The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 25 seconds with an average speed of 6 feet per second. Find the average speed of the swimmer if it takes 50 seconds to finish the race.

[tex](f \circ g)(x) = x+12[/tex]

Domain = [-3, infinity)

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Work Shown:

[tex]f(x) = x^2 + 9\\\\f(g(x)) = (g(x))^2 + 9\\\\f(g(x)) = (\sqrt{x+3})^2 + 9\\\\f(g(x)) = x+3 + 9\\\\f(g(x)) = x+12\\\\(f \circ g)(x) = x+12\\\\[/tex]

In step 2, we replaced every x with g(x)

In step 3, we plugged in g(x) = sqrt(x+3)

The domain of g(x) is [-3, infinity), so this is the domain of [tex](f \circ g)(x)[/tex] as well since the composite function depends entirely on g(x). Put another way: the input of f(x) depends on the output of g(x), so that's why the domains match up.

Answer:

2/3

Step-by-step explanation:

The fractions which are equivalent to the fraction [tex]\frac{9}{6}[/tex] from the given options are [tex]\frac{3}{2}[/tex] and [tex]\frac{12}{8}[/tex], which are options (A) and (C).

Given a fraction [tex]\frac{9}{6}[/tex].

It is required to find the fraction which is equivalent to the given fraction.

If two fractions are equivalent, then they will be proportional.

The fraction [tex]\frac{9}{6}[/tex] can be written as [tex]\frac{3*3}{2*3}[/tex].

Here, when 3 gets canceled, the resulting fraction is [tex]\frac{3}{2}[/tex].

So, [tex]\frac{3}{2}[/tex]  is equivalent to [tex]\frac{9}{6}[/tex].

And, [tex]\frac{3}{2}[/tex] is the simplest fraction that cannot be simplified further.

So, any number multiplied by it both on the numerator and denominator will be an equivalent fraction.

Multiplying both the numerator and denominator of the fraction [tex]\frac{3}{2}[/tex] by 4, the resulting fraction is [tex]\frac{12}{8}[/tex].

Hence, the correct options are (A) and (C).

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The complete question is given below.

Which fractions are equivalent to [tex]\frac{9}{6}[/tex]?

(A) [tex]\frac{3}{2}[/tex]

(B) [tex]\frac{4}{5}[/tex]

(C) [tex]\frac{12}{8}[/tex]

(D) [tex]\frac{10}{8}[/tex]

Answer:

hb=4√3

Step-by-step explanation:

Answer:

AB = 8, HB = 6, Area of ∆ABC = 8[tex]\sqrt{3}[/tex], Perimeter of ∆ABC = 12 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

To find AB:

∆ABC is an 30,60,90∆

Using the theorem, you can find AB = 2AC = 2*4 = 8

AB = 8

To find HB:

You need to find AH to subtract from AB

Construct CH, a perpendicular bisector to side AB

From before you can put together that m∠CAB = 60°

∆ACH is an 30,60,90∆

Using this method again, AH = AC/2 = 4/2 = 2

Then you subtract AH from AB = 8-2 = 6

HB = 6

To find the area of ∆ABC:

You use the (base*height)/2 method

base = AB = 8

to find the height, CH, you need to use the Pytha Theorem

and get [tex]AH^{2}+CH^{2}=AC^{2}[/tex]

then substitute, and get [tex]2^{2} + CH^{2} = 4^{2}[/tex]

calculate and get CH = 2[tex]\sqrt{3}[/tex]

then the height = CH =  2[tex]\sqrt{3}[/tex]

solve the area and get

Area of ∆ABC = 8[tex]\sqrt{3}[/tex]

(optional perimeter)

to find perimeter of ∆ABC:

you add AC + CB + AB

you find CB by using opposite to 30°

CB = CH*2 = 2[tex]\sqrt{3}[/tex]*2 = 4[tex]\sqrt3}[/tex]

so AC + CB + AB = 4 + 4[tex]\sqrt3}[/tex] + 8

Perimeter of ∆ABC = 12 + 4[tex]\sqrt3}[/tex]

Hope this helps!!

Answer:

42

Step-by-step explanation:

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Answer:

x-intercept = 3

y-intercept = - 6

Step-by-step explanation:

The intersection of the line with the x-axis is known as the x-intercept and it's calculated by making y = 0.

