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Marina CMI [18]
1 year ago
14

B

Mathematics
1 answer:
Pavlova-9 [17]1 year ago
3 0

Answer: R_{C, 180^{\circ}} \circ r_{m}

Step-by-step explanation:

The sequence is a reflection over line m followed by a rotation 180 degrees about point C.

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which function grows at fastest rate for increasing values of x? h(x) = 6x^2+1 , f(x) = 9x +14, g(x)= 4^x
mezya [45]
Hi there! The answer is g(x) = 4^x.

The function g(x) is an exponential function, and these functions grow faster than linear or quadratic formulas.
7 0
3 years ago
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Prove that one of every three consecutive positive integer is divisible by 3
Inessa05 [86]
Hello : 
all n in N ; n(n+1)(n+2) = 3a    a in  N  or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)

     n+1 </span>≡ 1 ( mod 3)...(2)
      n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3)  : n(n+1)(n+2) ≡ 0×1×2   ( mod 3)   : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)

     n+1 ≡ 2 ( mod 3)...(2)
      n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3)  : n(n+1)(n+2) ≡ 1×2 × 3  ( mod 3)   : ≡ 0 (mod 3) , 6≡ 0 (mod)
 3) n  ≡ 2 ( mod 3)...(1)

     n+1 ≡ 3 ( mod 3)...(2)
      n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3)  : n(n+1)(n+2) ≡ 2×3 × 4  ( mod 3)   : ≡ 0 (mod 3) , 24≡ 0      (mod3)
5 0
3 years ago
What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?
Dafna1 [17]

Step 1

<u>Find the slope of the given line</u>

we have

3x+4y=15

Isolate the variable y

Subtract 3x both sides

3x+4y-3x=15-3x

4y=-3x+15

Divide by 4 both sides

y=-\frac{3}{4}x+ \frac{15}{4}

the slope of the given line is

m=-\frac{3}{4}

Step 2

Find the equation of the line that passes through  the point (8,-2) and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

y-y1=m(x-x1)

we have

m=-\frac{3}{4}

(x1,y1)=(8,-2)

substitute in the equation

y+2=-\frac{3}{4}(x-8)

y=-\frac{3}{4}x+6-2

y=-\frac{3}{4}x+4  or  3x+4y=16

therefore

<u>the answer is</u>

y=-\frac{3}{4}x+4

or

3x+4y=16

8 0
3 years ago
50 POINTS! QUICKLY Are the pairs of variables x and y the solutions to the equation x^2–2y=7?
Fittoniya [83]

Hi there!

\large\boxed{(5,8) \text{ and } (1.2, -2.78)}}

We are given the equation:

x² - 2y = 7

To verify if each ordered pair is apart of the function, we can plug in their respective x and y values:

1. (5)² - 2(8) = 7

25 - 16 = 9 ≠ 7. This is NOT correct.

2. (-1)² - 2(-3) = 7

1 + 6 = 7. This is correct.

3. (-4)² - 2(-11.5) = 7

16 + 23 = 39 ≠ 7. This is NOT correct.

4. (1.2)² - 2(-2.78) = 7

1.44 +5.56 = 7. This is correct.

Thus, only 1 and 4 are the correct answers.

5 0
2 years ago
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I NEED HELP! Find the distance from(-4,4) to the line defined by y= -2x+6.Express as a radical or a number rounded to the neares
marysya [2.9K]
In radical form, the shortest distance from ( -4 , 4 ) and the line y = -2x + 6 is 2√5 units.


Attached below is the calculation to arrive at the answer as well as a graph.

8 0
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