What function is the inverse of the exponential function y = 3^x?

Given:

The polynomial function is

[tex]q(x)=6x^3+19x^2-15x-28[/tex]

Yuri thinks that [tex]\dfrac{3}{4}[/tex] is a root of the given function.

To find:

Why [tex]\dfrac{3}{4}[/tex] cannot be a root?

Solution:

We have,

[tex]q(x)=6x^3+19x^2-15x-28[/tex]

If [tex]\dfrac{3}{4}[/tex] is a root, then the value of the function at [tex]\dfrac{3}{4}[/tex] is 0.

Putting [tex]x=\dfrac{3}{4}[/tex] in the given function, we get

[tex]q(\dfrac{3}{4})=6(\dfrac{3}{4})^3+19(\dfrac{3}{4})^2-15(\dfrac{3}{4})-28[/tex]

[tex]q(\dfrac{3}{4})=6(\dfrac{27}{64})+19(\dfrac{9}{16})-\dfrac{45}{4}-28[/tex]

[tex]q(\dfrac{3}{4})=3(\dfrac{27}{32})+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]

[tex]q(\dfrac{3}{4})=\dfrac{81}{32}+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]

Taking LCM, we get

[tex]q(\dfrac{3}{4})=\dfrac{81+342-360-896}{32}[/tex]

[tex]q(\dfrac{3}{4})=\dfrac{-833}{32}\neq 0[/tex]

Since the value of the function at [tex]\dfrac{3}{4}[/tex] is not equal to 0, therefore, [tex]\dfrac{3}{4}[/tex] is not a root of the given function.

Answer:

Sensitivity = 66.7%  (C)

specificity= 98.0%  (E)

positive predictive value = 80.0%  (F)

Negative predictive value = 96.0%  (D)

accuracy of the test  = 94.5%  (A)

Step-by-step explanation:

Given the data in the question;

                                    Disease Present              Disease Absent        Total

Test Positive                      24                                        6                        30

Test Negative                    12                                       288                     300

Total                                   36                                       294                    330

so A = 24, B = 6, C = 12 and D = 288

sensitivity = [A/(A+C)]×100 = [24/(24+12)]×100 = [24/36]×100

Sensitivity = 66.7%  (C)

specificity= [D/(D+B)]×100 = [288/(288+6)]×100 = [288/294]×100

specificity= 98.0%  (E)

positive predictive value = [A/(A+B)]×100 = [24/(24+6)]×100

= [24/30]×100

positive predictive value = 80.0%  (F)

Negative predictive value = [D/(D+C)]×100 = [288/(288+12)]×100

= [288/300]×100

Negative predictive value = 96.0%  (D)

accuracy of the test = [A+D/(A+B+C+D)]×100 = [24+288/(24+6+12+288)]×100

= [312/330]×100

accuracy of the test  = 94.5%  (A)

Nothing 33.3% (B)

=====================================================

Work Shown:

Applying the tangent-secant theorem will allow us to solve for x

x*(x+5) = (x+2)^2

x^2+5x = (x+2)*(x+2)

x^2+5x = x^2+4x+4

5x = 4x + 4 ..... subtracting x^2 from both sides; terms cancel

5x-4x = 4

x = 4

------------------

Check:

Plug in x = 4

x*(x+5) = (x+2)^2

4*(4+5) = (4+2)^2

4*(9) = (6)^2

36 = 36

The answer is confirmed.

Answer:

I need answer too

Pleaseee help us

Answer:B

Step-by-step explanation:m is the slope and m=-3

Answer: Y=2/3x+4

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

Answer : -302.6

Step-by-step explanation:

Answer:

K = 15

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine x = 1/4

Cos² x = K / 16

K =?

Next, we shall determine the 3rd leg (i.e the adjacent) of the right angle triangle. This can be obtained as follow:

Sine x = 1/4

Sine x = Opposite / Hypothenus

Opposite = 1

Hypothenus = 4

Adjacent =?

Hypo² = Opp² + Adj²

4² = 1² + Adj²

16 = 1 + Adj²

Collect like terms

16 – 1 = Adj²

15 = Adj²

Take the square root of both side.

Adj = √15

Next, we shall determine Cos² x.

Adjacent = √15

Hypothenus = 4

Cos² x =?

Cos x = Adjacent / Hypothenus

Cos x = √15 /4

Square both side

Cos² x = (√15 /4)²

Cos² x = 15 / 16

Finally, we shall determine the value of K. This can be obtained as follow:

Cos² x = K / 16

Cos² x = 15 / 16

K / 16 = 15 / 16

K = 15

Answer:

6j(5k+3)

Step-by-step explanation:

18j+30jk

Factor out 6.

6(3j+5jk)

Consider 3j+5jk. Factor out j.

j(3+5k)

Rewrite the complete factored expression.

