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3 years ago

HELLPPPPPLSSSS SOMSE

Mathematics

1 answer:

Nina [5.8K]3 years ago

7 0

Answer:

Option F

Step-by-step explanation:

F). x + y = 3 -------(1)

x - 3y = -2 --------(2)

Equation (1) minus equation (2)

(x + y) - (x - 3y) = 3 - (-2)

4y = 5

y = 1.25

Hence, y is positive.

G). x + y = 3 --------(1)

x + y = -2 --------(2)

Both the equations represent parallel lines.

There are no solutions of the given equations.

H). x - 3y = -2 -------(1)

x + y = -2 -------(2)

Equation (2) minus equation (1)

(x + y) - (x - 3y) = -2 - (-2)

4y = 0

y = 0

Since, 0 is neither positive nor negative, y will be neither positive nor negative.

J). x + y = 3 -------(1)

x - y = 3 --------(2)

Equation (1) - Equation (2)

(x + y) - (x - y) = 3 - 3

2y = 0

Hence, y is neither negative nor positive.

Therefore, Option F is the answer.

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A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

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3 years ago

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Gala2k [10]

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3 years ago

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Write 54 + 63 as the product of the GCF of 54 and 63 and another sum

levacccp [35]

Answer:

9*(6+7)

Step-by-step explanation:

First, we have to find the Greatest Common Factor (GCF), to do this we have to see all the factors of 54 and 63 and find the greatest factor that they have in common.

Factors of 54

1,2,3,6,9,18,27,54

Factors of 63

1,3,7,9,21,63

The GCF is 9 because is the greatest factor that is common to both numbers.

Now we have to divide 54/9 and 63/9

54/9 = 6

63/9 = 7

So now we can write the product of the GCF and another sum:

9*(6+7)

We can prove this by solving both expressions:

54+63 = 9*(6+7)

117 = 9*13

117 = 117

The results are equal so we prove it is right.

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A trapezoid has 6 inches base 12“ x 6“ height

maw [93]

Do you have to find the area or perimeter?

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The leopard population in an African wildlife area is currently 17. Due to a new conservation effort, conservationists hope the

kykrilka [37]

Answer:

$a{_n} = 17 + (n - 1)4$ for n = 1, 2, . . . , 20.

Step-by-step explanation:

This is an arithmetic sequence, because the population is said to increase by 4 animals yearly. The formula for the nth term in an arithmetic sequence is given by:

$a{_n} = a{_1} + (n - 1)d$ where $a_n$ is the nth term, [/tex]a_1[/tex] is the first term, n = 1, 2, . . . and d is the common difference.

Since they are currently 17, this implies that the first number in the population sequence will be 17. In order words, the first term is 17.

Since they increase by 4 yearly, then the common difference is 4.

Since it's for 20years, the n = 1, 2, . . ., 20. The explicit formula is therefore:

$a{_n} = 17 + (n - 1)4$ for n = 1, 2, . . . , 20.

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3 years ago