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3 years ago

Rotate shape A 90° anti-clockwise with centre of rotation (0,0).

Mathematics

1 answer:

Oksanka [162]3 years ago

3 0

Answer:

(-6, 1) (-6, 3) (-5, 3) (-5, 2) (-3 2) -3, 1

Step-by-step explanation:

By rotating 90 degrees x become y and y becomes negative x

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A farmer saw some chickens and pigs in a field. he counted 30 heads and 84 legs. determine exactly how many chickens and pigs he

loris [4]

12 pigs×4 legs=48 legs
18 chickens×2 legs=36 legs
48 legs+36 legs=84 legs

12 are pigs and 18 are chickens

8 0

3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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3 years ago

At a school, 118 students play at least one sport. This is 40% of the students at the school. How many students are at the sc

REY [17]

There are 295 students.

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3 years ago

The variables xx and yy vary directly. use the values to find the constant of proportionality, kk. then write an equation that r

Sergeu [11.5K]

Direct variation means that changes in x will result to changes in y. If x increase, y also increases and vice versa.

y = kx
k = y / x

y = 45 ; x = 40

k = 45/40
k = 1.125

y = 1.125x

y will increase by 1.125 interval of x.

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3 years ago

Read 2 more answers

If the area of each of the triangular regions is as shown, what is the area of the polygon?

pochemuha

Answer:

Step-by-step explanation:

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3 years ago