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2 years ago

Make x the subject of the following relations. 2y+3=5x-18

Mathematics

1 answer:

nekit [7.7K]2 years ago

6 0

Step-by-step explanation:

2y+3=5x-18

swap both sides

5x-18=2y+3

add 18 to both sides

5x-18+18=2y+3+18

5x=2y+21

divide both sides by

5x/5=2y+21/5

X=2y+21/5

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Without using technology, describe the end behavior of f(x) = −3x38 + 7x3 − 12x + 13.

Vedmedyk [2.9K]

Second option: down on the left, down on the right.

Clearly when x is bigger than one the term -x^38 will dominate the result.

When absolute value of x grows, x^38 becomes a larger positive number and - x^38 a larger negative number. Then both ends of the function tend to negative infinity.

8 0

2 years ago

Read 2 more answers

1. Three friends pooled their money to purchase a new game system that costs $298. One person

iragen [17]

Answer:

First person: $107

Second person: $98

Third person: $93

Step-by-step explanation:

Let be "f" the amount of money (in dollars) that the first person contributed to the purchase, "s" the amount of money (in dollars) that the second person contributed to the purchase and "t" the amount of money (in dollars) that the third person contributed to the purchase.

With the information given in the exercise, you can set up the following equations:

Equation 1 → $f+s+t=298$

Equation 2 → $s=f-9$

Equation 3 → $t=f-14$

Substitute the Equations 2 and 3 into the Equation 1 and then solve for "f":

$f+(f-9)+(f-14)=298\\\\3f-23=298\\\\f=\frac{321}{3}\\\\f=107$

Finally, substitute the value of "f" into the Equation 2 and then into the Equation 3, in order to find the values of "s" and "t".

Therefore, you get:

$s=107-9\\\\s=98\\\\\\t=107-14\\\\t=93$

5 0

2 years ago

If candies are sold at 3 pcs for php.2.00.how many candies can melai get if she has php20.00?

Marrrta [24]

If you’re saying that 3 pieces costs 2.00 then the answer is 30. 2x10 is the $20.00 so 3x10 = 30 she can buy

8 0

2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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2 years ago

Ben says 7 9/100 must be less than 7. 2/10 because 9 hundredths is less than 2 tenths. Do you agree? Draw a line to support your

Marrrta [24]

Yes, I cannot draw a line because this is online. Sorry

5 0

2 years ago

Make x the subject of the following relations. 2y+3=5x-18​

Make x the subject of the following relations. 2y+3=5x-18