What's the inverse of ƒ(x) = x2 – 16?

Answer:

The solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Step-by-step explanation:

From Mathematics, we know that absolute values are defined by the following characteristics:

1) For [tex]x \ge 0[/tex], [tex]|x| = x[/tex]

2) For [tex]x < 0[/tex], [tex]|x| = - x[/tex]

Then, if [tex]|x| = x[/tex], then the solution set to the absolute value is:

[tex]S = \{x \in \mathbb{R}| x \ge 0\}[/tex] or [tex]S = [0, +\infty)[/tex]

Negative real numbers are not included in the solution set, as for [tex]x < 0[/tex], [tex]|x| = - x[/tex].

Answer:

12 and 12.5

Step-by-step explanation:

Answer:

The y-intercept of Function A is less than the y-intercept of Function B.

Step-by-step explanation:

Function A's y-intercept would be (0, -1) and Function B's y-intercept is (0, 4). Therefore, Function A's y-intercept is less than Function B's.

Answer:

3 /4

Step-by-step explanation:

The probability that selected person is a female Given she is married :

This is a conditional probability in the form ; A given B

P(A|B) = P(AnB) / P(B)

Let, Female = F ; Married = M

P(F|M) = P(FnM) / P(M) = 150 / 200 = 3 / 4

Answer:

C

Step-by-step explanation:  

 pedometers are devices that count the steps you take throughout the day. Seeing your daily step count can give you an idea of how active you are in a given day and give motivating feedback to help you achieve a daily step goal.

Answer:c i just took the test

Step-by-step explanation:

Answer:

the answer is in  

Step-by-step explanation:

The mean of 43,69,48,37,85,57,95,102 is 67

Answer:

x = 25

Step-by-step explanation:

3x-15 = 2x+10

x-15 = 10

x = 25

Answer:

x = 25 degree

Step-by-step explanation:

3x - 15 = 2x + 10 (their relation will be alternate interior angles if they [tex]l_{1}[/tex] and [tex]l_{2}[/tex] are parallel)

3x - 2x = 10 + 15

x = 25 degree

Answer:

253.5 ft³

Step-by-step explanation:

Volume of a pyramid = [tex] \frac{1}{3} [/tex]× base area × height

Volume of a prism = base area × height

Volume of the pyramid

= [tex] \frac{1}{3} [/tex]× (6×6.5÷2) × 9

= [tex] \frac{1}{3} [/tex]× 19.5 × 9

= 58.5 ft³

Volume of the prism

= (6×6.5÷2) × 10

= 195 ft³

Volume of the solid

= 58.5 + 195

= 253.5 ft³

Answer:

A

Step-by-step explanation:

the base is 19.5 feet squared

(6 * 6.5 / 2)

multiplied by 10 gives you 195 feet cubed for the lower solid

19.5 * 9 / 3

gives you 58.5 feet cubed for the upper solid

just add both volumes together

Answer:

It is 4

Step-by-step explanation:

1 times 1 for square

3 times 3 then divide by 2 = 3

add together

4

Answer:

a = 5.5 in²

Step-by-step explanation:

square

a = lw

a = 1 * 1

a = 1

Triangle

a = (1/2)bh

a = (1/2) * 3 * 3

a = 4.5

combined figure

a = 1 + 4.5

a = 5.5 in²

Answer:

a coin flip

Step-by-step explanation:

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero.

Answer:

b. The speed of the car is an explanatory variable

Step-by-step explanation:

In the scenario above, the variable which the researcher intends to measure is the a distance covered by a car using the speed information available. The measured variable is the dependent variable as it outcome depends on the variable with which it is being measured, this is called the independent or explanatory variable.

Therefore, car speed is the explanatory or independent variable

Distance is the dependent, response or measured variable.

Answer:

285 mi

Step-by-step explanation:

We can see that for every gallon, Josh drives 30 more miles. This means that he will drive 30*9.5 mi.

30*9.5 = 285

Step-by-step explanation:

15 may be

HOPE IT HELP U ...

Answer:

A. $15 is the mode.

Step-by-step explanation:

In order to answer this question, we need to know the definition of mode. "The mode of a set of numbers is the number that occurs the most" Since out of the four numbers, the one that appears the most is $15, then $15 is the mode.

Answer:

(My answers are not rounded!)

