Guest #3572

2 months ago

Remove the brackets:

Combine like terms:

Take out common factor 3:

Factorise (x² - 1):

Question

The football team is running a jackpot in which the prize will start at $2500 for the first game, and then increase $500 each game if there is no winner. If there are no winners, find the value of the jackpot at the end of their 16-game season.

Solution 1

The **value** of the **jackpot** at the end of the **16-game** season will be $10,000.

An **expression** contains one or more **terms** with addition, subtraction, multiplication, and division.

We always combine the **like** **terms** in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The **jackpot** **prize** starts at $2500 for the first game and **increases** by $500 for each game if there is no winner.

For the **second** **game**,

The prize will be $2500 + $500 = $3000.

For the **third** **game**,

The prize will be $3000 + $500 = $3500.

**Continuing** in this pattern, the prize for the 16th game will be:

$2500 + ($500 × 15)

= $2500 + $7500

= $10000

Therefore,

The **value** of the **jackpot** at the end of the **16-game** season will be $10,000.

Learn more about **expressions** here:

#SPJ3

Solution 2

10,500 because if you first add 2500 and 500 its already 1 so fifteen times mor and thats 10,500

Question

Ms. Bergstedt asked two students to come up with two different sequences. Jay created this sequence: The first term is 4 and each term after the first is 6 more than the preceding term. Joe created this sequence: The first term is 8 and each term after the first term is 5 more than the preceding term. What is the value of the first term that they have in common?

Solution 1

Well, create an equation.

y=6x+4 and y=5x+8

From there you would go to Desmos.com and find out. The answer is 4,28.

This means it's the fourth term and the number is 28.

y=6x+4 and y=5x+8

From there you would go to Desmos.com and find out. The answer is 4,28.

This means it's the fourth term and the number is 28.

Question

A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

Solution 1

For this case we have the following equation:

h = -16t ^ 2 + 184t + 20

Deriving we have:

h '= -32t + 184

We equal zero and clear t:

-32t + 184 = 0

32t = 184

t = 184/32

t = 5.75 s

Then, the maximum height is given by:

h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20

h (5.75) = 549 feet

**Answer:**

**It takes the boulder to reach its maximum height about:**

**t = 5.75 s**

**the boulder's maximum hieght is:**

**h (5.75) = 549 feet**

h = -16t ^ 2 + 184t + 20

Deriving we have:

h '= -32t + 184

We equal zero and clear t:

-32t + 184 = 0

32t = 184

t = 184/32

t = 5.75 s

Then, the maximum height is given by:

h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20

h (5.75) = 549 feet

Solution 2

**Answer:**

**The answer should be C.**

Question

A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun

Solution 1

For this case we have the following equation:

h = -16t ^ 2 + 32t + 6

Deriving we have:

h '= -32t + 32

We equal zero and clear t:

-32t + 32 = 0

32t = 32

t = 32/32

t = 1 s

Then, the maximum height is given by:

h (1) = -16 * (1) ^ 2 + 32 * (1) + 6

h (1) = 22 feet

**Answer:**

**It takes the ball to reach its maximum height about:**

**t = 1 s**

**The ball's maximum height is:**

**h (1) = 22 feet**

h = -16t ^ 2 + 32t + 6

Deriving we have:

h '= -32t + 32

We equal zero and clear t:

-32t + 32 = 0

32t = 32

t = 32/32

t = 1 s

Then, the maximum height is given by:

h (1) = -16 * (1) ^ 2 + 32 * (1) + 6

h (1) = 22 feet

Question

Grant is rolling a standard six sided number die eight times. how many outcomes are possible

Solution 1

We have been given that Grant is rolling a standard six sided number die eight times and we have to find the total number of outcomes.

Grant is rolling six sided number die. Hence, we can say that

Number of outcomes if rolled once = 6

Number of outcomes if rolled twice =

Number of outcomes if rolled thrice=

We can see that if rolled twice then we have exponent 2, when rolled trice then we have an exponent 3.

Hence, if rolled 8 times then we have an exponent 8 on 6.

Therefore, the possible number of outcomes should be

**Hence, the number of possible outcomes is 1679616**

Solution 2

There are 1679616 possible outcomes.

There are 6 possible outcomes for each roll; 6^8 = 1679616

There are 6 possible outcomes for each roll; 6^8 = 1679616

Question

Debate this math question 3-3x6+2

Solution 1

For this question BODMAS should be used

BODMAS = Bracket Of Division Multiplication Addition Subtraction

SO, in 3-3x6+2. multiplication should be done first

= 3-18+2 Next addition should be done

= 3-16 And now subtraction

= -13

**Answer = -13**

BODMAS = Bracket Of Division Multiplication Addition Subtraction

SO, in 3-3x6+2. multiplication should be done first

= 3-18+2 Next addition should be done

= 3-16 And now subtraction

= -13

Solution 2

The answer for 3-3x6+2 is 17. For this you need to use PEMDAS (Please Excuse My Dear Aunt Sally) to solve the problem. First, M stands for multiplication so you do 3x6 which is 18. Then, A is addition so add 2 to 18 which is 20. Lastly, S stands for subtraction so you subtract 3 from 20 and you get your answer, 17.

Question

Anyone know the answer to this simple little equation? It's giving me a bit of a tough time.. 3x^2 (4x-7)

Solution 1

12x2−13x−14 look it up on google to show you the graph

Solution 2

3x^2 (4x-7) = 12x^3 - 21x^2

Question

Given that a:12=4:10 find the value of a.

Solution 1

A:12=4:10

The extremes are a and 10

The middles are 12 and 4

We know that PRODUCT OF MIDDLE = PRODUCT OF EXTREMES

a*10=12*4

a = 48/10

a = 4.8

Therefore,**the value of a = 4.8**

The extremes are a and 10

The middles are 12 and 4

We know that PRODUCT OF MIDDLE = PRODUCT OF EXTREMES

a*10=12*4

a = 48/10

a = 4.8

Therefore,

Solution 2

A/12= 4/10

Cross multiply: 12*4= a*10

⇒ a= 12*4/10= 4.8

**Final answer: a= 4.8**

Cross multiply: 12*4= a*10

⇒ a= 12*4/10= 4.8

Question

True, false, or open. Explain. 45/x-14=22

Solution 1

45/x - 14 = 22

add 14 to both sides

45/x -14 +14 = 22 +14

45/x = 36

36 x = 45

x = 45/36 = 5/4 = 1.25

add 14 to both sides

45/x -14 +14 = 22 +14

45/x = 36

36 x = 45

x = 45/36 = 5/4 = 1.25

Question

What are the domain and range of f(x) = 2(3x)?

Solution 1

Its going to be all real numbers

or (- inf , inf)

or (- inf , inf)

Solution 2

**Answer:**

A) domain (-infinity, infinity); range (0, infinity)

**Step-by-step explanation:**

Domain is reading the x-axis left or right

Range is reading the y-axis up or down

Hope this helps!

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