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mixer [17]
3 years ago
14

1. Given the equation (x – 3)2 – 32 = 17 a)

Mathematics
1 answer:
m_a_m_a [10]3 years ago
6 0
We know that

The square root property<span> is one method that is used to find the solutions to a quadratic equation.  This method involves taking the square roots of both sides of the equation.  
</span>(x – 3)² – 32 = 17-------> (x – 3)² = 17+32-----------> (x – 3)² = 49
(x – 3)² = 7²--------> <span>will take the square root of each side
</span>so
√(x – 3)²=(+-)√7²------> <span>notice the use of the </span> sign (+-), this will give us both a positive and<span>  a negative root
</span>
then

x-3=7--------> x=10
x-3=-7-------> x=-4

the answer Part a) is
x=10
x=-4

Part b) Explain why the given equation has two solutions.

the answer part b) is
Because exist<span> the possibility of two roots for every square root, one positive and one negative</span>
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Find the inverse of f(x)=(x−5)/(−4x−2)
uysha [10]

Answer:

{f}^{ - 1} (x)= \frac{  5 - 2x }{ 4x  + 1}

Step-by-step explanation:

The given rational function is

f(x) =  \frac{x - 5}{ - 4x - 2}

Let

y =  \frac{x - 5}{ - 4x - 2}

Interchange x and y

x=  \frac{y- 5}{ - 4y - 2}

Cross multiply

x( - 4y - 2)= y- 5

Expand

- 4xy   - 2x= y- 5  \\ - 4xy  - y=  2x - 5 \\y( - 4x - 1)=  2x - 5

Solve for y;

y= \frac{  2x - 5}{ - 4x - 1}

or

y= \frac{  5 - 2x }{ 4x  + 1}

Therefore

{f}^{ - 1} (x)= \frac{  5 - 2x }{ 4x  + 1}

7 0
3 years ago
Raul has $460 in his checking account. Each month, $45 is automatically deducted from his account to pay for his cell phone plan
MissTica
X=number of months
how much is deducted total=number of months times amount deducted per m onth
amount deducted per month=45
number of months=x
how much deducted total=45x

460-deducted total is more than 100
460-45x>100
solve for x
add 45x to both sides
460>100+45x
subtract 100
360>45x
divide both sides by 45
8>x
answer is 7 months
if he does 8 months, then he will have exatly 100 and 100 is noe more than 100



answer is 7 months
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