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3 years ago

If u + t = 5 and u-t=2, what is the value of (u – t)(u² - 12) ?

Mathematics

2 answers:

chubhunter [2.5K]3 years ago

8 0

Answer:

(u – t)(u² - 12) is equal to 0.5.

Step-by-step explanation:

First let's find u and t:

Given u + t = 5, and u - t = 2

We'll substitute one of those into the other equation.

Let's solve the second one for u:

u - t = 2

u = 2 + t

Now we can substitute that definition into the first equation:

u + t = 5

(2 + t) + t = 5

2 + 2t = 5

2t = 3

t = 1.5

Now we can substitute that into either of the original equations to find u:

u = 2 + t

u = 2 + 1.5

u = 3.5

So t = 1.5 and u = 3.5. Now we can substitute them into the given expression to solve it:

(u – t)(u² - 12)

= (3.5 – 1.5)(3.5² - 12)

= (3.5 – 1.5)(12.25 - 12)

= 2 × 0.25

= 0.5

OLga [1]3 years ago

6 0

Answer:

0.5

Step-by-step explanation:

You know that u-t is 2, so it'll be 2( $u^{2}$ -12)

Now, system of equations to solve for u. if u+t=5, this means t=5-u, you can plug it in into u-t=2, so u-(5-u)=2. Now you know that u is 3.5, so do the calculations.

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3 years ago

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Question 2(Multiple Choice Worth 4 points)

leonid [27]

Answer:

p = 2

Step-by-step explanation:

using the rule of exponents

$(a^{m}) ^{n}$ = $a^{mn}$

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so value of p = 2

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2 years ago

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

sveticcg [70]

$16{ x }^{ 4 }-41{ x }^{ 2 }+25=0$

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

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.

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

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 (<span>fourth-degree <span>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 :
</span></span>
$t{ x }^{ 2 }+bx+c=0$

In our equation,

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

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

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

So the solution set :

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

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 :)

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

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

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 :)

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3 years ago

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