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9514 1404 393

Answer:

  [tex]f(x)=\left\{\begin{array}{cl}-x^2+11x-28&\text{for $4<x<7$}\\x^2-11x+28&\text{otherwise}\end{array}\right.[/tex]

Step-by-step explanation:

The absolute value function negates its contents when those contents are negative. Here, the quadratic factors as ...

 x^2 -11x +28 = (x -4)(x -7)

so will be negative when the factors have different signs. That will be the case for 4 < x < 7.

The piecewise function can be written in 3 parts, one part for x ≤ 4, another part for 4 < x < 7, and the remaining part for 7 ≤ x. The function expressions for x ≤ 4 and 7 ≤ x are identical.

In the answer above, we chose to write it with the part where the quadratic is negated being defined on the appropriate interval, and using "otherwise" for the rest of the function. It is a little unconventional to do it this way, but it is more compact and completely defines the function.

Answer:its the first one

Step-by-step explanation:

Answer:

Answer:

Order from Least to Greatest

-33/5 < -3.5 < 3.3 < 3 1/3

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

Answer:

Answer: Positive

Step-by-step explanation:

Answer:

It will read the same at F = -40.

Step-by-step explanation:

The relation between fahrenheit and celsius is given by the following equation:

[tex]C = \frac{5(F-32)}{9}[/tex]

At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?

This is F for C = F. So

[tex]C = \frac{5(F-32)}{9}[/tex]

[tex]F = \frac{5(F-32)}{9}[/tex]

[tex]9F = 5F - 160[/tex]

[tex]4F = -160[/tex]

[tex]F = -\frac{160}{4}[/tex]

[tex]F = -40[/tex]

It will read the same at F = -40.

Answer:

[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]

[tex]Cost = \$1.05[/tex]

Step-by-step explanation:

Given

[tex]Volume = 100in^3[/tex]

[tex]Cost =\$0.014[/tex] -- Top and Bottom

[tex]Cost =\$0.007[/tex] --- Sides

Required

What dimension of the cylinder minimizes the cost

The volume (V) of a cylinder is:

[tex]V = \pi r^2h[/tex]

Substitute 100 for V

[tex]100 = \pi r^2h[/tex]

Make h the subject

[tex]h = \frac{100 }{\pi r^2}[/tex]

The surface area (A) of a cylinder is:

[tex]A = 2\pi r^2 + 2\pi rh[/tex]

Where

[tex]Top\ and\ bottom = 2\pi r^2[/tex]

[tex]Sides = 2\pi rh[/tex]

So, the cost of the surface area is:

[tex]C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007[/tex]

[tex]C = 2\pi r(r * 0.014+ h * 0.007)[/tex]

[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]

Substitute [tex]h = \frac{100 }{\pi r^2}[/tex]

[tex]C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})[/tex]

[tex]C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})[/tex]

[tex]C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})[/tex]

[tex]C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})[/tex]

Open bracket

[tex]C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{2 *0.7}{r}[/tex]

[tex]C = 0.028\pi *r^2+ \frac{1.4}{r}[/tex]

[tex]C = 0.028\pi r^2+ \frac{1.4}{r}[/tex]

To minimize, we differentiate C w.r.t r and set the result to 0

[tex]C' = 0.056\pi r - \frac{1.4}{r^2}[/tex]

Set to 0

[tex]0 = 0.056\pi r - \frac{1.4}{r^2}[/tex]

Collect Like Terms

[tex]0.056\pi r = \frac{1.4}{r^2}[/tex]

Cross Multiply

[tex]0.056\pi r *r^2= 1.4[/tex]

[tex]0.056\pi r^3= 1.4[/tex]

Make [tex]r^3[/tex] the subject

[tex]r^3= \frac{1.4}{0.056\pi }[/tex]

[tex]r^3= \frac{1.4}{0.056 * 3.14}[/tex]

[tex]r^3= \frac{1.4}{0.17584}[/tex]

[tex]r^3= 7.96178343949[/tex]

Take cube roots of both sides

[tex]r= \sqrt[3]{7.96178343949}[/tex]

[tex]r= 1.997[/tex]

Recall that:

[tex]h = \frac{100 }{\pi r^2}[/tex]

[tex]h = \frac{100 }{3.14 * 1.997^2}[/tex]

[tex]h = \frac{100 }{12.52}[/tex]

[tex]h = 7.987[/tex]

Hence, the dimensions that minimizes the cost are:

[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]

To calculate the cost, we have:

[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]

[tex]C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)[/tex]

[tex]Cost = \$1.05[/tex]

Answer:

46 ft to yd conversion. A foot is a unit of length equal to exactly 12 inches or 0.3048 meters.

...

