All categories

3 years ago

Find the coordinates of the vertices of the triangle after a reflection across the line x= -1 and then across the line y = 1.

Mathematics

1 answer:

Digiron [165]3 years ago

7 0

Answer:

a. F'(0, 5), G'(1, 0), H'(-3, 3)

Step-by-step explanation:

Reflection across x = -1 gives you the transformation ...

(x, y) ⇒ (-2 -x, y)

Reflection across y = 1 gives you the transformation ...

(x, y) ⇒ (x, 2 -y)

Together, these give you the transformation ...

(x, y) ⇒ (-2 -x, 2 -y)

Applying this to point F, we have ...

F(-2, -3) ⇒ F'(-2 -(-2), 2 -(-3)) = F'(0, 5) . . . . . . matches choice A

_____

How we found the transformation

In general, if M is the midpoint between A and B, then you have ...

M = (A+B)/2

2M = A+B

B = 2M - A

So, if we want x=-1 to be the midpoint between x' and x, then we have ...

x' = 2(-1) -x = -2 -x

Likewise, if we want y=1 to be the midpoint between y' and y, then we have ...

y' = 2(1) -y = 2 -y

So, the transformation is ...

(x, y) ⇒ (x', y') = (-2 -x, 2 -y)

You might be interested in

18+m/4=24 solve for m

Gemiola [76]

18 + m/4 = 24

Subtract 18 from each side:

m/4 = 6

Multiply each side by 4 :

m = 24 

4 0

3 years ago

Read 2 more answers

Asking again because last time I didnt get an actual answer. What is the surface area of this composite figure?

Katyanochek1 [597]

Answer:

644 cm^2

Step-by-step explanation:

10*7*2+12*7*2+12*10=140+168+120=428

10*12-3*3=111

428+111=539

8*3*4+3*3=96+9=105

539+105=644

3 0

2 years ago

Im solving variables -4y + 7 = -10y+37

Ulleksa [173]

Answer:

Step-by-step explanation:

move the terms

collect like terms

calculate

divide both side

8 0

2 years ago

Read 2 more answers

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

RoseWind [281]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

Firstly we will calculate the general probability that of P(a < X < b)

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

2 years ago

A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defect

Vladimir79 [104]

The probability that the first two electric toothbrushes sold are defective is 0.016.

The probability of an event, say E occurring is:

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = favorable outcomes

N = total number of outcomes

Let X = the number of defective electric toothbrushes sold.

The number of electric toothbrushes that were delivered to a store is n = 20.

The number of defective electric toothbrushes is x = 3.

The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:

$(\left {{20} \atop {2}} \right. )$ $=\frac{20!}{2!(20-2)!} =\frac{20!}{2!18!} =\frac{20*19*18!}{2!*18!} = 190$

The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:

$(\left {{3} \atop {2}} \right. )$ $=\frac{3!}{2!(3-2)!} =\frac{3!}{2!1!} =\frac{3*2!}{1!2!} =3$

Compute the probability that the first two electric toothbrushes sold are defective as follows:

P (Selling 2 defective toothbrushes) = Favorable outcomes ÷ Total no. of outcomes

$\frac{3}{190}\\ =0.01579\\=0.016$

Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.

Learn more about probability here brainly.com/question/27474070

#SPJ4

4 0

1 year ago