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3 years ago

9x2 – 16 Factoring quadratic eqations

Mathematics

1 answer:

Strike441 [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Both are squares so

(3x - 4)2

You might be interested in

What is .07 times 1.22

lidiya [134]

.07×1.22 = ?
first take away the decimals in the question, 7×122 =854.
now add the decimals back to the answer, we had 4 decimal places in the questions so add 4 decimal places to 854 = 0.0854

answer= 0.0854

7 0

3 years ago

What is the circle's circumference? The diameter of a circle is 6 millimetres.

dolphi86 [110]

Answer:

C = 6pi or approximately 18.84 mm

Step-by-step explanation:

The circumference of a circle is

C = pi *d

C = pi *6

We can approximate pi by 3.14

C = 3.14*6

C =18.84

6 0

3 years ago

How do you find the limit?

coldgirl [10]

Answer:

2/5

Step-by-step explanation:

Hi! Whenever you find a limit, you first directly substitute x = 5 in.

$\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{5^2-6(5)+5}{5^2-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{25-30+5}{25-25}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{0}{0}}$

Hm, looks like we got 0/0 after directly substitution. 0/0 is one of indeterminate form so we have to use another method to evaluate the limit since direct substitution does not work.

For a polynomial or fractional function, to evaluate a limit with another method if direct substitution does not work, you can do by using factorization method. Simply factor the expression of both denominator and numerator then cancel the same expression.

From x²-6x+5, you can factor as (x-5)(x-1) because -5-1 = -6 which is middle term and (-5)(-1) = 5 which is the last term.

From x²-25, you can factor as (x+5)(x-5) via differences of two squares.

After factoring the expressions, we get a new Limit.

$\displaystyle \large{ \lim_{x\to 5}\frac{(x-5)(x-1)}{(x-5)(x+5)}}$

We can cancel x-5.

$\displaystyle \large{ \lim_{x\to 5}\frac{x-1}{x+5}}$

Then directly substitute x = 5 in.

$\displaystyle \large{ \lim_{x\to 5}\frac{5-1}{5+5}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{4}{10}}\\

\displaystyle \large{ \lim_{x\to 5}\frac{2}{5}=\frac{2}{5}}$

Therefore, the limit value is 2/5.

L’Hopital Method

I wouldn’t recommend using this method since it’s too easy but only if you know the differentiation. You can use this method with a limit that’s evaluated to indeterminate form. Most people use this method when the limit method is too long or hard such as Trigonometric limits or Transcendental function limits.

The method is basically to differentiate both denominator and numerator, do not confuse this with quotient rules.

So from the given function:

$\displaystyle \large{ \lim_{x \to 5} \frac{x^2-6x+5}{x^2-25}}$

Differentiate numerator and denominator, apply power rules.

Differential (Power Rules)

$\displaystyle \large{y = ax^n \longrightarrow y\prime= nax^{n-1}$

Differentiation (Property of Addition/Subtraction)

$\displaystyle \large{y = f(x)+g(x) \longrightarrow y\prime = f\prime (x) + g\prime (x)}$

Hence from the expressions,

$\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2-6x+5)}{\frac{d}{dx}(x^2-25)}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{\frac{d}{dx}(x^2)-\frac{d}{dx}(6x)+\frac{d}{dx}(5)}{\frac{d}{dx}(x^2)-\frac{d}{dx}(25)}}$

Differential (Constant)

$\displaystyle \large{y = c \longrightarrow y\prime = 0 \ \ \ \ \sf{(c\ \ is \ \ a \ \ constant.)}}$

Therefore,

$\displaystyle \large{ \lim_{x \to 5} \frac{2x-6}{2x}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{2(x-3)}{2x}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{x-3}{x}}$

Now we can substitute x = 5 in.

$\displaystyle \large{ \lim_{x \to 5} \frac{5-3}{5}}\\

\displaystyle \large{ \lim_{x \to 5} \frac{2}{5}}=\frac{2}{5}$

Thus, the limit value is 2/5 same as the first method.

Notes:

If you still get an indeterminate form 0/0 as example after using l’hopital rules, you have to differentiate until you don’t get indeterminate form.

8 0

3 years ago

If x=-7 and y=4 what would x^2-3xy=

Kruka [31]

Answer:

While x = -7 and y = 4, x² - 3xy = 133.

Step-by-step explanation:

x² - 3xy

Substitute variables.

(-7)² - 3(-7)(4)

Square -7 remembering that (-x)² = x².

49 - 3(-7)(4)

Multiply -7 and 4.

49 - 3(-28)

Multiply -3 and -28.

49 + 84

Add 49 and 84.

133

3 0

3 years ago

The function, p(d)equals=1plus+startfraction d over 33 endfraction d 33, gives the pressure, in atmospheres (atm), at a dep

Gelneren [198K]

Answer:

The pressure at 50 feet is 2.51515 atm

Step-by-step explanation:

we are given equation as

$p(d)=1+\frac{d}{33}$

where

p(d) gives the pressure, in atmospheres (atm)

a depth d in the sea (d is in feet)

We are given

d=50 feet

So, we can plug d=50 and find p

$p(50)=1+\frac{50}{33}$

$p(50)=2.51515atm$

So,

The pressure at 50 feet is 2.51515 atm

7 0

3 years ago

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