A sequence of patterns is made from circular tiles and square tiles. Here are the first three patterns in the sequence:
a) How many square tiles are needed to make Pattern Number 7? [2 MARKS]
b) How many circular tiles are needed to make Pattern Number 20? [2 MARKS]
c) When the pattern number is odd, the total number of tiles (SQUARE & CIRCULAR) needed to make the pattern: A - will always be even | B - will always be odd | C - could be even or odd | [2 MARKS]
!! PLEASE ANSWER ALL OF THE QUESTIONS !!
Answers
Answer:
a) 49
b) 84
c) (B) -- always odd
Step-by-step explanation:
We observe that the number of square tiles is the square of the pattern number. The number of circular tiles is 1 more than the pattern number on each side of the square.
square tiles = n²
circular tiles = 4(n +1)
__
a)7² = 49 square tiles are needed for pattern number 7.
__
b)4(20+1) = 84 circular tiles are needed for pattern number 20.
__
c)The parity of the number of square tiles matches the parity of the pattern number. (The square of a number has the same parity as the number.) Since 4 is a factor in the number of circular tiles, its parity is always even. The parity of the total number of tiles will match the parity of the pattern number.
When the pattern number is odd, the total number of tiles will always be odd. (B)
Related Questions
need to evaluate integral pls help me
Answers
Answer:
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegral NotationIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.[/tex]
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx[/tex][Integrand] Substitute in function: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1[/tex]Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)[/tex]Simplify: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
Step-by-step explanation:
[tex]\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx[/tex]
=[tex]\frac{9x^{10}}{10} |_0^1 + x^4|_1^2[/tex]
[tex]=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}[/tex]
Surface area of cone 5ft by 21ft
Answers
if the radius is 21 then the answer is 2809.61
Answer:
417.63
Step-by-step explanation:
Help help help math math
Answers
Answer:
The slope is 1
Step-by-step explanation:
Notice that for every 2 unit increase in y, there's a 2 unit increase in x. This determines our slope, or rate of change. So, the slope is Δy/Δx=2/2=1.
Answer:
1
Step-by-step explanation:
Write an eighth-degree polynomial in factored form that is decreasing at both ends , has a single root at -2, a double root at 3 and 0 and triple root at -1
Answers
Answer:
Step-by-step explanation:
y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)
The 8 degree polynomial for the given roots can be written as p(x) = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².
What is factor theorem?The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).
The roots of the polynomial are given as follows,
Number of roots at -2 = 1
Number of roots at 3 = 2
Number of roots at 0 = 2
And, number of roots at -1 = 3.
Now, the polynomial can be written using factor theorem as,
p(x) = x²(x + 2)(x - 3)²(x + 1)³
= x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)
= x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²
Hence, the polynomial for given roots can be written as p(x) = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².
To know more about factor theorem click on,
https://brainly.com/question/13547729
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Given mſn, find the value of x.
(6x+10)
>
(10x+10)
Answers
now,
6x+10+10x+10=180°[being cointerior angle]
16x=180-20
x=160%16
x=10°
One positive number is 7 more than twice another. If their product is 1425, find the numbers.
Answers
Answer:
25 and 57.
Step-by-step explanation:
Let the lowest number be x then the other is 2x + 7, So:
x(2x + 7) = 1425
2x^2 + 7x - 1425 = 0
2 * - 1425 = -2850 = -2 * 3 * 5 * 5 * 19
We need 2 numbers whose product is -2850 and whose sum is + 7.
These are 3 * 19 = 57 and -2* 5 * 5 = -50 so we write:
2x^2 - 50x + 57x - 1425 = 0 Now we factor by grouping:
2x(x - 25) + 57( x - 25) = 0)
(2x + 57) ( x - 25) = 0
x = -57, 25.
We ignore the negative as we are given that the number is positive,
x = 25 is one number and the other is 2(25) + 7 = 57.
Lella will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $46 and costs an additional $0.14 per mile driven. The
second plan has an initial fee of $51 and costs an additional $0.10 per mile driven
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DOES ANYONE KNOW PLEASE HELP ME I WILL MARK BRAINLIEST <3
Answers
Answer:
i got this i hope this is helpfulI'm sry I can't read and ans
Step-by-step explanation:
Electronic entry of medication orders through CPOE may reduce errors from poor handwriting or incorrect transcription. CPOE systems often include functionalities such as drug dosage support, alerts about harmful interactions, and clinical decision support, which may further reduce errors.
Please look for the question in the picture.
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Answer:
Step-by-step explanation:
Hello plz help with these two.
Answers
Problem 1
Answer: Choice D--------------
Explanation:
The vertices are (-12,0) and (12,0). Both of which are on the same horizontal line. Because of this, we have a hyperbola that opens leftward and rightward. Such hyperbolas are of the form
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
where (h,k) is the center and the a,b terms help set up the asymptotes.
