MATHEMATICS HIGH SCHOOL

The start of an arthmetic sequence is show Below. a) Work out the n term rule for this sequence. b) Work out the 30 term in this sequence. 4,13,22,31

Answers

Answer 1

Answer:

Step-by-step explanation:

Each term is 9 more than the previous term....the common difference, d = 9

an = a1 + 9(n-1) where a1 is the first term = 4

this reduces to: an = 4 + 9n-9

an = 9n - 5

the 30th term is then a30 = 9(30) - 5 = 265

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Simplifying rational expressions1. (c+8)(c-8)/(c-8)(c+3)
2. n^2+4n-12/n^2+2n-8
3. 42x^2y^3/28x^3y
4. m^2-3m-10/m-5

Answers

1. $((c + 8)(c - 8))/((c - 8)(c + 3))_,_$
   $(c + 8)/(c + 3)_,_$

2. $(n^(2) + 4n - 12)/(n^(2) + 2n - 8)_,_$
   $(n^(2) + 6n - 2n - 12)/(n^(2) + 4n - 2n - 8)_,_$
   $(n(n) + n(6) - 2(n) - 2(6))/(n(n) + n(4) - 2(n) - 2(4))_,_$
   $(n(n + 6) - 2(n + 6))/(n(n + 4) - 2(n + 4))_,_$
   $((n - 2)(n + 6))/((n - 2)(n + 4))_,_$
   $(n + 6)/(n + 4)_,_$

3. $(42x^(2)y^(3))/(28x^(3)y)_,_$
   $(3y^(2))/(2x)_,_$

4. $(m^(2) - 3m - 10)/(m - 5)_,_$
   $(m^(2) - 5m + 2m - 10)/(m - 5)_,_$
   $(m(m) - m(5) + 2(m) - 2(5))/(m - 5)_,_$
   $(m(m - 5) + 2(m - 5))/(m - 5)_,_$
   $((m + 2)(m - 5))/(m - 5)_,_$
   $m + 2_,_$

Estimate a 15% tip for a $27.60 bill.

Answers

Answer:

$4.2=tip value

$32.2=total value

Step-by-step explanation:

to estimate means to round to make it easier and i rounded 27.60 to 28 and 15% of 28 is 4.2, then to find the total value add the tip to the bill cost 4.2+28 to get 32.2 so its around 32.2 dollars

What is the correct solution to the equation? 5(x - 5) = 15 a. 50
b. 2
c. 8
d. 80

Answers

c. 8

You substitute 8 into x, which makes the equation 5(8-5) = 15. 8-5 is 3, and 5 x 3 = 15.

The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?

Answers

Answer:

The length of the diameter of the circle is 10 unit.

Step-by-step explanation:

Given : The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4).

To find : How long is the diameter of the circle?

Solution :

The center of a circle is at the origin i.e. $C=(x_1,y_1)=(0,0)$

An endpoint of a diameter of the circle is at $D=(x_2,y_2)=(-3,-4)$

The distance between the center and the end point of the diameter is the radius of the circle.

So, we find the radius with the help of distance formula,

$d=√((x_2-x_1)^2+(y_2-y_1)^2)$

Substitute the value in the formula,

$r=√((-3-0)^2+(-4-0)^2)$

$r=√(9+16)$

$r=√(25)$

$r=5$

Diameter is twice of radius $d=5* 2=10$

Therefore, The length of the diameter of the circle is 10 unit.

Use the distance formula
$√((-4-4)^2+(-3-3)^2) = √(100)=10$

24=9x+4-4x
Solve equation. Check your answer.

Answers

Answer:

x=4. Verified, Not wrong.

Step-by-step explanation:

24=9x+4-4x

24 = 5x+4

20-4

5x=20

(divide)

x=4

Step-by-step explanation:

24-4=9x-4x

20=9x-4x

20=5x

x=4

What is the focal length of the parabola with equation shown below?

Answers

patterns: vertical : y = a(x - h)² + k horizontal: x = a(y - k)² + h

Look at the patterns above and remember these key points.

1) if the x is squared, the parabola is vertical. It either opens up or down.
if the y is squared, the parabola is horizontal. It either opens left or right.

2) if a is positive, the parabola opens up or to the right.
if a is negative, the parabola opens down or to the left

3) the vertex is at (h,k). Be very careful. locations of h and k varies if the parabola is vertical or horizontal. its sign is also different in those positions

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Solve.–30 = 6za. –5b. –6c. –24d. –180

(05.02)A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half. Each bag of soil covers 20 square yards. How many bags should the farmer purchase? 1 bag 2 bags 3 bags 4 bags