Which line is parallel to line r?

line p
line q
line s
line t

The equations provided represent parabolas that have been translated or reflected from the standard form y = x^2. Without a given graph or additional details, we can't definitively determine which equation is correct.

Without a graph or specific details regarding the shape, position, and characteristics of the graph, we can't definitively choose one of the given equations. However, each equation represents a parabolic function that is translated and/or reflected from the standard form, y = x².

The equation y = (x + 4)² + 1 represents a parabola that is shifted 4 units to the left and 1 unit up from the origin.

The equation y = (x + 4)² − 1 is a parabola that is shifted 4 units to the left and 1 unit down.

For the equation y = (x − 4)² + 1, the parabola is shifted 4 units to the right and 1 unit up.

And lastly, the equation y = (x − 4)² − 1 describes a parabola that is shifted 4 units to the right and 1 unit down.

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Answer: B

Step-by-step explanation: The equation would be x^2+y^2=64 or 8^2

Answer:

B. Positive correlation

Step-by-step explanation:

Positive correlation is nothing but when the values of x increase, the corresponding y values are also increase.

When we look at the scatter plot, when x increase, the y also increase.

Therefore, it is a positive correlation.

Hope this will helpful.

Thank you.

Answer : The given polynomial equation can have 0,2 or 4 complex roots.

Explanation:-

Given polynomial equation is [tex]3x^5-2x+1=0[/tex] which is a polynomial of degree 5.

We know that the complex roots always occur in pair ,therefore the number of complex roots in any polynomial must be an even number but less than equal  to the degree of polynomial.

Thus, the given polynomial equation has 4 complex roots.

Answer:

The polynomial equation have 4 complex roots.

Step-by-step explanation:

We are given a polynomial equation as:

[tex]3x^5-2x+1=0[/tex]

clearly the polynomial equation is a equation of degree 5 hence, the polynomial equation has atmost 5 roots.

Now we find the roots of the equation by it's graph.

we could clearly see that the graph ofthe function passes through the point (-1,0). hence -1 is the root of the polynomial equation, other than this point the graph does not touches or pass through the x-axis.

Hence, the other four roots of the polynomial equation are complex.

Hence, the polynomial equation has 4 complex roots.

The graph that represents the solution of linear inequalities 3x + 2y >= 4 and x + 3y <= 2 is attached below. The shaded region represents the solution of the inequalities.

To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality. If given a strict inequality, use a dashed line for the boundary. If given an inclusive inequality, use a solid line. Next, choose a test point not on the boundary. If the test point solves the inequality, then shade the region that contains it; otherwise, shade the opposite side.

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Answer: Yes ΔRWS≈ΔQWT.

Step-by-step explanation:

We know that when two chords intersect each other inside a circle, the products of their segments are equal.

Therefore, [tex]QW\times WS=TW\times RW\\\Rightarrow\frac{QW}{RW}=\frac{TW}{WS}[/tex]

Now in triangle QWT and triangle RWS

∠QWT=∠RWS     [Vertically opposite angles]

[tex]\frac{QW}{RW}=\frac{TW}{WS}[/tex]

Therefore, By SAS similarity rule

ΔRWS≈ΔQWT

Therefore, yes ΔRWS≈ΔQWT.

On the second day, Andrea will still win by 0.026 seconds and the other girl will be at 99.75 meters on the track.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Andrea and Sula ran a race on a track that was 100 meters long.

Let us assume that Andrea completed the 100m race in 10 secs.

∴  Andrea's speed is (100/10) = 10m/sec.

Also given that Sula was exactly 5 meters behind her.

∴ In 10 secs she completed 95 meters, and her speed is

= (95/10) = 9.5m/sec.

The next day they ran another race and Andrea agreed to start 5 meters behind the starting line and both the girls run at the same speed,

∴  Andrea has to run 105 meters, so she'll complete the race in

(105/10) secs.

= 10.5 secs.

Sula has to run only 100 meters, so the time needed for her to complete is,

= (100/9.5) secs.

= 10.526 seconds.

So, on the next day, Andrea will win again by (10.526 - 10.5) secs

= 0.26 secs.

∴ When the winner crosses the finish line the other girl will be,

(10.5×9.5) meters = 99.75 meters on the track.

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32 is your answer hope it helped :) welcome

The amount of tip I would leave for the waiter is  $24.89

A tip is a form of payment that is given to someone who renders a service. The amount of tip that was given is a percentage of the total bill at the restaurant.

The value of the tip can be determined by multiplying the percentage of tip by the total bill at the restaurant

Value of the tip = percentage tip x total bill at the restaurant

20% x  $24.89

0.2 x  $24.89 = $4.98

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Answer:

  The product of an odd number of negative factors is negative.

Step-by-step explanation:

The factor -1 can be factored from any negative number. Then the product of some number of negative numbers is the product of that number of positive numbers and -1 raised to that power.

An even power of -1 is 1.

An odd power of -1 is -1. So, the product of an odd number of negative factors is negative.

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Comment on this result

This is helpful to remember when considering the solutions to polynomial inequalities. Once the factored form of the polynomial is found, the solution will depend on the signs of the factors. For example, consider ...

  (x +4)(x -2)(x -3) < 0

The zeros of these factors are -4, 2, 3. At each of these values of x, the sign of one of the factors will change. For x<-4, all three factors are negative, so the inequality is true. For -4<x<2, only two of the factors are negative, so the inequality is false. For 2<x<3, one of the factors is negative, so the inequality is again true. For 3<x, all factors are positive, so the inequality is false. Then the solution is (x < -4) ∪ (2 < x < 3).

See the graph for a plot of this polynomial and the solution to the inequality.

After a 270-degree counterclockwise rotation, the first car on the ferris wheel originally located at (0, 40) will be at (40, 0).

If the first car of a ferris wheel is located at the point (0, 40) on a coordinate plane and undergoes a rotation of 270 degrees counterclockwise about the origin, the new coordinates of the first car can be determined by applying a rotation transformation. To perform a 270-degree counterclockwise rotation, we rotate the point 90 degrees clockwise. This equivalent action simplifies the calculation, as rotating (0, 40) 90 degrees clockwise results in the point moving to (40, 0). Therefore, after a 270-degree counterclockwise rotation (which is equivalent to a 90-degree clockwise rotation), the new coordinates of the first car on the ferris wheel are (40, 0).

Final answer:

By adding the fractions of votes for the museum (5/12) and zoo (5/24), converting them to a common denominator, and subtracting from the whole, we find that 3/8 of the class voted for the nature park.

Explanation:

To determine what fraction of the class voted for the nature park, we first need to add up the fractions of the class that voted for the museum and the zoo, and then subtract that sum from the whole class, which is represented as 1 (or 12/12). Since 5/12 of the class voted for the museum and 5/24 of the class voted for the zoo, we need to find a common denominator to add these fractions together. The lowest common denominator for 12 and 24 is 24.

First, we convert 5/12 to a fraction with a denominator of 24, which would be 10/24 (since 5 × 2 = 10 and 12 × 2 = 24). Now we can add the two fractions:

10/24 (votes for the museum)

5/24 (votes for the zoo)

Therefore, 10/24 + 5/24 = 15/24. After that, we subtract the sum from the whole to find out what fraction voted for the nature park:

12/12 - 15/24 = 24/24 - 15/24 = 9/24.

Hence, 9/24 of the class voted for the nature park. However, we can simplify 9/24 by dividing the numerator and the denominator by their greatest common divisor, which is 3, giving us 3/8.

Therefore, 3/8 of the class voted for the nature park.

42 received an A
 so 40-42 = 38 did not

the fraction would be 38/80, divide both numbers by 2

38/80 reduces to 19/40 did not receive an A

Out of 80 students, 38 did not receive an A, resulting in the fraction who did not receive an A being 19/40 after simplifying.

In a class of 80 students, if 42 received a grade of A, then the number of students who did not receive an A is the total number of students minus the number who did receive an A. So, 80 students − 42 students = 38 students. The fraction of the class that did not receive an A is 38 out of 80, which can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2.

Therefore, the reduced fraction is 19/40.

The fraction of the class that did not receive an A is 19/40 which, if we converted into a percentage, would be 47.5%.