8. Look at the growing pattern below. How many squares will it
take to make the nth figure in this pattern?
Answers
Step-by-step explanation:
the first thing we notice is : there are always 2 "extra" squares (1 added to the bottom left, and 1 added to the top right).
and then we see that we have a "core" of n+1 squares that are added n-1 times.
e.g. for n=2 we get (2+1)(2-1) = 3×1 = 3 squares in the middle.
for n=3 we get (3+1)(3-1) = 4×2 = 8 squares in the middle.
just to verify for n=1 : that would be (1+1)(1-1) = 2×0 = 0. meaning no middle squares, which is correct.
so, the formula for n is
squares(n) = (n+1)(n-1) + 2 = n² - 1 + 2 = n² + 1
The number of squares that it takes to make the nth figure in this pattern will be n² + 1.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The growing pattern will be
⇒ (n+1)(n-1) + 2
⇒ n² - 1 + 2
⇒ n² + 1
Where n is the integer number.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Related Questions
Here are all the ways to make 5 except for one. Which one is missing?
5 + 0 = 5
2 + 3 = 5
4 + 1 = 5
3 + 2 = 5
0 + 5 = 5
Answers
Answer:
1 + 4 = 5
Step-by-step explanation:
You did duplicates of all numbers, other than that one! :)
Hope this helps!!
How many gallons of 35% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 40%
alcohol solution?
There needs to be____
gallons of 35 % alcohol solution and____
gallons of 50 % solution.
Answers
There needs to be 6 gallons of 35 % alcohol solution
and 3 gallons of 50 % solution.
======================================================
Explanation:
x = number of gallons of the 35% solution
y = number of gallons of the 50% solution
The two amounts must add to 9 gallons, so x+y = 9
This solves to y = 9-x
Since we want 9 gallons of 40% alcohol solution, this means we want 0.40*9 = 3.6 gallons of pure alcohol.
----------------
0.35x = amount of pure alcohol from the first batch
0.50y = amount of pure alcohol from the second batch
0.35x+0.50y = total amount of pure alcohol
Set that expression equal to the 3.6 figure calculated earlier (the total amount of pure alcohol we're after) and we get this equation
0.35x+0.50y = 3.6
----------------
Next, we replace y with 9-x and then solve for x.
0.35x+0.50y = 3.6
0.35x+0.50(9-x) = 3.6
0.35x+4.5-0.50x = 3.6
-0.15x+4.5 = 3.6
-0.15x = 3.6-4.5
-0.15x = -0.9
x = -0.9/(-0.15)
x = 6
We'll need 6 gallons of the 35% solution
Use this x value to find y
y = 9-x
y = 9-6
y = 3
We'll also need 3 gallons of the 50% solution
Jen traveled from Boston to Cape Cod at 60 mph. On her way back, the
traffic was bad and her return trip took 3 times as long. What was Jen's
average speed on the round trip?
