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2 years ago

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Select the statement that is true. Group of answer choices There are integers s and t such that 2=102⋅s+72⋅t . here are integers

s and t such that 8=102⋅s+72⋅t . There are integers s and t such that 1=102⋅s+72⋅t . There are integers s and t such that 6=102⋅s+72⋅t .

1 answer:

LekaFEV [45]2 years ago

3 0

Answer:

Step-by-step explanation: true

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Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2

Marina86 [1]

Answer: The correct options are

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.

Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.

The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).

And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).

<u>Option (A) Rotation 90°:</u>

We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.

So, rotation of 90° anticlockwise is a correct option.

<u>Option (B) Rotation 180°:</u>

If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.

So, rotation of 180° is NOT a correct option.

<u>Option (C) Rotation 270°:</u>

If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.

So, rotation of 270° clockwise is also a correct option.

<u>Option (D) (x, y) → (–y, x):</u>

We see that the co-ordinates of both the triangle follow the transformation

X(0, 0) ⇒ X'(0, 0)

Y(0, -2) ⇒ Y'(2, 0)

Z(-2, -2) ⇒ Z'(2, -2).

So, the transformation is (x, y) ⇒ (-y, x).

Therefore, the transformation (x, y) → (–y, x) is a correct option.

<u>Option (E) (x, y) → (y, -x):</u>

We see that the co-ordinates of both the triangle does NOT follow this transformation

For example, suppose this transformation is correct. Then, we have

Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.

Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.

Thus, the correct options are:

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

9 0

1 year ago

Read 2 more answers

Sharon wants to make key chains with different colored beads. Each key chain will look the same. Sharon will use a total of 20 g

skelet666 [1.2K]

20 green and 20 red ?

8 0

2 years ago

Read 2 more answers

dr.drazzle collected 70 liters of ocean water to test for antibacterial properties. he split the water into 100 samples . how mu

Annette [7]

Answer:

Each sample contains 0.70 liters of water.

Step-by-step explanation:

Dr Drazzle collected 70 liters of water of ocean water to test and he split the water into 100 samples.

So by unitary method we can calculate the amount of water in each sample.

∵ 100 samples contain the amount of water = 70 liters

∴ 1 sample contains the amount of water = 70/100 = 0.70 liters

So the answer is 0.70 liters in each sample.

8 0

1 year ago

Suppose again that we are counting the ways to distribute exams to TAs and it matters which students' exams go to which TAs. The

abruzzese [7]

The question is incorrect.

The correct question is:

Three TAs are grading a final exam.

There are a total of 60 exams to grade.

(c) Suppose again that we are counting the ways to distribute exams to TAs and it matters which students' exams go to which TAs. The TAs grade at different rates, so the first TA will grade 25 exams, the second TA will grade 20 exams and the third TA will grade 15 exams. How many ways are there to distribute the exams?

Answer: 60!/(25!20!15!)

Step-by-step explanation:

The number of ways of arranging n unlike objects in a line is n! that is ‘n factorial’

n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1

The number of ways of arranging n objects where p of one type are alike, q of a second type are alike, r of a third type are alike is given as:

n!/p! q! r!

Therefore,

The answer is 60!/25!20!15!

6 0

1 year ago

In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC a

geniusboy [140]

Answer:

BC:BN=8:3

Step-by-step explanation:

ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.

Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD

But, BC= BN+NC

Therefore, BC:BN=(BN+NC):BN

⇒BC:BN=(3+5):3

⇒BC:BN=8:3

4 0

1 year ago