Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
Answers
Answer:
No. There should be 210 small triangles
Step-by-step explanation:
The number of small triangles in these figures forms a sequence
Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)
So the nth figure should have 1+2+3+.....+(n-1)+ n
1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210
Related Questions
Construct a truth table for the following symbolic statement.
Use the type of truth table where each variable or operator in the given expression has its own column. Fill in the rows of the truth table one at a time.
Answers
The truth table is completed for each column as T T F F T T T
What is a truth table?A truth table is a mathematical table which shows all the truth values of a given combination of logic statements.
Analysis:
The truth table is shown in the attached file
in the attached file, the first two columns were given,
The third column is the negation of p, and P is true(T) which means its negation is false(F).
The fourth column is the negation of Q, which means Q is true(T) so its negation is false(F).
In the fifth column, negation P is implies negation Q. The truth table for implication, is only false if Q is false, else it is True.
Same as in the sixth column.
The last column is bi-implication, the truth table for this only true, if both statements are false or both are true else, it is false.
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Passengers under the age of 8 and whose height is less than 57 inches must be in the _________ seat of a vehicle.
Answers
Passengers under the age of 8 and whose height is less than 57 inches must be in the back seat of a vehicle.
When you journey in the backseat of a automobile, you take a seat within the row of seats behind the motive force. Kids once in a while combat over the front seat, not wanting to take a seat within the backseat. you may tour within the backseat of a car except you're the driver or are using a two-seat sports activities vehicle.
The cushion in which the driving force or passenger sits is either known as a horizontal cushion or seat cushion. The back of the automobile seat is called the seat again however it could additionally be called a backrest.
An infant protection seat every so often referred to as an toddler protection seat, infant restraint device, baby seat, child seat, car seat, or booster seat is a seat designed particularly to shield youngsters from injury or death throughout automobile collisions.
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2
A B
-10-9-8
5
Point A
Point B
Point C
Point D
6
ch point on the number line represents the product (-4)(-2)(-1)?
8
012
9
10
C D
5 6 7 8 9 10
59:3
Answers
We can actually deduce here that the point on the number line that represents the product (-4)(-2)(-1): -8.
What is number line?Number line is actually known to be a horizontal or vertical line that is graduated with both negative and positive numbers. A number line is known to have both negative and positive numbers.
We see here that if we multiply out the brackets, (-4)(-2)(-1) = (8)(-1) = -8.
Thus, the answer is -8.
See attached image.
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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
Answers
The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.
Given the table
x f(x)
-2 -46
-1 -22
0 -10
1 -4
2 -1
We have to choose which statement describes better about function
Let us assume [tex]f(x)=ab^x+c[/tex]
at x=0, f(0)=-10
So, -10 =a+c
Similarly, by satisfying the above table in the f(x)
[tex]f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}[/tex]
[tex]f'(x) > 0[/tex]
So we can say that f(x) is an increasing function.
[tex]g(x) = - 18 (\frac{1}{3} )^ x + 2[/tex]
[tex]g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)[/tex]
ln(1/3) < 0
So, g^ \prime (x) > 0
So, g(x) is an increasing function.
For any x∈f(x) and x∈g(x) [tex]g'(x) > f'(x)[/tex]
So, g increases at a faster average rate
Thus, Both functions are increasing, but function g increases at a faster average rate.
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what is the mean of 4,7
Answers
Answer:5.5
Step-by-step explanation:first we have to plus 4 and 7 and then we to divide the answer we get by 2 because there are only 2 digits and then the mean is 5.5
hope it helps
25:50=4x:8. What is the value of X
Answers
Answer: X = 1
Step-by-step explanation:
25/50 = 4x/8
First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.
25*8/50 = 4x*8/8
25*8/50 = 4x
25*8 = 200
200 divided by 50 = 4
4 = 4x
After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.
4/4 = 4x/4
1 = x
X = 1
Hope I helped! :]
Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
6 m
Step-by-step explanation:
[tex]sin22 = x/16\\x = 16sin22\\x = 6[/tex]
what is te equation of the line that passes through the point (6, -5) and is perpendicular to the line represented by y= 3/4x +2?
