Ask question

Ask question

All categories

3 years ago

7

Two intersecting lines l and m form an angle of 56° with each other. The reflection of a point (–4, 1) along the line l followed

by a reflection along line m will cause a ________ rotation. Question 18 options: A) 56° B) 112° C) 180° D) 28°

1 answer:

Tasya [4]3 years ago

7 0

Answer:

B) 112°

Step-by-step explanation:

After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:

2·56° = 112°

_____

In the attached, lines l and m are separated by 56°, as required by the problem statement.

You might be interested in

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounc

Ludmilka [50]

Answer:

$\mu = 12.1\\\sigma = 0.3$

a) Find the probability that the drink is less than 11.9 fluid ounces

We are supposed to find P(x<11.9)

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

Refer the z table

So, P(z<-0.67) = 0.2514

Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514

b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces

x= 11.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.6-12.1}{0.3}$

$z=-1.67$

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

We are supposed to find P(11.6<x<11.9)

So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

Refer the z table

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

P(-1.67<z<-0.67)= 0.2514-0.0475

P(-1.67<z<-0.67)= 0.2039

So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.

c)Find the probability that the drink is more than 12.6 fluid ounces

We are supposed to find P(x>12.6)

x= 12.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{12.6-12.1}{0.3}$

$z=1.67$

Refer the z table

P(x>12.6)=1-P(x<12.6)

P(z>1.67)=1-P(z<1.67)

P(z>1.67)=1-0.9525

P(z>1.67)=0.0475

Hence the probability that the drink is more than 12.6 fluid ounces is 0.0475

d) Is the drink containing more than 12.6 fluid ounces an unusual event?

Since p value is less than alpha (0.05)

Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.

3 0

3 years ago

Four people equally share 3 4 of a whole pizza. What fractional part of the whole pizza does each person receive?

murzikaleks [220]

Answer:

3/16

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Question 7 50 points

meriva

Answer:

1f 2×4 -3×³ 12k is divided by × - 3 the remainder is 21 find the value of k

8 0

2 years ago

Read 2 more answers

Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².

Liula [17]

Step-by-step explanation:

Let $y(x)=f(x)g(x)h(x)$ where

$f(x) = x^4$

$g(x)= (1 -2x^5)^6$

$h(x)= (5 - 8x^3)^2$

so that

$y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2$

Recall that the derivative of the product of functions is

$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$

so taking the derivatives of the individual functions, we get

$f'(x) = 4x^3$

$g'(x) = 6(1 - 2x^5)^5(-10x^4)$

$h'(x) = 2(5 - 8x^3)(-24x^2)$

So the derivative of y(x) is given by

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)$

or

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)$

3 0

2 years ago

A butcher is mixing ground turkey breast that is 98% lean and beef that is 90% lean to make a blend that is 92.4% lean. Determin

Paul [167]

See brainly.com/question/8613376 for one way to work mixture problems.

The proportion of beef will be
.. (98 -92.4)/(98 -90) = 5.6/8 = 0.7

70 pounds of beef and 30 pounds of turkey are needed.

_____
1. I would prefer to use "t" and "b" as variables, rather than x and y. That way I can more easilly keep straight that they represent pounds of turkey and pounds of beef, respectively.

2. t + b = 100 . . . . . we want 100 pounds of mix

3. 98%*t +90%*b = 92.4%*100 . . . . . total pounds of lean meat

4. Using subsitution for t, we have
.. 98%*(100 -b) +90%*b = 92.4%*100
.. b*(98 -90) -98*100 = -92.4*100 . . . . . . multiply by -100, collect b terms
.. b = (98 -92.4)*100/(98 -90) . . . . . . . . . add 98*100 and divide by b coefficient
note that this expression is exactly the one we used to write down the answer above.
.. b = 5.6*100/8 = 70 . . . . . . . y, if you like
.. t = 100 -b = 30 . . . . . . . . . . x, if you like

70 pounds of beef and 30 pounds of turkey are needed.

7 0

3 years ago