Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6, 10, and 15. Is there a direct variation between a triangular number and its position in the sequence?

Answers

Answer 1

Answer: As observed in the given triangular numbers, 1, 3, 6, 10, and 15, the first two differ by 2. The second and the third, differ by 3. The third and fourth differ by 4 and the last two differ by 5. From this, it can be concluded that the difference between the triangular numbers from an arithmetic sequence with 2 as the first term and common difference of 1.

Answer 2

Answer:

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

Equation is 3p+4=25

p=7

Step-by-step explanation:

Isolate the variable

3p + 4 - 4 = 25 - 4

Simplify

3p = 21

Solve for p

3p/3 = 21/3

p=7

A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.

Answers

Answer:

Part a) $120\pi\ (rad)/(min)$

Part b) $960\pi\ (in)/(min)$

Step-by-step explanation:

we have

60 rev/min

Part a) Find the angular speed in radians per minute

we know that

One revolution represent 2π radians (complete circle)

$1\ rev=2\pi \ rad$

To convert rev to rad, multiply by 2π

$60\ (rev)/(min)=60(2\pi)=120\pi\ (rad)/(min)$

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=8\ in$ ----> given problem

substitute

$C=2\pi(8)$

$C=16\pi\ in$

Remember that

One revolution subtends a length equal to the circumference of the circle

$1\ rev=16\pi\ in$

To convert rev to in, multiply by 16π

$60\ (rev)/(min)=60(16\pi)=960\pi\ (in)/(min)$

4+1=5 2+5=12 3+6=21 8+11=?

Answers

most of these are wrong....?
4+1=5
2+5 is not 12, it is 7
3+6 is not 21, it is 9
8+11= 19

4+1=5+2+5=12+3+6=21+8+11= Total =40

Solve the following exponential equations 4^x=1024

Answers

$4^x=1024 \n\nx\neq 0\n \n4^x=4^5\n \nx=5$

$4^x=1024\n \n 2^(2x)=2^(10)\n \n 2x=10\n \n x=(10)/(2)\n \n \boxed{x=5}$

The Foil method is used for__a determining the order of operations in a standard algebra problem
b factoring quadratic equations
c simplifying factor sets that contain variables
d solving inequalities

Answers

Factoring Quadratic Equations.
U use the FOIL method to factor trinomials into binomial that would then allow you to find the solutions to the problem

4. Here are the ingredients needed to make 12 shortcakes.Shortcakes
Makes 12 shortcakes
50 g of sugar
200 g of butter
200 g of flour
10 ml of milk
Liz makes some shortcakes.
She uses 25 ml of milk.
(a) How many shortcakes does Liz make?