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3 years ago

Help please thank you!

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

6 0

Answer:

g(f(x)) = x

Yes, the functions are inverses.

Step-by-step explanation:

Hi there!

We're given:

$f(x) = 8x-7$

$g(x)=\displaystyle\frac{x+7}{8}$

To solve for g(f(x)), plug f(x) into g(x) as x:

$g(f(x))=\displaystyle\frac{(8x-7)+7}{8}\\\\g(f(x))=\displaystyle\frac{8x-7+7}{8}\\\\g(f(x))=\displaystyle\frac{8x}{8}\\\\g(f(x))=x$

Because g(f(x)) = x, the two functions are inverses.

I hope this helps!

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Un jardín rectangular de 50 cm de largo por 34 m de ancho está rodeado por un camino de arena uniforme.Halla la anchura de dicho

Anastasy [175]

Answer:

5.85 m

Step-by-step explanation:

The width of the sand road can be calculated knowing its area and the dimensions of the rectangular garden as follows:

$A_{g} = a.b$

Where:

Ag: is the area of the rectangular garden

a: is the length of the rectangular garden = 50 cm = 0.5 m

b: is the width of the rectangular garden = 34 m

$A_{s} = 540 m^{2}$

Where:

As: is the area of the sand road

The relation between the area of the sand road and the area of the rectangular garden is the following:

$A_{s} + A_{g} = (a+2x)*(b+2x)$

$540 m^{2} + 0.5m*34m = ab + 2ax + 2bx + 4x^{2}$

$557 m^{2} = ab + 2x(a + b) + 4x^{2}$

$557 m^{2} - 17m^{2} - 2x(34.5 m) - 4x^{2} = 0$

$540 - 69x - 4x^{2} = 0$

By solving the above equation for x we have two solutions:

x₁ = -23.10 m

x₂ = 5.85 m

Taking the positive value, we have that the width of the sand road is 5.85 m.

I hope it helps you!

7 0

3 years ago

Two tailors, Valentina and Laura, sit down to do some embroidery. Valentina can embroider 2 shirts per hour, and Laura can get t

mina [271]

Answer:

Valentina and Laura finished the same total number of shirts in $4$ hours.

Total number of shirts finished by Valentina $=23$

Total number of shirts finished by Laura $=23$

Step-by-step explanation:

Suppose that Valentina and Laura finished the same total number of shirts in $t$ hours.

Valentina can embroider 2 shirts per hour and Valentina has already completed 15 shirts.

Total number of shirts finished by Valentina $=2t+15$

Laura can get through 3 shirts per hour and Laura has completed 11 shirts.

Total number of shirts finished by Laura $=3t+11$

Therefore,

$2t+15=3t+11\\3t-2t=15-11\\t=4$

So,

Valentina and Laura finished the same total number of shirts in $4$ hours.

Total number of shirts finished by Valentina $=2(4)+15=8+15=23$

Total number of shirts finished by Laura $=3(4)+11=12+11=23$

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3 years ago