The midpoint of the vertices (-12,0) and (12,0) is the point (0,0). This is the center. So we know that h = 0 and k = 0.
For left/right opening hyperbolas, the asymptotes can be described as the equations:
y = (b/a)x
y = (-b/a)x
Or we can condense them into [tex]y = \pm \frac{b}{a}x[/tex]. Compare this to the given equation [tex]y = \pm\frac{5}{12}x[/tex] to see that b = 5 and a = 12.
Therefore, we get the following:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{12^2}-\frac{(y-0)^2}{5^2}=1\\\\\frac{x^2}{144}-\frac{y^2}{25}=1[/tex]
That points us to choice D.
You chose the correct answer.
=============================================================
Problem 2
Answer: Choice A--------------
Explanation:
Divide both sides by 3600 so we can turn that "3600" into "1". Then our goal is to get that "1" to its own side like so:
[tex]25x^2-144y^2 + 3600 = 0\\\\\frac{25x^2-144y^2 + 3600}{3600} = \frac{0}{3600}\\\\\frac{25x^2}{3600}-\frac{144y^2}{3600} + \frac{3600}{3600} = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} + 1 = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} = -1\\\\-\frac{x^2}{144}+\frac{y^2}{25} = 1\\\\-\frac{x^2}{12^2}+\frac{y^2}{5^2} = 1\\\\[/tex]
We see that a = 12 and b = 5 like earlier, so we end up with the same asymptotes as before. The only difference is that this hyperbola opens upward/downward rather than left/right.
You made the correct choice in picking answer A. Both of your answers are correct. Nice work.
Determine whether a triangle with the given side lengths is a right triangle.
Answers
Answer:
See answer below.
Step-by-step explanation:
This is true for all right triangle a² + b² = c² were c = the largest number
9, 12, 15 A right triangle
21, 28, 35 A right triangle
9, 13, 16 Not a right triangle
10, 11, 15 Not a right triangle
Last week, the price of oranges at the farmers market was $1.75 per pound. This week, the price has decreased by 15%. What is the price of
oranges this week?
Answers
Answer:
11.6 (6 is repeating)
Step-by-step explanation:
1.75 divided by 15% of 75
Find m
∠
J
L
K
∠JLK.
Answers
Answer:
m∠JLK° = 62°
Step-by-step explanation:
∠JLK = ∠KJL
SO
56°+2(∠JLK)° = 180°
2(∠JLK)° = 180-56
2(∠JLK)° = 124
∠JLK° = 62°
so m∠JLK° = 62°
Answer:
m∠JLK = 62°
Step-by-step explanation:
180 - 56 = 124
124 ÷ 2 = 62
write 321.51 to the nearest whole
Answers
Answer:
322.
Hope that helped. x
Step-by-step explanation:
We have 321.51,
So what we need to do is check the number straight after the decimal point and see if it is less than 5 or 5 and above. (5 and above mean increasing the number, less than 5 means decreasing the number.)
Since the number is 5 we change the 1 to a 2. So the answer is 322.
Waluigi's Towing Service charges $38.51 for its hook-up fee plus $35.21 for every mile, m, they tow your car. The equation that models the total cost (T) is T(m) = 35.21m + 38.51. Which value in the equation represents the rate of change?
A .. The number of miles towed
B .. $38.51
C .. $35.21
D .. $73.72
Answers
Answer:
c 35.21
Step-by-step explanation:
rate of change is=to slope
in y=mx+b
m is slope(rate of change)
x the variable such as miles
b is y intercept
leading coefficient of the polynomial 4x^2−x^6+2x−6
Answers
Answer: The leading coefficient is -1.
Step-by-step explanation: Coefficients are the numbers than procede each term with a variable (in this instance, x) in the equation.
[tex]-x^6+4x^2+2x-6\\[/tex]
There are four terms in this equation, which has been reordered in the correct form, which is from the highest term to the lowest term (based on exponent values).
Thus, there are three coefficients in this equation, which, in order, are as follows:
[tex]-1, 4, 2[/tex]
What is the equation of the line in slope intercept form perpendicular to the y axis and has the point (-4,5)
Answers
Answer:
y=5
Step-by-step explanation:
If it is perpendicular to the y-axis, that means it is a horizontal line so the slope m=0.
Use the equation
y-y=m(x-x)
y-5=0(x-(-4))
y-5=0
y=5
Answer:
y=5
Step-by-step explanation:
Is it possible to arrange 152 books on a shelf so that the first shelf has 7 fewer books than the second shelf and 11 more than the third shelf?
Answers
Using a system of equations, it is found that since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.