Also, the intersection of the line with the y-axis is known as the y-intercept and it's calculated by making x = 0.  

Given the following data;

Equation of straight line is [tex]y = 2x - 6[/tex]

To find the intersection;

When y = 0, the equation crosses the x-axis.

y = 0;

Substituting into the equation, we have;

0 = 2x - 6

2x = 6

x = 6/2 = 3

x = 3

(x, y) = (3, 0) on the x-axis.

When x = 0, the equation crosses the y-axis.

x = 0;

Substituting into the equation, we have;

y = 2(0) - 6

y = 0 - 6

y = -6.

(x, y) = (0, -6) on the y-axis.

Therefore, the coordinates of the intersection of the graph is (3, 0) and (0, -6).

Answer:

108quartz

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

If A cylindrical container can hold 4 quarts of water, then;

4 = πr²h ...... 1

Let the volume be x of the radius and height at tripled

h1 = 3h

r1 = 3r

X = πr1²h1

X = π(3r)²(3h)

X = 9πr²(3h)

X = 27πr²h .... 2

Divide 1 by 2

4/x = πr²h/27πr²h

4/x = 1/27

Cross multiply

x = 4×27

x = 108

Hence the container can hold 108quartz of water of the radius and height was tripled.

Answer:

11

Step-by-step explanation:

i was born one year before you

Answer:

x= -4

Step-by-step explanation:

c? i think its c (Sorry if iim wrong)

Answer:

The answer is D

Step-by-step explanation:

Answer:

C. -3/4

Step-by-step explanation:

The Slope is always rise over run or

rise

___

run

so with X you rise up 3 and Y, you run down 4 so the slope is C.

-3/4

Answer:

The slope would be 2

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

because u deleting this app

Answer:

1/4 en pedazos seria 1/4 en pedazos

Step-by-step explanation:

la pregunta no tiene sentido

Answer: La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan cuatro piezas para formar un todo". La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan 4 piezas para formar un todo".

Step-by-step explanation:

Answer:

-33

Step-by-step explanation:

2(-2)^3 -7(-2)^2 -5(-2) +1

-16 -28 +11

= -33

Answer:

X=38(8m)#7=274*€7£

Step-by-step explanation:

There you go my answer is pretty much the explanation

not sure what grade this is but if this is collage than that would be the answer

Answer:

4

Step-by-step explanation:

7 + (-3)

= 7 - 3

Answer:

the answer is 4

Step-by-step explanation:

Answer:

3/4   and  2/5 have a common denominator of 20, so re-write

15/20x - 2 = 8/20       Now multiply both sides by 20

15x-40 = 8

Step-by-step explanation:

Answer:

The minimum amount of time required is 74.7 seconds.

Step-by-step explanation:

The question can be solved in two cases:

i. diagonal swimming of Brandon across the river

ii. Running of the rest distance by Brandon.

Case I: Since he would swim diagonally across the river, then the diagonal distance can be determined by applying appropriate trigonometric function.

Let the diagonal be represented by x, an included angle θ = [tex]45^{o}[/tex] is formed at his starting point (angle formed by the diagonal and the length of the width of the river).

So that:

Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos [tex]45^{o}[/tex] = [tex]\frac{70}{x}[/tex]

x = [tex]\frac{70}{Cos 45^{o} }[/tex]

  = 98.995

x = 99 m

The diagonal distance covered by Brandon is 99 m.

The time to cover this distance can be calculated by:

speed = [tex]\frac{distance}{time}[/tex]

time = [tex]\frac{distance}{speed}[/tex]

Given that his swimming rate is 2 m/s, then:

time = [tex]\frac{99}{2}[/tex]

        = 49.5

The time taken by Brandon to swim diagonally is 49.5 seconds.

Case II: Since he want to cover a total distance of 250 m;

remaining distance to be covered = 250 - 99

                                                         = 151

time = [tex]\frac{distance}{speed}[/tex]

Given that he runs at 6 m/s, then;

time = [tex]\frac{151}{6}[/tex]

       = 25.1667

The time taken by Brandon to run the remaining distance is 25.2 seconds.

