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algol [13]
3 years ago
11

Solve 0 = (x – 4)2 – 1 by graphing the related function.

Mathematics
1 answer:
fomenos3 years ago
8 0

Answer:

Therefore, the solutions of the quadratic equations are:

x=5,\:x=3

The graph is also attached.

Step-by-step explanation:

The solution of the graph could be obtained by finding the x-intercept.

y=\left(x-\:4\right)^2-1

Finding the x-intercept by substituting the value y = 0

so

y=\left(x-\:4\right)^2-1

\:0\:=\:\left(x\:-\:4\right)^2\:-\:1        ∵ y = 0

\left(x-4\right)^2-1=0

\left(x-4\right)^2-1+1=0+1

\left(x-4\right)^2=1

\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

\mathrm{Solve\:}\:x-4=\sqrt{1}

\mathrm{Apply\:rule}\:\sqrt{1}=1

x-4=1

x=5

\mathrm{Solve\:}\:x-4=-\sqrt{1}

\mathrm{Apply\:rule}\:\sqrt{1}=1

x-4=-1

x=3

So, when y = 0, then x values are 3, and 5.

Therefore, the solutions of the quadratic equations are:

x=5,\:x=3

The graph is also attached. As the graph is a Parabola. It is visible from the graph that the values of y = 0 at x = 5 and x = 3. As the graph is a Parabola.

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Stells [14]
80+10x is the expression. To find the cost for 9 guests, simply plug in 9 for x. This becomes an equation reading 80+10(9)=170. The total cost for 9 guests is $170.00.


4 0
3 years ago
Carlos is using the quadratic formula to find the solutions of y=3x^2-5x-2. Which of the following will simplify to the correct
Nana76 [90]

Answer:

Fx=\frac{5\pm\sqrt{25+24} }{6}

Step-by-step explanation:

A quadratic equation in one variable given by the general expression:

ax^2+bx+c

Where:

a\neq 0

The roots of this equation can be found using the quadratic formula, which is given by:

x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}

So:

y(x)=3x^2-5x-2=0

As you can see, in this case:

a=3\\b=-5\\c=-2

Using the quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(3)(-2)} }{2(3)}=\frac{5\pm\sqrt{25+24} }{6}

Therefore, the answer is:

Fx=\frac{5\pm\sqrt{25+24} }{6}

4 0
3 years ago
Solve each of the following equations for xx using the same technique as was used in the Opening Exercise.
Brrunno [24]

Answer:

The value of the x is 1/9.  

Step-by-step explanation:

Data provided in the question is:

3^2/x=81

To find out:-        

the value of x.

Solution for the equation:-    

3^2/x = 81\\9/x=81\\9/81=x\\1/9=x\\

On solving the given question or equation by using  mathematics of algebra we find out the value of x to be 1/9.

7 0
3 years ago
Can you answer this question ?
Elden [556K]

Answer:

k = -14

Step-by-step explanation:

We should cross-multiply

9/(k -  7)  =  6 / k

9*k  = 6 * (k - 7)

9k = 6k  - 42

9k - 6k = -42

3k = -42

k = -14

7 0
2 years ago
Choose the correct correspondence.​
Alex

Answer:

B

Step-by-step explanation:

idk I think its correct

4 0
3 years ago
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