Look at the three functions below. Which of the functions are equivalent? Two of them? None of them? All of them? Show/explain how you
know!
Function 1: x2-x-2
Function 2: (x + 1)(x - 2)
Function 3: (x -0.5)^2 - 2.25​

Functions with all real numbers as their domain include polynomial functions, sine and cosine functions, and exponential functions. For example, the function f(x)=x², f(x) = sin(x), or f(x) = cos(x) and f(x)=a^x (where a>0).

In Mathematics, the domain of a function is the set of values that can be plugged into the function. There are multiple functions that have a domain of all real numbers, some of them are polynomial functions, sine and cosine functions, and exponential functions.

For example, the function f(x)=x² is a polynomial function where any real number can be inputted for x, hence its domain is set of all real numbers.

Similarly, sine and cosine functions, represented as f(x) = sin(x) or f(x) = cos(x), have a domain of all real numbers, because sine and cosine are periodic and their values repeat over every interval of 2π.

Furthermore, the exponential functions, represented in the form f(x)=a^x (where a>0), have also their domains as the set of all real numbers.

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Answers)

27=6

30=82

33=24

Answer:

-4p³+3p²-17p

Step-by-step explanation:

(-3p³+5p²-2p)+(-p³-8p²-15p)

-3p³+5p²-2p-p³-8p²-15p

-3p³-p³+5p²-8p²-2p-15p

=-4p³+3p²-17p

Answer: The car is 6.6 years old.

Step-by-step explanation:

Hi, to answer this question we have to replace the values in the equation given:

Y = 1/2 (half the value)

A = 1 (total value)

r =10% = 0.10 (decimal form)

Replacing:

y = A(1-r)^t

1/2 = 1 (1-0.10)^t

Solving for t:

(1/2)/1 = 0.9^t

1/2 = 0.9^t

log 1/2 = log 0.9^t

log 1/2 = (t) log 0.9

(log 1/2)/ log 0.9 = t

6.57 =t

6.6 years (rounded)

We have been given that in an assembly line, 56 out of 60 randomly selected parts have no faults. We are asked to predict the number of parts that will have no faults in a similar batch of 12,000 parts.

We will use proportions to solve our given problem.

[tex]\frac{\text{Not faulty parts}}{\text{Total parts}}=\frac{56}{60}[/tex]

[tex]\frac{\text{Not faulty parts}}{12,000}=\frac{56}{60}[/tex]

[tex]\frac{\text{Not faulty parts}}{12,000}\times 12,000=\frac{56}{60}\times 12,000[/tex]

[tex]\text{Not faulty parts}=56\times 200[/tex]

[tex]\text{Not faulty parts}=11,200[/tex]

Therefore, approximately [tex]11,200[/tex] parts will have no faults in a similar batch of 12,000 parts.

Answer:

Around 202.08

Step-by-step explanation:

The formula for the surface area of a pyramid is [tex]a^2 +2a\sqrt{\frac{a^2}{4}+h^2}=9^2+2\cdot 9\sqrt{\frac{9\cdot 9}{4}+5^2}=81+18\sqrt{45.25}\approx 202.08[/tex]. Hope this helps!

Answer:

pooooooo

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Answer:

Option B 15/16

Step-by-step explanation:

calculate the volume of the cone and the volume of the cylinder and then put them in a fraction with the cone over the cylinder, afterwards put that fraction in a calculator and see what you get. once you get the answer input each one of the options into the calculator until one of the fractions gives you the same product as the cone/cylinder fraction.

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Answer: A

Explanation: x is your independent variable and is time, so it is unlikely to have negative amounts of time.

The time will be 2.25 seconds. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given below.

h(x) = – 16x² + 100

Where x is the time in seconds and h(x) is the height at x.

Let the height is y feet.

Then the value of y will be

y = 84 – 65

y = 19 feet

Then the time will be

   19 = – 16x² + 100

16x² = 100 – 19

16x² = 81  

  4x = 9    

    x = 2.25 seconds

Then the correct option is D.

More about the function link is given below.