The minimum amount of time required = time taken by Brandon to swim diagonally + time taken by Brandon to run the remaining distance

                                 = 49.5 + 25.2

                                 = 74.7

The minimum amount of time required is 74.7 seconds.

Minimum amount of time to reach the desired point is   79.5 s

Brandon is on one side of a river

The width of the river =  70 m

Brandon wants to reach a point that is 250 m downstream of opposite side as quickly as possible by swimming diagonally across the river then running the rest of the way.

The swimming speed of Brandon =   2 m/s

The speed of running of Brandon = 6 m/s

Let us consider that the included angle be 45°

[tex]\rm cos \; \theta = \dfrac{70}{x} \\\\cos \; 45 = \dfrac{70}{x} \\\x = \dfrac{70}{0.707} \approx 99[/tex]

So the distance traveled by Brandon in water is 99 m

As the swimming speed of Brandon is given 2 m/s

So the time taken by Brandon to cross the river is given as follows

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

[tex]\rm Time \; to\; cross\; the\; river = \dfrac{99}{2} = 49.5 \; s[/tex]

Let the horizontal distance covered by Brandon by swimming is H

So from Pythagorean theorem we can write

[tex]\rm H = \sqrt{99^2 -70^2 } = 70[/tex]

The distance that is left to be traveled by running is  250 - 70 = 180 m  

So  Time taken in running to reach the point by running = 180/6 = 30 s

So the  time to reach the desired point = 49.5 + 30 =   79.5 s

For more information please refer to the link given below

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Answer:

5 twenty's 1 five

Step-by-step explanation:

20 x 5 = 100

100 = 5 = 105

Answer:

The correct option is d.

Step-by-step explanation:

The directional hypothesis is:

[tex]H_{a}:\mu>\mu_{0}[/tex]

The sample size is, n = 40.

The significance level is:

[tex]\alpha =1-0.95=0.05[/tex]

Use the t-table to compute the right-tailed t-critical value as follows:

[tex]t_{\alpha,\ (n-1)}=t_{0.05, (40-1)}[/tex]

             [tex]=t_{0.05, 39}\\\\\approx t_{0.05, 40}\\\\=1.684\\\\\approx 1.685[/tex]

The value is positive since the directional hypothesis suggests that the test is right tailed.

The correct option is d.

there could be a calculator online to solve it

Answer:

There is a 50% chance of a blue marble

20% chance of a red marble

30% chance of a blue marble

Answer:

82.19

Step-by-step explanation:

Answer:

t = 20°

Step-by-step explanation:

Recall that the base angles of an isosceles ∆ are equal to each other.

This means that:

<NMO and <NOM of ∆MNO are congruent to each other.

Thus,

m<NMO = ½(180 - m<N) = ½(180 - 70)

m<NMO = ½(110)

m<NMO = 55°

Also, <PMO and <POM are congruent to each other. Thus:

m<PMO = ½(180 - m<P) = ½(180 - 110)

m<PMO = ½(70)

m<PMO = 35°

Therefore,

m<NMO = t + m<PMO (angle addition postulate)

55° = t + 35° (substitution)

Subtract 35 from each side

55° - 35° = t

20° = t

t = 20°

I hope it is helpful for you

Answer:

the answer is 1

Step-by-step explanation: i took the test on k12 hope this helps

Answer:

4.5 ounces of yellow and 7.5 ounces of blue will create 12 ounces of the perfect shade of green.

Step-by-step explanation:

1.5 + 2.5 = 4 ounces.

Multiply by 3

4.5 + 7.5 = 12 ounces

So, she needs 4.5 ounces of yellow.

Answer:

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that is hard but the answer is 1,256 I think that is right

Answer: I believe it’s 24

Step-by-step explanation: if not sorry

Answer:

Note that 6 is 4 plus 2,  

              10 is 6 plus 4, or 6 plus 2^2

               16 is 10 plus 6

Given the first term, 4, we find the second term by adding 2 to 4, obtaining 6.

Given the 2nd term, 6, we find the third term     by adding 4 to 6, obtaining 10.

Given the 3rd term, 10, we find the fourth term  by adding 6 to 10:  16

What's the next term?  Find the fifth term           by adding 8 to 16:  24 (answer)

Step-by-step explanation:

24 would be the answer hope this helps ya :)