5. Purple Bricks are stacked according to the pattern below. Each row contains 2 more bricks than the row above it!
Part A.
Determine a Quadratic Function to model the total number of bricks in the stack, f(x), given a number of rows X.
Part B.
If there are 50 rows in the stack, how many bricks would there be ? Use your quadratic function to determine the number of rows. Show your work and explain your reasoning
Answers
Answer:
Part A
The Quadratic Function to model the total number of bricks the stack is f(x) = x²
Part B
The number of bricks we will have for 50 rows is 2500 bricks
Step-by-step explanation:
Part A
Let the Quadratic Function to model the total number of bricks the stack, f(x), where x is the number of rows be f(x) = a·x² + b·x + c
We have;
When x = 0, f(x) = 0, therefore, f(0) = a×0² + b×0 + c = 0 + 0 + c = 0
∴ c = 0
When x = 1, f(x) = 1, therefore, f(1) = a×1² + b×1 + 0 = 1
∴ a + b = 1...(1)
When x = 2, f(x) = 4, therefore, f(2) = a×2² + b×2 = 4
∴ 4·a + 2·b = 4...(2)
Multiply equation (1) by 2, and subtract it from equation (2) gives;
4·a + 2·b - 2×(a + b) = 4 - 2 × 1
2·a = 2
a = 1
From equation (1), we have;
b = 1 - a = 1 - 1 = 0
b = 0
∴ f(x) = a·x² + b·x + c = 1·x² + 0·x + 0 = x²
Therefore, the Quadratic Function to model the total number of bricks the stack, f(x), where x is the number of rows be f(x) = x²
Part B
If there are 50 rows in the stack, then we have, x = 50
Therefore;
f(50) = 50² = 2500
The number of bricks we will have for 50 rows is f(50) = 2500 bricks
Related Questions
A coffee table is on sale for 20% off the original price of $115.
If there is 7.5% sales tax, what is the final price of the coffee table?
Enter your answer in the box.
Answers
Answer:
$98.90
Step-by-step explanation:
20% off of 115 is 92 then when you add the sales tax of 7.5% you get $98.90.
You are going to pay $6.90 in sales tax.
PLEASE MARK BRAINLIEST
Answer:
$98.90
Step-by-step explanation:
20% off of 115 is 92 then when you add the sales tax of 7.5% you get $98.90.
You are going to pay $6.90 in sales tax.
What is the measure of angle five and what vocabulary word is it?
Answers
Answer: The measure of 5 is 90 degrees and it is a right angle
Step-by-step explanation:
Explanation above
A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 8 granola bars and each large box has 24 granola bars. How many granola bars are there in 8 small boxes and 6 large boxes? How many granola bars are there in ss small boxes and ll large boxes?
Answers
Answer:
208
Step-by-step explanation:
8 times 8 +6 times 24=208
Express this amount in dozens. (Use decimal form.) 75 cupcakes
Answers
Answer:
6.25 dozens for 75 cupcakes
Step-by-step explanation:
(used a calculator... if I'm wrong, I'm sorry TmT
Answer:
6.25 dozens
Step-by-step explanation:
1 dozen = 12
75 / 12 = 25 / 4
25 / 4 = 6 1 /4 = 6.25
Find the next two numbers in the pattern
Answers
Answer:
They are -6 and positive 3
I need help please
Answers
Answer:
help on what like whats ur question
Step-by-step explanation:
Answer:
I hope this helps
Step-by-step explanation:
need more letters
Problem #18
I have a box that is 5 inches wide, 2 inches deep, and 4 inches tall that I want
to fill with sand. How much sand can I fit inside my box?
Answers
Answer:
40in^3Step-by-step explanation:
Step one:
given data
dimension of the box
lengh= 5 in
width= 2 in
height =4 in
Required
the volume of the box
the expression for the volume is
V=L*W*H
V=5*2*4
V=40 in^3
Hence the volume of sand the box can take is 40in^3
A biker can travel 8 miles in one hour. How long will it take him to travel 32 miles?
Create a table. Highlight the unit rate. State your answer clearly with a label.
Answers
Answer:
4hrs
Step-by-step explanation:
Given parameters:
Rate of the biker = 8mph
Unknown:
Time taken to travel 32miles = ?
Solution:
We have been given the speed of the bike which is 8mp.
Speed is the distance covered per unit of time. It is mathematically expressed as;
Speed = [tex]\frac{distance}{time}[/tex]
So,
Time = [tex]\frac{distance }{speed }[/tex]
Now, insert the parameters and solve;
time = [tex]\frac{32}{8}[/tex] = 4hrs
What is the rate of change of the following equation?
y=x-5
Answers
Step-by-step explanation:
rate of change =y/x
= _5
rate of change = 1
What is rate of change?Rate of Change: The speed at which a variable changes over a specific period of time. It is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another. Graphically, this ratio is represented by the slope of a line.
Given equation:
y = x - 5
rate of change = m = ?
Comparing the equation with slope intercept form of line
y = mx + c
slope m = 1
c = -5
Hence the rate of change (slope m) = 1
Learn more about rate of change here:
https://brainly.com/question/29518179
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What is the area of the figure?
Answers
Answer:
252 in 2
Step-by-step explanation:
break the big figure up and get 108, 90, and 54 add them all togther and get 252
Reed has made 78 of 90 attempted free
throws last season. How many
consecutive free throws must he make to
bring his free throw percentage to 90%?
Answers
Answer: 81 consecutive free throws
Step-by-step explanation: Since 78 of 90 attempted free throws equals to 88.89%, then try adding 3 to 78, (78 + 3) which equals to 81. If you convert 81/90 to a percentage, you get 90%. So your final result or answer is 81 consecutive free throws.
Tip: To convert a fraction to a percentage, divide the denominator by the numerator and you should get a decimal quotient. Lastly, just add a percentage sign.
Harry took a loan from the bank.
D represents Harry's remaining debt (in dollars) after t months.
D=200t + 9000
What was the size of Harry's loan?
Answers
If y varies directly with x and y=8 when x=12, what will be the value of y when x=18
Answers
Answer:
y will equal 12 as 18 is 1.5x 12, 12 is 1.5x 8
Step-by-step explanation:
What is the expanded form of 5(3m + 7)?
Answers
Answer: the answer is 15m + 35
Step-by-step explanation:
Answer:
y= 5(3m+7)
Step-by-step explanation:
F(x)=5x + 4
When f(x) =54
Answers
Answer:
274
Step-by-step explanation:
5(54)+4 = 274
An arrow is shot vertically upward from a platform 35 ft high at a rate of 166 ft/sec. When will the arrow hit the ground? Ignore the air resistance. Use the formula ℎ = −16 2 + 0 + ℎ0. Round your answer to the nearest tenth.
Answers
Answer:
The arrow will hit the ground approximately 10.5 seconds after launch.
Step-by-step explanation:
The arrow experiments a free fall motion, which is a particular form of uniform accelerated motion due to gravity and in which air friction and effects from Earth's rotation can be neglected. Then, the height as a function of time ([tex]h(t)[/tex]), measured in feet, is obtained by the following kinematic formula:
[tex]h(t) = h_{o}+v_{o}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}[/tex] (1)
Where:
[tex]h_{o}[/tex] - Initial height of the arrow, measured in feet.
[tex]v_{o}[/tex] - Initial velocity of the arrow, measured in feet per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
If we know that [tex]h(t) = 0\,ft[/tex], [tex]h_{o} = 35\,ft[/tex], [tex]v_{o} = 166\,\frac{ft}{s}[/tex] and [tex]g = -32.174\,\frac{m}{s^{2}}[/tex], then the following polynomial is obtained:
[tex]35+166\cdot t -16.087\cdot t^{2}=0[/tex] (2)
Lastly, we find the roots of the given expression by the Quadratic Formula:
[tex]t_{1}\approx 10.526\,s[/tex] and [tex]t_{2} \approx -0.207\,s[/tex]
Time is a positive variable and then we conclude that the only solution that is physically reasonable is approximately 10.526 seconds.
The arrow will hit the ground approximately 10.5 seconds after launch.
PLZ HELP ASAP
What is the value of the 11th term in the following geometric sequence?
-5, -10, -20, -40
-100
-19,531,250
-180
-5,120
Answers
Answer:
No thanks give me my points back ;)
Step-by-step explanation:
Hi can someone help me with this. Find the slope
Answers
Answer:
5/2
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
goes 2 to the right then up 5
Jack left a tip of $5.75 for his waiter. If this represents 20% of his meal, what was the cost, in dollars, of Jack’s meal without the tip?
Answers
Answer:
Step-by-step explanation:
This is a commission problem. Here is the formula:
P x R
= 5.75 x 0.20
= $1.15
Jack's tip was $1.15. :D
Key: P = Original Price R = Commission Rate
If trianglePTS ~ trianglePQR, find the value of x.
Answers
Answer:
bei2uer22vv
Step-by-step explanation:
Identify the independent and dependent variable for the given situation. The amount of
distance covered by a car in a certain amount of time.
Answers
Answer:
distance = independant; time = dependant
Step-by-step explanation:
You are able to change the distance you travel, making it the independant. As you go farther, the time increases, so it is dependant on the distance traveled, therefore it is the dependant.
Select ALL of the answers that are true about the equation: y= 6x-2
A)The slope is negative.
B)The Y-Intercept is negative.
C)The slope is 6.
D)The Y-Intercept is +2.
Answers
Answer:
B and C
:)))))
Evaluate the distance between each pair of integers
Answers
Answer: number one is 24
Step-by-step explanation: all you have to do is just minus i’m pretty sure and for the negative ones add the negative number and the other number together. If they are both negative then just act like the negative sign is not there and add the sign back after you find the distance
PLEASE HELP DUE MIDNIGHT
Answers
Answer: 26
Step-by-step explanation: Since you are given the measures of two legs which are 24 (XY) and 10 (XS), you just need to use the formula a^2+b^2=c^2 to find the hypotenuse which is RY.
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
26 = c
RY = 26
plz solve marked brainlist
Answers
Answer:
No solution
Step-by-step explanation:
There is one variable. so it can't be two solutions. To the rest, we need to solve the equation.
5-2x=3+x-4-3x
5=3-4
5=-1
Impossible!!!
so no solution.
Hope this helps plz mark brainliest :D
Multiple Choice 1. Which type of correlation is suggested by the scatter plot? Positive correlation negative correlation Equal correlation no correlation
Answers
Answer:
negativo correlation
Step-by-step explanation:
because is parrallel
At Star Market, you can buy 3 pints of raspberries for $12.00. What is the cost per pint?
Answers
Answer:
$4 per pint
Step-by-step explanation:
Take $12 and divide by 3 pints.
:)
Answer: x= 12/3
Step-by-step explanation:
The answer to your problem is $4.00 per pint
Tell whether the relationship shown in the mapping diagram is a function or not.
Answers
Answer:
It is a function
Step-by-step explanation:
The x-values do not repeat so it is a function.
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP ME THIS DUE RIGHT NOW AND IF I FAIL MATH I GOING GET KICK OUT OF SOCCER TEAM PLZZZZZ HELP!!
1. Evaluate │-9│+ │11│ - │-15│ + │-6│ *
5 points
11
41
10
-19
2. Shin has a balance on her credit card of $212.45. She writes a check for $165.45. After she has paid (check), how much more money will she need to pay to have zero balance? *
5 points
$47
$165.45
$377.90
$118.45
3. The price of a share of a stock in ABC Company started the day at $27, rose $6 the first hour, dropped $4 the second hour, dropped $1.50 the third hour, and dropped $5 the fourth hour. Which of the following expressions describe the above statement? *
5 points
27 + 6 + 4 + 1.50 + 5
27 + 6 + (-4) + 1.50 + (-5)
27 + 6 + (-4) + (- 1.50) + ( -5)
27 + (-6) + (-4) + (-1.50) + 5
4. On January 1st, Rose's bank balance was $200. During the month, she wrote checks for $115.25 and $350.00 and made one deposit of $150.50. Which best represents her checking account balance at the end of the month? *
5 points
$815.75
- $114.75
- $415.75
$114.75
5. Which expression has the smallest value? *
5 points
A. |-19|
B. |-34|
C. |22|
D. |47|
6. Simplify this expression. 3/7 - 1/7 + 5/7 - 9/7 *
5 points
- 18/7
- 10/7
- 6/7
- 2/7
7. Which of the following is the correct solution to the problem below? - 9/3 + (-51)/17 *
5 points
1
- 3
0
- 6
8. Simplify −36 ÷ ( − 3) + 2(27 ÷ 3 × 2) *
5 points
21
48
108
252
9. Simplify - 15/35 x (-7) *
5 points
- 7 3/7
- 3
3
7 3/7
10. Which statement best describes the expression: -36/2 ÷ - 4 1/2 *
5 points
It is equal to 4 because -4 /-1 is equal to 4/1.
It is equal to 1/4 because -1/-4 is equal to 1/4.
It is equal to -4 because -4/-1 is equal to -4/1
It is equal to -1/4 because -1/-4 is equal to -1/4
11. Simplify: 8 (6 + 1/4) *
5 points
14 1/4
49 1/2
50
48 1/4
12. Which of the following division problems has a result that is negative? *
5 points
- 10 ÷ (-2)
- 9 ÷ 3
-│4│÷ - │-2│
│-6│ ÷ │3│
13. Evaluate (-2)(3)(-4) *
5 points
- 2
24
- 3
- 9
14. Which of the following is equivalent to 1 5/8 *
5 points
0.158
1.625
1.58
15.8
15. On Monday, Greg walks the entire length of a trail that is 3 1/2 miles long. On Tuesday he walks the entire length of a trail that is 4.6 miles long. On Wednesday, he starts out on a trail that is 2 1/5 miles long, but he does not walk the final 1.7 miles. How many miles does Greg walk in total on Monday, Tuesday, and Wednesday? *
5 points
8 3/5
8 3/50
10 3/10
10 3/100
Answers
Answer:
-13
Step-by-step explanation:
-13
The evaluated value of the given function is -
│-9│+ │11│ - │-15│ + │-6│= 11.
What is function? What is modulus function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
We can define the modulus function as -
|x| = - x {x < 0}
|x| = x {x > 0}
Given is to evaluate the expression -
│-9│+ │11│ - │-15│ + │-6│
We can evaluate the function as -
│-9│+ │11│ - │-15│ + │-6│
9 + 11 - 15 + 6
20 - 9
11
So, we can write -
│-9│+ │11│ - │-15│ + │-6│= 11
Therefore, the evaluated value of the given function is -
│-9│+ │11│ - │-15│ + │-6│= 11.
To solve more questions on functions, visit the link below-
https://brainly.com/question/30194223
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Solve for x.
5x - 6 = 4x + 8
Answers
Answer:
x = 14
Step-by-step explanation:
5x - 6 = 4x + 8
+6 +6
5x = 4x + 14
-4x -4x
x = 14
Answer:
5x-6=4x+8
5x=4x+8+6
5x=4x+14
x=14
I hope this is good enough:
