Gary draws this sequence of patterns of white and grey squares. The sequence is continued. How many grey squares will there be with 16 white squares?
Answers
Answer:
20 gray squares
Step-by-step explanation:
Given
See attachment for squares
Required
Number of gray squares when white = 16
First, we calculate the equation that represents both squares.
The white squares
[tex]a = 2[/tex] --- initial
[tex]d = 4 - 2 = 6 - 4[/tex]
[tex]d = 2[/tex] -- difference between successive gray squares
So, the nth term is:
[tex]W_n = a + (n - 1)d[/tex]
[tex]W_n = 2 + (n - 1)*2[/tex]
[tex]W_n = 2 + 2n - 2[/tex]
[tex]W_n = 2n[/tex]
The gray squares
[tex]a = 6[/tex] --- initial
[tex]d = 8-6=10-8[/tex]
[tex]d = 2[/tex] -- difference between successive gray squares
So, the nth term is:
[tex]G_n = a + (n - 1)d[/tex]
[tex]G_n = 6 + (n - 1) *2[/tex]
[tex]G_n = 6 + 2n - 2[/tex]
[tex]G_n = 4 + 2n[/tex]
When the white squares is 16
[tex]W_n = 16[/tex] --- Calculate n
[tex]W_n = 2n[/tex]
[tex]16 = 2n[/tex]
[tex]8 = n[/tex]
[tex]n = 8[/tex]
To get the number of gray squares;
Substitute [tex]n = 8[/tex] in [tex]G_n = 4 + 2n[/tex]
[tex]G_n = 4 + 2 * 8[/tex]
[tex]G_n = 20[/tex]
Related Questions
Mateo has 60 wooden tiles in the shape of diamonds as shown below. He plans to glue these tiles side by side onto a tabletop. What will the area of the tabletop be?
Answers
If sin θ =8/9. Find cot θ.
Answers
Step-by-step explanation:
✧ [tex] \underline{ \underline{ \large{ \tt{G\: I \: V \: E\: N}}} }: [/tex]
[tex] \large{ \tt{sin \: \theta = \frac{8}{9}}} [/tex] Here , Perpendicular ( p ) = 8 & hypotenuse ( h ) = 9♨ [tex] \underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I\: N\: D}}}} : [/tex]
[tex] \large{ \tt{cot \: \theta}}[/tex]♨ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T\: I\: O \: N}}}} : [/tex]
First, Find the base ( b ) using Pythagoras theorem :☪ [tex] \boxed{ \bf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]
~Plug all the known values and then simplify!
⇾ [tex] \large{ \bf{ {9}^{2} = {8}^{2} + {b}^{2} }}[/tex]
⇾ [tex] \large{ \bf{81 = 64 + {b}^{2} }}[/tex]
⇾ [tex] \large{ \bf{64 + {b}^{2} = 81}}[/tex]
⇾ [tex] \large{ \bf{ {b}^{2} = 81 - 64}}[/tex]
⇾ [tex] \large{ \bf{ {b}^{2} = 17}}[/tex]
⇾ [tex] \large{ \bf{b = \sqrt{17}}} [/tex]
Now , Find the value of cot θWe know ;
⟿ [tex] \large{ \bf{cot \theta = \frac{b}{p} = \boxed{ \bf{ \frac{ \sqrt{17} }{8}}}}} [/tex]
⤷ [tex] \boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : { \tt{ \frac{ \sqrt{17} }{8} }}}}}}}[/tex]
( Correct me if I'm wrong )
Hope I helped ! ♡
Have a wonderful day / night ! ツ
☄ Let me know if you have any questions regarding my answer !
[tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎
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What are the slope and the y-intercept of the linear function that is represented by the equation Y --10x+1?
BARE
O The slope is -10, and the y-intercept is -1.
O The slope is -10, and the y-intercept is 1.
The slope is -1, and the y-intercept is -10.
O The slope is 1, and the y-intercept is -10.
Answers
Answer:
The slope is -10, and the y-intercept is 1.
Step-by-step explanation:
Assuming that the equation is y = -10x+1, the easiest way to identify slope and the y-intercept is by knowing the equation for slope-intercept (y = mx+b)
Equation for slope-intercept (y = mx+b) explained:
The equation is y = mx+b, let's break it down.
y = The line
m = The slope
b = The y-intercept
Now that we know the equation and broke it down you can identify them in your equation
Slope (m)= -10
y-intercept = 1
Conclusion: The slope is -10, and the y-intercept is 1.
Pls I need help and do not post that link thank you
Answers
Answer:
4 the one
hope 5hid will you
you deposit $50 in checks in your account with $100 cash amount, what is your total deposit? (answer in only numbers) $
I’ll give brainiest
Answers
Its 150 dollars because your adding 50 +100
4. Based on the original question, how many quarters and dimes must Jada have?
Answers
identify the zeros of the polynomial function .
Answers
Step-by-step explanation:
To start, every term has an
x
in common, so we can factor that out. Doing this, we get
x
(
x
2
+
x
−
42
)
=
0
What I have in blue can be factored by a thought experiment. What two numbers have a sum of
1
and a product of
−
42
?
After some trial and error, we arrive at
−
6
and
7
. Thus, this business can be factored as
x
(
x
−
6
)
(
x
+
7
)
=
0
We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get
x
=
0
,
x
=
6
, and
x
=
−
7
If you know how to do this problem, please help me out!
Answers
Step-by-step explanation:
Parallel
[tex]y = - \frac{2}{5} x + 3[/tex]
Perpendicular
[tex]y = \frac{5}{2} + 4[/tex]
Answer:
Slope of a parallel line: 2/5
Slope of a perpendicular line: 5/2
Explanation:
Parallel lines function
1. y = -2/5x+(R-4)
Perpendicular line function
2. y = 5/2x
NO ONE IS HELPINGGGGGGGG
You found Genie hidden in a dungeon. Genie is offering two different options for you as a reward for finding him. There are two options shown for you to choose. Which option would you choose? Explain your reasoning using the key features of exponential functions. (e.g. initial value, growth rate/growth factor, domain, range, etc)
Answers
Answer:
:D
Step-by-step explanation:
Which of the following correctly completes the square for: x^2+2x=48
A. (x+2)^2=52
B. (x+1)^2=49
C. (x+2)^2=47
D. (X-1)^2=26
Answers
Answer:
(x+1)²= 49, the answer is B
Step-by-step explanation:
x² + 2x = 48
x² + 2x + (2/2)² - (2/2)²= 48 --[what we are trying to do is to complete a square by adding (2/2)² - (2/2)²]
(x+1)²= 49, the answer is B
Answer:
hey I'm pretty sure it's B. (x+2)²=49
Step-by-step explanation:
x²+2x+(2\2)²=48 + (2\2)²
(x+1)²=49
2 over 2 by the power of 2 = 1
Jeff bought a canoe for $333.75. The sales tax was 5%. What was his total cost?
Answers
Answer:
Jeff bought a canoe for $333.75. The sales tax was 5%. What was his total cost?
Step-by-step explanation:
The total cost of jeff purchase was approximately $351.27.
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
The right answer is third option 68°.
3. Find the products.
a) (a? + 4) (a? – 4)
Answers
Answer:
a^2-16
Step-by-step explanation:
you just a.a+a.-4+4.a+4.-4=a^2-16
Plz help me! And no links!
Answers
Answer:
hi
Step-by-step explanation:
A line passes through the points (0, 3) and (10, 2). What is its equation in slope-intercept form?
Answers
Answer:
1. Find slope.
slope(m)
[tex] = \frac{y2 - y1}{x2 - x1} \\ [/tex]
[tex] \frac{2 - 3}{10 - 0} = \frac{ - 1}{10} [/tex]
2. Substitute any point. (either (0,3) or (10,2) to find the y-intercept (b)
y=mx+b
3=-1/10+b
b=31/10 or 3.1
so the final answer is
y= - 1/10 + 31/10 or y= - 0.1 + 3.1
You have been evaluating cell phone providers. Double Mint Mobile has a $100 startup
fee and costs $30 per month for a cell phone plan. BT&T has a $20 startup fee and costs
$50 per month for a similar cell phone plan.
After how many months will both cell phone plans cost the same?
Answers
Answer:
4 months
Step-by-step explanation:
Let
x = number of months
Double Mint Mobile = 100 + 30x
BT&T = 20 + 50x
After how many months will both cell phone plans cost the same?
Equate the cost of both phone plans
Double Mint Mobile = BT&T
100 + 30x = 20 + 50x
100 - 20 = 50x - 30x
80 = 20x
x = 80/20
x = 4 months
Number of months = 4 months
PLEASE HELP
Write the equation of a line that has the point (5,2) and y-intercept of -3
Answers
Because the slope is 2-(-3)/5-0= 5/5= 1 and the y intercept is -3
What is the relationship between the exterior angle of a triangle and its remote
interior angles?
Answers
Answer:
The sum of the interior angles of a triangle is always 180 degrees. The exterior angle is the angle between any side of a shape, and a line extended from the next side. The sum of an exterior angle and its adjacent interior angle is also 180 degrees.
The relationship between the exterior angle of a triangle and its remote
interior angle is the exterior angle is equal to the sum of the two remote interior angles.
Which is known as the Exterior Angle Theorem.
What is a triangle?
A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
In a triangle, the exterior angle is formed when one side of the triangle is extended.
The exterior angle and the two remote interior angles (angles adjacent to the exterior angle on the triangle) form a linear pair, which means they add up to 180 degrees.
More specifically, the exterior angle is equal to the sum of the two remote interior angles.
This relationship is known as the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
For example, if one of the remote interior angles of a triangle measures 40 degrees, and the exterior angle adjacent to it measures 120 degrees, then the other remote interior angle measures 180 - 40 - 120 = 20 degrees.
Thus,
The relationship between the exterior angle of a triangle and its remote
interior angle is the exterior angle is equal to the sum of the two remote interior angles.
This relationship is known as the Exterior Angle Theorem.
Learn more about triangles here:
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a +19 =43
can someone help me
Answers
Answer:
A= 24!
Step-by-step explanation:
just subtract 19 from 43, and that will give you what A equals!
Answer:
24
Step-by-step explanation:
43-19= 24
24+19= 43
Please help if you want brianleist!!! Tyyy!! :}
Answers
Hey love! <3
Answer:
The area of the following figure would be A = 312cm^2
Step-by-step explanation:
To begin solving for the area of this question we should first calculate the triangles.
The triangles width are 10cm each, and the length for each triangle is 12/2, or 6. Remember the formula for finding the area of a triangle is length times width divided by 2
After calculating all four triangles you should get 30+30+30+30, or 120.
Now, lets calculate the large central rectangle, the formula for this is the basic length times width, so that would equal 192.
Thus, 192+120=312cm^2
Hope this makes things a little easier for you! ◕‿◕ Sincerely, Kelsey from Brainly.
~ #LearnWithBrainly ~
My father invests $5000 in a new bank that has an annual
interest rate of 3.8%. Find the balance
after 10 years if it is compounded yearly. Round your answer to
the nearest whole dollar.
$
Answers
$5000+3.8%=$5190
$190x10=$1900
$5000+$1900=$6900
4. What is the slope of the line that passes
through the points (-6, -30) and (12, 24)?
Answers
(24-(-30))/(12-(-6)) = (24+30)/(12+6)
(54)/(18) = 3
The slope is 3
And I’m back lol. Or did I never leave to begin with?-
Answers
Answer:
61 is ur answer
Step-by-step explanation:
Since this was a 90 degree angle you would just subtract 29 from the 90 degrees and get your answer.
Find the area of the shaded polygons
PLS HELP ASAP AGAIN!!!
