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3 years ago

Find the inverse function of (Show work) f(x)=x^2-4

Mathematics

1 answer:

Olegator [25]3 years ago

4 0

Answer:

The answer to your question is $f(x) = \sqrt{x+ 4}$

Step-by-step explanation:

f(x) = x² - 4

Process

1.- Change f(x) for y

y = x² - 4

2.- Change "x" for "y" and "y" for "x".

x = y² - 4

3.- Make "y" the object of the equation

y² = x + 4

$y = \sqrt{x+ 4}$

4.- Change "y" for f(x)

$f(x) = \sqrt{x+ 4}$

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The diagonal of a side of rhombus are of equal length. Find the measures of angles of the rhombus.

sergij07 [2.7K]

Explanation:

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus i.e,

⇛AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

⇛AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

⇛∠ BAC=∠ABC= ∠ACB =60°→→→Eqn(i)

Similarly in ∆DAC ,

DA=DC=AC

⇛∠DAC=∠ACD=∠ADC=60°→→→Eqn(ii)

From eqn(i) and eqn(ii)

∠A=∠BAC+∠DAC=60°+60°=120°

and

∠B= ∠ABC = 60°.

and

∠C=∠ACB+∠ACD=60°+60°=120°

and

∠D =∠ADC=60°

∴ ∠A = 120° , ∠B = 60° ,∠C = 120° & ∠D = 60°

Answer:-The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°.

Note: [Figure refers in the attached file.

7 0

2 years ago

Y = -8 Y = -2x - 12 Solve this equation by substitution

aliina [53]

Answer:

x = - 2

Step-by-step explanation:

- 8 = - 2x - 12

- 8 + 12 = - 2x - 12 + 12

- 2x = 4

- 2x ÷ - 2 = 4 ÷ - 2

x = - 2

5 0

3 years ago

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

scZoUnD [109]

Answer:

Option B m<ZA+m<ZB = 155° is correct option.

Step-by-step explanation:

We know that sum of angles of triangle is equal to 180°

And Isosceles triangle, 2 angles are same

So, let Angle 1 = x

Angle 2 = x

Angle 3 = 130°

Finding values of angle x

x+x+130=180

2x=180-130

2x=50

x=25

So, Angle 1 = 25 °

Angle 2 = 25°

As, angle B is greater than 90°, the sum of angles added must be greater than 90°

So, Option A, C and D can't be correct, as their sum is less than 90°

Option B m<ZA+m<ZB = 155° is correct option.

Verify:

m<ZA = 25° (as found earlier)

m<ZB = 130° (given)

So, m<ZA+m<ZB = 155°

25°+130° = 155°

8 0

3 years ago

Henry rolls a fair dice 42 times. How many times would Henry expect to roll a number greater than 5?

Sonja [21]

Answer:

7 times

Step-by-step explanation:

There is one number greater than 5 on a dice - that is the number 6.

So probability of throwing a six = 1/6.

So it is 42 * 1/6.

5 0

3 years ago

Amanda is having new tile installed in her kitchen. TileAll charges a flat fee of $378.00 plus $15.00 per tile. Kitchen Plus cha

myrzilka [38]

Answer:

$C = 495 + 13.05x$

60 tiles.

Step-by-step explanation:

$15.00 per tile plus a flat fee of $378.00 that charges Tile All.

Therefore, for x number of tiles, the total cost of installation will be

C = 378 + 15x ........... (1)

Again, $14.50 per tiles plus a flat fee of $550.00 that charges Kitchen Plus. Amanda has at Kitchen Plus, a 10% discount coupon.

Therefore, for x tiles installation the charges will be

$C = (550 + 14.5x)(1 - \frac{10}{100}) = 495 + 13.05x$ .......... (2) (Answer)

Now, if for x number of tiles both the company charges the same, then

378 + 15x = 495 + 13.05x (From equations (1) and (2)}

⇒ 1.95x = 117

⇒ x = 60 tiles. (Answer)

3 0

3 years ago