Problem A:

Area: 285 cm^2

Perimeter: 70 cm

Problem B:

Area: 30 m^2

Perimeter: 30 m

Problem C:

Area: 28 m^2

Perimeter: 24 m

Problem D:

Lateral Area: 150 in^2

2 (l + w) h

= 2 (11 + 4) 5

= 2(15)5

= 30(5)

= 150

Surface Area: 238 in^2

2 (lw + hl + hw)

2 (11 x 4 + 11 x 5 + 5 x 4)

= 2 ( 44 + 55 + 20)

= 2 (119)

= 238

Volume: 220 in^3

Length x width x height (rectangular prism)

use formula: 11 x 5 x 4 = 220

Problem E:

Area: 379.94 m^2

Formula: πr^2 (circle)

3.14(11^2)

= 3.14(121)

= 379.94

Circumference: 69.08 m

Formula: 2πr

= 2(3.14)11

= 6.28(11)

=69.08

Problem F:

Area: 49 m^2

length x width

7 x 7 = 49

Perimeter: 28 m

2 (l + w)

= 2 (7 + 7)

= 2(14)

= 28

Problem G:

Area: 1,056 cm^2

length x width

48 x 22 = 1,056

Perimeter: 140 cm

2 (l + w)

2 (48 + 22)

2(70)

=140

Problem H:

Lateral Area: 94.2 in^2

2πrh

= 2(3.14) x 1.5(10)

= 6.28 x 15

= 94.2

Surface Area: 108.33 in^2

2πrh+2πr2

=2(3.14) 1.5(10) + 2(3.14) 1.5^2

= 108.33

Volume: 70.65 in^3

πr2h

= 3.14(1.5^2) 10

= 3.14(2.25) 10

= (7.065) 10

= 70.65

Answer:

0.83333333333

Step-by-step explanation:

One-half plus one-third equals 5/6 or 0.8333.

Given that:

Expression: 1/2 + 1/3

To add one-half (1/2) and one-third (1/3), to find a common denominator and then add the fractions together.

The least common denominator (LCD) of 2 and 3 is 6. To convert the fractions to have a common denominator of 6, multiply the numerator and denominator of 1/2 by 3, and the numerator and denominator of 1/3 by 2:

1/2 × 3/3 = 3/6

1/3 × 2/2 = 2/6

Now that the fractions have a common denominator of 6, add them:

3/6 + 2/6 = 5/6

3/6 + 2/6 = 0.8333

Therefore, one-half plus one-third equals 5/6 or 0.8333.

Learn more about Divisor here:

https://brainly.com/question/30925934

#SPJ6

Answer:

If I understand this right I think it would be 8 and 6?

Step-by-step explanation:

Sorry if this is wrong I'm really bad at math, please tell me if this is right.

9514 1404 393

Answer:

Step-by-step explanation:

Modern graphing calculators have a derivative function available, so using a calculator to find the next value of x is pretty simple.

The Newton's Method iterator for finding the next approximation to the root (x') is ...

  x' = x -f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x).

The attachment shows the first 3 iterations (4 approximations). We observe that the starting point is pretty far from the root, and on the wrong side of some wiggles in the function, so convergence is pretty slow.

The desired approximations are shown above and in the table below.

__

Additional comment

To 12 significant figures, the only real root is −1.10305899649. When the calculator can interactively produce a next guess, you can type the next guess value into the iterator function even as it is showing you the next value. This lets you find the best-precision result as fast as you can type it.

For a calculator like a TI-84, the iterator function can make repeated use of "Ans" as an argument. It usually doesn't take more than 3 or 4 iterations to get a best-precision result, since the number of good decimal places is about doubled on each iteration. (Of course, you have to start with a better approximation than the one given in this problem.)

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2*x+2*3=x-4

2x+6=x-4

2x-x=-4-6

x=-10

Answer:

[tex]x = - 10[/tex]

Step-by-step explanation:

Let's solve:

[tex]2(x+3)=x−4[/tex]

Step 1: Simplify both sides of the equation.

[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]

Step 2: Subtract x from both sides.

[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]

Step 3: Subtract 6 from both sides.

[tex]x+6−6=−4−6 \\ x=−10[/tex]

Answer:

The nth term of this sequence is [tex]a_{n} = -2n + 2[/tex]

Step-by-step explanation:

In this sequence we keep adding -2 on to get the next term. This sequence is called an arithmetic sequence, a sequence that uses addition to keep increasing.

The formula for the nth term of an arithmetic sequence is

[tex]a_{n} = d[/tex] · [tex]n + a_{1} - d[/tex]

[tex]a_{1}[/tex] stands for the first term in the sequence, and [tex]d[/tex] stands for the difference between each number in the sequence.

[tex]a_{1} = 0[/tex] and [tex]d[/tex] = -2, so :

[tex]a_{n} = -2[/tex] · [tex]n + 0 - (-2)\\[/tex]

[tex]a_{n} = -2n + 2[/tex]

Therefore, to find the nth term in this sequence you would use the formula

[tex]a_{n} = -2n + 2[/tex]

Answer:

Perimeter: 18.28

Area: 22.28

Step-by-step explanation:

1. Approach

An easy method that can be used to solve the given problem is the partition the given figure into two smaller figures. One can divide this figure into a square and a semi-circle. After doing so, one can find the area of the semi-circle and the area of the square. Finally, one can add the two area together to find the final total area. To find the perimeter of the figure, one can add the lengths of three of the sides of the square and then one can add half of the circumference of the circle to the result. The final value will be the perimeter of the entire figure.

