Gabby buys a new purse for $33. The sales tax in her state is 6%. How much is the sales tax?

What is the image point of (1,-2)after a translation right 4 units and down 4 units?

den301095 [7]

By applying the concept of translation, we conclude that the image point of (1, - 2) is equal to the point (5, - 6).

<h3>What is the image of a point by rigid translations?</h3>

In this problem we have a point set in a Cartesian plane, which has to be translated to determine the coordinates of a resulting point. Translations are examples of rigid transformations, these are, transformations applied on geometric loci such that Euclidean distance is conserved.

Vectorially speaking, translations are modelled by the following formula:

P'(x, y) = P(x, y) + T(x, y) (1)

Where:

P(x, y) - Original point
P'(x, y) - Resulting point
T(x, y) - Translation vector

If we know that P(x, y) = (1, - 2) and T(x, y) = (4, - 4), then the resulting point is:

P'(x, y) = (1, - 2) + (4, - 4)

P'(x, y) = (5, - 6)

By applying the concept of translation, we conclude that the image point of (1, - 2) is equal to the point (5, - 6).

To learn more on rigid transformations: brainly.com/question/1761538

#SPJ1

5 0

1 year ago

The answer to this problem for my hw

Darya [45]

Okay. So, Marianna has 16 yards of fabric. Subtract 2 2/3 from 16, because those are the leftovers. 16 - 2 2/3 is 13 1/3. 13 1/3 / 3 1/3 is 4. Mariana made 4 pieces of 3 1/3 yard fabric. The answer is C: 4.

5 0

3 years ago

Which of the following is the equation for the graph shown?a. x^2/144+y^2/95=1b. x^2/144-y^2/95=1c. x^2/95+y^2/144=1d. x^2/95-y^

Andrews [41]

e follSOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

$\frac{\mleft(x-h\mright)^2}{a^2}+\frac{(y-h)^2}{b^2^{}}=1$

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

$\begin{gathered} 2a=24,a=\frac{24}{2}=12 \\ 2b=20,b=\frac{20}{2}=10 \end{gathered}$

STEP 3: Get the equation of the ellipse

$\begin{gathered} By\text{ substitution,} \\ \frac{(x-h)^2}{a^2}+\frac{(y-h)^2}{b^2}=1 \\ \frac{(x-0)^2}{12^2}+\frac{(y-0)^2}{10^2}=1=\frac{x^2}{144}+\frac{y^2}{100}=1 \end{gathered}$

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as:

$\frac{x^2}{144}+\frac{y^2}{95}=1$

OPTION A

8 0

1 year ago

Find the point on the line y = 2x + 3 that is closest to the origin.

Ludmilka [50]

I believe the answer is (-1,1) . The origin is the same as (0, 0) so I drew the line on a quick graph and if you are talking about distance, then the answer should be correct.
Hope this helped :)

6 0

3 years ago

The sum of 5 consecutive odd numbers is 145. What is the third number in this sequence

vredina [299]

Answer: The 3rd number in the sequence is 29.

Step-by-step explanation: What we have is a sequence of “ODD” numbers and they are consecutive, which means they come one after another with regular intervals. We don’t have any of the numbers but we can start by saying ‘let x represent the first number in the sequence’

With this in mind, we can now assume all other four numbers in the sequence. Therefore if the 1st number is x, the 2nd number would be x + 2, and the the 3rd number would be x + 4, 4th number would be x + 6 while the 5th number would be x + 8.

The reason is that, every odd number is an addition of two to the previous odd number. For instance, if you start with 3, the next odd number would be 3+2 (5), and so on.

Therefore we can now write our consecutive odd numbers as follows;

x + (x + 2) + (x + 4) + (x + 6) + (x + 8)

Remember that all the numbers add up to 145. Therefore,

x + x + 2 + x +4 + x + 6 + x + 8 = 145

5x + 20 = 145

Subtract 20 from both sides of the equation

5x = 125

Divide both sides of the equation by 5

x = 25.

The first odd number is 25, which means the 3rd odd number is 25 + 4.

Therefore the 3rd odd number is 29.

5 0

3 years ago