Practice
1. Hyatt Home Improvement uses H-shaped tile Design 1 Design 2
Design 3
designs on their buildings, advertisements, and
vehicles. The designs they use follow a specific
pattern. The first three designs are shown.
a. Describe the pattern in the designs.
b. Write two different expressions to represent
the number of tiles used in Design n. Use
algebraic properties to prove the two expressions are equivalent.
c. Explain how you could use technology to prove the two expressions in part (b)
are equivalent.
d. Create a table that displays the number of tiles used in each of the first 6 designs.
e. Create a graph of the data points in your table on the coordinate plane shown. Draw a smooth
curve to connect the points.
f. Do all of the points on the smooth curve make sense in terms of the problem situation? Explain
your reasoning.
g. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.
h. The owner of Hyatt Home Improvement wants to put one of their designs on an empty
rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. If he
Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:
The pattern is that the number of tiles increases as the design number increasesThe expressions for the number of tiles are [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]The expression can be proved to be equivalent using graph technology The points on the curve make sense in this scenario because all values are positiveThe pattern is quadratic.The largest design number that can enter an empty 10 by 12 ft sign is design number 8The pattern
The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)
The expressions for the number of tiles
The design number and the number of tiles is represented as follows
[tex]1 \to 7[/tex]
[tex]2 \to 12[/tex]
[tex]3 \to 19[/tex]
From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.
Design 1 has 1 tile at the center and 6 tiles at either sides.
So, we have:
[tex]1 \to 1 + 6[/tex]
[tex]2 \to 4 + 8[/tex]
[tex]3 \to 9 + 10[/tex]
Expand
[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]
[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]
[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]
Notice the pattern,
The number of tiles in design n will be:
[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]
Open bracket
[tex]Tiles = n^2 + 2n + 4[/tex]
Hence, the expressions for number of tiles in design n are:
[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]
Technology to prove that both expressions are equivalent
To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared
The table and graph for the first 6 designs
The table entry for the first 6 designs is calculated as follows:
[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]
[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]
[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]
[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]
[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]
[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]
So, we have:
[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]
See attachment for the graph of the above table
All the points on the curve make sense in this scenario because all values are positive.
The pattern type
We have:
[tex]Tiles = n^2 + 2n + 4[/tex]
When an equation has a degree of 2, the equation is quadratic.
Hence, the pattern is quadratic.
The largest design that an empty sign of 10ft by 12ft can contain.
From the first three designs:
The number of tiles on a complete row and column are always the same.
Design 1 has 3 tiles in its complete row and column
Design 2 has 4 tiles in its complete row and column
Design 3 has 5 tiles in its complete row and column
The relationship between the design number (d) and the number of complete tiles (t) is:
[tex]d = t - 2[/tex]
For the 10ft by 12ft empty sign
[tex]t = 10[/tex] because [tex]10 < 12[/tex]
So, we have:
[tex]d = t - 2[/tex]
[tex]d = 10 - 2[/tex]
[tex]d = 8[/tex]
Hence, the largest design number is design 8
Read more about patterns at:
https://brainly.com/question/13382968
32600÷9330?
Please answer:(
Answer:
3.49410504
It is the answer hope it helps.
Mark me as Brainliest plz
Answer:
3.49410503751
Step-by-step explanation:
But as a smaller version it is
3.494
1. Which of the following is an example of like
terms?
a. - 16 and - 16x
b. x and x2
C, 50y and y
d. 20a and 2
r-6
--------- = - 3
- 3
Answer:
r=0
Step-by-step explanation:
ɪ ɴᴇᴇᴅ ʜᴇʟᴘ ᴡɪᴛʜ ᴛʜɪꜱ !
ᴍᴀᴛʜ ᴇxᴘᴇʀᴛꜱ ᴏɴʟʏ
If (x + 4)^2 = 49 and x < 0. what is the value of x?
Answer:
x = -11
Step-by-step explanation:
To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.
