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3 years ago

PLEASE HELP ASAP 20 POINTS!!!!!!

Mathematics

2 answers:

Jet001 [13]3 years ago

6 0

1 A. 2A. 3 D. 4 C. 5 B

tankabanditka [31]3 years ago

4 0

Number 1.
Subtracting Negative Is The Same As Adding.
So, It Would Be Equivalent To A
Number 2:
Subtracting From A Negative Is Making The Negative Number Larger.
So, It Would Be A
Number 3:
Positive Plus Positive Makes Larger Positive:
37 + 13 = 50.
So, 3 Is D.
Number 4:
Adding Negative Is Making Positive Numbers Smaller.
So, It Is C.
Number 5:
This Is C, Because -30 + 30 = 0 + 1 = 1

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2 years ago

A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

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2 years ago

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3 years ago

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3 years ago

On Naomi's cell phone plan, the amount she pays each month for international text messages is proportional to the number of inte

Lostsunrise [7]

A) The constant of proportionality in this proportional relationship is $k = \frac{y}{x}$

B) The equation to represent this proportional relationship is y = 0.2x

<h3>Solution:</h3>

Given that,

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Therefore,

This is a direct variation proportion

$\text{ amount Naomi pays each month } \propto \text{ number of international texts she sends that month}$

Let "y" be the amount that Naomi pays each month

Let "x" be the number of international texts she sends that month

Therefore,

$y \propto x$

y = kx -------- eqn 1

Where, "k" is the constant of proportionality

Thus the constant of proportionality in this proportional relationship is:

$k = \frac{y}{x}$

Last month, she paid $3.20 for 16 international texts

Therefore,

y = 3.20

x = 16

Thus from eqn 1,

$3.20 = k \times 16\\\\k = \frac{3.20}{16}\\\\k = 0.2$

Substitute k = 0.2 in eqn 1

y = 0.2x

The equation would then be y = 0.2x

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3 years ago