Sequences and equations:Position = 10, 11, 12, 13, 14
Value of term = 28, 31, 34, 37

Answers

Answer 1

Answer: Sequences
Sequence: a function whose domain is a set of consecutive integers.
Domain: the position of the term (1st, 2nd, 3rd, and so on).
Range: the terms of the sequence.
Terms: the numbers in the sequence.
Finite Sequence: a sequence that has a last term.
Infinite Sequence: a sequence that continues without stopping.
Rule for the nth term: means to write an equation of the arithmetic sequence.
Look at the following sequences:
an = 2, 4, 6, 8 an = 2, 4, 6, 8, …..
If n represents the position of the term, then a2 refers to the 2nd term.
Writing Terms of Sequences
To write the first six terms of a sequence, plug the numbers 1 – 6 in for n.
Example 1: Write the first six terms of the sequence.
a) an = 5 – n b) f(n) = 5n
Example 2: Write the next term in the sequence.
a) 1, 4, 9, 16, 25, ______, … b) 5, 25, 125, ______, … c) 456 , , , _____,...
789
d) 0, 3, 8, 15, 24, ______, … e) 1, 2, 5, 10, 17, ______, …

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Eleanor and Billie make 752 brownies then give them to their nine friends to share how many will they have leftover what impacted the remainder have on the answer

Use the figure to identify each pair of angles as complementary angles, supplementary angles, vertical angles, or none of these.A: angles 1 and 5
B: angles 3 and 5
C: angles 3 and 4

Answers

Complimentary means parts of a 90* angle. So 1 and 5. Then 3 and 5 are vertical, and 3&4 supplementary because they make up a 180*. So comp=90, supp=180, and vertical are opposite sides of an X shape

A right triangle has side length 9,40, and 41 as shown below. Use these lengths t find cos Y, and tan Y, and sin Y.

Answers

Trigonometric functions are applicable to the right-angled triangles. The value of the Sin(Y), Cos(Y), and Tan(Y) are 0.976, 0.219 and 4.445.

What are Trigonometric functions?

$\rm Sin \theta=(Perpendicular)/(Hypotenuse)\n\n\nCos \theta=(Base)/(Hypotenuse)\n\n\nTan \theta=(Perpendicular)/(Base)$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

XY = 41

YZ = 9

XZ = 40

In ΔXYZ for ∠Y,

$\rm Sin \theta=(Perpendicular)/(Hypotenuse)\n\n\rm Sin (\angle Y)=(XZ)/(XY)\n\n\rm Sin (\angle Y)=(40)/(41)\n\n$

$\rm Cos \theta=(Base)/(Hypotenuse)\n\n Cos (\angle Y)=(ZY)/(XY)\n\n Cos (\angle Y)=(9)/(41)$

$\rm Tan \theta=(Perpendicular)/(Base)\n\nTan \theta=(XZ)/(ZY)\n\nTan \theta=(40)/(9)$

Hence, the value of the Sin(Y), Cos(Y), and Tan(Y) are 0.976, 0.219 and 4.445.

Learn more about Trigonometric functions:

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Final answer:

The cos Y, sin Y, and tan Y of a right triangle with side lengths of 9, 40, and 41 can be calculated using trigonometric ratios. Cos Y equals 9/41, sin Y equals 40/41, and tan Y equals 40/9.

Explanation:

In a right-angled triangle, we use the concept of trigonometric ratios which involves sine (sin), cosine (cos) and tangent (tan). Here, the side length 9 would be considered the adjacent side (a), the side length 40 would be considered the opposite side (b), and the side length 41 would be the hypotenuse (c).

The trigonometric ratios can be determined as follows:

Cosine (cos) Y = adjacent/hypotenuse = 9/41
Sine (sin) Y = opposite/hypotenuse = 40/41
Tangent (tan) Y = opposite/adjacent = 40/9

This would be the solution to finding the cos Y, tan Y, and sin Y with respect to angle Y.

Learn more about Trigonometric Ratios here:

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What is solution for the following system of equations, 2x+8y=4 and x=-3y+51) X=14 Y=-3
2) X=2 Y=-3
3) X=-3 Y=-3
4)X=12 Y=5

Answers

Answer:

1) x=14 and y=-3

Step-by-step explanation:

To solve the system of equations, substitute x = -3y+5 into the equation 2x + 8y = 4 for x. This becomes 2(-3y+5) +8y = 4. To solve, apply the distributive property, combine like terms and isolate y.

2(-3y+5)+8y=4

-6y+10+8y=4

10+2y=4

10-10+2y=4-10

2y=-6

y=-3

Then to find x, substitute y =-3 into x =-3y+5.

x = -3(-3) + 5

x = 9 + 5

x = 14

Payton plays 15 games of fortnight in 15 minutes. If he maintains this rate, how many games will he play in 3 hours

Answers

Payton will play 180 games in 3 hours.

Step-by-step explanation:

Given,

Games played in 15 minutes = 15 games

We will find unit rate;

15 minutes = 15 games

Dividing both sides by 15

$(15)/(15)\ minutes=(15)/(15)\ games\n\n1\ minute = 1\ game$

Time = 3 hours = 3*60 = 180 minutes

180 minutes = 180*games per minute

180 minutes = 180*1 games

180 minutes = 180 games

Payton will play 180 games in 3 hours.

Keywords: unit rate, multiplication

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Please help :)1. Does x < 4 mean the same thing as 4 > x?

2. Give 3 numbers that would work for the value of x if x < 1

3. Give 3 numbers that would work for the value of x if x ≤ -2

Write these statements as inequalities: Use symbols ≤ ≥ < or >.

4. I have at least 4 homework assignments tonight. ___________

5. You must be at most 10 years old to swim in the baby pool. ____________

6. I can spend a maximum of $20 on lunch today. ___________

Answers

Answer:

1: No x < 4 is not the same thing as 4 > x.

2: 0, -2, -10

3: -2, -4, -22

4: x ≥ 4

5: x ≤ 10

6: x ≤ $20

Step-by-step explanation

Do you need an explanation?

The body of a person who weighs 50 kilograms contains around 2 × 10^2 grams of sodium chloride. How much sodium chloride is contained in the bodies of 1.8 × 10^3 people who each weigh 50 kilograms? Represent the answer in scientific notationA. 3.6 × 10^5 gramsB. 1.1 × 10^1 gramsC. 36 × 10^5 gramsD. 11 × 10^1 grams