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Debora [2.8K]
2 years ago
11

A figure in the first quadrant is rotated 180° counterclockwise about the origin. In which quadrant will the rotated figure appe

ar?
Mathematics
2 answers:
d1i1m1o1n [39]2 years ago
8 0
The rotated figure will appear in quadrant I.
bagirrra123 [75]2 years ago
4 0
For every point A = (x,y) in your figure, a 180 degree counterclockwise rotation about the origin will result in a point A' = (x', y') where:
x' = x * cos(180) - y * sin(180)
y' = x * sin(180) + y * cos(180)

Happy-fun time fact: This is equivalent to using a rotation matrix from Linear Algebra!

Because a rotation is an isometry, you only have to rotate each vertex of a polygon, and then connect the respective rotated vertices to get the rotated polygon.

You can rotate a closed curve as well, but you must figure out a way to rotate the infinite number of points in the curve. We are able to do this with straight lines above due to the property of isometries, which preserves distances between points.
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Simplify 2p × 3p2 ×4p3​
stepladder [879]

Answer: 24p^6

<em>How to: </em><u><em>Simplify the expression.</em></u>

<em>Have a great day ! Sorry if it's wrong :)</em>

6 0
2 years ago
A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his
Karolina [17]

Answer:

a) The ratio of passenger cars to pickup trucks is \frac{5}{7}

The ratio of pickup trucks to passenger cars is \frac{7}{5}

The ratio of passenger cars to total vehicles is \frac{5}{12}

The ratio of pickup trucks to total vehicles is \frac{7}{12}

b) The tape diagram is shown in the attached picture.

c) The tape diagram has 12 equal-sized parts.

d) The total quantity that the tape diagram represent is 192.

e) The value of each individual part of the tape is 16.

f) There were registered 80 passenger cars and 112 pickup trucks.

Step-by-step explanation:

a) According to the information in the problem, that for every 5 passenger cars registered, there were 7 pickup trucks registered.

So the ratios are:

Passenger cars to pickup trucks: \frac{5}{7}

Pickup trucks to passenger cars: \frac{7}{5}

If we calculate the total vehicles: 5+7=12

So, we can get two ratios more:

Passenger cars to total vehicles is \frac{5}{12}

Pickup trucks to total vehicles is \frac{7}{12}

b) We make a tape diagram where each box represents a vehicle so we draw 5 boxes for cars and 7 boxes for pickup trucks.

c) If we count the total quantity of boxes, there are 12.

d) This diagram represents the total quantity of registrations in August which is 192.

e) To get the representation of each part of the tape diagram we have to divide 192 by 12. 192÷12=16

f) Finally, we multiply 16 by the number of boxes of each type of vehicle:

Cars: 16×5=80

Pickup trucks: 16×7=112

6 0
2 years ago
Cindy found a collection of baseball cards in her attic worth $8,000. the collection is estimated to increase in value by 1.5% p
Sergio [31]
A]
Exponential function is given by the form:
y=a(b)ˣ
where:
a=initial value
b=growth factor
From the question:
a=$8000, b=1.015, 
thus the exponential growth function of this situation is:
y=8000(1.015)ˣ

b] The value of the collection after 7 years will be:
x=7 years
Using the formula:
y=8000(1.015)ˣ
plugging the values we get:
y=8000(1.015)⁷
y=8,878.76

Answer: $8,878.76
7 0
2 years ago
Lincoln Middle School has a total of $200 to spend on notebooks and tablets for the school board meeting. Notebooks cost $7 each
Anton [14]
The school can buy fifteen notebooks and nineteen tablets.  15X7=105 and 5X19=95.  95+105=200.  The first thing you want to do is realize that 5Xanything will give you an answer that has a 0 or a five at the end, so you want to find a product by 7 that ends with a 0 or 5 too.
4 0
2 years ago
The sampling distribution of certain statistical measures shows a normal distribution which of the following is an unbiased esti
svlad2 [7]

Answer:

A) Proportion.

Step-by-step explanation:

The distribution of sample proportions leads or may tends to approximate a normal distribution and is an unbiased estimator that has a graph that is usually distributed and is not skewed. In other words, simply, we can also say that the population proportion is basically defined to be as the mean of the sample proportion. The population proportion is basically equaled the expected value of the sample proportion.

4 0
1 year ago
Read 2 more answers
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