How would I solve 16x^4-41x^2+25=0 ???

Answers

Answer 1

Answer: $16{ x }^( 4 )-41{ x }^( 2 )+25=0$

${ x }^( 4 )={ ({ x }^( 2 )) }^( 2 )\n \n 16{ ({ x }^( 2 )) }^( 2 )-41{ x }^( 2 )+25=0$

First of all to make our equation simpler, we'll equal $x^(2)$ to a variable like 'a'.

So,

${ x }^( 2 )=a$

Now let's plug $x^(2)$ 's value (a) into the equation.

$16{ ({ x }^( 2 )) }^( 2 )-41{ x }^( 2 )+25=0\n \n { x }^( 2 )=a\n \n 16{ (a) }^( 2 )-41{ a }+25=0$

Now we turned our equation into a quadratic equation.

(The variable 'a' will have a solution set of two solutions, but 'x' , which is the variable of our first equation will have a solution set of four solutions since it is a quartic equation (fourth-degree equation) )

Let's solve for a.

The formula used to solve quadratic equations ;

$\frac { -b\pm \sqrt { { b }^( 2 )-4\cdot t\cdot c } }{ 2\cdot t }$

The formula is used in an equation formed like this :

$t{ x }^( 2 )+bx+c=0$

In our equation,

t=16 , b=-41 and c=25

Let's plug the values in the formula to solve.

$t=16\quad b=-41\quad c=25\n \n \frac { -(-41)\pm \sqrt { -(41)^( 2 )-4\cdot 16\cdot 25 } }{ 2\cdot 16 } \n \n \frac { 41\pm \sqrt { 1681-1600 } }{ 32 } \n \n \frac { 41\pm \sqrt { 81 } }{ 32 } \n \n \frac { 41\pm 9 }{ 32 }$

So the solution set :

$\frac { 41+9 }{ 32 } =\frac { 50 }{ 32 } \n \n \frac { 41-9 }{ 32 } =\frac { 32 }{ 32 } =1\n \n a\quad =\quad \left\{ \frac { 50 }{ 32 } ,\quad 1 \right\}$

We found a's value.

Remember,

${ x }^( 2 )=a$

So after we found a's solution set, that means.

${ x }^( 2 )=\frac { 50 }{ 32 }$

and

${ x }^( 2 )=1$

We'll also solve this equations to find x's solution set :)

${ x }^( 2 )=\frac { 50 }{ 32 } \n \n \frac { 50 }{ 32 } =\frac { 25 }{ 16 } \n \n { x }^( 2 )=\frac { 25 }{ 16 } \n \n \sqrt { { x }^( 2 ) } =\sqrt { \frac { 25 }{ 16 } } \n \n x=\quad \pm \frac { 5 }{ 4 }$

${ x }^( 2 )=1\n \n \sqrt { { x }^( 2 ) } =\sqrt { 1 } \n \n x=\quad \pm 1$

So the values x has are :

$\frac { 5 }{ 4 }$ , $-\frac { 5 }{ 4 }$ , $1$ and $-1$

Solution set :

$x=\quad \left\{ \frac { 5 }{ 4 } \quad ,\quad -\frac { 5 }{ 4 } \quad ,\quad 1\quad ,\quad -1 \right\}$

I hope this was clear enough. If not please ask :)

Answer 2

Answer: 16x⁴ - 41x² + 25 = 0
16x⁴ - 16x² - 25x² + 25 = 0
16x²(x²) - 16x²(1) - 25(x²) + 25(1) = 0
16(x² - 1) - 25(x² - 1) = 0
(16x² - 25)(x² - 1) = 0
(16x² + 20x - 20x - 25)(x² - x + x - 1) = 0
(4x(4x) + 4x(5) - 5(4x) - 5(5))(x(x) - x(1) + 1(x) - 1(1)) = 0
(4x(4x + 5) - 5(4x + 5))(x(x - 1) + 1(x - 1)) = 0
(4x - 5)(4x + 5)(x + 1)(x - 1) = 0
4x - 5 = 0 or 4x + 5 = 0 or x + 1 = 0 or x - 1 = 0
    + 5 + 5    - 5 - 5 - 1 - 1 + 1 + 1
   4x = 5 4x = -5 x = -1    x = 1
      4    4    4 4
   x = 1¹/₄ x = -1¹/₄

The solution set is equal to {(1¹/₄, -1¹/₄, -1, 1)}.

