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.

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

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

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.

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

Answer:

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:

The angle between AB and AC is:

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

The distance between the boats is 197.93 km.

The process capability index for the process is 0.1754.

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

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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Answer:

35 Floors in 6 Hours

Step-by-step explanation:

20 / 4 = X Floors Per Hour

floors per hour = 5

6*5 = 35 Floors

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

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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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

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:

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:

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

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

The equivalent expression to given expression is 1/3.

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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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.

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

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

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

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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The vertex of this angle is point S.

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! (:

Answer:

C. (-2.2, -3)

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

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.

Answer:

I think it’s C

Step-by-step explanation:

I think

Answer: -24

Step-by-step explanation:

See attached image.

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

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