MATHEMATICS HIGH SCHOOL

A pattern of letter arrangements begins with the 3 steps below, A
ABA
ABCBA

what are the next 3 steps, how many letters are in the 3 above and how many letters are in the 10th step?

Answers

Answer 1

Answer:

The 10th step have 19 letters.

What is Arithmetic Progression?

We can define an arithmetic progression (AP) in two ways:

An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.
An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term.

In first pattern

number of letters= 1

In second pattern

number of letters= 3

In third pattern

number of letters= 5

so, we can create a series as

1,3,5,.....

a=1, d= 2

Now, for a_10= a+ 9d

=1 + 9*2

=1+18

=18

Hence, the 10th step have 19 letters.

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Answer 2

Answer:

next 3 steps:

ABCDCBA
ABCDEDCBA
ABCDEFEDCBA

Patern: add 2 letters

1. 1
2. 3
3. 5
4. 7
5. 9
6. 11
7. 13
8. 15
9. 17
10. 19

The 10th step has 19 letters

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11.68 - 0.48 ÷ (-1.6) =
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In a certain triangle, the measure of the largest angle is 20 degrees more than twice the measure of the smallest angle. Five times the measure of the smallest angle equals the sum of the measures of the other two angles. Find the measures of the three angles.

Answers

Let the medium angle be B degrees the small angle be A degrees the large angle be C degrees Then C = 2 B + 20 ..................X 5 B = A + C ..................Y Sum of all angles A + B + C = 180 .............Z Applying Y in Z 5 B + B = 180 6 B = 180 B = 30 From X C = 2 x 30 + 20 = 60 + 20 = 80 From Y 5 x 30 = A + 80 150 = A + 80 150 - 80 = A = 70 Hence medium angle B = 30 degrees the small angle A = 70 degrees the large angle C = 80 degrees

Final answer:

To solve the problem, we apply the properties of a triangle and make a system of linear equations. Setting up appropriate mathematical expressions for angles and solving the equation gives the angles as 30, 80 and 70 degrees.

Explanation:

This problem involves angles in a triangle and can be solved through linear equations. We know from the problem that the largest angle is 20 degrees more than twice the smallest angle, and 5 times the smallest angle equals the sum of the measures of the other two angles.

Let's denote the smallest angle as x. Thus the largest angle becomes 2x + 20.
The third angle, due to the property that the sum of angles in a triangle equals 180, would be 180 - x - (2x + 20).
You can insert the expression of the third angle into the second equation from problem statement, which gives: 5x = x + 2x + 20. Solving this equation gives x = 30.
Therefore, the angles are: 30 degrees, 2*30 + 20 = 80 degrees and 180 - 30 - 80 = 70 degrees.

Solution verification:

The sum of all angles is indeed 180 degrees.
The largest angle is indeed 20 degrees more than twice the smallest one.
Five times the smallest angle is indeed equal to the sum of the two other angles.

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Find value of x and y

2.) 4x+13y=40
4x+3y=-40

Answers

$\left\{\begin{array}{ccc}4x+13y=40\n4x+3y=-40&/\cdot(-1)\end{array}\right\n+\left\{\begin{array}{ccc}4x+13y=40\n-4x-3y=40\end{array}\right\n-----------\n.\ \ \ \ \ \ 10y=80\ \ \ \ /:10\n.\ \ \ \ \ \ y=8\n\n4x+3\cdot8=-40\n4x+24=-40\n4x=-40-24\n4x=-64\ \ \ \ /:4\nx=-16\n\nSolution:x=-16\ and\ y=8.$

4x + 13y = 40
4x + 3y = -40
using elimination method
10y = 80
y = 8
substitute y in eq1
4x + 13(8) = 40
4x + 104 = 40
4x = 40 - 104
4x = - 64
x = -16

What is the degree of each monomial? 7m^6n^5

A. 5
B. 11
C. 6
D. 7

Answers

The answer is B. 11

If the polynomial contains more than one variable, then the degree of the monomial is equal to the sums of all their exponents. 6+5 = 11

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Final answer:

The degree of a monomial is the sum of the exponents of its variables. For the given monomial 7m^6n^5, adding the exponents gives us a degree of 11. Thus, the correct choice is B. 11.

Explanation:

The degree of a monomial is the sum of the exponents of all its variables. If we look at the monomial 7m^6n^5, we see that m is raised to the exponent 6 and n to the exponent 5. Adding these exponents together, we find that the total degree of this monomial is 11. Therefore, the correct answer is B. 11.

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PLEASE HELP i really need the answer asap

Answers

Answer:

its 16

Step-by-step explanation:

8 /x = 10/20

20 * 8 =160

10 * x =10x

10x = 160

x=16

The answer is
X is 16

Delilah received a stipend of $1,000 for the extra work she does on the job. She is going to deposit the money into her bank account that receives 4% simple interest.The account balance after year 3 is what

Answers

Answer:

$1,120

Step-by-step explanation:

Interest I = PRT/100 where P = amount deposited, R = rate percent and T = time.

So I = (1000 * 4 * 3) / 100

= $120.

So the account balance is 1,120 dollars.

Shana sells
t-shirts. It costs Shana $6.50 to buy
each t-shirt. She also pays $150 each
month to rent equipment to add print to the t-shirts.

Shana sells each
t-shirt for $12.

Write an
inequality that can be used to determine the number of t-shirts (T) Shana must
sell each month in order to make a profit for the month.