6j(5k+3)

Answer:

The answer is A, good luck on the test! :D

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. In geometry, a cylinder is a three-dimensional shape with a circular base, ... So using the volume of cylinder formula we can find the volume of i

Answer:

[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]

Step-by-step explanation:

Given

[tex]t= thickness[/tex]

[tex]h =height[/tex]

From the first statement, we have that:

[tex]t\ mm \ge 0.1 * h\ cm[/tex]

Convert mm to cm

[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]

[tex]t\ *0.1 \ge 0.1 * h[/tex]

Divide both sides by 0.1

[tex]t \ge h[/tex]

From the second statement, we have that:

[tex]Cost \le 12.2[/tex]

Substitute 0.2 + t + 0.5h for Cost

[tex]0.2 + t + 0.5h \le 12.2[/tex]

Collect Like Terms:

[tex]t + 0.5h \le 12.2-0.2[/tex]

[tex]t + 0.5h \le 12.0[/tex]

So, the inequalities are:

[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]

Answer: it's a, the answer

Step-by-step explanation:

Answer: 414

Step-by-step explanation: 414 is a palindrome that is divisible by 18 because it’s an even number and that it’s one less than 415 which is a multiple of 5.

Kayla's number is 414 and this can be determined by using the given data and also by using the arithmetic operations.

Given :

The following steps can be used in order to determine Kayla’s number:

Step 1 - Remember palindrome means 'reads the same left-to-right as it does right-to-left'.

Step 2 - The digit should be between 0 to 9 and according to the given data, the number is one than a multiple of 5 that is, the first and last digit must be 4 or 9.

Step 3 - So, the number which is divisible by 18 is 414.

For more information, refer to the link given below:

https://brainly.com/question/25277954

Answer:

(5, 5.25) , (10, 6.50) , (20, 9)

Step-by-step explanation:

As given ,

y = 0.25x + 4

Now,

if x = 5

⇒ y = 0.25(5) + 4

      = 1.25 + 4

     = 5.25

⇒ y = 5.25

∴ the ordered pair be (x, y) = (5, 5.25)

if x = 10

⇒ y = 0.25(10) + 4

      = 2.5 + 4

     = 6.50

⇒ y = 6.50

∴ the ordered pair be (x, y) = (10, 6.50)

if x = 20

⇒ y = 0.25(20) + 4

      = 5 + 4

     = 9

⇒ y = 9

∴ the ordered pair be (x, y) = (20, 9)

Answer:

48 square in.

Step-by-step explanation:

so first off you do 4x6 and you get 24 now you want t do 24x2 and get 48

Answer:

Step-by-step explanation:

9 : 16 :: M : 32

Means of extremes = means of means

= 9 x 32 = 16 x M

= 288 = 16M

288/16 = M

18 = M

Answer:

273

Step-by-step explanation:

63 ÷ 30% = 210

210 + 63 = 273

therefore your total is 273

hope this is right, and that it helps :)

Answer:

Becky and her brother made 90+63=153 masks in total

Step-by-step explanation:

Percentages

Let's call x=number of masks Becky's brother made.

We know Becky made 30% less than the number of masks her brother made.

30% of x is calculated by:

30*x/100 = 0.3x

Now subtracting from x:

x - 0.3x = 0.7x

Becky made 63 carnival masks, this means that:

0.7x = 63

Dividing by 0.7:

x = 63/0.7 = 90

Becky's brother made 90 masks.

Becky and her brother made 90+63=153 masks in total

Answer:

this question is not complete. need another equation

Step-by-step explanation:

give another equation then I can solve

[tex] \frac{3}{8} x = \frac{17}{24} - \frac{1}{3} y \\ x = \frac{17}{9} - \frac{8}{9} y[/tex]

Answer:

7 centimeters

Step-by-step explanation:

Standard size of a coffee cup is 7 centimeters

7 meters is too big

7 kilometers  is bigger than 7 meter

7 millimeters is too small

Answer:

Aug 16th

Step-by-step explanation:

Answer:

oof

Step-by-step explanation:

Question- What method would you happen to be using to solve this problem?

Answer:

Triangle

Step-by-step explanation:

Option D. triangle

Answer:

Add maybe

Step-by-step explanation:

add the 500+400+200 try that hope it helps have a great day

Answer:

Step-by-step explanation:

S, S, E.

Come on, do I have to spell it out for you?  :)

First let's review how to expand this!

(ax+b)^2=a^2*x^2+2abx+a^2

In this case

(2x^2+1/2)^2=2^2*x^2+2*1/2*2x+(1/2)^2

=4x^2+2x+1/4

Done!

Answer:

150 ft^2

Step-by-step explanation:

The formula is (30*10)/2 which is equal to 150.