Help me pls
Answers
Since both lines are perpendicular, then their product is -1
y = 3/4x. +. 2
M= 3/4
M. M2 = -1
3/4 . M2 = -1
M2 = -4/3
M2=y-y1/x- x2
Since th
M2=y - (-5). /. x- 6
-4/3 = y+5. / x-6
-4(x-6) = 3(y+5)
-4x + 24 = 3y + 15
3y= -4x+24-15
3y = -4x + 9
y= -4/3x + 3
Answer is y= -4/3x + 3
2m² + 2m – 12 = 0
m=?
a. 2,-12
b. 3,1
c. 1.-3
d. -2.2
Answers
Step-by-step explanation:
F1/A1 = F2/A2
10/2=F2/4
5=F2/4
F2=5x4
F2=20
The first term of an arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the last term is 81.
Answers
Answer:
n = 53
Step-by-step explanation:
the sum to n terms of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 3 and a₅ = 9 , then
3 + 4d = 9 ( subtract 3 from both sides )
4d = 6 ( divide both sides by 4 )
d = 1.5
then solving for n
3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )
1.5(n - 1) = 78 ( divide both sides by 1.5 )
n - 1 = 52 ( add 1 to both sides )
n = 53
there are 53 terms in the progression
Answer:
53 terms
Step-by-step explanation:
Finding common difference :
a = 3a + 4d = 94d = 6d = 1.5Solving :
a_{n} = a + (n - 1)d81 = 3 + 1.5n - 1.579.5 = 1.5nn = 53what is the measure of
Answers
Answer:
C. Ф = 4 radians
Step-by-step explanation:
Given,
Radius of the Circle (r) = 3cm
Length of the Arc (S) = 12cm
In any circle of radius r, the arc length S to the circumference equals the ratio of the angle θ subtended by the arc at the centre and the angle in one revolution. Thus, measuring the angles in radians, S=rθ.
Therefore, S = r*Ф
12 = 3*Ф
Hence, Ф = 4 radians
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Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
The direct distance from A to C is more than yards.
Answers
The direct distance form A to C is represented by the inequality
AC < 40 yards.
What is a Triangle ?A triangle is a polygon with three sides , three vertices and three angles.
It is given that
Distance form point A to B is 15 yards
Distance form point B to C is 25 yards.
Distance AC = ?
In a Triangle the sum of two sides is always greater than the third side.
Therefore
AC < 15 +25
AC < 40 yards.
Therefore the direct distance form A to C is represented by the inequality AC < 40 yards.
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HELP PLEASE GIVING BRIANLEST
Answers
Answer:
Maybe the answer will be C. P (A and B )
Ans: C
Explanation:
I think it is option c , P(A and B)
as this is the only option which has the value of 80, which we got from the table
An object travels along a circular path so that it completes one revolution in 8 seconds. If the linear velocity of the object is 90pi inches per minute, what is the diameter, in inches, of the circular path?
Answers
Answer:
Using the concept of speed-distance-time, we find that the diameter of the circular path is 12 inches.
Step-by-step explanation:
Given that the object completes one revolution in 8 seconds. So, the circular speed of the object is 2πr/8 = πr/4 inches per seconds, where r is the radius of the circular path. The speed can be written as:
πr/4 inches per seconds = 60πr/4 inches per minute = 15πr inches per minute.
But, it is given that the circular speed of the object is 90π inches per minute. So,
90π = 15πr
r = 6 inches
Since, diameter is the double of radius, d = 2r = 12 inches.
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Assessing the regression model on data other than the sample data that was used to generate the model is known as _____. Group of answer choices approximation cross-validation graphical validation postulation
Answers
Assessing the regression model on data other than the sample data that was used to generate the model is known as cross-validation
How to complete the blank?From the question, we have the following highlights:
Sample data, not usedThe model is a regression modelWhen the sample data is not used in a regression model, then the term is known as cross-validation.