2. Find the circumference of the semi-circle

The circumference of a circle is the two-dimensional distance around the outer edge of a circle, in essence the length of the arc around a circle. The formula to find the circumference of a circle is as follows,

C = 2(pi)r

Since a semi-circle is half of a circle, the formula to find its circumference is the following,

C = (pi)

Where (pi) is the numerical value (3.1415) and (r) is the radius of the circle. By its definition, the radius of a circle is the distance from a point on the circle to the center of the circle. This value will always be half of the diameter, that is the distance from one end of the circle to the other, passing through the center of the circle. The radius of a circle is always half of the diameter, thus the radius of this semi-circle is (2). Substitute this into the formula and solve for the circumference;

C = (pi)r

C = (pi)2

C ~ 6.28

3. Find the area of the semi-circle

The formula to find the area of a circle is as follows,

A = (\pi)(r^2)

As explained earlier, a semi-circle is half of a circle, therefore, divide this formula by (2) to find the formula for the area of a semi-circle

A = ((pi)r^2)/(2)

The radius of this circle is (2), substitute this into the formula and solve for the area of a semi-circle;

A = ((pi)r^2)/(2)

A = ((pi)(2^2))/(2)

A = (pi)2

A = 6.28

4. Find the area and perimeter of the square,

The perimeter of a figure is the two-dimensional distance around the figure. Since the semi-circle is attached to one of the sides of a square, one only needs to add three sides of the square to find the perimeter of the square;

P = 4+4+4

P = 12

The area of a square can be found by multiplying the length by the width of the square.

A = l*w

Substitute,

A = 4*4

A=16

5. Find the area and the perimeter of the figure,

To find the perimeter of the figure, add the value of the circumference to the vlalue of the perimeter of the square;

A = C+P

A = 6.28+12

A = 18.28

To find the area of the figure, add the value of the area of the circle to the area of the square;

A = 6.28+16

A = 22.28

Answer:

Square tables used

Step-by-step explanation:

x represents the number of square tables used since it is being multiplied times 8 which is the number of people a square table can fit

Answer:

answer in pictures

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Based on your math expression:

7-15 = -8

-2*(-8) = 16

16 / 4 = 4

Answer:

4

Step-by-step explanation:

-2(7-15)

=-14+30

=16÷4

=4

Answer:

[tex]\text{D. }464\:\mathrm{ft^2}[/tex]

Step-by-step explanation:

The surface area of the prism consists of four rectangles and two trapezoids. The sum of the areas of these polygons will give the total surface area of the prism:

Rectangle 1 (top base): [tex]12\cdot 14=168[/tex]

Rectangle 2 (bottom base): [tex]6\cdot 14 = 84[/tex]

Trapezoids 1 and 2 (lateral): [tex]2\cdot 9 \cdot 4=72[/tex]

Rectangles 3 and 4 (lateral): [tex]2\cdot 14\cdot 5=140[/tex]

Thus the total surface area is equal to

[tex]168+84+72+140=\boxed{\text{D. }464\:\mathrm{ft^2}}[/tex]

Answer:

see below

Step-by-step explanation:   6  5  17  43

Volume of a sphere = 121.5 π mm³   Find r

Vol Sphere = (4π r³) / 3     solve for r

Vol Sphere × 3 = (4π r³)

(Vol Sphere × 3) / 4π = r³

∛((Vol Sphere × 3) / 4π)  = r

∛((121.5 π mm³× 3) / 4π)  = r         the pi terms cancel

∛((121.5  mm³× 3) / 4)  = r

∛((364.5  mm³) / 4)  = r

∛((91.125  mm³) )  = r

       4.5   =  r

Answer:

[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]

Step-by-step explanation:

From the question we are told that:

Diameters has endpoints: [tex](-14. -3, -6) & (-4, 7, 4)[/tex]

Generally the equation for Center of The sphere is mathematically given by

 [tex]C=(\frac{-14+(-4)}{2},\frac{-3+(7)}{2},\frac{-6+(4)}{2})[/tex]

 [tex]C=(9,2,-1)[/tex]

Generally the equation for Radius of the sphere is mathematically given by

 [tex]R=\sqrt{(9-2)^2+(2-9)^2+(-1-2)^2}[/tex]

 [tex]R=\sqrt{107}[/tex]

Therefore the Equation of the Sphere is

 [tex](x-9)^2+(y-2)^2+(z+1)^2=107[/tex]

 [tex](x^2-18x+81)+(y^2-4y+4+(z^2+2z+1))=107[/tex]

 [tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]

Answer:

Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.

Step-by-step explanation:

The perimeter of the sector is equivalent to the length of the rope which is 18 meters

Perimeter of the sector= 2 x radius + length of the arc

But length of arc= radius x central angle in radian

18= 2(3.5)+ 3.5(central angle in radians)

18=7+3.5 (central angle in radians)

18–7=3.5(central angle)

11=3.5(central angle)

central angle =11/3.5=3.14 radians or pi radians

Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees

Therefore the central angle = 180 degrees because pi radians is half of 2pi radians which is half of 360 degrees

Notes: This sector shape is a semicircle because the central angle is 180 degrees

Check: Length of Arc for semicircle =3.5(pi radians)=11 meters

Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.