1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ExtremeBDS [4]
2 years ago
5

Four runners start at the same point; Lin, Elena, Diego, Andre. For each runner write a multiplication equation that describes t

heir journey.
Lin runs for 29 seconds at 7.2 meters per second. What is her finish point?

7.2*?=29

29*7.2=?

?*29=7.2

Elena runs for 26 seconds and finishes at 240 meters. What is her velocity?

240*26=?

26*?=240

?*240=26

Diego runs for 33 seconds at -6.1 meters per second. What is his finish point?

-6.1 • ? = 33

33*?=-6.1

-6.1*33=?

Andre runs for 38 seconds and finishes at -295 meters. What is his velocity?

-295*38=?

38*?==-295

?*-295=38
Mathematics
1 answer:
Natalka [10]2 years ago
6 0

Answer:

See the answers in the explanation

Step-by-step explanation:

Lin runs for 29 seconds at 7.2 meters per second. What is her finish point?

time= 29 seconds

speed= 7.2 m/s

distance= speed*time

distance= 7.2*29

distance=208.8 m

Elena runs for 26 seconds and finishes at 240 meters. What is her velocity?

time= 26 seconds

distance= 240meters

velocity= distance/time

velocity= 240/26

velocity=9.23 m/s

Diego runs for 33 seconds at -6.1 meters per second. What is his finish point?

time= 33 seconds

velocity

distance=velocity*time

distance=33*6.1

distance= 33*6.1

distance=201.3 m

Andre runs for 38 seconds and finishes at -295 meters. What is his velocity?

time= 38 seconds

distance= 295m

velocity= distance/tim

velocity= 295/38

velocity= 7.76m/s

You might be interested in
show that thw roots of the equation (x-a)(x_b)=k^2 are always real if a,b and k are real. Please I really need help with this
VLD [36.1K]

Answer:

see explanation

Step-by-step explanation:

Check the value of the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real

• If b² - 4ac = 0 roots are real and equal

• If b² - 4ac < 0 then roots are not real

given (x - a)(x - b) = k² ( expand factors )

x² - bx - ax - k² = 0 ( in standard form )

x² + x(- a - b) - k² = 0

with a = 1, b = (- a - b), c = -k²

b² - 4ac = (- a - b)² + 4k²

For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0

Hence roots of the equation are always real for a, b, k ∈ R


           

8 0
3 years ago
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

3 0
1 year ago
Which are the soultions of the quadratic equation? x^2=7x+4
Vesnalui [34]

Answer:

Answer in image below

Step-by-step explanation:

3 0
3 years ago
What is Q3 for this data set?
Kisachek [45]

The same as last time

Step-by-step explanation:

8 0
1 year ago
Read 2 more answers
Find the slope and y intercept of the line represented by each table
charle [14.2K]

Step-by-step explanation:


6 0
3 years ago
Other questions:
  • If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(x + 1)?
    15·2 answers
  • I NEED HELP ON THIS CONSTRUCTED RESPONSE QUESTION! :(
    10·1 answer
  • What does ii and i mean in math?
    5·2 answers
  • Which is not a correct way to name the angle? A. ∠P B. ∠1 C. ∠QRP D. ∠QPR
    9·1 answer
  • Round 415,203 to the nearest thousands place
    10·1 answer
  • A rectangular pool has dimensions of 40ft and 60 ft. The pool has a patio
    14·2 answers
  • Question 1 - work out the value of 300
    8·2 answers
  • I neeed helppppppppppp
    11·2 answers
  • Need help!!!!!!!!!!!!!!!!
    9·2 answers
  • The box plot represents the distribution of speeds, in miles per hour, of 100 cars as
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!