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3 years ago

Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)

Mathematics

2 answers:

IceJOKER [234]3 years ago

6 0

Answer:

Hi! Todo HEre!!

Step-by-step explanation:

Given the function f(x)=x 2 +2x+1, find: a) f(−7) Start with f(x) = x 2 + 2x + 1 1. Take out all the x's, and replace them with open parentheses f( )= ( ) 2 + 2( ) + 1 2. Put -7's in the parentheses: f(-7)= (-7) 2 + 2(-7) + 1 Leave the left side as it is and simplify the right side: f(-7)= 49 - 14 + 1 f(-7)= 36 -----

Have a GREAT day!!!

Setler [38]3 years ago

5 0

6 Why because my brain is huge

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Evaluate the expression when x = 32 and y = 2 x/4y a. 1/16 b. 16/21 c. 2 d. 4

ohaa [14]

32/4 (4)
32/16 = 2

it is c. 2

4 0

3 years ago

Read 2 more answers

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.

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

3 0

3 years ago

Given the line a and b are parallel angles 1 and5 are congruent because they are

kakasveta [241]

Answer:

Step-by-step explanation:

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.

figure51

Vertical angles are always congruent, which means that they are equal.

Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap.

figure52

The size of the angle xzy in the picture above is the sum of the angles A and B.

Two angles are said to be complementary when the sum of the two angles is 90°.

figure53

Two angles are said to be supplementary when the sum of the two angles is 180°.

figure54

If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal

When a transversal intersects with two parallel lines eight angles are produced.

figure55

The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Example

figure56

The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

6 and 8 are vertical angles and are thus congruent which means angle 8 is also 65°.

6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.

6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.

4 0

3 years ago

Write 30x3+5x in factored form.

yaroslaw [1]

5x(6^2 +1)
Is 30x3+5x in factored form

3 0

2 years ago

Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5

sashaice [31]

The question is incomplete.

This is the complete question as I found in internet:

Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10

these are the points:

-1,5

1,5

0,-5

0,5

Answer: (0, -5)

Explanation:

point x y 5x - 2y = 10 ?

-1,5 -1 5 5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution

1,5 1 5 5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution

0,-5 0 -5 0 -2(-5) = 10 ⇒ a solution

0,5 0 5 0 - 2(5) = - 10 ≠ 10 ⇒ not a solution

7 0

3 years ago

Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)​

Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)