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Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest and gives him the ability to make ATM withdrawals from that bank’s ATMs. Putting the money in an online savings account will earn him 4.85% annual interest, but he will be charged $3 every time he makes an ATM withdrawal. Assuming that Gareth’s ATM withdrawals do not affect the amount of interest he earns, roughly how many ATM withdrawals must Gareth make every year for the local savings account to be a better deal than the online savings account?

Answers

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest.

Interest earned in local bank = 2000 * 22.2% = 2000 * 0.022 = 44

Putting the money in an online savings account will earn him 4.85% annual interest

Interest earned in online account = 2000 * 4.85% = 2000 * 0.0485 = 97

He will be charged $3 every time he makes an ATM withdrawal.

In online account, the interest is 97 . If he withdraws 18 times then

Total ATM fee is 18 * 3= 54 . so 97 - 54 = 43

43 is lower than 44 that is interest of local account.

Therefore, 18 ATM withdrawals make local savings account to be a better deal than the online savings account every year.

Answer:

Gareth should make 18 ATM withdrawals every year for better deal.

Step-by-step explanation:

Consider the provided information.

Gareth has $2,000 to invest and local bank will earn him 2.2% annual interest.

The amount earned by local bank is: $\$2000* (2.2)/(100)=\$44$

The money in an online savings account will earn him 4.85% annual interest, but he will be charged $3 every time he makes an ATM withdrawal.

The amount earned by online account $\$2000* (4.85)/(100)=\$97$

Savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.

Let x is the number of times he withdrawal money.

$97-3x=44\n3x=53\nx=17.67\approx 18$

Hence, Gareth should make 18 ATM withdrawals every year for better deal.

What is the solution set of negative X equals -8

Answers

Answer:

Step-by-step explanation:

the unknown can NEVER be negative

so you wont see an answer like

-b= 7, -a=98; -k= -9

so,

-x= -8 (change their positions so that the unknown, x, is positive)

x=8

When you use the distance formula, you are calculating the length of the _____ of a right triangle. A.hypotenuse B.longer leg C.perimeter D.shorter leg

Answers

You are finding the hypotenuse. :)

Answer:

A.hypotenuse

Step-by-step explanation:

When you use the distance formula, you are calculating the length of the hypotenuse of a right triangle

What is the midpoint of the x-intercepts of f(x) = (x – 2)(x – 4)? A)(–3,0)
B)(–1,0)
C)(1,0)
D)(3,0)

Answers

Answer:

The correct option is D.

Step-by-step explanation:

The given function is

$f(x)=(x-2)(x-4)$

From the given graph it is clear that x-intercepts of the graph are (2,0) and (4,0).

The midpoint of x-intercepts is

$Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))$

$Midpoint=((2+4)/(2),(0+0)/(2))$

$Midpoint=((6)/(2),(0)/(2))$

$Midpoint=(3,0)$

The midpoint of x-intercepts is (3,0). Therefore the correct option is D.

The x-intercepts are readily identified on the graph: (2,0) and (4,0). The midpoint of a line connecting those 2 points would be (3,0).

This is relay hard i need help 19 point available

Answers

order of operations
PEMDAS
parenthaseees
exponents
multiplication or division whichever comes first
addition or subtraction whichever comes first

parenthases first
inner to outer
left to right
treat a/b as (a)/(b) so simplify the fraction top and bottom as much as possible
the parenthaseese we have to simplify are
(20-5^2), (16+2^2), (3*2^2)

(20-5^2)
exponents first
5^2=25
now we have
(20-25)
subtract
20-25=-5
other parenthasees

16+2^2
exponent,
2^2=4
16+4=20

next
3*2^2
exponent
2^2=4
3*4=12

so the equaiton we have now is
$((-5)(20))/(-2^(3)+(12))$

exponents
-2^3 =-1 times 2^3
exponent first
2^3=8
-1 times 8=-8

now we hav
$((-5)(20))/(-8+(12))$
treat the numberator and denomenator as if they are in parenthasees so try to simplify them next
(-5)(20)=-100
-8+12=4

now we have
$(-100)/(4)$
division
-100/4=-25

If the nth term of a sequence is
4n + 3 what is the 6th term?

Answers

Answer:

27 is the answer to the question

Step-by-step explanation:

4(6)+3=24+3=27

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