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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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6 0
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A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground
Vlad1618 [11]

Answer:

34.78 feet

Step-by-step explanation:

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Once I found x, I used the pythagorean theorem to get 34.78 feet

3 0
3 years ago
Can someone help with math?
algol [13]

Answer:

A. {4,3}

Step-by-step explanation:

x -2y = -2

    y = - 3x +15

x - 2(-3x+15) = -2

x +6x - 30 = -2

7x = 28

x = 4

y = - 3x +15 = - 3*4 + 15 = -12 + 15 = 3

{4,3}

5 0
3 years ago
Can any one solve this.?
SpyIntel [72]

Answer:

x = 1

Step-by-step explanation:

Expand brackets

2x + 16 - 4x = 10x + 4

Rearrange so that x's are on one side and whole numbers are on the other

2x - 4x - 10x = 4 - 16

Simplify

-12x = -12

Make x on its own

x = 1

3 0
3 years ago
In rectangle MNOP, MO = 4x - 10 and NP = 2x + 4.<br> What is the length of a diagonal?
slega [8]

Answer:

18

Step-by-step explanation:

From the rectangle, M O = NP

4x - 10 = 2x+4

4x-2x = 4 + 10

2x = 14

x = 14/2

x = 7

SInce MO and NP are the diagonal

Length of diagonal = 4x- 10

Length of diagonal = 4(7) - 10

Length of diagonal = 28 - 10

Length of diagonal = 18

hence the required length is 18

6 0
3 years ago
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