All categories

1 month ago

Select all the sequences of reflections that produce an image equivalent to the image r(180°, O)(△BCD).

Mathematics

1 answer:

tester [12.3K]1 month ago

8 0

Answer:

The operation r(180°,0) represents a 180° rotation around the origin.

This rotation shifts our shape to the opposite quadrant (effectively translating it across two quadrants).

Thus, this can be seen as:

A reflection across the x-axis followed by a reflection across the y-axis.

Alternatively.

It can also be depicted as a reflection across the y-axis followed by a reflection across the x-axis.

There exists another reflection method, contingent upon the position of our figure.

When the figure is situated in either the first or third quadrant, reflecting over the line y = -x yields a result equivalent to the rotation.

Conversely, if the figure lies in the second or third quadrant, reflecting over the line y = x corresponds to the rotation.

We can merge these two approaches into a single expression:

A reflection over the line y = (-1)^n*x.

Here, n indicates the number identifying the quadrant containing the figure.

You might be interested in

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tuli

Zina [12379]

B. 5 Step-by-step explanation: The greatest common factor of 85 and 15 is 5, leading to a ratio of red to white tulips of 17:3. Red tulip ratio becomes 85/5 = 17, while white tulip ratio turns out to be 15/5 = 3.

4 0

1 month ago

Happy is four times as old as Grumpy. The sum of their age is 100. How old are Happy and<br> Grumpy?

PIT_PIT [12445]

Answer:

Grumpy's age is 20 while Happy's age is 80.

Step-by-step explanation:

5 0

2 months ago

Read 2 more answers

Which formula can be used to describe the sequence? -2/3,-4,-24,-144...

lawyer [12517]

The formula that describes the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

Step-by-step explanation:

The nth-term formula for a geometric sequence is $a_{n}=a(r)^{n-1}$ , where

a represents the first term of the sequence
r signifies the common ratio between any two consecutive terms
$r=\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$

∵ The sequence is $\frac{-2}{3}$ , -4, -24, -144,.......

∵ The first term is $\frac{-2}{3}$

∵ The second term is -4

∴ $\frac{-4}{\frac{-2}{3}}=6$

∵ The third term is -24

∴ $\frac{-24}{-4}=6$

∵ The fourth term is -144

∴ $\frac{-144}{-24}=6$

∵ $\frac{a_{2}}{a_{1}}$ = $\frac{a_{3}}{a_{2}}$ = $\frac{a_{4}}{a_{3}}$ = 6

∴ There is a consistent ratio between two consecutive terms

∴ The sequence qualifies as a geometric sequence

∵ The formula for the nth term of the geometric sequence is $a_{n}=a(r)^{n-1}$

∵ a = $\frac{-2}{3}$

∵ r = 6

∴ The equation for the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

The formula that can be employed to outline the sequence is $a_{n}=\frac{-2}{3}(6)^{n-1}$

Learn more:

You can explore more about sequences in

8 0

2 months ago

The product of two whole numbers is 196 and their sum is 35. what are the two numbers

Svet_ta [12734]

A) The product of x and y equals 196. Thus, A) x is equal to 196 divided by y.

B) The sum of x and y is 35. By substituting A) into B), we have
B) 196 divided by y plus y equals 35. Multiplying both sides by y yields
B) 196 plus y squared equals 35y. This results in B) y squared minus 35y plus 196 equals 0.
Therefore, the solutions are X1 = 28 and X2 = 7.

8 0

3 months ago

A bag of garden soil weighs 38 pounds and holds 4 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags

Svet_ta [12734]

Answer:

The total weight of 15 bags is 258.21 kilograms.

The combined volume of 15 bags is 2.222 cubic yards.

Step-by-step explanation:

In terms of dimensions, a pound is equivalent to 0.453 kilograms, and a cubic yard is equal to 27 cubic feet. We'll calculate the weight and volume for 15 bags by utilizing these conversions:

Weight

$x = 15\,bags \times \frac{38\,lb}{1\,bag}\times \frac{0.453\,kg}{1\,lb}$

$x = 258.21\,kg$

The total weight of 15 bags equals 258.21 kilograms.

Volume

$x = 15\,bags \times \frac{4\,ft^{3}}{1\,bag} \times \frac{1\,yd^{3}}{27\,ft^{3}}$

$x = 2.222\,yd^{3}$

The total volume of 15 bags sums up to 2.222 cubic yards.

7 0

2 months ago