Hence, the term that completes blank is cross-validation
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How do you calculate the minimised dimensions: length width and height of a rectangular prism with the given volume of 10m^3?
Answers
The length, width and height of the rectangular prism is ∛10
How to determine the dimensions?The volume is given as:
Volume, V = 10m^3
For a minimised volume, we have:
Length = Width = Height
This means that:
V = L^3
So, we have:
L^3 = 10
Take the cube root of both sides
L = ∛10
Hence, the length, width and height of the rectangular prism is ∛10
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HELP FACTORISE ITS DUE IN TODAY PPLEASE
Answers
Answer:
ab(7a+b-2)
Step-by-step explanation:
see the common and take out the common parr
Answer:
its all about the formula =
(a+b)2 =a2 +2ab=b2
Step-by-step explanation:
Express cos L as a fraction in simplest terms
Answers
Answer:
cos L = [tex]\frac{23}{25}[/tex]
Step-by-step explanation:
cos L = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{JL}[/tex] = [tex]\frac{23}{25}[/tex]
I need this Asap Please and Thank you
Answers
Answer:
[tex]a= 10,\:\: b=6[/tex]
Step-by-step explanation:
[tex]\frac{7^2\:.\:7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex][tex]\rightarrow\frac{7^{2+8}}{7^4}=\frac{7^a}{7^4}=7^b[/tex][tex]\rightarrow\frac{7^{10}}{7^4}=\frac{7^a}{7^4}=7^b[/tex][tex]\rightarrow {7^{10-4}}={7^{a-4}}=7^b[/tex][tex]\rightarrow {7^{6}}={7^{a-4}}=7^b[/tex][tex]\rightarrow 6=a-4=b[/tex] (Bases are equal so exponents will also be equal)[tex]\rightarrow 6=a-4,\:\: 6=b[/tex][tex]\rightarrow 6+4=a,\:\: 6=b[/tex][tex]\rightarrow a= 10,\:\: b=6[/tex]Marquis wrote the linear regression equation y = 1.245 x minus 3.684 to predict the cost, y, of x songs purchased. marquis spent $40 on songs. which is the best estimate of the number of songs that marquis purchased? 29 32 35 46
Answers
Answer:
35
Step-by-step explanation:
1. Write the equation
y = 1.245x - 3.684
2. Set y = 40, since that is the cost of the songs he purchased.
40 = 1.254x - 3.684
3. Add 3.684 to both sides
43.684 = 1.254x
4. Divide by 1.254
x = 35.0875502
Answer:
Answer is C.) 35
Step-by-step explanation:
Kelly brought a pair of sneakers for 35.00 she also brought a pile of different laces. Each set of laces,l, costs 3.00. Write a variable expression to show how Kelly could calculate her total cost
Answers
Answer:
35+3I
Step-by-step explanation:
35+3I
i need a little help please i am so bad with exponents right now -
Answers
Answer:
the answer is -1/8
Step-by-step explanation:
find the total surface area of this triangular prism 21cm 29cm 20cm 22cm
Answers
Answer:
[tex]\huge\boxed{SA=1960cm^2}[/tex]
Step-by-step explanation:
We have:
2 rectangular triangles with legs 20cm and 21cm3 different rectangles 20cm × 22cm, 21cm × 22cm and 29cm × 22cmThe formula of an area of
a rectangular triangle:[tex]A_\triangle=\dfrac{a\cdot b}{2}[/tex]
a, b - legs
a rectangle a × b:[tex]A_{\square}=a\cdot b[/tex]
Calculate:
Rectangular triangle
[tex]A_\triangle=\dfrac{20\cdot21}{2}=210(cm^2)[/tex]
Rectangles:
[tex]A_{\square1}=20\cdot22=440(cm^2)\\\\A_{\square2}=21\cdot22=462(cm^2)\\\\A_{\square3}=29\cdot22=638(cm^2)[/tex]
Total surface:
[tex]SA=2A_\triangle+A_{\square1}+A_{\square2}+A_{\square3}\\\\SA=2\cdot210+440+462+638=1960(cm^2)[/tex]
Given two points of a line, find its slope.