-11 + 4 = -7
(-7)^2 = 49
Answer:
x = -11
Step-by-step explanation:
To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.
midpoint (12, -9), endpoint (19, 0) the other endpoint is
Answer:
(5, -18)
Brainliest, please!
Step-by-step explanation:
(12, -9)(19, 0)
x distance: 7, y distance: 9
To get the other endpoint, we must apply the opposite.
x distance: -7, y distance: -9
(12, -9)
12 - 7 = 5, -9 - 9 = -18
(5, -18)
what is ????????????????? 21x+28<10-3x
Answer:
x < -3/4
Step-by-step explanation:
21x + 3x < 10 - 28
24x < -18
x < -18/24
x < -3/4
a + 1 = 3000
a = ?
This is my first question, I know the answer. I just wanna test the platform.
Answer:
2999
Step-by-step explanation:
a + 1 = 3000
=> Subtracting 1 from both sides,
=> a + 1 - 1 = 3000 - 1
=> a = 2999
30, 32, and 34 Please! I WILL GIVE BRAINLIEST
Answer:
see explanation
Step-by-step explanation:
Since AL bisects ∠ KAT then ∠ 1 = ∠ 2
(30)
7x + 3 = 6x + 7 ( subtract 6x from both sides )
x + 3 = 7 ( subtract 3 from both sides )
x = 4
(32)
SAT is a straight line , then
∠ 1 + ∠ 2 + ∠ 3 = 180° , then
x + x + 4x = 180
6x = 180 ( divide both sides by 6 )
x = 30
(34)
Similar to (32)
x + 12 + x + 12 + 6x - 20 = 180 , that is
8x + 4 = 180 ( subtract 4 from both sides )
8x = 176 ( divide both sides by 8 )
x = 22
Answer:
30) x= 4
32) x=30
33) x=22
Step-by-step explanation:
All step by step explainations are in pic below
Joanne a total score for a round of darts was -42 she had thrown 6 darts and scored the same each throw How many points did Joanne score on each throw
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Ok, so we know 42 is the number of points added up, and we know that she threw 6 darts all scoring the same. Now, all we have to do is figure out what number(for example x) multiplied by 6 equals 42. Or in the form of an equation:
6x = 42
Now, to finish the equation, all we have to do is divide:
6x/6 = 42/6
42/6 = 7
x = 7
1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.
Let the small , medium and large baskets be denoted by s,m & l
Formulating the equations
s+m+l= 80--------- equation1
$15.75s+ $25 m + $32.5l = $2086.25------equation2
2s=l---------equation 3
Using the technology s=15, m=35 and l= 30
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
2(15)=(30)---------equation 3
Yes because multiple variables can be easily calculated through matrices using technology
In Matrix form
[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex] = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]
Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]
B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]
Z= A⁻¹ B
A⁻¹= A mod/ det A
det A= -1
Using the technology s=15, m=35 and l= 30
15 small baskets,
35 medium baskets
30 large baskets were sold.
Part C:
15+35+30= 80--------- equation1
$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2
236.25+ 875+ 975=$2086.25
$2086.25=$2086.25
2(15)=(30)---------equation 3
Answer 2:
Yes because multiple variables can be easily calculated using technology.
N.B There is a typing error in question its $2086.25 not 52086.25
find the determinant of 2P-3Q if P=(2/3-1/4) and Q=(2/0-3/5)
(1/2)^x=2^-x could anyone tell me why
Answer:
Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4
Step-by-step explanation:
Someone answer this
Answer:
1st box is "a 90°clockwise rotation about the origin
2nd box is "a 180° rotation about the origin
3rd box is "a 90° counterclockwise rotation about the origin
Is the set of real numbers closed under addition? Explain why or why not. If it is not closed, give an example
Answer: Yes, the set of real numbers is closed under addition.