Answers
Jen's average speed on the round trip will be 20mph
Distance and spedThe formula for calculating speed is expressed as:
Speed = Distance/Time
d = st
Let the time taken on Jen's way to Cape Cod be "t"
The time taken back to Boston will be t + 3
d1 = 60t
d2 = 60(t+3)
Since he traveled the same distance to and fro, hence;
Average speed = 60/3
Average speed = 20mph
Hence Jen's average speed on the round trip will be 20mph
Learn more on speed here: https://brainly.com/question/4931057
Answer:
30 mph
Step-by-step explanation:
is cot 4 a is equal to tan (a - 20) where 4a is an acute angle find the value of a
Answers
Answer:
a = 22
Step-by-step explanation:
[tex]cot \: 4a = tan \: (a - 20)....(given) \\ \\ \implies \: tan(90 - 4a) = tan \: (a - 20) \\ [\because \: cot \theta = tan(90 \degree - \theta) ]\\ \\ \implies (90 - 4a) = tan(a - 20) \\ \\ \implies \: 90 + 20 = 4a + a \\ \\\implies \: 110 = 5a \\ \\ \implies \: a = \frac{110}{5} \\ \\ \huge \red{ \boxed{\implies \: a = 22}}[/tex]
Will give Brainlist pls answer
Answers
Answer:
Negative
Step-by-step explanation:
From the number line we see that [tex]m[/tex] is negative and [tex]n[/tex] is positive
The expression in the parentheses, [tex](-m . n^2)[/tex] is positive since
[tex]-m[/tex] is the negative of a negative number and the sign of that is positive
[tex]n^2[/tex] is positive since a positive (or negative) number squared is always positive
[tex]\frac{m}{n}[/tex] is a negative number. If you divide a negative number, the sign of the result is negative
So evaluating the whole expression [tex]\frac{m}{n} .( m . n^2)[/tex]
gives us a negative number multiplied by a positive number and the result is a negative number
What is the percent difference in height between a building that is 600 feet tall and a tree that is 72
Answers
Answer:
730%
Step-by-step explanation:
600 - 72 = 528
528/72 = 7.3
7.3 * 100 = 730%
PLEASE HELP ME
ILL MARK AS BRAIN LIEST!!!!!
Answers
Answer:
C 377
Step-by-step explanation:
I simply typed in "surface area of cone calculator" in chrome and did it that way, since there is quite a complex formula for finding it out on your own.
(This is the formula : pi * r^2 + pi * r * sqrt (r^2+h^2)
There are 15 more girls than boys in the auditorium. If there are 91 students in the auditorium, how many are girls?
Answers
Answer:
53 Girls
Step-by-step explanation:
X is the number of girls and Y is the number of boys:
(X + 15) + Y = 91
91 - 15 = 76
76 ÷ 2 = 38
38 + 15 = X
X = 53
(38 + 15) + 38 + 91
The length of a rectangle is 5 m less than six times its width. If the perimeter is 200 m, find the length and width of the rectangle.
Answers
Answer:
Let W be the width of the rectangle. The length will then be 6W (six times the width). The area is length times width. if this equals 216, then you have an equation
(6W)(W) = 216
6W2 = 216
W2 = 36
W = 6.
The width is 6 ft and the length must then be 6W = 36 ft.
To find the perimeter, use the formula
P = 2L + 2W.
Plug in:
P = 2(36) + 2(6) = 72 + 12 = 84 ft.
The perimeter is 84 ft. (Remember that area has units length units squared and perimeter has units same as length.)
Step-by-step explanation:
PLZ HELP ILL MARK AS BRAINLEITS
Answers
[tex]SA=\pi rs+\pi r^2\\r=8\div2=4\\s=7 \\SA=3,14\times4\times7+3,14\times4^2=138,16\:\text{in}^2\approx138\:\text{in}^2[/tex]
Answer: 138 in²
Brainliest if correct
Answers
Answer:
y=3
Step-by-step explanation:
We can solve this using substitution (substitute 4 for x)...
4+y=7
Subtract 4 from both sides
y=3
Answer:
y = 3
Step-by-step explanation:
x + y = 7
x = 4
4 + y = 7
y = 7 - 4
y = 3
divide sh 810,000 among Sarah, John, Monica in ratio 4:3:2 respectively.
Answers
Answer:
Step-by-step explanation:
Let,4x,3x, and 2x be the share .
Now we have,
[tex]4x+3x+2x=810000\\\\9x=810000\\\\x=\frac{810000}{9} \\\\x=90000[/tex]
Again,
Share of Sarah=4x=4×90000=360000
Share of John=3x=3×90000=270000
Share of Monica=2x=2×90000=180000
EASY!!! What is (8+4)+24 / 2^3
Answers
Answer:
4 1/2.Step-by-step explanation:
Given equation:
(8 + 4) + 24 ÷ 2³.Solve:
(8 + 4) + 24 ÷ 2³= 12 + 24 ÷ 2³= 36 ÷ 2³= 36 ÷ 8= 4 R4= 4.5= 4 1/2.calculate the measure of each angle. find X
Answers
Solution:
Note that:
4x - 27 = 3x + 4 (Vertically opposite angles)Using the equation (4x - 27 = 3x + 4), solve for x.
4x - 27 = 3x + 4=> -3x + 4x - 27 = 3x + 4 - 3x=> x - 27 = 4=> x - 27 + 27 = 4 + 27=> x = 31The measure of x is 31.
Solve for X ~
[tex] \bf4x - 27 = 3x + 4[/tex]
[tex] \bf \: 4x - 3x = 4 + 27[/tex]
[tex] \boxed{ \bf \: x = 31}[/tex]
Now, Finding each angle⤵️[tex] \tt \: ∠1 = 2x + 21 \\ \tt \: = 2 \times 31 + 21 \\ \tt \: ∠1= 83 \degree[/tex]
[tex] \tt \: ∠2 = 4x + 27\\ \tt \: = 4\times 31 - 27 \\ \tt \: ∠2= 97 \degree[/tex]
[tex] \tt \: ∠3 = 3x + 4 \\ \tt \: = 3\times 31 + 4 \\ \tt \: ∠3= 97 \degree[/tex]
Puzzle Three
In order to complete the following puzzle you will need to use your
answers to fill in the questions that follow. For example your answer to
number one you will have to fill in for number two and so on. Be sure to
take your time as one mistake will mess up the entire puzzle.
1) (152 - 10) =
x
2)
(4x - 5) + 2x =
3) 7x +
x - 2x -x=
X
4) - 20
x + 4) + 5x =
x-
5) - (x+12) + 2(–3x + 4) = x -
Code: Find the mean of the following:
Mithin the 2019
Your answer
This is a required question
Answers
Step-by-step explanation:
hope this helps you!
-s.
In this swimming pool design, explain how to find the area of the pool's surface.
Answers
Answer:
Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.
Step-by-step explanation:sample
What’s 106 divided by 4 showing answer as mixed number
Answers
Answer:
Step-by-step explanation:
106/4 = 26[tex]\frac{2}{4\\}[/tex] = 26[tex]\frac{1}{2}[/tex]
Hope this helps!
Anyone pls help me in qn 11 in simultaneous equations
Answers
Answer: 19 cents
Step-by-step explanation:
Let's say that the cost of a lemon be L and the cost of an orange is O
We get the equation
4L + 3O = 5.45
7L + 4O = 9.30
The first equation can be made into the equation
28L + 21O = 38.15
And the second be made into
28L + 16O = 37.20
The second equation - The first question
5O = 0.95
O = 0.19
The decrease in the worth of Kenzie's car can be represented by the function m(t)=23,000(0.97)t, where t is the time in years, and m is the car's value in dollars.
What is the average rate of change of the car's value in dollars per year (rounded to the nearest dollar) during the first 4 years Kenzie owns it?
660
2638
−2638
−660
Answers
Answer:
-660
Step-by-step explanation:
The value of X is 36 degrees less than the value of y. Find the values of X and Y!!
Answers
Answer:
x=72, y=108
Step-by-step explanation:
y-36=x
[tex]\left \{ {{y-x=36} \atop {y+x=180}} \right.[/tex]
⇒ 2y=216
y=108108-36=x
x=72Adding both
2x=144=>x=72Put in eq(1)
y=180-72=108°A motorist covers distance of 180km in 3hours.calculate the speed at which the motorist was driving
Answers
Answer:
60 Km / hour
Step-by-step explanation:
average speed (S) is calculated as
S = [tex]\frac{D}{T}[/tex] ( D is distance and T time in hours )
here D = 180 and T = 3 , then
S = [tex]\frac{180}{3}[/tex] = 60 Km / hour
heather ate 3/6 of a box of cookies. Melody ate 3/5, who ate
more?
Answers
Answer:
Melody
Step-by-step explanation:
3/6 = 0.5
3/5 = 0.6
i.e. If it has the same numerator but different denominator the one with the smaller denominator will be bigger
Answer: Melody ate more.
Step-by-step explanation:
So, it would be Melody who ate more because
Over here:
Heather: ate 3 OUT of 6
Melody: ate 3 OUT of 5
Melody ate more because if you count up to 5 theres two cookies left, while Heather had 3 cookies left.
Hope this answers your question!
What is the slope of the line that passes through the points (6,-5) and (6,-4)?
Write your answer in simplest form.
Answers
Answer:
[tex] \boxed{\tt \: m = \boxed{\tt Undefined}}[/tex]
Step-by-step explanation:
Given Two Points are:
[tex] \sf \: \tt (6,-5) \: \sf and \: \tt (6,-4)[/tex]
We need to Find:
[tex] \longrightarrow \sf \: The \: Slope[/tex]
Solution:-We know that,
[tex] \sf \: Slope = \tt \: Rise/Run \: , \: \sf \: i.e. \: \: \boxed{\tt\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex] \sf \: Slope= \boxed{\tt\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Where,
[tex] \tt \: y_2= -4[/tex]
[tex]\tt y_1= - 5[/tex]
[tex]\tt x_2=6[/tex]
[tex] \tt \: x_1=6[/tex]
So Substitute their values accordingly:
[Important Note: Slope is denoted as m generally.]
[tex] \tt\implies \: m = \cfrac{ - 4 -( - 5)}{6 - 6} [/tex]
Now Simplify it.[Follow BODMAS Rule strictly while simplifying]
[tex] \tt \implies m = \cfrac{ - 4 + 5}{0} [/tex]
[tex]\tt \implies m = \cfrac{ 1}{0} [/tex]
Here, We can find that 1 is divided by 0.
We know that any expressions divided by 0 is undefined .
Hence, the slope[m] would be undefined.
[tex] \rule{225pt}{2pt}[/tex]
I hope this helps!
Let me know if you have any questions! :)
Solve the proportion using cross products.
14/6 = d/15
Answers
Answer:
D=35
Step-by-step explanation:
First, find a common multiple of both 15 and 6, we get 30, 14/6*5=70/6 meaning that 14/6=35/15
what is the answer I had wanted to make sure if this was the answer
Answers
Answer:
area of the entire figure: 21 cm²
Step-by-step explanation:
bottom rectangle:
length * width
3 * 2
6 cm²
upper rectangle:
length * width
3 * 4
12 cm²
triangle area:
1/2 * base * height
1/2 * 2 * 3
3 cm²
Total area: 6 cm² + 12 cm² + 3 cm² = 21 cm²
4. What will be the coordinates of L' given the following transformation?
J(-2,2), KT-1, 2), 1(-1, -2), M( -3, -1); (3,2)
A) (-5,0
B) (-1,4)
C) (2, 4)
D) (2,0)
Answers
What is the value of u?
Answers
Answer:
W/m²K by-step explanation:
I will give brainliest to correct answer
Answers
Answer:
less than 1 bag
Step-by-step explanation:
[tex] \sf{12 \: sq \: yds \: require = 7.5 \: bags}[/tex]
[tex] \implies\sf{1 \: sq \: yd \: will \: require = \frac{7.5}{12} \: bags} \\ = \sf{ \underline{0.625}}[/tex]
which is less than 1.
Implies that, each square yard requires about less than 1 bag of mulch.
What’s the correct answer for this question?
Answers
Answer:
Slope = 3
y- intercept = (0, 10)
Step-by-step explanation:
the equation is given by y=mx+c where m is the slope
- At y-intercept, x is equal to 0
Therefore, y = 3(0) + 10
y = 0 + 10
y = 10
I am trying to solve this problem then simplify
Answers
Answer:
3x^2+11x+6
Step-by-step explanation:
3x +2
x 3x^2 2x
+3 9x 6
3x^2+9x+2x+6
=
3x^2+11x+6