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3 years ago

Find the least common denominator for these two rational expressions. x²/x²+2x+1 and 5/x²+4x+3

1 answer:

5 0

Factor each denominator:

x^2 + 2x + 1 = (x+1)^2

x^2 + 4x + 3 = (x+3)(x+1)

Now take the common and non common factors with the highest exponents and multiply them.

(x+3).(x+1)^2 is the least common denominator.

If you expand that product you will get x^3 + 5x^2 + 7x +3

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The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?

kirill [66]

Answer:

Step-by-step explanation:

Let's organise our information :

the function is (1/2)x²+2x+3

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

(1/2)x²+2x+3=x+7

(1/2)x²+2x+3-x-7=0
(1/2)x²+x-4=0

Now let's solve this equation :

a= 1/2
b= 1
c= -4

Δ=1²-4*(1/2)*(-4)

= 9

So we have two solutions :

$\left \{ {{y=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.$

y= -4
x= 2

So the solutions are -4 and 2

3 0

3 years ago

10. On a Math test, there are 60 questions. Juanita answered 50 questions correctly. A) What percent did she answer incorrectly?

Travka [436]

Answer:

83.3

Step-by-step explanation:

4 0

3 years ago

Find d / dx ( e^in(x)).

Lena [83]

let's first off apply a log rule of cancellation, keeping in mind that, first off is ln(), not in(), and that ln() is just a shortcut to logₑ.

$\bf \textit{Logarithm Cancellation Rules}
\\\\
log_a a^x = x\qquad \qquad \stackrel{\stackrel{\textit{we'll use this one}}{\downarrow }}{a^{log_a x}=x}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
e^{ln(x)}\implies e^{log_e(x)}\implies x
\\\\\\
\cfrac{d}{dx}\left[ e^{ln(x)} \right]\implies \cfrac{d}{dx}[x]\implies 1$

5 0

3 years ago

Use the 3 digits 5, 3, and 2 only once in each number how many 3 digit numbers can you make?

Dmitrij [34]

Answer:

532

523

325

352

235

253

so you can make 6

3 0

3 years ago

Brainiest If Correct + 50pts ---The cylinder with base radius 5 and height 12 is inscribed in a right rectangular prism. Find th

Romashka [77]

Answer:

SA = 680 units^2

V =1200 unit^3

Step-by-step explanation:

If the radius is 5 then the diameter is 2r = 2*5 = 10

The height would remain the same

Surface area of a prism is given by

SA = 2 (lw+lh+hw)

l =d = 10 w = d = 10 h = 12

SA = 2 ( 10*10 + 10 * 12+ 12* 10)

SA = 2( 100+120+120)

SA = 2(340)

SA = 680 units^2

V = l*w*h = 10*10*12 =1200 unit^3

4 0

3 years ago