One number is five more than five times another. If their sum is decreased by four, the result is twenty-five. Find

PLEASE HELP

TiliK225 [7]

5 0

2 years ago

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Find the inverse of square root f(n) = n – 3.

pogonyaev

Answer:

$f'(n) = n + 3$

Step-by-step explanation:

Given

$f(n) = n - 3$

Required

The inverse

$f(n) = n - 3$

Replace f(n) with y

$y = n - 3$

Swap positions of y and n

$n = y - 3$

Make y the subject

$y = n + 3$

Replace y with f'(n)

$f'(n) = n + 3$

4 0

3 years ago

Please Help! Will give Brainlest!

Marina86 [1]

Answer:

amplitude = 2

Step-by-step explanation:

the amplitude is the distance from the x- axis(midline ) to the maximum value , that is

amplitude = 2

4 0

1 year ago

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4 The ratio of corresponding dimensions of two similar solids is 3/4. The surface

White raven [17]

4.

The ratio is 3/4 for corresponding dimensions, the ratio of their surface areas is equal to the square of this ratio:

$\sf (\dfrac{3}{4})^2=\dfrac{S}{96}$

Simplify the exponent:

$\sf \dfrac{9}{16}=\dfrac{96}{S}$

Cross multiply:

$\sf 9S=1536$

Divide 9 to both sides:

$\sf S\approx 170.7~m^2$

So the surface area of the second solid is 54 square meters.

The ratio is 3/4 for corresponding dimensions, the ratio of their volumes is equal to the cube of this ratio:

$\sf (\dfrac{3}{4})^3=\dfrac{720}{V}$

Simplify the exponent:

$\sf \dfrac{27}{64}=\dfrac{720}{V}$

Cross multiply:

$\sf 27V=46080$

Divide 64 to both sides:

$\sf V\approx 1706.7~m^3$

5.

A globe is a sphere, use the formula for the volume of a sphere:

$\sf V=\dfrac{4}{3}\pi r^3$

The radius is half of the diameter, so the radius here is 40/2 = 20. Plug it in the formula, use 3.14 to approximate for Pi:

$\sf V=\dfrac{4}{3}(3.14)(20)^3$

Simplify the exponent:

$\sf V=\dfrac{4}{3}(3.14)(8000)$

Multiply:

$\sf V\approx \boxed{\sf 33,493~in^3}$

6 0

3 years ago

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Determine whether each of the binary relation R defined on the given sets A is reflexive, symmetric, antisymmetric, or transitiv

ki77a [65]

Answer:

In explanation

Please let me know if something doesn't make sense.

Step-by-step explanation:

a)

*This relation is not reflexive.

0 is an integer and (0,0) is not in the relation because 0(0)>0 is not true.

*This relation is symmetric because if a(b)>0 then b(a)>0 since multiplication is commutative.

*This relation is transitive.

Assume a(b)>0 and b(c)>0.

Note: This means not a,b, or c can be zero.

Therefore we have abbc>0.

Since b^2 is positive then ac is positive.

Since a(c)>0, then (a,c) is in R provided (a,b) and (b,c) is in R.

*The relation is not antisymmretric.

(3,2) and (2,3) are in R but 3 doesn't equal 2.

b)

*This relation is reflective.

Since a^2=a^2 for any a, then (a,a) is in R.

*The relation is symmetric.

If a^2=b^2, then b^2=a^2.

*The relation is transitive.

If a^2=b^2 and b^2=c^2, then a^2=c^2.

*The relation is not antisymmretric.

(1,-1) and (-1,1) is in the relation but-1 doesn't equal 1.

c)

*The relation is reflexive.

a/a=1 for any a in the naturals.

*The relation is not symmetric.

Wile 4/2 is an integer, 2/4 is not.

*The relation is transitive.

If a/b=z and b/c=y where z and y are integers, then a=bz and b=cy.

This means a=cyz. This implies a/c=yz.

Since the product of integers is an integer, then (a,c) is in the relation provided (a,b) and (b,c) are in the relation.

*The relation is antisymmretric.

Assume (a,b) is an R. (Note: a,b are natural numbers.) This means a/b is an integer. This also means a is either greater than or equal to b. If b is less than a, then (b,a) is not in R. If a=b, then (b,a) is in R. (Note: b/a=1 since b=a)

6 0

2 years ago