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natka813 [3]
3 years ago
12

Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. Square A B C D and triangle B U C are attached at sid

e B C to create trapezoid A U C D. What is the measure of angle DCU?
a.45o
b.90o
c.120o
d.135o
Mathematics
2 answers:
Art [367]3 years ago
5 0

Answer:

d) 135º

Step-by-step explanation:

Note that the angle DCU is the sum of the angles DCB and BCU. The angle DCB is 90º because A B C D is a square, then all its angles are equal to 90º.

After attaching B U C to A B C D, we obtain a trapezoid A U C D. Since A U C D has at least one pair of parallel sides, then AU should be parallel to CD, thus the angle CBU must be 90º.

B U C is isoceles, so we conclude that other two angles must have the same size, and due to the sum of the angles of a triangle being 180º, then both BUC and BCU are equal to 45º

As a result, the angle DCU is equal to 90º+45º = 135º. Option d is the correct one.

ch4aika [34]3 years ago
4 0

Answer:

135

Step-by-step explanation:

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The word "less than" represent what operation?
bixtya [17]

Answer:

  • The term 'less than' is used to indicate the relationship between two values.
  • The term 'less than' symbolically represented as '<'.

Step-by-step explanation:

  • The term 'less than' is used to indicate the relationship between two values.

It expresses that one value will be lesser than the other.

The term 'less than' symbolically represented as '<'.

We can implement certain operations like comparing values, heights, and numbers.

For example, there are 3 pencils in one bag A, and 8 pencils in bag B.

When we compare the two, we can easily observe that bag A has fewer pencils than bag B.

Thus,

Pencils in Bag A       <         Pencils in Bag A

           3                     <                    8

4 0
3 years ago
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Svetlanka [38]

Answer:

63.2

Step-by-step explanation:

90+26.6=116.8

180-116.8=63.2

8 0
2 years ago
Read 2 more answers
The researcher trains a sample of 16 individuals in mindfulness and then collects data on how long they spend eating per day. Th
Mila [183]

Answer:

The calculated t-value is t=0.47.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>"Americans typically eat quickly and do not spend time enjoying their meal. A researcher plans to test if those trained in mindfulness will take more time to enjoy their meal (that is, they will spend more time eating than the general population). The general population spends an average of 68 minutes per day combined eating their three meals. The researcher trains a sample of 16 individuals in mindfulness and then collects data on how long they spend eating per day. The sample mean for those trained in mindfulness equals 74; the SS = 150. What is the calculated t-value? Round your answer to two decimal places."</em>

The degrees of freedom are (n-1)=(16-1)=15

The standard deviation is:

s=\sqrt{\frac{SS}{n-1}}=\sqrt{\frac{150}{16-1}}=\sqrt{10}=3.16

The t-value can be calculated as:

t=\frac{M-\mu}{\sigma/\sqrt{n}} =\frac{74-68}{3.16/\sqrt{16}} \\\\t=\frac{6}{3.16*4}=\frac{6}{12.64}= 0.47

4 0
3 years ago
the graph of a liner relationship has a slope of -5 and passes through the point (2, -12). write tge equation of the liner in th
bixtya [17]

Answer:

y = -5x - 2

Step-by-step explanation:

equation formula: y = mx + c

m = -5

-12 = -5(2) + c

c = -2

⇒ y = -5x - 2

5 0
2 years ago
Consider the vector x: x &lt;- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Opti
Nookie1986 [14]

<u>Completed Question</u>

Outputs to be matched to the functions are:

  • 1,2,3,4,5
  • 1,5,3,2,4
  • 1, 4, 3, 5, 2
  • 2, 18, 27, 43, 96

Answer:

  • sort(x): 2, 18, 27, 43, 96
  • order(x): 1, 5, 3, 2, 4
  • rank(x) : 1, 4, 3, 5, 2
  • none of these :  1, 2, 3, 4, 5

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

<u>Sort</u>

In R, the sort(x)  function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

<u>Rank</u>

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

  • 2 has a rank of 1
  • 43 has a rank of 4
  • 27 has a rank of 3
  • 96 has a rank of 5
  • 18 has a rank of 2

Therefore, the output of rank(x)  is: 1, 4, 3, 5, 2

<u>Order</u>

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

  • 2 was in the 1st position
  • 18 was in the 5th position
  • 27 was in the 3rd position
  • 43 was in the 2nd position
  • 96 was in the 4th position

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

7 0
3 years ago
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