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3 years ago

Some one help me i cant get it

Mathematics

1 answer:

Novay_Z [31]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

(a)

Under a rotation of 180° about the origin

a point (x, y ) → (- x, - y)

the coordinates of P, Q and R are

P(1, -1 ), Q(3, - 2 ), R(3, - 4 )

Hence under the given rotation

P(1, - 1 ) → P'(- 1, 1 )

Q(3, - 2 ) → Q'(- 3, 2 )

R(3, - 4 ) → R'(- 3, 4 )

(b)

Under a reflection in the x-axis

a point (x, y ) → (x, - y ), hence

P(1, - 1 ) → P''(1, 1 )

Q(3, - 2 ) → Q''(3, 2 )

R(3, - 4 ) → R''(3, 4 )

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2 years ago

alisha [4.7K]

Answer:

$d=3\sqrt{2}\ units$

Step-by-step explanation:

The complete question is

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{9-5}{7-3}$

$m=\frac{4}{4}=1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=1\\point\ (3,5)$

substitute

$y-5=(1)(x-3)$

isolate the variable y

$y=x-3+5$

$y=x+2$ -----> equation A

step 2

Find the equation of the perpendicular line to the given line L that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

The slope of the given line L is $m=1$

The slope of the line perpendicular to the given line L is

$m=-1$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=-1\\point\ (2,10)$

substitute

$y-10=-(x-2)$

isolate the variable y

$y=-x+2+10$

$y=-x+12$ ----> equation B

step 3

Find the intersection point equation A and equation B

$y=x+2$ -----> equation A

$y=-x+12$ ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(2,10) and (5,7)

substitute

$d=\sqrt{(7-10)^{2}+(5-2)^{2}}$

$d=\sqrt{(-3)^{2}+(3)^{2}}$

$d=\sqrt{18}\ units$

simplify

$d=3\sqrt{2}\ units$

see the attached figure to better understand the problem

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3 years ago

75 out of 300 oranges in a basket are bad. what percent age of the oranges are (a) bad (b)good

Likurg_2 [28]

Answer:

a) 25% are bad

b) 75% are good

Step-by-step explanation:

We know that there are 300 oranges total and that 75 are bad. That means that the rest are good (implied).

300 - 75 = 225 good oranges.

So to find the percentage we have to take the selected amount divided by the total amount.

Bad Apples: Good Apples:

75 / 300 = 0.25 225/300 = 0.75

However, that's a decimal or a number out of 1, we need a percent or a number out of 100. So we have to multiply both numbers by 100.

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2 years ago

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Nimfa-mama [501]

It says Sandeep has twice as much as Sonia. Thus, let Sandeep's amount be 2x and Sonia's amount be x.

Now, together they have 150.

Thus, the equation;

x+2x=150

Now let's solve the equation;

3x=150

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Thus, Sonia has 50

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3 years ago