MATHEMATICS HIGH SCHOOL

The graph of which function has a minimum located at (4, –3)?f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35

Answers

Answer 1
Answer:

Answer:

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

f(x)=a(x-h)^(2)+k

where

(h,k) is the vertex of the parabola

case A) we have

f(x)=x^(2)+4x-11

In this case the x-coordinate of the vertex will be negative

therefore

case A is not the solution

case B) we have

f(x)=-2x^(2)+16x-35

This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point (4,-3)but is not a minimum

see the attached figure

therefore

case B is not the solution

case C) we have

f(x)=x^(2)-4x+5

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-5=x^(2)-4x

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-5+4=(x^(2)-4x+4)

f(x)-1=(x^(2)-4x+4)

Rewrite as perfect squares

f(x)-1=(x-2)^(2)

f(x)=(x-2)^(2)+1 --------> vertex form

The vertex is the point (2,1)

therefore

case C is not the solution

case D) we have

f(x)=2x^(2)-16x+35  

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)-35=2x^(2)-16x

Factor the leading coefficient

f(x)-35=2(x^(2)-8x)

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)-35+32=2(x^(2)-8x+16)

f(x)-3=2(x^(2)-8x+16)

Rewrite as perfect squares

f(x)-3=2(x-4)^(2)

f(x)=2(x-4)^(2)+3 --------> vertex form

The vertex is the point (4,3)

therefore

case D is not the solution

The answer to the question will be the function

f(x)=2x^(2)-16x+29

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A system in a noisy environment transmits 11111 or 00000 when 1 or 0 are transmitted to decrease the probability of error. Suppose the probability that one of the 5 transmitted bits is corrupted from 1 to 0 is 0.3 and the probability that a bit is corrupted from 0 to 1 is 0.1. Given that the probability that the system transmits a 0 or a 1 is equally likely, if 01101 was received what is the probability that a 1 was transmitted.

Answers

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Step-by-step explanation:

The attachment below simply explains how to solve it using Bayer's rule

Please help me figure this out .


2x+10(340/139)=-18

Answers

Answer:

To solve the equation 2x + 10(340/139) = -18, we can follow these steps:

1. Distribute the 10 to the terms inside the parentheses:

2x + (10 * 340/139) = -18

2x + 3400/139 = -18

2. Combine like terms:

2x + 3400/139 = -18

3. Move the constant term to the other side of the equation by subtracting 3400/139 from both sides:

2x = -18 - 3400/139

4. Simplify the right side of the equation:

2x = (-18 * 139 - 3400) / 139

5. Calculate the right side of the equation:

2x = (-2502 - 3400) / 139

2x = -5902 / 139

6. Divide both sides by 2 to isolate the variable x:

x = -5902 / (2 * 139)

x = -5902 / 278

x = -21.2115 (rounded to four decimal places)

Therefore, the solution to the equation 2x + 10(340/139) = -18 is x = -21.2115.

Slope-intercept from two points (1,4) and (2,2)​

Answers

Answer:

y=-2x+6

Step-by-step explanation:

Equation of the line

First, we find the slope of the line.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\displaystyle m=(y_2-y_1)/(x_2-x_1)

The two points are (1,4) and (2,2), thus:

\displaystyle m=(2-4)/(2-1)=(-2)/(1)

m=-2

The equation of a line passing through (h,k) and slope m is:

y-k=m(x-h)

y-4=-2(x-1)

Note we used the point (1,4). If we used the other point, the result would have been the same. Operating the equation:

y-4=-2x+2

Adding 4:

y=-2x+6

The slope-intercept form of the line is

\boxed{y=-2x+6}

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Answers

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Is the set of multiples of 4 closed under addition? Explain why or provide a counterexample if not.A. Yes, because the sum of any two multiples of 4 is also a multiple of 4.


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Answers

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