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
can someone help I need help lol
Aisha wants to paint the wall of the room. She knows that each can of the paint contain one gallon. A half gallon will completetly cover a 55 square feet of wall. Each of the four wall of the room is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 ft wide. How many one gallons buckets of paint does aisha need to buyin order to paint the room ?
Answer:
It doesn't say what to do with that 0.1 of a gallon. I would buy another gallon or dilute what I had so it came to exactly 9.1 gallons. In math, I suppose the answer is 9.
In reality it would be 10.
You have to choose. What has been done with other questions like this.
Step-by-step explanation:
1 can covers 55 square feet.
h = 10
w1 = 10 feet
w2 = 10 feet
w3 = 15 feet
w4 = 15 feet
Total area = Area of wall 1 + wall 2 + wall 3 + wall 4
Total area = 10*10 + 10*10 + 10*15 + 10* 15
Total area = 100 + 100 + 150 + 150
Total area = 500 feet^2
1 gallon / 55 ft^2 = x / 500 ft^2 Cross multiply
55 * x = 500 Divide by 55
x = 500/55
x = 9.1 gallons.
In real life you would buy another gallon.
A student’s incorrect attempt to simplify an exponential expression is show in the box
What is his mistake!!!!!
Answer:
A
Step-by-step explanation:
x^a/x^b=x^(a-b). General rule of exponents
c=2, f(x)= {3-x, x<2
2, x=2
x/2, x>2
Answer:
ball$
Step-by-step explanation:
<3
(
a. Find the distance around the park to the nearest yard.
39
The distance is about
yards.
b. A new path and a bridge are constructed from point Q to the midpoint M of PR Find QM to the nearest yard.
QM
yd
c. A man jogs from P to Q to M to R to Q and back to P at an average speed of 150 yards per minute. To the neare
long does it take him to travel the entire distance?
It takes about
minutes
Type here to con
We have that the distance around the park to the nearest yard,QM to the nearest yard and the Time of travel for man's jog is given respectively as
[tex]X=190yd[/tex][tex]QM=40yd[/tex][tex]T=1.5minutes.[/tex]From the Question we are told that
[tex]PQ=(50-10)=40\\\\QR=(80-10)70[/tex]
Generally the equation for the Resultant PR is mathematically given as
[tex]PR=\sqrt{PQ^2+QR^2}\\\\PR=\sqrt{70^2+40^2}\\\\PR=80yd[/tex]
a)
Generally the equation for the Distance around they park is mathematically given as
[tex]X=PQ+QR+PR\\\\X=80+70+40\\\\[/tex]
[tex]X=190yd[/tex]
b)
Generally the equation for the Path QM is mathematically given as
From the diagram we see that
[tex]QM=PM=MR\\\\QM=\frac{80}{2}\\\\[/tex]
[tex]QM=40yd[/tex]
c)
From the question we are told
Average speed of [tex]150yd/m[/tex]
Total distance traveled
[tex]D_t=40+40+40+70+40\\\\D_t=230yd[/tex]
Therefore
Time
[tex]T=\frac{D_t}{V}\\\\T=\frac{230}{150}[/tex]
[tex]T=1.5minutes.[/tex]
in conclusion
The distance around the park to the nearest yard,QM to the nearest yard and the Time of travel for man's jog is given respectively as
[tex]X=190yd[/tex][tex]QM=40yd[/tex][tex]T=1.5minutes.[/tex]For more information on this visit
https://brainly.com/question/15356513
l find it difficult to solve this problem. Please help.
Answer:
27 square are there in the given figure
Determine if the expression 8a – a4 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
The given expression
va polynomial.
represents
does NOT
represent
attempt 1 out of 2 / problem 1 out of max 1
Answer:
Represents
Step-by-step explanation:
Going over the basic definition of polynomial, an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division, we can see that the expression is indeed a polynomial.
What type of number is 80i?
Jaulas father throws Kayla a graduation party that costs $773. He pays the DJ $250, $75 for the cake, and $4 per party guest for food. How many guests were at the party?
Answer:
112 guests
Step-by-step explanation:
I. If her total cost is 773$
When Total = DJ + Cake + Guest
773 = 250 + 75 + 4(x)
773 = 325 + 4(x)
773 - 325 = 4(x)
448 = 4x
x = 448/4
x = 112
That makes guests are 112
Marley made three full pitchers of lemonade. Eachpitcher holds exactly five cups of liquid. How many ounces of lemonade did Marley make?
Answer:
120 fluid ounces
Step-by-step explanation:
1 cup = 8 fluid oz
Multiply 15 on both sides (since there is 3 pitchers and each is 5 cups, so 3 * 5 = 15 cups in total for all 3 pitchers) and we get 15 cups = 120 fluid oz.
So that's our answer
Hope this helped!
[I know this is a bit rude asking, but can I please have a Brainliest?]
13 Points Plz Help Me
Step-by-step explanation:
y+x-2-6x = y-5x-2
2x+3-x-4 = x-1
5xy+4x-5xy-3 = x
PLEASE HELP!! i can’t figure this out!
Given the point A(-3,-3) and B(5,1), find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio of 3:1.
Answer:
1,-1
Step-by-step explanation:
midpoint is (-3)+5÷2 ; (-3)+1÷2
=1;-1
20 PTS + Brainliest. Please find the size of the blue area, explain your work.
here is answer, hope u understand:)
solve 4m plus 2n equals 5n for m.
Answer:
m = (3/4) n
Step-by-step explanation:
4m + 2n = 5n
The subtraction property of equality states that we can subtract 2n from both sides to isolate the m and its coefficient to get
4m = 3n
The division property of equality states that we can divide 4 from both sides to isolate only the m (we divide by 4 because anything divided by itself equals 1) to get
m = (3/4) n
What is the answer ?
Answer:
27
Step-by-step explanation:
36 divided by 4 equals 9 which is what the sea turtle can swim in 1 second. Multiply 9 by 3 and you'll get 27.
Answer:
Step-by-step explanation:
Solve for W.
4w=5.12
Answer:
x =1.28
Step-by-step explanation:
4w=5.12
Divide each side by 4
4w/4 = 5.12/4
x =1.28
At a charity fund-raiser, adult tickets were sold for $10 each and children's tickets were sold for $4 each. Write an algebraic expression for the total amount of money raised from the sale of tickets. How much money was raised if the fundraiser sold 244 adult tickets and 387 children's tickets?
Answer:
the all adult tickets made out 2440$
the all children tickets made out 1548
Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5
Answer:
It is y = x - 5
Step-by-step explanation:
General equation of a line:
[tex]{ \bf{y = mx + c}}[/tex]
m is the gradient, and c is y-intercept.
For gradient:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]
substitute:
[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]
m = 1
for y-intercept:
consider point (6, 1):
[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]
therefore:
[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]
2(k + 1) = -4(k - 2)
Answer:
1
Step-by-step explanation:
2(k + 1) = -4(k - 2)
2k + 2 = --4k+8
2k+4k=8-2
6k=6
k=6/6
k=1
(−2x + 8) + (−8x^2− 8x)
Answer:
-8x^2 -10x + 8
Step-by-step explanation:
there is no multiplying just adding
someone help me asap
Answer:
19/20 cups
Step-by-step explanation:
Add the amounts together
1/4 + 7/10
Get a common denominator of 20
1/4 *5/5 + 7/10 *2/2
5/20 + 14/20
19/20
Answer:
19/20
Step-by-step explanation:
find a common denominator then do the same with the numerator then add.
If 2 – x > x – 2 then the solution of x is
[tex]\\ \sf\longmapsto 2-x\gt x-2[/tex]
[tex]\\ \sf\longmapsto 2+2\gt x+x[/tex]
[tex]\\ \sf\longmapsto 4\gt 2x[/tex]
[tex]\\ \sf\longmapsto x\lt \dfrac{4}{2}[/tex]
[tex]\\ \sf\longmapsto x\lt 2[/tex]
What is the domain in roster notation(numerical order) x= -2,-1,1,3,3 y=3,-3,0-3,3
Answer:
Domain is {x|x = -2, -1, 1, 3}
Step-by-step explanation:
I. When domain is x.value and renge is y.value
Got more question or something to discuss? leave comment below
PLS HELP WILL MARK AS BRAINLIEST
Answer:
SEE THE IMAGE FOR SOLUTION .
HAVE A GREAT DAY
Answer:
11. D
12. C
13. D
14. B
15. E
Step-by-step explanation:
11.
1/3 + 1/2 = 2/6 + 3/6 = 5/6
A is 3/4
B is 2/3
C is 9/10
D is 4/5
E is 2/5
the closest to 5/6 is 4/5.
12.
this is totally easy. just simply additions and one subtraction (to see what is left).
8+10+9 = 27
so, he has
60 - 27 = 33 hours left
13.
the mean value of a series of equal weighted numbers is simply their sum divided by the amount of numbers.
so,
(2+5+3+6+4)/5 = 20/5 = 4
14.
a scale factor is always applied to all dimensions, otherwise the result will be distorted. and that would be especially bad for a map.
so, clearly the width of the larger map is 3 times the width of the smaller map. therefore, the length of the larger map has to be also 3 fine the length of the smaller map.
3×6 = 18
15.
3t - 10 = 8
3t = 18
t = 6
Can someone tell me the asnwer to this ASAP?
Answer:
[tex]2\sqrt{2} \\2[/tex]
Step-by-step explanation:
[tex]\sqrt{8} = \sqrt{4*2} = \sqrt{4} * \sqrt{2} = 2*\sqrt{2} = 2\sqrt{2} \\\\\sqrt[3]{8} = \sqrt{2*2*2} = 2[/tex]
Answer:
I noticed that [tex]\sqrt{8\\}[/tex] does not have 3 on it like the second one. And i wonder that the answers would be different from each other
[tex]2\sqrt{2}[/tex]
2
Translate the sentence into an inequality.
Eight subtracted from b is less than or equal to 27.
THIS IS MY LASY!! 20Points
Step-by-step explanation:
Note that less means (-) and less than or equal means ≤
b - 8 ≤ 27
[tex]b - 8 \leqslant 27[/tex]
Hope it help youFind the sum of
2x^2- 8x– 6 and 9x^2-8
Answer:
11x^2-8x-14
Step-by-step explanation:
(2x^2- 8x– 6)+(9x^2-8) = 11x^2-8x-14
Answer:
11x^2-8x-14
Step-by-step explanation:
2x^2- 8x– 6 and 9x^2-8
solution:
2x^2- 8x– 6 +(9x^2-8)
=2x^2-8x–6+9x^2-8
=2x^2+9x^2-8x-6-8
=11x^2-8x-14
Solve 29 – 3:= 5x + 5 for x.
Answer:
x=4.2
Step-by-step explanation:
29-3=5x+5
21=5x, x=21/5=4.2
93. Let f(x) = 3x - 1 and g(x) = x + 5. Evaluate the following limits. (a) lim x→3 f(g(x)]
(b) lim x→3 g[f(x)]
Answer:
a) 23 and b) 13
Step-by-step explanation:
I. If f(g(x)) is composit function
Find fog and gof
fog = 3(g) - 1
= 3(x+5) -1
= 3x + 15 -1
= 3x + 14
gof = (f) + 5
= (3x - 1) +5
= 3x + 4
II. Fill in a) and b) question
lim x -> 3 fog
= 3(x) + 14
= 3(3) + 14
= 9 + 14
a) = 23
lim x-> 3 gof
= 3x + 4
= 3(3) + 4
= 9 + 4
b) = 13
Got more question or something to discuss, leave comment below
Pls help me I’m not very smart
Answer:
39.90
Step-by-step explanation:
multiply 95x42, ur not smart if you think u arent.