Explanation:
Let x and y be two real numbers. Their sum x+y is some other real number. This is what it means when we say the set of real numbers is closed under addition. Taking any two numbers and adding them will get us some other real number.
There is no way to have x+y be nonreal while x,y are both real.
What’s the answer???
Answer:
Step-by-step explanation:
5. After paying a tax of 8 palsa per rupee a man saves Rs. 18,400 per month Then his monthly income is 2 Points) 20,000
Answer:
92% of Income is Rs 18400
Step-by-step explanation:
I = 18400/.92 = Rs 20000
Marking brainliest
What else should I add
Step-by-step explanation:
........Student
........ Cousin
......... Child
Answer:
Step-by-step explanation:
daughter cousin (if you have any).mother (if you are one)family member (if it applies)best friend.factors of 15,17 ,26 & 80
Answer:
Factors of 15: 1, 3, 5 and 15.
Factors of 17: 1 and 17.
Factors of 26: 1, 2, 13 and 26
Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.
Actually you can find all the answers in the Internet.
what is the purpose?
[tex] \\ [/tex]
Answer:
I hope it will helpful.
Step-by-step explanation:
I hope it will help you.
A truck can be rented from Company A for $120 a day plus $0.20 per mile. Company B charges $60 a day plus $0.40 per mile to rent the same truck. Find the number of miles in a day at which the rentals cost for company A and company B are the same.
please help..
Answer:
12 miles in a day.
Step-by-step explanation:
Variable x = number of miles
Company A: 120 + 0.20x
Company B: 60 + 0.40x
Set up an equation:
120 + 0.20x = 60 + 0.40x
60 + 0.20x = 0.40x
60 = 0.20x
12 = x
Simplify the answer has to be a positive exponent Please help!
5^4 /5
Use the exponent rule x^a/x^b = x^a-b
5^4/5 = 5^4-1 = 5^3
Answer as a positive exponent is 5^3
Anyone know the answers 11 through 14?Please help me.I’m tired
Answer:
11. [tex]x^{5}[/tex]
12. 5*[tex]x^{2}[/tex]
13. x+21
14. 2x-8
Step-by-step explanation:
If(2x,x+y)=(y,9)find x and y.
Answer:
the value of X is 3 and y is 6 .
Solve for x: 4x + 1/2 (2x + 4) > 12
( 9th grade Algebra 1)
Answer:
x > 2
Step-by-step explanation:
Distribute and cross-simplify 1/2 with parenthesis
4x + x + 2 > 12
Solve left side
5x + 2 > 12
Subtract 2 from both sides
5x > 10
Divide both sides by 5
x > 2
if the 6th term of an A.p is 11and its first term is 1 find the common diferent
Answer:
2
Step-by-step explanation:
In an AP, Tn = a + (n - 1)d
T6 = a + 5d = 11
The first term = a = 1
∴ T6 = 1 + 5d = 11
5d = 11 - 1
5d = 10
∴ d = 2
I hope this will help you :-)
Answer:
[tex]x6 = 11 \\ x1 = 1 \\ x6 \: can \: be \: written \: as \: x6 = x1 + 5d \\ x6 = 1 + 5d \\ 11 = 1 + 5d \\ 10 = 5d \\ d = \frac{10}{5} \\ d = 2 \\ thank \: you[/tex]
The value of tan1°tan2ºtan3⁰ (a) 0 (b)-1 (c) 1 (d) 2 tan890 is equal to
Step-by-step explanation:
Answer-
b) 1
where can i find the answers?
Answer:
I don't know where can you find this question's answer.
I divide my favorite number by its reciprocal , the quotient is 10 times as large as my favorite number. My favorite number is..
A. 1/10
B. 1/5
C. 1/2
D. 10
Answer:
1/10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
x is the favorite number
x÷[tex]\frac{1}{x}[/tex] = 10x (flip the fraction and multiply)
[tex]x^{2}[/tex]=10x (divide both sides by x)
x=10
