1. 10x + 5 + 3x + 1<br> # of terms<br> list like terms

The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls out of a drum with 69 balls and

Doss [256]

Answer: a) 11,238,513 and b) 292,201,338

Step-by-step explanation:

Since we have given that

Number of white balls = 69

Number of white balls drawn = 5

Number of red balls = 26

Number of red balls drawn = 1

According to question, The Powerball jackpot is won by matching all five white balls in any order and the red Powerball.

So, a) Possible different ways of Powerball tickets can be purchased is given by

$^{69}C_5\\\\=11,238,513$

And

b) Number of possible ways of different winning Poweball tickets are there would be

$26\times ^[69}C_5\\\\=292,201,338$

Hence, a) 11,238,513 and b) 292,201,338

7 0

3 years ago

Koran is spending $12 on games and rides at another carnival, where a game costs $0.25 and a ride costs $1.

Vlad [161]

Answer:

$0.25x+y=12$

Step-by-step explanation:

Let

y ----> the number of rides

x ---> the number of games

we know that

The number of rides multiplied by $1 plus the number of games multiplied by $0.25 must be equal to $12 (the dollar amount Koran is spending)

so

The equation that represent this situation is

$0.25x+y=12$

5 0

3 years ago

A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true? A. ABCD is

Dima020 [189]

Hey There!!

The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).

Hope It Helped!~ ♡

ItsNobody~ ☆

7 0

3 years ago

How do I solve this equation by linear combinations

Tatiana [17]

What’s the equation given ?

7 0

3 years ago

Dave is three times as old as his sister. In seven years the sum of their ages will be 38. How old are they now?

bija089 [108]

Answer:

Dave is 18 and his sister is 6.

Step-by-step explanation:

If you do 38 -7x2 you can work out the combined ages of them now which is 24 (you have to do 7x2 because there are two of them and its seven years in the future). Then you can work out their ages using a ratio. Dave’s age : his sister’s age is 3:1 so if you divide 24 by 4 (3+1 = 4 so your can work out one portion of their age) you can find out how old the sister is which is 6. Times that by 3 to get Dave’s age which is 18. A formula for this (where x is his sisters age) would be 3x=38-7x2 which cancels down to 6.

7 0

4 years ago

1. 10x + 5 + 3x + 1 # of terms list like terms