The equation of the line? ​

Answer:

a)  f(5) = 24

b) The inverse of given function

              f⁻¹ ( x ) = √x+1

c)    f⁻¹ ( 8 ) = √9 =3

Step-by-step explanation:

Explanation:-

Given  f(x) = x² - 1

a)

      f(5) = 5² -1 = 25-1 =24

b)      

put y =  f(x) = x² - 1

   ⇒   y =  x² - 1

 ⇒     x² = y + 1

⇒     x = √y+1

⇒ f⁻¹ ( y ) = √y+1      ( ∵ f⁻¹ ( y) =x)

The inverse of given function

              f⁻¹ ( x ) = √x+1

c)   put x=8

             f⁻¹ ( 8 ) = √8+1 = √9 =3

Answer: The answer is -19.5

Step-by-step explanation: This is because 1/2 is .5 in decimal form. A negative PLUS a positive = is negative since the -20 is larger than .5

Answer:

the answer would be -19.5 :)

Step-by-step explanation:

[tex]16 - 3 \times 5 {}^{2} \div 5[/tex]

[tex]16 - 3 \times 5 {}^{2} \div 5 {}^{1} [/tex]

[tex]16 - 3 \times 5 {}^{2} \div 5 {}^{ - 1} [/tex]

[tex]16 - 3 \times 5 {}^{2 - 1} [/tex]

[tex]16 - 3 \times 5 {}^{1} [/tex]

[tex]16 - 3 \times 5[/tex]

[tex]16 - 15[/tex]

[tex]1[/tex]

HopeItHelps you

#CarryOnLearning

Answer:

1/6 of the tomatoes

Step-by-step explanation:

So first, after she uses 5/9 she has 1 - 5/9 = 4/9 of her tomatoes left. Then, she uses 5/8 of that 4/9 to make a salad, so she used 5/8 * 4/9 = 5/18 of her tomatoes overall.  That means that she has 4/9 - 5/18 = 8/18 - 5/18 = 3/18 = 1/6 of her tomatoes saved.

Answer:

2 and 21/32

Step-by-step explanation:

Answer:

Step-by-step explanation:

P represents the original price of the sandwich

1.5 represents the discount

Answer:

im taking a nap

Step-by-step explanation:

9514 1404 393

Answer:

  80.67 fps

Step-by-step explanation:

1 mi/h = 22/15 ft/s

Multiplying this equation by 55, we get ...

  55 mi/h = 1210/15 ft/s = 80 2/3 ft/s ≈ 80.67 ft/s

Answer:

18/3 is 6

-18/3 is -6

-18/(-3) is 6

18/(-3) is -6

Answer:

379.94 square inches, or 379.94 in².

Step-by-step explanation:

The area of a circle is π r². The diameter of the circle is listed as 22 inches, and the radius, or "r", is equal to half of the diameter. So, half of 22 is 11.

Since the formula says r², 11 needs to be squared, or multiplied once by itself.  11 x 11 = 121, so the last part of the equation is to multiply 121 by π. Because pi is an irrational number that never ends, it is commonly accepted to use 3.14, or the first three digits of pi, as the value of pi in an equation.

With that, 121 x 3.14 = 379.94, giving a final answer of 379.94 in².

Let me know if I need to change or clarify anything. I hope this helps! :D

Answer:

19.6ft2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The are similar. That means that one could have its sides measured in miles and the other measured in a few inches. All three angles could be equal, but they are not congruent.

You need at least one properly placed side to make them congruent.

Answer:

don't know

.....................

Answer:

x = 12

Step-by-step explanation:

Consider three orthogonal triangles (see picture)

1. The smallest triangle

2. The medium triangle

3. The big triangle that holds both triangles.

All are orthogonal (or right triangles) so you can use Pythagoras Theorem:

"The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides"

Use Pythagoras theorem on triangle 1.

[tex]a^{2} = 3^{2} + 6^{2} = 45[/tex]

Now user Pythagoras on triangle 2.

[tex]b^{2} = x^{2} + 6^{2} = x^{2} + 36[/tex]

Now use Pythagoras on triangle 3 (the big triangle).

[tex](3 + x )^{2} = a^{2} + b^{2}\\x^{2} + 6x + 9 = a^{2} + b^{2}[/tex]

Now replace the values for [tex]a^{2}[/tex] and [tex]b^{2}[/tex] from the two equations derived from triangle 1 and 2:

[tex]x^{2} + 6x + 9 = 45 + x^{2} + 36[/tex]

The two [tex]x^{2}[/tex] get cancelled out, so:

[tex]6x + 9 = 45 + 36\\x = 12[/tex]

TA DA!

Answer:

$19,000 after five years

Step-by-step explanation:

1900 * .5 = 3800    one year

5 * 3800 = 19,000

Answer:

whats the subject? science?

Step-by-step explanation:

Answer:

3g + 8 = T

Step-by-step explanation:

3g + 8 = T because since Deanna estimates 3 slices for each guest, you would times the # of guests by 3, which is 3g. Then you would add 8 because Deanna will need extra 8 slices for the unexpected guests. This equation would tell you how many slices Deanna needs in total.

Hope this helps :D

Answer:

15%

5%

24%

40%

32%

80%

32%

54%

60%

66%

9%

89%

Step-by-step explanation:

Answer: P(4) - 4/12,1/3,33%,0.33

Step-by-step explanation:

My teacher went over the answers

Solution :

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

This is a valid probability distribution.