For the system, we consider that:
x is the number of books on the first shelf.y is the number of books on the second shelf.z is the number of books on the third shelf.In total, there are 152 books, hence:
[tex]x + y + z = 152[/tex]
The first shelf has 7 fewer books than the second shelf, hence:
[tex]x = y - 7[/tex]
Also, it has 11 more books than the third shelf, hence:
[tex]x = z + 11[/tex]
Then:
[tex]y - 7 = z + 11[/tex]
[tex]z = y - 18[/tex]
Then, replacing in the first equation:
[tex]x + y + z = 152[/tex]
[tex]y - 7 + y + y - 18 = 152[/tex]
[tex]3y = 177[/tex]
[tex]y = \frac{177}{3}[/tex]
[tex]y = 59[/tex]
The number of books in each shelf has to be countable, that is, cannot be decimal.
Then, since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.To learn more about system of equations, you can take a look at https://brainly.com/question/14183076
I need help with this, can anybody help me? thank you, have. a great day!
Answers
Answer:a
Step-by-step explanation:
Answer:
As a mixed number, it is 3 5/8.
As an improper fraction it is 29/8.
Hope that helps you. x
Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answers
The cost of each bag of apple is $6.35
Let the cost of a bag of apple be xIf Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount
The correct equation that represents the statement will be given as:
6.17 + 8x = 56.97Make x the subject of the formula
8x = 56.97 - 6.17
8x = 50.8
x = 50.8/8
x = 6.35
Hence the cost of each bag of apple is $6.35
Learn more on equations here: https://brainly.com/question/2972832
What is the answer to this question in SSS, SAS, AA, or none
Answers
Answer:
Step-by-step explanation:
40/32 ?=? (40 + 12.5) / (32 + 10)
1.25 ?=? 52.5 / 42
1.25 = 1.25
similar via SAS
Which pair of expressions are equivalent?
A
3x+2+2x and 7x
B
8(x−3) a
nd 8x−24
C
4(x+1) and 4x+1
D
3(5x) and 8x
Answers
Description of a turn for those who have never done math / for a child
Answers
Answer:
Step-by-step explanation:
1+1=2
2+2=4
3+3=6
4+4=8
5+5=10
Write a function rule for that table.
Answers
Answer
f(x) = x - 2
Step-by-step explanation:
If you subtract 2 from each x, you get the answer in f(x)
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Pythagorean theorem )
Answers
Answer:
5 sqrt(6) = x
Step-by-step explanation:
The pythagorean theorem states
a^2 + b^2 = c^2
Where a and b are the legs and c is the hypotenuse
7^2 + (sqrt(101))^2 = x^2
49+101 = x^2
150 = x^2
Take the square root of each side
sqrt(150) = sqrt(x^2)
sqrt(25*6) = x
5 sqrt(6) = x
In six years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answers
Answer:
72
Step-by-step explanation:
Tim wants to create a circle graph showing the number of physicians whose specialty is aerospace medicine. He knows the following information.53 male physicians are under 35 years of age. 8 female physicians are under 35 years of age. 155 male physicians are between 35 and 44 years of age. 17 female physicians are between 35 and 44 years of age. 145 male physicians are between 45 and 54 years of age. 10 female physicians are between 45 and 54 years of age. 98 male physicians are over 54 years of age. 2 female physicians are over 54 years of age. If he wants to include each of the eight groups in his graph, how many degrees would he use for the central angle of the "45-54 year-old Males" sector? Express your answer to the nearest whole number.
Answers
Answer:
107 :)
Step-by-step explanation:
In total there are 53+8+155+17+145+10+98+2=488 physicians of aerospace medicine. 45-54 year-old males account for 145/488 of this population, so they should account for that fraction of the central angle of the circle graph also. Since there are 360 degrees in the central angle to divide up among the groups, the 45-54 year-old male group should get 145/488 x 360 which rounds to about 107 degrees.
subtract the polynomials (4x^2-9x-7)-(3x^2-5x-6)
Answers
Answer:
x^2 - 4x - 1
Step-by-step explanation:
Which characteristics did early Japanese, Chinese, and Korean civilizations share?
They were friendly nations that shared culture and customs.
They were nations at war that shared a common religion.
They were neighboring countries that shared a common history.
They were countries with dissimilar culture and customs.
Answers
Answer:They were nations at war that shared a common religion.
Step-by-step explanation:
edge
Answer:
B. They were nations at war that shared a common religion.
Explanation: I got it right.
What is the slope of the linear equation that has the values shown in the table
Answers
Answer:We noted above that a linear function has the form f(x)= mx+b, f ( x) = m x + b, where m m is the slope of the line, and b b is the y y -intercept. Since m m and b b can take on various values
Step-by-step explanation: