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riadik2000 [5.3K]
3 years ago
11

From the following figure, how many ways can you show that lines l and m are parallel? At least 4 ways One way Two ways Three w

ays

Mathematics
2 answers:
antiseptic1488 [7]3 years ago
8 0

You can show it 4 ways by rotating the paper and if that is not an option, then the answer is 2.



Lynna [10]3 years ago
8 0

Answer:

The correct answer is: At least 4 ways.

At least 4 ways.

Step-by-step explanation:

There are 4 basic ways of showing that two lines are parallel.

  • Show that corresponding angles are equal.
  • Show that alternative interior angles are equal.
  • Show that consecutive interior angles are supplementary.

Show that consecutive exterior angles are supplementary.

Clearly from the figure we can show the first four properties easily.

Hence, the answer is:

At least 4 ways.

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10. Which transformations result in a preimage and image with opposite orientations?
Airida [17]
Reflections and glide reflections both give you a transformation where the preimage and image have opposite orientations.
3 0
3 years ago
Read 2 more answers
A pond has 150 fish and the population decreases by 8% each day. How many days before there are 30 fish
nlexa [21]

Answer:

19 days

Step-by-step explanation:

Given

a = 150 --- initial

r = 8\% -- rate

Required

Days when the fish gets to 30

The function is exponential and as such it follows;

y = ab^x

Where x represents the number of days and y the number of fishes

Because the fishes decreases;

b = 1 - r

So, we have:

b = 1 - 8\%

Express as decimal

b = 1 - 0.08

b = 0.92

In y = ab^x

a =150

y = 30

b = 0.92

So, we have:

30 = 150 * 0.92^x

Divide both sides by 150

0.2 = 0.92^x

Take log of both sides

log(0.2) = log(0.92^x)

Apply law of logarithm

log(0.2) = x\ log(0.92)

Make x the subject

x = \frac{log(0.2)}{log(0.92)}

x = \frac{-0.6990}{-0.0362}

x = 19.309

x \approx 19

<em>Hence, it takes approximately 19 days</em>

3 0
3 years ago
What is the equation of the line parallel to the line with the equation −x+3y=−3
mezya [45]

Answer:

y = 1/3x - 19/3

Step-by-step explanation:

3y = x -3

y = 1/3x -3

Slope = 1/3

Point= (1,-6)

y-intercept = -6 - (1/3)(1) = -6 - 1/3 = -19/3

5 0
2 years ago
Makers Corp. had additions to retained earnings for the year just ended of $205000. The firm paid out $185000 in cash divends, a
forsale [732]

Answer:

3.9

Step-by-step explanation:

The retained earnings for the year is $205,000

The firm paid out $185,000 in cash dividend

It has total equity of$4.90 million

100,000 common shares are outstanding

Therefore the earnings per share van be calculated as follows

= 205,000+185,000/100,000

= 390,000/100,000

= 3.9

Hence the earnings per share is $3.9

6 0
3 years ago
What is the standard form of the equation of a line for which the length of the normal segment to the origin is 8 and the normal
jeka57 [31]
Slope of line = tan(120) = -tan(60) = - &radic;3
Distance from origin = 8

Let equation be Ax+By+C=0
then -A/B=-&radic;3, or
B=A/&radic;3.
Equation becomes
Ax+(A/&radic;3)y+C=0

Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/&radic;3)y+C)/sqrt(A^2+(A/&radic;3)^2))
Substitute coordinates of origin (x,y)=(0,0)  =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/&radic;(4/3) => C=8*2/&radic;3 = (16/3)&radic;3

Therefore one solution is
x+(1/&radic;3)+(16/3)&radic;3=0
or equivalently
&radic;3 x + y + 16 = 0

Check:
slope = -1/&radic;3  .....ok
distance from origin
= (&radic;3 * 0 + 0 + 16)/(sqrt(&radic;3)^2+1^2)
=16/2
=8  ok.

Similarly C=-16 will satisfy the given conditions.

Answer  The required equations are
&radic;3 x + y = &pm; 16 
in standard form.

You can conveniently convert to point-slope form if you wish.




4 0
3 years ago
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