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2 years ago

Rearranging literal equations!! really confused ASAPplease

Mathematics

1 answer:

valina [46]2 years ago

7 0

Answer:

b = $\frac{8a-55}{5-a}$

Step-by-step explanation:

To clear the radicals square both sides

$\frac{1}{6-a}$ = $\frac{8+b}{b-7}$ ( cross- multiply )

(6 - a)(8 + b) = b - 7 ← expand factors on left using FOIL

48 + 6b - 8a - ab = b - 7 ( subtract 48 from both sides )

6b - 8a - ab = b - 55 ( add 8a to both sides )

6b - ab = b - 55 + 8a ( subtract b from both sides )

6b - ab - b = 8a - 55, that is

5b - ab = 8a - 55 ← factor out b from each term on the left side )

b(5 - a) = 8a - 55 ← divide both sides by (5 - a)

b = $\frac{8a-55}{5-a}$

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Step-by-step explanation:

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3 years ago

The graph of f(x) = 2x^2 + 20x + 48 is shown

Free_Kalibri [48]

Answer:

a) The equation in intercept form by factoring is (x+6)(x+4)

b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.

c) The solutions of $2x^2+20x+48=0$ is $(x+6)(x+4)=0$ that is x= -6 and x = -4.

Step-by-step explanation:

The given quadratic equation is $f(x)=2x^2+20x+48$

Put the function f(x) = 0 , then $f(x)=2x^2+20x+48=0$

a) The equation in intercept form by factoring is ,

Consider the given function,

$f(x)=2x^2+20x+48=0$

$\Rightarrow 2x^2+20x+48=0$

taking 2 common, we get,

$\Rightarrow 2(x^2+10x+24)=0$

$\Rightarrow x^2+10x+24=0$

The above is a quadratic equation of the form $ax^2+bx+c=0$

Solving quadratic equation using middle term splitting method,

$\Rightarrow x^2+6x+4x+24=0$

$\Rightarrow x(x+6)+4(x+6)=0$

$\Rightarrow (x+6)(x+4)=0$

Thus, The equation in intercept form by factoring is (x+6)(x+4).

b) From the given graph x- intercepts are (-4,0) and (-6,0) .

Zeroes / roots of a function are those points where the value of the function is zero.

Put f(x) = 0 as solved above

that is $(x+6)(x+4)=0$

$\Rightarrow (x+6)=0$ or $\Rightarrow (x+4)=0$

$\Rightarrow x=-6$ or $\Rightarrow x=-4$

Thus, zeros (roots) of the function are -6 and -4.

For checking put x = -6 and -4 in the function we get f(x) =0 .

c) The solutions of $2x^2+20x+48=0$ is $(x+6)(x+4)=0$ that is x= -6 and x = -4 as shown above.

8 0

2 years ago