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2 years ago

If ƒ(x ) = 3x + 1 and and ƒ -1 = , then the ordered pair of ƒ -1(10) = (10, 31) (10, 3) (3, 10)

1 answer:

6 0

      f(x) = 3x + 1
   y = 3x + 1
      y - 1 = 3x + 1 - 1
<u>y - 1</u> = <u>3x</u>
       3    3
¹/₃y - ¹/₃ = x
   y = ¹/₃x - ¹/₃
    f⁻¹(x) = ¹/₃x - ¹/₃
    f⁻¹(10) = ¹/₃(10) - ¹/₃
    f⁻¹(10) = 3¹/₃ - ¹/₃
    f⁻¹(10) = 3
It is equal too (10, 3).

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A city survey of two neighborhoods asked residents whether they would prefer a new playground or a dog park.

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Answer:

so if it is asking about the exact percentage then the answer is B but if it is the percentage in all the answer is D.

Step-by-step explanation: My reasoning behind is that 70 percent of the neighborhood wants a playground if it is 40 to 17

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1 year ago

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A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat

allsm [11]

Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 = 3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h

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1 year ago

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

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Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

$5+5^{2}=30$ (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

$5^{1}+5^{2}+5^{3}+...+5^{x}>19000$ (II)

Buscamos el valor de $x$ que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

$5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000$

$19530>19000$

El valor de $x$ que satisface (II) es $x=6$ .

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro $x=6$ , el número de horas que pasaron son 5 horas (1 menos que el valor de $x$ )

Todo el pueblo se habrá enterado en 5 horas de la noticia.

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2 years ago

Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the numbe

Ede4ka [16]

Answer:

N + D = 175

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Step-by-step explanation:

You need a system of equations to get the correct answer that applies to both constraints.

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1 year ago

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From home, Mary’s work is two thirds along the way to training. Training is 2.5km from work. Mary normally goes to work, then tr

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First thing to do is to illustrate the problem, Since it was mentioned that work was along the way to training, the order is shown in the picture. Mary's home and workplace are nearer compared to her training center. It is also mentioned that the distance between work and home, denoted as x, is 2/3 of the total distance from home to training. The total distance is (x + 2.5). Thus,

x = 2/3(x+2.5)
x = 2/3 x + 5/3
1/3 x = 5/3
x = 5 km

Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,

Total distance = 2(5km) + 7.5 km
Total distance = 17.5 km

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1 year ago