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seropon [69]
2 years ago
10

Using the 0,1,6,8, and 9, write down all the possible three-digit numbers that have rotational symmetry. the digits can be used

more then once
Mathematics
1 answer:
Hunter-Best [27]2 years ago
4 0

Assuming 1 is written rotationally symmetrical, using 0,1,6,8,9 to make numbers that have a degree of symmetry of 2 (i.e. 180 degrees), we can say

one digit numbers: 0,1,8


two digit numbers: 11, 69, 96

(18 becomes 81, so not admissible, similarly for 19, 91,16,61, etc)

(00 is not considered generally as a two-digit number)


three digit numbers:

(000, 010, 080 are not considered generally as a three-digit number)

101, 609, 808, 906,

replace the middle digit successively by 1 and 8 gives

111, 619, 818, 916,

181, 689, 888, 986

for a total of 12 numbers

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Find a1, for the arithmetic series<br> with S14 = - 420 and d = -6.
faust18 [17]

\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} n = 14\\ d= -6 \end{cases} \\\\\\ a_{14}=a_1+(14-1)(-6)\implies a_{14}=a_1+(13)(-6)\implies a_{14}=a_1-78 \\\\[-0.35em] ~\dotfill

\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ \cline{1-1} n= 14\\ S_{14}=-420\\ a_{14}=a_1-78 \end{cases}\implies S_{14}=\cfrac{n(a_1+a_{14})}{2} \\\\\\ -420=\cfrac{14[a_1+(a_1-78)]}{2}\implies -420=7(2a_1-78)\implies \cfrac{-420}{7}=2a_1-78 \\\\\\ -60=2a_1-78\implies 18=2a_1\implies \cfrac{18}{2}=a_1\implies 9=a_1

8 0
3 years ago
Can someone help me with this plss
DIA [1.3K]

Answer:

6. Quadrant four

7. Quadrant three

8. Quadrant one

Step-by-step explanation:

These questions give you points to graph and then asks which quadrants they are graphed in. Here is a visual.

6 0
1 year ago
What is 6 1/2 times -3
AleksAgata [21]

Answer:

-14.5

Step-by-step explanation:

6.5 * -3 = -14.5

- * + = -

5 0
3 years ago
Read 2 more answers
What is the least common denominator of the fraction 3 x over x plus 1 plus the fraction x plus 1 over 2 x plus the fraction 5 o
Hoochie [10]
3x/(x+1) + (x+1)/(2x) + (5/x)

To find the least common denominator, we multiply the denominators that cannot factor into eachother. x, the denominator in 5/x, fits into 2x, so we do not need to multiply this number.
Therefore, the least common denominator is:
2x(x+1) 

The first term will be multiplied by 2x/2x
The second term will be multiplied by (x+1)/(x+1)
The third term will be multiplied by 2(x+1)
3 0
3 years ago
Given sin A = 12/13 and that angle A is in Quadrant 1,
UkoKoshka [18]

We have been given that \text{sin}(A)=\frac{12}{13} and angle A is in quadrant 1. We are asked to find the exact value of \text{cot}(A) in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}

Now we will find adjacent side using Pythagoras theorem as:

\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2

\text{Adjacent}^2=13^2-12^2

\text{Adjacent}^2=169-144

\text{Adjacent}^2=25

Let us take positive square root on both sides:

\sqrt{\text{Adjacent}^2}=\sqrt{25}  

\text{Adjacent}=5

Therefore, adjacent side of angle A is 5 units.

\text{cot}(A)=\frac{5}{12}

Therefore, the exact value of cot A is \frac{5}{12}.

5 0
2 years ago
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