Answers
9514 1404 393
Answer:
9 square units
Step-by-step explanation:
Pick's theorem is a useful relationship in circumstances like these. It tells you the area is ...
A = i + b/2 - 1
where i is the number of interior points (8), and b is the number of points on the border (4).
The area of this figure is ...
A = 8 + 4/2 -1 = 9
The area of the polygon is 9 square units.
_____
You can also get there by realizing the bounding rectangle is 4 units square. From that, corner triangles are cut. CW from upper left, those triangles have (base, height) dimensions of (3, 2), (1, 3), (3, 1), and (1, 2). So, the total of their areas is (1/2)(6 +3 + 3 +2) = 7 square units. The shaded area is then 16-7 = 9 square units, same as above.
I need help please is for tomorrow):
Answers
Answer:
Step-by-step explanation:
If a number gets increased by scale factor = k
Then k > 1
If the number gets decreased by a scale factor 'k'
Then 0 < k < 1
Let numbers gets increased by the scale factor = 2,
And decreased by the scale factor = [tex]\frac{1}{2}[/tex]
Numbers Scale up by 2 Scale down by [tex]\frac{1}{2}[/tex]
0.05 0.05 × 2 = 0.1 0.05 × [tex]\frac{1}{2}[/tex] = 0.025
[tex]\frac{1}{2}[/tex] [tex]\frac{1}{2}\times 2 = 1[/tex] [tex]\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}[/tex]
7 7 × 2 = 14 7 × [tex]\frac{1}{2}[/tex] = 3.5
13 13 × 2 = 26 [tex]13\times \frac{1}{2}=6.5[/tex]
25 25 × 2 = 50 [tex]25\times \frac{1}{2}=12.5[/tex]
102 102 × 2 = 204 [tex]102\times \frac{1}{2}=51[/tex]
One day a retail store received a box of 24 shirts. If this shipment had 6 defective shirts, what can the store expect for upcoming shipments?
F.
A box of 32 shirts will have 12 defective shirts.
G.
A box of 40 shirts will have 10 defective shirts.
H.
A box of 48 shirts will have 3 defective shirts.
J.
A box of 64 shirts will have 8 defective shirts.
Answers
Answer:
the answer is H.
Step-by-step explanation:
Jonny has $50 in a savings account. Each week, he deposits $13 in the account. Jonny's brother has $90 in a saving account. Each week, he deposits $11 in the account. Write an algebraic expression to describe how much money Jonny and his brother will have in their accounts after m months.
Answers
Answer:
140 + 96 m
Step-by-step explanation:
There are 4 weeks in 1 month.
Therefore:
Jonny has $50 in a savings account. Each week, he deposits $13 in the account.
$50 + $13 × 4m
The algebraic expression is given as:
50 + 52m
Jonny's brother has $90 in a saving account.
Each week, he deposits $11 in the account.
The algebraic expression is given as:
$90 + $11 × 4m
90 + 44m
An algebraic expression to describe how much money Jonny and his brother will have in their accounts after m months is written as:
Amount Jonny has + Amount his brother has
50 + 52m + 90 + 44m
= 50 + 90 + 52m + 44m
= 140 + 96 m
1) Mrs. Pinkard is wrapping a present in a box. What is the total amount of wrapping paper he will need if the dimensions of the box are 4 inches in height, 8 inches in width, and 12 inches in length? *
Answers
Answer:
2,304
Step-by-step explanation:
4x8x12
4x8=32
32x12=384
384x6=2,304
bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00. leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00. how much does it cost to bowl a game
Answers
The cost to bowl a game is $2.5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let g represent the cost of bowling a game and s represent the cost of renting shoes.
Bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00
3g+s=9..(1)
Leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00.
5g+s=14..(2)
Subtract equation 2 from 1
3g+s-5g-s=9-14
-2g=-5
Divide both sides by 2
g=2.5
Hence, the cost to bowl a game is $2.5.
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Math but tell me don’t make me click on som link
Answers
Answer:
theres no question lol
Step-by-step explanation: