e) If the cheetah made a round-trip and took half the amount of time on the return trip as on the front end of the trip, what would be the relationship between the average rates on each leg of the trip? Using a complete sentence, explain how you arrived at this conclusion.

Answers

Answer 1

The relationship between the average rates is that ; The average rate of return trip is twice the average rate of front trip.

How to determine algebra relationship?

From the complete question seen online, we can say that;

Time taken on front trip = t

Time taken on return trip = 1/2 × t = t/2

Relationship between speed(Rate) and time is;

Rate ∝ 1/time

This means that Rate is inversely proportional to time.

Thus, for the front trip, the rate is; r = 1/t

For return trip, the rate is; R = 1/(t÷2)

R = 1 × 2/t

R = 2/t

Rate of front trip = 1/t

Rate of return trip = 2/t

Thus, we can say that the average rate of return trip is twice the average rate of front trip.

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Related Questions

I need help on this question don't understand this at all

Answers

Answer:

F (3)=-1

Step-by-step explanation:

The domain consists of the pre-images and the range has the images. We have the f (3)=-1 since -1 is the image of 3. When we are looking for the function of a number and we are given a diagram of such, we just need to take the value of the number it is pointing to.

sally sweeps 20 floors in 4 hours , at the same rate , how many floors can sally sweep in 6 hours ?

Answers

Answer:

35 Floors in 6 Hours

Step-by-step explanation:

20 / 4 = X Floors Per Hour

floors per hour = 5

6*5 = 35 Floors

can anybody help me?

Answers

f(-2) = 2(-2)² - 8(-2) + 6 = 30

f(-1) = 2(-1)² - 8(-1) + 6 = 16

f(0) = 2(0)² - 8(0) + 6 = 6

f(1) = 2(1)² - 8(1) + 6 = 0

f(2) = 2(2)² - 8(2) + 6 = -2

Make m the subject of the equation
(a) 5(m + y) = 4(m - 3y)

Answers

Answer:

m=(-5y-3y)

Step-by-step explanation:

5m+5y=4m-3y

5m-4m=-5y-3y

m(5-4)=-5y-3y

m=(-5y-3y)/1

please help me
I'll mark you brainlist ​

Answers

Answer:

There are 16 notes of 20 paise's and 12 notes of 5 paise's.

Explanation:

The amount of notes for of 20 paise and 5 paise coins are not given.

So let there be x 20 paise's coins and y 5 paise's coins.

Equation buildup:

20x + 5y = 380 ___eq 1

20y + 5x = 380 - 60

20y + 5x= 320 ___ eq 2

Make x the subject for both:

1st

[tex]\rightarrow \sf 20x + 5y = 380[/tex]

[tex]\rightarrow \sf 20x = 380-5y[/tex]

[tex]\rightarrow \sf x = 19-0.25y[/tex]

2nd

[tex]\sf \rightarrow 20y + 5x = 320[/tex]

[tex]\sf \rightarrow 5x = 320-20y[/tex]

[tex]\sf \rightarrow x= 64-4y[/tex]

Solve them simultaneously:

[tex]\sf \rightarrow 64-4y =19 - 0.25y[/tex]

[tex]\sf \rightarrow -4y+0.25y =19 -64[/tex]

[tex]\sf \rightarrow -3.75y =-45[/tex]

[tex]\sf \rightarrow y =12[/tex]

Find x:

[tex]\sf \rightarrow x = 64-4y[/tex]

[tex]\sf \rightarrow x = 64-4(12)[/tex]

[tex]\sf \rightarrow x = 16[/tex]

The sum of two consecutive even numbers is 38. What is the smaller number?

Answers

Even numbers = 2x +2

Consecutive even numbers = 2x+4

then

(2x+2) + (2x+4)= 38

2x + 2 + 2x + 4 = 38

2x + 2x + 2 + 4 = 38

    4x + 6 = 38

                   4x = 38 - 6

                     x = 32 :4

                    x = 8

2x+ 2 = 2(8)+2 = 16 + 2 = 18

2x+4 = 2(8) +4 = 16 + 4 = 20

The smallest number is 18

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

18 is the smaller number

Step-by-step explanation:

Let us take X for the first even number (it will also be the smallest)

x, x+1, x+2, so on..

the consecutive even number of x+2 is the next even number after x.

so you now get this equation...

x+(x+2) = 38

2x + 2 = 38

2x = 36

x=18

Select the correct answer.
Using synthetic division, find (2x + 4x³ + 2x² + 8x + 8) + (x + 2).
O A. 2x3 + 2x + 4
OB.
2x4 + 2x² + 4x
OC. 2x3 + 2x + 4 +
I
OD.
2x3 + 2x² + 4
1
+ 2

Answers

The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

Division of the polynomial

The division of the polynomial is determined as follows;

(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)

                           

                     2x³ + 2x + 4

                   -------------------------

     x + 2   √(2x⁴ + 4x³ + 2x² + 8x + 8)

                - (2x⁴ + 4x³)

                 -------------------------------------

                                        2x² + 8x + 8

                                     - (2x² + 4x)

                                   ------------------------

                                                  4x + 8

                                               - (4x + 8)

                                              -------------------

                                                       0

Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

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A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 millimeters and an upper specification limit of 23.1 millimeters. The standard deviation is 0.19 millimeters and the mean is 22.9 millimeters. What is the process capability index for the process? Note: Round your answer to 4 decimal places.

Answers

The process capability index for the process is 0.1754.

How to calculate the index?

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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What subjects together do more than half of the class like?

Math 9 people
Science 3 people
Art 5 people
Writing 3 people
History 1 person

Math and Writing
Science and History
Art and Science
History and Math

Answers

Answer:

Math and Writing

Step-by-step explanation:

Well if we add up all the people we get (9 + 3 + 5 + 3 + 1) = 21. Half of that is 10.5 so the sum of the two subjects must be at least 11. The amount of people that like Math and Writing is 11 people so the two subjects that more than half the class like are Math and Writing.

Answer:

Math and Writing

Step-by-step explanation:

Number of students who like each subject:

Math = 9Science = 3Art = 5Writing = 3History = 1

Total number of students = 9 + 3 + 5 + 3 + 1 = 21

Half of 21 = 21 ÷ 2 = 10.5

Therefore, more than half the class would be > 10.5 students

Total number of students who like:

Math and Writing = 9 + 3 = 12Science and History = 3 + 1 = 4Art and Science = 5 + 3 = 8History and Math = 1 + 9 = 10

Therefore, the only combination of subjects that more than 10.5 students like is Math and Writing as 12 > 10.5

difference between compounded annually, monthly and daily.

Answers

Answer:

With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.

Raphael graphed the system of equations shown.

y = – 3
y = x – 0.8

A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?

(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)

–3x + StartFraction one-half EndFractiony = –3

b =

2
4
6
8

Answers

Answer:

C. (-2.2, -3)

Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between the both boats after two hours.

Answers

Answer:

197.93 km

Step-by-step explanation:

Let the base camp is point A and boats' locations after two hours are points B and C.

By connecting the three points together we get a triangle ABC with sides:

AB = 50*2 = 100 kmAC = 70*2 = 140 km

The angle between AB and AC is:

60 + 50 = 110 degrees (opposite directions from south)

We are looking for the distance BC, which can be found by using the law of cosines:

BC² = AB² + AC² - 2AB*AC*cos ∠BACBC² = 100² + 140² - 2*100*140*cos 110°BC²  = 39176.56 (rounded)BC = √39176.56 = 197.93 km (rounded)

The distance between the boats is 197.93 km.

Which pair of functions are inverses of each other?

Answers

f(x) = 10x -5 and g(x) = (x+5)/10  are inverses of each other , Option D is the correct answer.

What is a Function ?

A function is a mathematical statement which relates two variables , a dependent and an independent variable.

The inverse of a function is found by replacing every y by x and vice versa , and then solve for y

The equation

f(x) = 4/x - 3

or

y= 4/x -3

Replacing y by x

x = 4/y -3

x +3 = 4/y

y = 4/(x+3)

Which do not correlate with the given inverse

f(x) = 10x -5

y = 10x -5

for finding inverse

10y -5 = x

10y = x+5

y = (x+5)/10

g(x) = (x+5)/10

Therefore , Option D is the correct answer.

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PLEASE PLEASE HELP WILL MARK BRAINLIEST!!
Which choice is equivalent to the product below when x > 0?

A. x/9
B. 1/3
C. x/3
D. 1/9

Answers

The equivalent expression to given expression is 1/3.

What is Equivalent Expression?

Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.

Here, given expression

    [tex]\sqrt{2/x^2} X \sqrt{x^2/18}[/tex]

=   [tex]\sqrt{2 X x^2/18x^2}[/tex]

=    [tex]\sqrt{1/9}[/tex]

=   1/3

Thus, the equivalent expression to given expression is 1/3.

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The function h(x) is given below.

h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}

Which of the following gives h–1(x)?
{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}

Answers

The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.

What is inverse of a function?

Suppose that the given function is

f:X → Y

Then the inverse of the considered function will be

f⁻¹: Y → X

The function h(x) is given below.

h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}

Then the coordinate of the inverse function gets swapped.

h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

Then the correct option is B.

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Given the function f(x) = −5x2 − x + 20, find f(3).

Answers

Answer:

-28

Step-by-step explanation:

put 3 where is x

f(x) = −5(3)^2 − (3) + 20

exponents flrst

(−5*9) − (3) + 20

-45 -3 +20

-48 + 20

-28

Help yalllll question is in the pic

Answers

Answer: D) -304

Step-by-Step Solution:

=> f(x) = 5x - 1
=> g(x) = 2x^2 + 1
=> Find value of (f * g)(-3)

First Substitute x as -3 in f(x) and g(x) :-

f(x) = 5x - 1
f(-3) = 5(-3) - 1
f(-3) = -15 - 1
=> f(-3) = -16

g(x) = 2x^2 + 1
g(-3) = 2(-3^2) + 1
g(-3) = 2(9) + 1
g(-3) = 18 + 1
=> g(-3) = 19

Now Multiply f(-3) with g(-3) :-

= f(-3) * g(-3)
= -16 * 19
=> -304

Therefore, (f * g)(-3) = -304

Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. ​

Answers

Answer:

y = -3x + 1

Step-by-step explanation:

The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.

You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.

DOWN3 and OVER1 is the slope -3/1, which is equal to -3.

Fill in -3 in place of the m in the equation.

y = -3x + 1

Done!

Answer:

y = -3x + 1

Step-by-step explanation:

The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)

The slope can be found by taking any two points on the line,  (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)

If you look at the line 2 points on the line are P(2,-5) and (0,1)

Slope = (-5-1)/(2-0) = -3

The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1

Therefore equation is
y = -3x + 1

You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value

For example, in the graph we see that at x = 1, y = -2

Indeed -3(1) + 1 = -3 + 1 = -2 also

4sin2xcosx+sin3x=sin<3,14+x>

Answers

The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}

How to solve the equation?

The equation is given as:

4sin2xcosx+sin3x=sin<3,14+x>

Rewrite properly as:

4sin(2x)cos(x)+sin(3x)=sin(3.14+x)

Next, we split the equation as follows:

y = 4sin(2x)cos(x)+sin(3x)

y = sin(3.14+x)

Next, we plot the graph of both equations (see attachment)

From the attached graph, we have:

x = nπ, where n = ±{0, 0.5, 1, 1.5....}

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Which table represents a linear function?
2
3
4
5
(J1
10
15
20
25

Answers

Answer:

I think it’s C

Step-by-step explanation:

I think


The graph represents a function.
2
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (2, -1) O (-5,2) O (2,-5) (-2,5)

Answers

(-5, 2) is the only point which we plot in given graph then it still represent a function.

What is Function?

A function is a special type of relation in which each and every element of set A have a unique image in its codomain set B.

Here, Given points on graph

{(-4, 2), (-2, -3), (2, 3), (3, -1)}

2 and -2 are already available in given ordered pair.

so only (-5, 2) is the only option which satisfies the definition of function.

Thus, (-5, 2) is the only point which we plot in given graph then it still represent a function.

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Triangle 304 degrees and 115 degrees work out x

Answers

a straight line make an angle of 180° ,

so 115+y=180

y=65°

for the top part of the triangle it makes an angle of 360° , so 304+y=360

y=56

sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .

so

65+56+y= 180

121+y=180

y=59( the angle next to X)

X+59=180( together they make an angle of 180)

x=121°

Hope it helps

please give brainliest

what equation describes a linear function

Answers

Answer: y = f(x) = a + bx y = f(x) = a + bx y = f(x) =

explanation: The following is the formula for a linear function. y = f(x) = a + bx y = f(x) = a + bx y = f(x) = One independent variable and one dependent variable make up a linear function.

Answer:

I don't knowwwwwwwwwwwwwwww

I think of a number and divide it by 3. The result is 2 less than the number I first thought of. Find the number I first thought of.​

Answers

Answer:

Let the number be x

so, x/4 = x-3

x = 4(x-3)

x= 4x-12

x-4x = -12

-3x = -12

x= 12/3

x = 4

Step-by-step explanation:

Hope this helps! (:

Please mark me Brainliest!

HI PLEASE ANSWER THIS QUESTION THANK YOU!
(NO TROLLS PLEASE!)

Answers

Not 100% sure but it might be B

identify the coefficient of -24x7y3

Answers

Answer: -24

Step-by-step explanation:

See attached image.

please help me guys its math

Answers

58 because she is increasing 8 minutes a day

The vertex of this angle is:
R
T
S

Answers

The vertex of this angle is point S.

i need help asapppppp

Answers

Answer:

a

Step-by-step explanation:

2^3 = 8; 4^3 = 64; 8/64 = 1/8

(g^5)^3 = g^15

(h^2)^3 = h^6

g^15/8h^6

Asap please!!!!!!! if jkl=rst, which congruences are true by cpctc? check all that apply.

a. l=r
b. jk=rs
c. k=s
d. j=s
e. kl=st
f. jl=rs

Answers

Answer:

  b, c e

Step-by-step explanation:

A congruence statement lists corresponding parts in the same order. CPCTC says corresponding parts are congruent.

__

To see if any particular statement is consistent with CPCTC, identify the locations of the referenced parts in the congruence statement. If they match, the congruence is true

  a. l = r ... jkl = rst . . . . not in the same place

  b. jk = rs ... jkl = rst . . . . a match; true

  c. k = s ... jkl = rst . . . . a match; true

  d. j = s ... inconsistent with (c)

  e. kl = st ... jkl = rst . . . . a match; true

  f. jl = rs ... inconsistent with (b)

Statements b, c, e are consistent with the congruence statement, and are true by CPCTC.

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