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The value of the inverse function f⁻¹(x) at x = 3 is 0.631.

The inverse function is defined as a function obtained by reversing the given function.

The function f(x) = 3ˣ is a one-to-one function, which means it has an inverse function denoted by f⁻¹(x).

To find the value of f⁻¹(x) at x = 3, we need to solve the equation f(x) = 3ˣ = 3 for x.

3ˣ = 3

Divide both sides by 3:

3ˣ/3 = 3/3

Simplify:

3ˣ-1 = 1

Take the natural logarithm of both sides:

ln(3ˣ-1) = ln(1)

Simplify:

ln(3ˣ-1) = 0

Now we can solve for x:

ln(3ˣ-1) = 0

3ˣ-1 = e⁰ = 1

3ˣ = 2

x = log₃(2)

So, f⁻¹(3) = log₃(2) ≈ 0.631.

Therefore, the value of f⁻¹(x) at x = 3 is 0.631.

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Answer:

115 degrees

Step-by-step explanation:

The third angle will measure 115° so option (A) will be correct.

The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Sum of all three internal angles of the triangle = 180°

Sum of two angles + third angle = 180°

Given that,

Two angles of a triangle add up to 65° so

65° + third angle = 180°

Third angle = 180 - 65°

Third angle = 112°

Hence the third angle will be 112° measure.

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Answer: Choice C) 6x+5y = -20

You have the correct answer. Nice work.

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Work Shown:

y = (-6/5)x - 4

5y = 5*( (-6/5)x - 4 )

5y = 5*(-6/5)x - 5*4

5y = -6x - 20

6x+5y = -20

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Explanation:

In the second step, I multiplied both sides by 5 to clear out the denominator. Two steps later (step 4), we have 5*(-6/5)x turn into -6x, so the fraction goes away.

In the last step, I added 6x to both sides to get the equation into standard form Ax+By = C. In this case, A = 6, B = 5, and C = -20.

Answer: 4 miles = 16 min

4 miles : 16 min

Step-by-step explanation:

You have to multiply by the same number

The unit rate that describes Mr. Roble's trip to the store is 0.25 miles per minute.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Mr. Roble is traveling to the store and drives 4 miles in 16 minutes.

∴  The unit rate that describes Mr. Roble's trip to the store is,

= (4/16) miles per minute.

= 1/4 or 0.25 miles per minute.

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Answer:

Its gonna equal itself which is 14n^4

Step-by-step explanation:

14n4

=14*n4

=14*(n*n*n*n)

=14n4

Answer:

5,2

Step-by-step explanation:

Here, we want to find the point that is a solution to the system of inequalities

From what we have, the points that lie in the dark brown patch represent the solution to the system

Hence the coordinates lying in these parts are the solution to the system

An example of such coordinates is the point (5,2)

Step-by-step explanation:

Given

Total spending =$230

The cost of the skirt  is $15

The Cost of the shirt  is $10

Suppose she buys x skirts and y shirts

So, sum of the spending on skirts and shirts must be less than or equal to the $230

[tex]15x+10y\leq230[/tex]

Answer:

Additive inverse: a+(-a)=0

Additive identity: a+0=a

Multiplicative inverse: a•1/a=1

Multiplicative identity: a•1=a

Step-by-step explanation:

Answer:

i think it is a but i am not sure please let me know

Step-by-step explanation:

good luck!

Answer:

Step-by-step explanation:

4. D. 4

5. D. 10a + 10

6. 11 and 71

7.  27.5 and 39.25

Answer:  So  Reina and Sam are multiplying (84)5 (73)9 and their work are (84)5 (73)9 = 84 + 573 + 9 = 89712 Reina's (84)5 (73)9 = 84-573-9 = 820727

So Sam's Actually they are doing or multiplying using exponents. Reina's work (8*)s(7³)º=8*+5+ 73+9= 8° 712 This is incorrect because she added exponents instead of multiplying exponents Sams work (8*)5 (7³)º=84x5 73x9= 820 727 This is correct because Sam multiplied exponents correctly Exponents are multiplied not added.

Step-by-step explanation: Have a blessed  day and hope this helps.

My reasoning is in there. I calculated I hope that is helps a lot. god bless you

Answer:

399.8 feet

Step-by-step explanation:

Since the angle of elevation of the top of the tower from the building is Ф = 37°, and the distance between the tower and the building is x = 275 feet. Let the upper part of the tower be h. These three components from a right-angled triangle with opposite side = h and adjacent side = x. So, by trigonometric ratios,

tanФ = h/x

h = xtanФ

= 275 feet × tan37°

= 275 feet × 0.7536

= 207.23 feet

Also, the angle of depression of the bottom of the tower from the building is Ф' = 35°, and the distance between the tower and the building is x = 275 feet. Let the lower part of the tower be h'. These three components from a right-angled triangle with opposite side = h' and adjacent side = x. So, by trigonometric ratios,

tanФ' = h'/x

h' = xtanФ'

= 275 feet × tan35°

= 275 feet × 0.7002

= 192.56 feet

So, the height of the tower, H = h + h'

= 207.23 feet + 192.56 feet

= 399.79 feet

≅ 399.8 feet

Answer:

k=-2

Step-by-step explanation:

2(6k+8)-6k=4

12k+16-6k=4

6k+16=4

6k=-12

k=-2

Answer:

Step-by-step explanation:

2193.67

10%=219.367

5%=109.6835

1%=21.9367

21.9367 +21.9367 +21.9367 +109.6835 +219.367=394.8606

394.87 rounded to 2dp

Answer:

B

Step-by-step explanation:

Answer:

its B I TOOK TEST

Step-by-step explanation:

Answer:

$64.00

Step-by-step explanation:

64-75%

Answer:

Well -19 is less than -21 so it's the other three.

So it's -30, -100 and -25

Answer:

dhjshsjshshhshsgsgsgsggdd

Answer:

yes

Step-by-step explanation:

yes because the large bottle has 42ml more than the small bottle

Answer:

262.50

i think thats the answer.

Answer:

$162.50

Step-by-step explanation:

75% of 150 is 112.5

112.5 + 150 = 162.5

Answer:

Follow the rule of BODMAS (brackets, of, division, multiplication, addition, subtraction)

Ans: 58

Step-by-step explanation:

42 + 4(6 - 2)                           Process --> 6 - 2 = 4

= 42 + 4 * 4                            Process --> 4 * 4 = 16

= 42 + 16                                Process --> 42 + 16 = 58

= 58

Hope this helps :)

Answer:

it is posible...because tha polynomial have expression than two algebriac

Answer:

219.50

Step-by-step explanation

9.75% can be converted into 0.0975 so multiply  0.0975 by 200 you get 19.5. add 19.5 to 200 and you get 219.50

Answer:

21 and 30

Step-by-step explanation:

x + y = 51

x - y = 9

add the two equations and y's will cancel out

2x = 42  divide by 2

x = 21   so put 21 in for x in the top equation and solve

21 + y = 51

y = 30

Answer:

6x+50 is the answer if u simplify it

Step-by-step explanation:

Answer:

6x+50

Step-by-step explanation:

Distribute the 5 and add

5x+50+x=6x+50