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marusya05 [52]
1 year ago
11

Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the in

tersection of lines k and m, the bottom right angle is 93 degrees. Given the information in the diagram, which theorem best justifies why lines j and k must be parallel? a) alternate interior angles theorem b) alternate exterior angles theorem c) converse alternate interior angles theorem d) converse alternate exterior angles theorem

Mathematics
2 answers:
Nutka1998 [239]1 year ago
8 1

Answer:

b) alternate exterior angles theorem

Step-by-step explanation:

When two lines are cut by a transversal, the alternate exterior angles are congruent. In the first diagram:

  • x and y are congruent
  • a and b are congruent

Comparing with our given lines, j, k and m.

We can see that the two given angles are in the same position as in the first image. Therefore, lines j and k are parallel by the alternate exterior angles theorem.

Guest
1 year ago
this one was wrong for me
klemol [59]1 year ago
8 0

Answer:

converse of the alternate interior angles theorem

Step-by-step explanation:

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A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard
Sauron [17]

Answer:

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $393.50

Standard deviation r = $50.30

Number of samples n = 25

Confidence interval = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

$393.50+/-1.96($50.30/√25)

$393.50+/-1.96($10.06)

$393.50+/-$19.7176

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

5 0
1 year ago
a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft.
satela [25.4K]

Answer:

t=2.47\ s  

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is

h(t) = h_0 + s_0t -16t ^ 2

Where h_0 is the initial height, s_0 is the initial velocity and t is the time in seconds.

We know that the initial height is:

h_0 = 4.5\ ft

The initial speed is:

s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s

So the equation is:

h (t) = 4.5 + 37.62t -16t ^ 2

The ball hits the ground when when h(t) = 0

So

4.5 + 37.62t -16t ^ 2 = 0

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

at^2 +bt + c

The quadratic formula is:

t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}

In this case

a= -16\\\\b=37.62\\\\c=4.5

Therefore

t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}

t_1=-0.114\ s\\\\t_2=2.47\ s  

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

4 0
2 years ago
Two pence coins are used to make a square. If one millioncoins were used, what would be the length of the sides of the square?
Slav-nsk [51]

Answer:

i dont know the answer

Step-by-step explanation:

just put a random answer and hope for the best

7 0
2 years ago
Jalen inherited a collection of vintage comic books. An appraiser separated the comic
sladkih [1.3K]

Jalen has total 63 comic books.

Step-by-step explanation:

Given,

Total value of comic books = $3135

Let,

Number of $45 comic books = x

Number of $65 comic books = y

According to given statement;

45x+65y=3135     Eqn 1

x=y+33                  Eqn 2

Putting value of x from Eqn 2 in Eqn 1

45(y+33)+65y=3135\\45y+1485+65y=3135\\110y=3135-1485\\110y=1650\\

Dividing both sides by 110

\frac{110y}{110}=\frac{1650}{110}\\y=15

Putting y=15 in Eqn 2

x=15+33\\x=48

Total comic books = x+y

Total comic books = 48+15 = 63

Jalen has total 63 comic books.

Keywords: addition, elimination method

Learn more about elimination method at:

  • brainly.com/question/10879401
  • brainly.com/question/10940255

#LearnwithBrainly

7 0
1 year ago
Jackson has ten dollar bills and one dollar bills in his pocket. The number of ten dollar bills is five more than six times the
Katyanochek1 [597]

Answer:

Let t be the number of ten dollar bills.

o×6+5=t

If you need it without t, then it's:

o×6+5

Step-by-step explanation:

Let t be the number of ten dollar bills.

o×6+5=t

We get this because the question said that there were more ten-dollar bills than 6 times the number of one-dollar bills.

5 0
1 year ago
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