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Answer

Inequality=100x+275≥775       Answer=5 or more

Step-by-step explanation:

Answer:

area of a sector = 14.13 yards²

Step-by-step explanation:

XYZ is a sector of a circle. The radius YZ is 6 inches .The angle of the sector is given as 45°. The area of the sector can be solved as follows.

area of a sector = ∅/360 × πr²

where

r = radius

∅ = center angle

r = 6 inches

∅ = 45°

area of a sector = 45/360 × 3.14 × 6²

area of a sector = 45/360 × 3.14 × 36

area of a sector = 45/360 × 113.04

area of sector = 1/8 × 113.04

area of a sector = 14.13 yards²

Answer:

14.13

Step-by-step explanation:

i know

Answer: D

Step-by-step explanation:

No two coordinates can have to same input(x) and different outputs(y)

Option A represents y as a function of x because each x-value is associated with only one y-value.

To determine if a set of ordered pairs represents y as a function of x, we need to check if each x-value is associated with a unique y-value. In option B) {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)}, we can see that the x-value 3 is associated with two different y-values, 9 and 16. Therefore, option B) does not represent y as a function of x.

The correct answer is option A) {(0, 0), (-1, 2), (-1, -2), (-2, 4), (-2, -4)}. In this set, each x-value is associated with only one y-value. For example, x = -1 is associated with y = 2 and y = -2. Since no x-value is repeated with different y-values, this set represents y as a function of x.

Option C) {(0, 0), (0, 1), (0, 2), (0, -1), (0, -2)} and option D) {(0, 0), (-1, -0.5), (-2, -1), (-3, -1.5), (-4, -2)} both have repeated x-values with different y-values, so they do not represent y as a function of x.

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Answer:

[tex](p-10)^2[/tex]

Step-by-step explanation:

[tex]p^2-20p+100=\\(p-10)^2[/tex]

Hope this helps!

p − 10 ) 2

Step-by-step explanation:

Answer:

Width: 9 inches

Step-by-step explanation:

1. We can see that the height increased by 6 inches, provided a difference of 15 and 9. If the question states that the frame's dimensions were proportionately enlarged, perhaps the height's enlargment could be benificial

2. If we were to take a ratio where the increased height is over the previous height (height enlargment/prior height) that would be 6/9, or in other words, can be simplified to be 2/3

3. We can see that if the width were to be enlarged, we might be able to determine how much it should be enlarged through a proportionality, provided the frame's dimensions are proportionately enlarged. Now if x ⇒ the width enlargment: 2 / 3 = x / 5.4

4. Through cross multiplication, let us solve for x:

2 * 5.4 = 3 * x,

10.8 = 3 * x,

x = 3.6 inches by which the width should be enlarged

5. If we are to determine the new width of the frame after enlargment, add 5.4 to 3.6 ⇒ the width of the frame ⇒ 9 inches

Answer:

14000/100*105 = 14,700

Step-by-step explanation:

10x−3+3≥2+3

10x≥5

(10x10)/2≥(5/10)

x≥1/2

Answer:

I think the answer is B.

Answer:

b.) [tex]50,48,14[/tex]

Step-by-step explanation:

To find if a set of lengths makes a right triangle, use the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

If a and b squared equal c squared, then the set makes a right triangle. C (the hypotenuse) is the largest number of the set because the hypotenuse is always the largest side in a right triangle.

Use the options:

a.) insert values:

[tex]8^2+14^2=17^2\\64+196=289\\260\neq 289[/tex]

260 does not equal 289, so a is wrong.

b.) insert values:

[tex]14^2+48^2=50^2\\196+2304=2500\\2500=2500[/tex]

2,500 equals 2,500, so b is correct.

Finito.

f(x) = ax + b

(0, -4):

           f(0) = a•0 + b

           f(0) = b      ⇒     b = -4

(12, 0):

           0 = a•12 + b

           0 = 12a - 4

           4 = 12a

           [tex]a=\frac4{12}=\frac13[/tex]

The equation of the green line:

                                                   [tex]\underline{\,y=\frac13x-4\,}[/tex]

or:      [tex]y=\frac13x-4[/tex]

         [tex]-\frac13x+y+4=0\\\\\underline{x-3y-12=0}[/tex]    

Answer:

3

Step-by-step explanation:

5+3=8

8-5=w

Answer:

Step-by-step explanation:

hello :

x²+6x + y²– 12y = 36

completed to suqard :(x²+6x) + (y²– 12y) = 36 means :

(x²+6x+9)-9 + (y²– 12y+36)-36 = 36

(x+3)²+(y-6)² = 9².... standard form when the radius is : 9

The volume is approximately 33.51 [tex]cm^3[/tex], option B.

