2.333

Solving a Single Variable Equation :

3.3 Solve : 3x+8 = 0

Subtract 8 from both sides of the equation :

3x = -8

Divide both sides of the equation by 3:

x = -8/3 = -2.667

Supplement : Solving Quadratic Equation Directly

Solving 9x2+45x+56 = 0 directly

A teacher is evaluating the typing speeds of students in the class. Carl types 108 words in 2 minutes. Max types 260 words in 5 minutes. Jason types 177 words in 3 minutes. Calculate the unit rate of words per minute for each student. Then, order the names of the students from slowest to fastest based on their typing speeds?