All categories

3 years ago

Which statement about polygon PQRST and its image after dilation, polygon P'Q'R'S'T', is correct?

Mathematics

1 answer:

solniwko [45]3 years ago

6 0

Answer:

The length of diagonal PS and diagonal P'S' are in the ratio 1:3.

Step-by-step explanation:

Comparing the coordinates of the vertices,

P(0, -3)→P'(0, -9); Q(3, -2)→Q'(9, -6); R(3, 1)→R'(9, 3); S(0, 2)→S'(0, 6); T(-2, 0)→T'(-6, 0)

We can see that the pre-image points have been multiplied by a scale factor of 3. This means comparing the pre-image sides to the image sides, the ratio is 1:3. However, we must compare corresponding sides; the only choice comparing corresponding sides with a ratio of 1:3 is PS to P'S'.

You might be interested in

1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

Ad libitum [116K]

Answer: (a) The ratio of spirit to varnish is 1 : 3

(b) You will need 80 ml of mineral spirits

Step-by-step explanation: (a) If you have to mix 25% mineral spirit to the varnish as required in the question, then the whole solution would effectively contain 25 percent spirit and 75 percent varnish, giving you a hundred percent solution. To express both quantities in ratio can be done as follows;

Ratio = Spirit : Varnish

Ratio = 25 : 75

Ratio = 1 : 3

(b) Next, if you use 240 ml of varnish, this quantity would constitute 75 percent or ratio 3 out of 4 of your total solution. Therefore 240 ml of varnish can be expressed as follows;

240 : x = 3 : 4

Where x is the total solution and the right hand side (3 : 4) expresses the ratio of varnish in relation to the total solution. Hence,

240/x = 3/4

By cross multiplication you now have,

3x = 240 * 4

x = 960/3

x = 320

If x is the total solution which is 320 ml, and varnish constitutes 240 ml, then spirit equals,

Spirit = Total solution - varnish

Spirit = 320 - 240

Spirit = 80.

Therefore, you would need 80 ml of mineral spirits.

(c) Robson's tapestries all measure 1.5 m by 1 m. This can be expressed in whole numbers by first eliminating the decimal. Multiplying both dimensions by 10 results in,

1.5 (10) x 1 (10)

15 x 10

If both measurements can also be expressed as 15 m by 10 m, then reducing to the least terms would result in 3 by 2. That is,

15/5 by 10/5

3 by 2

Expressed as a ratio, this now becomes

Ratio = 3 : 2

6 0

4 years ago

teacher gives 5 students a multiple choice test, in which each problem is worth 1 point and there is no penalty with negative po

mamaluj [8]

The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order

The correct values as response to the questions are;

The minimum possible top score is 21

The maximum possible top score is 32

The minimum of the possible standard deviation is approximately 1.26

The maximum of the possible standard deviation is approximately 11.7

The reason the above values are correct are as follows:

The given parameters are;

The number of students that take the test, n = 5

The amount of points for each problem = 1 point

The median score = 9

The mean Score = 10

Required:

The minimum possible score;

The maximum possible top score

The minimum of the possible standard deviations

The maximum of the possible standard deviations

Solution:

Given that there is a score (the median) which is 9, we have;

The scores obtainable in the test is Scores ≥ 9

Therefore, for a score of 10, we have;

The minimum total points obtainable = Mean × Number of students

Therefore;

Total minimum total points obtainable by the 5 students = 5 × 10 = 50

The minimum possible top score

By arrangement, with the median at the middle, the minimum possible top score is given as follows;

0, 0, 9, 20, 21

Therefore, the minimum possible top score is 21

The maximum possible top score

The maximum possible top score is similarly given by arrangement of the numbers as follows'

0, 0, 9, 9, 32

The maximum possible top score is 32

The minimum standard deviation

By arrangement and selection, the minimum standard deviation is given as follows;

The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ 1.26

The maximum of the possible standard deviation

The maximum of the possible standard deviation is given as follows;

The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ 11.7

Learn more about mean and median here:

brainly.com/question/17012793

8 0

3 years ago

Dianna made several loaves of bread yesterday. Each loaf required 2 cups of flour. All together, she used 135 cups of flour. How

irinina [24]

Answer:

The answer is not in the options, it is 67.5

Step-by-step explanation:

135/2 = 67.5

4 0

4 years ago

Which characteristics describe the scatterplot? Check all that apply.

denpristay [2]

Answer:

1. Negative Correlation

3. Strong Correlation

5. Linear

Step-by-step explanation:

We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.

Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.

We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.

We can also see that the slope of the line connecting all data points is approximately $-1$ , which represents a strong negative correlation, therefore, 3rd option is correct as well.

If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.

6 0

3 years ago

Read 2 more answers

If the cone itself is 7 inches long, and the radius of the cone is 2 inches, what is the entire volume of ice cream in the cone

stepladder [879]

So if you use the volume of 7 inch and 2 inch your value is 14 volume

4 0

2 years ago

Read 2 more answers