The question asks us to determine the closest volume to a golf ball with a diameter of approximately 4 centimeters. To find the volume of a sphere (which is the shape of a golf ball), we use the formula:

V = (4/3)π[tex]r^3[/tex],

where r is the radius of the sphere. Since the diameter of the golf ball is given as 4 cm, the radius would be half of that, which is 2 cm. Plugging in the radius into the formula, we have:

[tex]V = (4/3)\pi(2 cm)^3 = (4/3)\pi(8 cm^3) = (32/3)\pi cm^3,[/tex]

Now, we calculate the value using the approximation π = 3.14:

V = (32/3) × 3.14 [tex]cm^3[/tex] = 33.51 [tex]cm^3[/tex] (approximately).

Therefore, the volume that is closest to the actual volume of the golf ball is 33.51 [tex]cm^3[/tex], option B.

Answer:

[tex]t \approx 4.501\,s[/tex]

Step-by-step explanation:

The second-grade equation must be rearragend into its standard form:

[tex]-16\cdot t^{2} + 70\cdot t + 9 = 0[/tex]

Roots can be found with the help of the General Equation for Second-Order Polynomial:

[tex]t = \frac{-70\pm \sqrt{70^{2}-4\cdot (-16)\cdot (9)}}{2\cdot (-16)}[/tex]

[tex]t = 2.188 \pm 2.313[/tex]

[tex]t_{1} \approx 4.501\,s[/tex]

[tex]t_{2} \approx -0.125\,s[/tex]

Only the first root offers a reasonable solution.

[tex]t \approx 4.501\,s[/tex]

Answer: part of the alphabet

Step-by-step explanation: nice

Answer:

[tex]144\pi[/tex]

Step-by-step explanation:

Circumference = [tex]\pi d[/tex]

Diameter = [tex]2r[/tex]

Area of a circle = [tex]\pi r^2[/tex]

From our first equation, we can find our value for our diameter:

We do this by dividing [tex]24 \pi[/tex] by [tex]\pi[/tex] to get 24.

[tex]c=\pi d[/tex]

[tex]d=\frac{c}{\pi } = \frac{24\pi }{\pi } =24[/tex]

Using our second equation, we can find out the value for our radius:

[tex]d=2r[/tex]

[tex]r=\frac{d}{2} =\frac{24}{2} =12[/tex]

Now we have a value for our radius, we can use our third equation to find out our area:

[tex]A=\pi 12 ^2 = 144 \pi[/tex]

Given that:

To Find:

We know that:

Where,

Finding the radius of the circle:

Circumference of a circle = 24π

⟶ 2πR = 24π

⟶ 2πR = 2π × 12

Cancelling 2π.

⟶ R = 12

∴ Radius of the circle = 12 ft.

Finding the area of the circle:

⟶ Area = πR²

⟶ Area = π(12)²

⟶ Area = π × 12 × 12

⟶ Area = π × 144

⟶ Area = 144π

Hence,

Answer: 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).

Step-by-step explanation:

This question is a system of equations. First, we will define our variables:

Let x= number of pints of the first fruit drink (60% pure fruit juice), and then y = the number of pints of the second fruit drink(85% pure fruit juice).

We know that there are 160 total pints of the mixture. Therefore,

x + y = 160 .......... equation i

We are also aware that 70% of those 160 pints will be pure fruit juice, and they will come from either x or y.

For x pints of the first juice, there is

0.6x of pure fruit juice and for y pints of first juice, there is 0.85y of pure fruit juice. Therefore, we will have:

0.6x + 0.85y = 160 × 0.7

0.6x + 0.85y = 112

Multiply through by 100 to remove decimal. This will be:

60x + 85y = 11200 ........... equation ii

Combine both equations

x + y = 160 .......... i

60x + 85y = 11200 ........ ii

Multiply equation i by 60

Multiply equation ii by 1

60x + 60y = 9600 ........ iii

60x + 85y = 11200 ......... iv

Subtract iv from iii

-25y = -1600

y = 1600/25

y = 64

Since x + y = 160

x = 160 - 64

x = 96

Therefore , we will need 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).

Q=rational number=1/6

2/3+q=1/2=1/6

Answer:

The answer is A - a. -6a^2/b  b. 5y^3