Convert 46 Feet to Yards.

ft yd

46.00 15.333

46.01 15.337

46.02 15.34

46.03 15.343

ft yd

46.00 15.333

46.01 15.337

46.02 15.34

46.03 15.343

46.04 15.347

46.05 15.35

46.06 15.353

46.07 15.357

46.08 15.36

46.09 15.363

46.10 15.367

46.11 15.37

46.12 15.373

46.13 15.377

46.14 15.38

46.15 15.383

46.16 15.387

46.17 15.39

46.18 15.393

46.19 15.397

46.20 15.4

46.21 15.403

46.22 15.407

46.23 15.41

46.24 15.413

ft yd

46.25 15.417

46.26 15.42

46.27 15.423

46.28 15.427

46.29 15.43

46.30 15.433

46.31 15.437

46.32 15.44

46.33 15.443

46.34 15.447

46.35 15.45

46.36 15.453

46.37 15.457

46.38 15.46

46.39 15.463

46.40 15.467

46.41 15.47

46.42 15.473

46.43 15.477

46.44 15.48

46.45 15.483

46.46 15.487

46.47 15.49

46.48 15.493

46.49 15.497

ft yd

46.50 15.5

46.51 15.503

46.52 15.507

46.53 15.51

46.54 15.513

46.55 15.517

46.56 15.52

46.57 15.523

46.58 15.527

46.59 15.53

46.60 15.533

46.61 15.537

46.62 15.54

46.63 15.543

46.64 15.547

46.65 15.55

46.66 15.553

46.67 15.557

46.68 15.56

46.69 15.563

46.70 15.567

46.71 15.57

46.72 15.573

46.73 15.577

46.74 15.58

ft yd

46.75 15.583

46.76 15.587

46.77 15.59

46.78 15.593

46.79 15.597

46.80 15.6

46.81 15.603

46.82 15.607

46.83 15.61

46.84 15.613

46.85 15.617

46.86 15.62

46.87 15.623

46.88 15.627

46.89 15.63

46.90 15.633

46.91 15.637

46.92 15.64

46.93 15.643

46.94 15.647

46.95 15.65

46.96 15.653

46.97 15.657

46.98 15.66

46.99 15.663

Step-by-step explanation:

Hope this helps <3

Answer:

A,D,C

Step-by-step explanation:

Answer:

28 and 32 or B And C

Step-by-step explanation:

Answer:

y=1.3x-3

or

y=4/3x-3

Step-by-step explanation:

1.3 is the slope (the change in between points)

-3 is the y intercept (the point on the y-axis)

Answer: 0,16,32,48,64

Step-by-step explanation: the equation 16b means you will multiple 16 by whatever is in the b box. For the first b is equal to 0 so 16x0 = 0, the second b is equal to 1 so 16x1 = 16

Answer:

The required function is:

Please check the attached graph.

Step-by-step explanation:

We need to write a function to match the function machine  multiply the input by -3, then  subtract 2.

Let 'x' be the input.

Therefore, multiply the input by -3, then  subtracting 2 would give us the result:

f(x) = 3x - 2

Therefore, the required function is:

Please check the attached graph.

Answer:

Step-by-step explanation:

discriminant = (-13)² - 4·2·15 = 49

discriminant > 0 so there are two real roots

Answer:

7 = 49.....

Step-by-step explanation:

7 * 7. = 49

ok....

thanks

Answer:

easy...

132.75total cost

4.75 for each book  

Step-by-step explanation:

not a) it would be far to large

not b) again to large

maybe c) not to big but still small

not d) to big yet again

id assume c? im not to smart tho

Answer:

Convert Equation 1 to slope-intercept form.

y

=

−

x

+

4

The two equations have the same slope,  

m

=

−

1

, therefore they are perpendicular and there is no solution to this linear system. The two lines have no points in common.

graph{(x+y-1)(x+y-4)=0 [-10, 10, -5, 5]}

Step-by-step explanation:

Answer:

m<7

Step-by-step explanation:

Answer:

m<7

Step-by-step explanation:

9514 1404 393

Answer:

  >

Step-by-step explanation:

We know that 5 + 3 = 8, so 5 2/3 +3 = 8 2/3.

This problem has you adding 3 3/4, not 3, so the sum will clearly be "greater than" 8 2/3.

  5 2/3 + 3 3/4 > 8 2/3

Answer:

theres nothing there

Step-by-step explanation:

Answer:

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 40

Given that standard deviation of the Population = 15

Let 'x' be the random variable in normal distribution

Let 'X' = 25

[tex]Z = \frac{x-mean}{S.D} = \frac{25-40}{15} = -1[/tex]

Let 'X' = 55

[tex]Z = \frac{x-mean}{S.D} = \frac{55-40}{15} = 1[/tex]

Step(ii):-

The probability that between 25 and 55

P( 25 ≤ X≤ 55) = P( -1≤z≤1)

                       = A(1) - A(-1)

                      = A(1) + A(1)

                     = 2 × A(1)

                    = 2× 0.3413

                   = 0.6826

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

Final answer:-

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

Answer:

D

Step-by-step explanation:

Since Jackson has 7 1/2 hours to spend at the amusement park, he has already spent 1 1/2 of those hours at the water park (We will need this shortly). Since he has 6 hours remaining and 3 parks to go, he can't spend more than 7 1/2 hours at the park. This means that the answer will have to be less than or equal to. Finally, it would be D because he can spend any amount of time at the other 3 parks (x) plus the 1 12 hours he already spent.

Answer:

The first 4

Step-by-step explanation:

any that are whole numbers

Answer: 9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3 x 3 = 9 :)

Answer:

im pretty sure 1 and 5 are correct i dont know the 3rd one though

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

Twenty five times the sum of ten and three.

Answer:

You did but you forgot to turn it back into a whole number! Your final answer would be 1  and 1/3 Step-by-step explanation: 15 goes into 20 once which gives you the 1. You are then left with 5/15 which can be simplified into 1/3. 1 and 1/3