 admin # Find the sum of (3x^2+16x+9) and (-16x-12)

2 months ago

## Solution 1 Guest #3572
2 months ago Remove the brackets: Combine like terms: Take out common factor 3: Factorise (x² - 1): ## 📚 Related Questions

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. ### What is an expression? 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.

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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.
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

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
Solution 2

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

It takes the ball to reach its maximum height about:

t = 1 s

The ball's maximum height is:

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
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

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
Solution 2
A/12= 4/10

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

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)
Solution 2

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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