In the question it is given that call for a response of Y for short of a sample of people aged between 19 years to 25 years.

Also the event that describes the value of call for response greater than 3 i.e. (Y < 3) is a randomly chosen people between the age 19 to 25 years old who has gone to fitness center or did exercise fewer than 3 days.

Valid probability models add up to 1

The probability is a valid probability model

The probability model is given as:

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

To determine if the model is a valid probability model, or not

We make use of:

[tex]\mathbf{\sum P(x) = 1}[/tex]

So, we have:

[tex]\mathbf{0.68 + 0.05 + 0.07 + 0.08 + 0.05 + 0.04 + 0.01 + 0.02 = 1}[/tex]

Add the probabilities

[tex]\mathbf{ 1= 1}[/tex]

The above equations shows that:[tex]\mathbf{\sum P(x) = 1}[/tex]

Hence, the probability is a valid probability model

Read more about probability models at:

https://brainly.com/question/9965602

Answer:

(-2,0) and (1,0)

Hope this helps!

Answer:

either 2/3

or 3/2

but its probably 2/3

thanks for the easy points!

Step-by-step explanation:

Answer:

Proved all parts below.

Step-by-step explanation:

As given ,

|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]

To prove- a) For any real number x , | x | ≥ 0 . Moreover, | x | = 0 ⇒ x = 0

                 b) For any two real numbers x and y , | x | ⋅ | y | = | x y | .

                 c) For any two real numbers x and y , | x + y | ≤ | x | + | y | .

Proof -

a)

As given x is a real number

Also , by definition of absolute value of x , we get

| x | ≥ 0

Now,

if |x| = 0

⇒ x = 0 and -x = 0

⇒ x = 0 and x = 0

⇒ x = 0

∴ we get

| x | = 0 ⇒  x = 0

Hence proved.

b)

To prove - | x | ⋅ | y | = | x y |

As we have,

|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]

|y| = [tex]\left \{ {{y , y\geq 0} \atop {-y, y< 0}} \right.[/tex]

|xy| = [tex]\left \{ {{xy , x,y > 0 and x,y < 0} \atop {-xy, x > 0, y< 0 and x <0 , y > 0}} \right.[/tex]

We have 4 cases : i)  when x > 0 , y > 0

                              ii) when x > 0 , y < 0

                              iii) when x < 0, y > 0

                              iv) when x < 0, y < 0

For Case I - when x > 0 , y > 0

⇒ |x| = x, |y| = y

⇒|x|.|y| = xy

For Case Ii - when x > 0 , y < 0

⇒ |x| = x, |y| = -y

⇒|x|.|y| = -xy

For Case Iii - when x < 0 , y > 0

⇒ |x| = -x, |y| = y

⇒|x|.|y| = -xy

For Case IV - when x < 0 , y < 0

⇒ |x| = -x, |y| = -y

⇒|x|.|y| = (-x)(-y) = xy

∴ we get , from all 4 cases

| x | ⋅ | y | = | x y |

Hence Proved.

c)

To prove - | x + y | ≤ | x | + | y |

Let

|x| = |x + y - y|

    ≥ |x + y| - |y|     ( Triangle inequality)

⇒ |x| + |y| ≥ |x + y|

Hence Proved.

Answer:

the slope is 4,3 and the y intercept is 2

Answer:

Niiger

Step-by-step explanation:

The area of figure will be;

⇒ 105.56 km²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The figure is shown.

Now,

The area of figure is find as;

Total area = (12 × 7) + (π × 4² / 4) + (3 × 3)

               = 84 + 3.14 × 4 + 9

               = 93 + 12.56

               = 105.56 km²

Thus, The area of figure will be;

⇒ 105.56 km²

Learn more about the area visit:

https://brainly.com/question/11564229

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Answer:

20:60 12:36 2:6

Step-by-step explanation:

The second number is going to be 3 times as big as the first ine

What was the answer

Answer:D

Step-by-step explanation:

Answer:

[tex]\frac{x-5}{x+1}[/tex], [tex]x\neq -1, x\neq -9[/tex]

Step-by-step explanation:

x^2 + 4x - 45

= (x+9)(x-5)

x^2 + 10x + 9

= (x+9)(x+1)

So the fraction goes to

[tex]\frac{(x+9)(x-5)}{(x+9)(x+1)}[/tex] which is [tex]\frac{x-5}{x+1}[/tex].

Since the denominator cannot be 0, x^2 + 10x + 9 cannot be equal to 0. Therefore x cannot be -1 or -9.

Answer:

4.16x+6y=1

Step-by-step explanation:

The given equation of the line is:

      8x + 3y  = 1

From this line, we need to re-arrange and write in the form of the equation of  a straight line.

        The equation of a straight line is given as:

         y  = mx + c

  8x + 3y  = 1

         3y = -8x + 1

          y  = [tex]\frac{-8x}{3}[/tex]  + [tex]\frac{1}{3}[/tex]  

 The slope of the line is [tex]\frac{-8}{3}[/tex]

  Any line from the given choices that will be parallel to the is must have the same slope as it is.

That line is 16x + 6y  = 1

                         6y  = -16x + 1

                            y = [tex]\frac{-16x}{6}[/tex]  + [tex]\frac{1}{6}[/tex]  

                           y = [tex]\frac{-8x}{3}[/tex]  +  [tex]\frac{1}{6}[/tex]  

9/3. 5/14 hope that's the right awnser

0.36.  i just had this question and got it right. :)