Ask question

Ask question

All categories

2 years ago

5

Joseph drove to Carly’s house for dinner. He was away from his house for 2 hours. He spent 50minutes at Carly’s house. Driving t

o and from Carly’s house he drove at a speed of 45mph. How far away from Carly does Joseph live?

1 answer:

Klio2033 [76]2 years ago

7 0

70 miles

Hope this helps

-Millie

You might be interested in

The vertex form of the equation of a vertical parabola is given by y= 1/4p(x-h)^2 , where (h, k) is the vertex of the parabola a

Brrunno [24]

Answer:

See diagram, attached.

Part A: Equation of the directrix is y= -2

Part B: point of intersection A of directrix & line of symmetry A(6,-2)

Part C: y = (1/12) (x-6)^2<em>+1</em>

or on simplifying

12y = x^2 -12x +48

(Note: given instructions omitted the <em>+k</em> term.)

part D: The parabola opens upwards becaus p>0.

Part E: The value of p is the difference of y coordinates of F minus the y-coordinate of A, all divided by 2, which is positive.

Part F: p = (4 - (-2))/2 = +3

Part G: y = (1/12)(x-6)^2 + 1

Part H: See attached diagram below

Part I : y = (1/12) (x-6)^2 + 1 where h=6, k=1, or V(6,1).

It fits with the given formula, provided we include the +k term.

Step-by-step explanation:

The vertex form of the equation of a vertical parabola is given by y= 1/4p(x-h)^2 , where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.

Part A: Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line? (y=-2)

Part B: Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola? A(6,-2)

Part C: Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.

We know that the equation in vertex form is

y = (1/(4p)(x-h)^2+k where V(h,k) are the coordinates of the vertex.

From points F and A, we know that the distance from directrix to focus is 6.

Therefore p=3.

The vertex, V(h,k) is located at the mid point between the segment joining the directrix and the focus, namely A & K, which has coordinates V(6,1), thus h=6, k=1.

The equation of the parabola is therefore

<em>y = (1/(4p) * (x-h)^2 </em>+k<em>) = (1/(4*3))(x-6)^2 </em>+1 <em>= (1/12) (x-6)^2+1</em>

(note: given instructions omitted the +k term.)

Simplifying

12y = x^2 -12x +36+12

<em>12y = x^2 -12x +48</em>

Part D: Which way will the parabola open? Explain.

The parabola opens upwards becaus p>0.

Part E: How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.

The value of p is the difference of y coordinates of F minus the y-coordinate of A, all divided by 2, which is positive.

Part F: What is the value of p for your parabola?

p = (4 - (-2))/2 = +3

Part G: Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.

y = (1/12)(x-6)^2 + 1

Part H: Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.

See attached diagram below

Part i: Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.

1.33...x^2 - 16x -16y = -64

Multiply all by 3/4

x^2-12x-12y=-48

rearrange

12y = x^2-12x+36 +12

Factor

12y = (x-6)^2 + 12

Divide by 12 all through

y = (1/12) (x-6)^2 + 1 where h=6, k=1, or V(6,1).

It fits with the given formula, provided we include the +k term.

6 0

2 years ago

he data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. {5, 3

sergeinik [125]

The best measure of center tendency for this set of data would be the median. It is the best measurement because the data set has an outlier. The outlier is the 30. So to find the median we first order the data set and then find out if the set is an even or odd set. This set is even so we just chose the middle number. If the set was even, we would add the two center number and divide them by 2.

3, 3, 4, 4, 4, 5, 5, 5, 30

The center tendency = 4

8 0

2 years ago

Read 2 more answers

Which angles form a linear pair? AnglePRL and AngleLRM AngleORP and AngleMRN AngleMRN and AngleNRO AngleLRP and AngleORP

Andrew [12]

Answer: C (AngleMRN and AngleNRO)

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect. Two angles are linear if they are adjacent angles (angles next to each other) formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

AngleMRN and AngleNRO together is 180 degrees

I'm not very good at explaining but hope this helps ! :)

4 0

2 years ago

A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is cor

Nady [450]

Answer:

a) S ~ N ( 0 , 48 )

b) P ( S > 10 ) = 0.0745

Step-by-step explanation:

Given:-

- We have n = 100 MCQs

- 5 options for every MCQs

- probability to guess each MCQ correct is independent from one another.

- Right Answer points= +4

- Wrong answer points= -1

Find:-

a) Find ????(S).

b) Find P(S>10). Write your answer as a math expression, then use the code cell below to find its numerical value and provide it along with your math expression.

Solution:-

- The probability (p) of guessing a correct answer for each question is:

p ( correct answer ) = 1 / 5 = 0.2

- The mean number of correct and incorrect answers can be determined by:

( Mean correct answers) = n*p = 100*0.2 = 20

( Mean incorrect answers) = n*(1-p) = 100*0.8 = 80

- The mean score for correct answers would be:

Sc ( u ) = (Points for right answer)*(Mean correct answers)

Sc ( u ) = ( +4 )*(20)

Sc ( u ) = 80 points

The mean score for incorrect answers would be:

Si ( u ) = (Points for wrong answer)*(Mean incorrect answers)

Si ( u ) = ( -1)*(80)

Si ( u ) = -80 points.

- The mean score attained by a student would be S (u):

S (u) = Sc(u) + Si(u)

S (u) = 80 - 80 = 0

- The variance of the correct and incorrect answers can be determined by:

Var ( correct answers ) = n*p*q = 100*0.2*0.8 = 16

Var ( in-correct answers ) = n*p*q = 100*0.2*0.8 = 16

- The variance of points of correct answers can be:

Sc (Var) = Var ( correct answer ) * (Points for right answer)

Sc (Var) = 16*(+4) = +64 points

- The variance of points of incorrect answers can be:

Si (Var) = Var ( incorrect answer ) * (Points for wrong answer)

Si (Var) = 16*(-1) = -16 points

- Since the probabilities of guessing correct answers are independent. Then as per law of independence:

S ( Var ) = Sc (Var) + Si (Var)

= 64 - 16

= +48 points

- The standard deviation for the distribution (s.d) of points (S) is:

S ( s.d ) = √S (Var) = √48 = 6.9282

- The number of points (S) attained by a student by guessing on the test containing MCQs would have a mean u = 0 points and s.d = + 48 points.

- The random variable (S) can be modeled by normal distribution as follows:

S ~ N ( 0 , 48 )

- To find the required probability P(S>10).

Compute the Z-value of S = 10 points:

Z - value = ( S - u ) / s.d

= ( 10 - 0 ) / 6.9282

= 1.4434

Use the standardized Z-table for normal distribution:

P ( Z > 1.4434 ) = 0.0745

The probability is:

P ( S > 10 ) = P ( Z > 1.4434 ) = 0.0745

5 0

2 years 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

2 years ago