(3, 1), (7,4)
Answers
Answer:
3/4 is the slope
Step-by-step explanation:
PLEASE ANSWER ASAP!!!!!!!!
Sally plots (−4,π)on the polar plane.
How does she proceed?
Drag a phrase to each box to correctly complete the statements.
Is this correct???
Answers
The drag phase you have given the interference would be a positive x-axis.
As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis.
The first block then should be the negative x-axis if r is positive and on the positive x-axis if r is negative.
What is the interference form?
It is a phenomenon in which two or more waves superimpose to form a resultant wave of greater or lower amplitude.
My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence.
Which would mean interference from the above statements, from the drag phase you have given the interference would be a positive x-axis.
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Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.65 How many of each type of coin do they have?
Answers
The number of quarters or nickels Kevin and Randy Muise have in the jar is 27 and 38 respectively.
Simultaneous equationA nickel = 5 centsA quarter = 25 centsn + q = 65
0.05n + 0.25q = 8.65
From equation (1)
n = 65 - q
substitute n = 65 - q into (2)
0.05n + 0.25q = 8.65
0.05(65 - q) + 0.25q = 8.65
3.25 - 0.05q + 0.25q = 8.65
- 0.05q + 0.25q = 8.65 - 3.25
0.20q = 5.40
q = 5.40/0.20
q = 27
Substitute into (1)
n + q = 65
n + 27 = 65
n = 65 - 27
n = 38
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whats the answer to this?
Answers
[tex](x)(x^{2} +9x+8)[/tex]
Step-by-step explanation:GCF is a way to simplify a polynomial by separating out one factor.
GCF
GCF stands for greatest common factor. This means the GCF is the largest number that is a factor of each term.
For example, the GCF of 15 and 25 is 5 because that is the greatest common factor between the 2 numbers.
Finding the GCF
To find the GCF, first look at the coefficients of each term.
In order, the coefficients are 1, 9, and 8These numbers have no shared factors besides 1, which doesn't help because factoring out 1 does nothing.
However, next, we can move on to the variables. You can factor out variables the same way you do constants.
All of the terms share a GCF of x.Factoring Out X
The question states that we only need to do GCF to solve. So, we can just factor out x. Remember that factoring is like dividing each term by x.
The completely factored expression is:
[tex](x)(x^{2} +9x+8)[/tex]Here we have divided each term by x and then added x as a new factor in the expression.
Answer:
X(x+1)(x+8)
Step-by-step explanation:
U just have to find the comment number
help______________________________________
Answers
The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.
Meaning of Simultaneous Equation.A simultaneous equation can be defined as an equation that possesses two unknowns and one constant.
The solution to the problem can only be gotten by solving it side by side with another equation of the same format.
In conclusion, The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.
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Select all the correct locations on the graph. Oliver is riding his bike to visit some friends. Every two minutes, he bikes 1,760 feet. Identify the pair of points you can use to create the line representing how far he has traveled in terms of time spent biking.Select all the correct locations on the graph. Oliver is riding his bike to visit some friends. Every two minutes, he bikes 1,760 feet. Identify the pair of points you can use to create the line representing how far he has traveled in terms of time spent biking.
Answers
Answer:
(0, 0) and (2, 1760)Step-by-step explanation:
Pretty sure that is the answer.
whats 555 divided by 5
Answers
Answer:
111
Step-by-step explanation:
555÷5=111
and just to check, 5×111=555
Answer:
555 divided by 5 = 111
Step-by-step explanation:
This is common knowledge. The 5 in the hundreds place is divisible by 5 to get a quotient of 1. The 5 in the tens place is also divisible by 5 to get a quotient of 1 and the same is equally true for the 5 in the ones place.
Hence, the quotient of 555/5 = 111
Hope this helps! :D
