What is In(3x)=2 ? Pre-Calc/Calc

Answers

Answer 1

The final value of the equation is x=e²/3

A natural log is a logarithm with the base "e." It is represented by the symbol "ln." In other words, loge = ln. In other words, the natural logarithm lacks a base. When "ln" is recognized automatically, "e" is assumed to be its base. The same set of logarithmic rules applies to all logarithms, including the natural logarithm. As a result, the following are the key natural log rules (also known as ln rules):

ln (mn) = ln m + ln nln (m/n) = ln m - ln nln mn = n ln mln a = (log a) / (log e)ln e = 1ln 1 = 0log∨b m = x ⇒ m = b∧xlog∨e(3x)=23x=e²x=e²/3

Therefore the final answer for the given question is x=e²/3

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Related Questions

How do division properties help you evaluate expressions?

Drag a word or number to the box to correctly complete the statement.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the Response area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the

Answers

The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

How to explain the information?

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

Step-by-step explanation:

f(x)=2x^2-6
Find f(7)

Answers

Answer:

f(7) = 92

Step-by-step explanation:

f(7) means what is the value of f(x) when x = 7

substitute x = 7 into f(x)

f(7) = 2(7)² - 6 = 2(49) - 6 = 98 - 6 = 92

y
X
-9
-6
3
9
x - 1
x
3
у

Answers

Answer:

see explanation

Step-by-step explanation:

-9x = -3y

-6x = 2  1/5y

3x = 0y

9x = 2y

Is 5,707,460 divisible by 10?

Answers

Answer:

Yes

Step-by-step explanation:

Every number is divisible by 10, in this case you just need to tale of the zero at the end. 570,746 is the answer.

an angle measures 101.4 less then the measure of supplementary angles. what is the measure of each angle

Answers

Answer:

39.3°, 140.7°

Step-by-step explanation:

supplementary angles means that together they have 180°.

so, when we have 2 angles, x and y.

x + y = 180

x = y - 101.4

using the second equation in the first

y - 101.4 + y = 180

2y - 101.4 = 180

2y = 281.4

y = 281.4/2 = 140.7°

x = y - 101.4 = 140.7 - 101.4 = 39.3°

so, the starting angle is 39.3°, and every supplementary angle is then 140.7°.

Assume the statements below are true. If exactly two of the students went to the movies, who did NOT go to the movies?
If Catherine goes to the movies, then Jessika will go.
If Jessika goes to the movies, then Jorge will go.
If Jorge goes to the movies, then Mike will go.

Answers

Answer:Jorge and  Mike

Step-by-step explanation:

Nobody goes if Mike goes

I need to find the error in the equation

Answers

Answer:

20 - i

Step-by-step explanation:

Addition of complex numbers:

In complex number addition/subtraction, add the imaginary part and add the real part separately.

The error is while adding imaginary part, you have to combine the coefficients of the imaginary numbers. So, -3 +2 will give us -1. So, the result is -i.

16  - 3i + 4+  2i = 16 + 4  -3i + 2i

                         = 20 - i

Answer:

20 - i

Step-by-step explanation:

The error made during second step:

When adding or subtracting expression, we add or subtract like terms.

(16 - 3i) + (4 + 2i) get rid of parenthesis

16 - 3i + 4 + 2i add/subtract like terms

20 - i (the mistake is made here, instead of "i" they typed i^2)

Which of the following Statements are true?

Statement 1: A right triangle can be an equilateral triangle.

Statement 2: An equilateral triangle can be a right triangle.

Answers

Step-by-step explanation:

both statements are wrong.

a right (or right-angled) triangle has a 90° angle. that is all.

an equilateral triangle has 3 equally long sides.

but that also implies that the 3 angles must be equal too.

the sum of all angles in a triangle must be 180°.

if all angles are equally large, that means

180 = 3×angle

angle = 180/3 = 60°.

that means none of the angles can be 90°, so, no right-angled triangle can be equilateral.

and no equilateral triangle can be right-angled.

By eating one egg one cupcake and one slice of pizza a child consumes 303 mg of cholesterol. if the child eats three cupcakes in four slices of pizza he or she takes in 93 mg of cholesterol. by eating two eggs in 1 cup cake a child consumes 569 mg of cholesterol. how much cholesterol is in each item?

Answers

The amount of cholesterol that is in each is given as  c = 19, E = 275 and P = 9

How to solve for the cholesterol

We have to define the variables as:

E + C + P = 303

3C + 4P = 93,

we have to make pizza, P the subject

4P = 93 - 3C,

P = (93 - 3C) / 4

2E + C = 569,

2E = 569 - C

E = (567-C) / 2

We have to form the equation

(569-C)/2 + C + (93-3C)/4 = 303

We have to multiply the equation by 4

(569-C)2 + 4C + 93-3C = 1212

1138 - 2c + 4c + 93 - 3c = 1212

-C = 1212- 93 -1138

-c = -19

hence c = 19 mg for 1 cupcake

E = (569- 19)/2

275 for 1 egg

P =  (93-3C)/4

P = 93 - 57 / 4

= 36 / 4

= 9 for one pizza

Hence we would have c = 19, E = 275 and P = 9

19 + 275 + 9 = 303 (proves it to be correct)

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19+274 + 7 = 300 mg

14x^2-9x+11-8x^2+8x^6


Combine like terms

Answers

Answer:

8x^6 + 6x^2 - 9x + 11

Step-by-step explanation:

Well, I combined like terms.

There's only two terms you can combine here anyhow; those being 14x^2 and -8x^2.

The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.

Answers

The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

When time equals 0, why is the height of the cannonball not equal to 0?

From the graph, we have the y-intercept to be

y-intercept = (0, y), where y > 0

This means that the graph starts above the origin

This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)

Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground

Describe the domain and the range of this function

In this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height

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What is the answer for this question 2 (6² +2²)÷4-10 ​

Answers

Step-by-step explanation:

2 . (6² + 2²) ÷ 4 - 10

= 2 . (36 + 4) ÷ 4 - 10

= 2 . 40 ÷ 4 - 10

= 80 ÷ 4 - 10

= 20 - 10

= 10

Find the LCM and
GCF of: 25 and 100

Answers

Answer:

Look below

Step-by-step explanation:

The LCM of 25 and 100 is 100

The GCF of 25 and 100 are 25.

The LCM of 25 and 100 is 100.

find the prime factorization of 25:
25= 5x5

find the prime factorization of 100:
100= 2x2x5x5

Multiply each factor the greater number of time it occurs in steps above to find the LCM:

2x2x5x5

LCM= 100

You are installing 250 feet of PVC conduit. Each​ 100-foot section takes 1/2 can of PVC​ cement, and each​ 50-ft section takes 1/4 can. How much cement do you​ need? Your answer should be in the form of a mixed​ number, with any remaining fraction in its lowest terms.

Answers

While installing 250 feet of PVC conduit given the details we have in the question, The amount of cement needed is 1 1/4  can of PVC cement

How to find quantity of cement needed

Given data

PVC conduit required to be installed =  250 feet

Each 100-foot section takes 1/2 can of PVC cement

Each 50-ft section takes 1/4 can of PVC cement

250 feet will be split into two which is 200 feet and 50 feet. We solve for each separately then add up

solving for 200 feet

200 feet contains how many 100-foot, this is solved as follows:

= 200 / 100

= 2

And each 100-foot takes 1/2 can of PVC cement, therefore:

2 * 1/2 = 1

solving for 50 feet

50 feet takes 1/4 can of PVC cement

= 1/4

The sum: 1 + 1/4 = 1 1/4 ( mix number )

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18:5=5/18 true or false

Answers

i responded to this already but it it is FALSE

Answer: False

Step-by-step explanation: Ratio is A:B = A/B

(05.01)Which statement best describes the area of the triangle shown below?
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.

Answers

A statement that best describes the area of the triangle is It is one-half the area of a square of side length 4 units.

What is the area of the triangle?

The area of a triangle can be found by the formula:
= 1/2 x base x height

The base is 4 units and the height if 4 units.

Area of the triangle is:

= 1/2 x 4 x 4

= 8 units²

The area of a square of side length 4 units. is:

= 4 x 4

= 16 units²

In conclusion, option B is correct.

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In Earnest's yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
A.It rained 2 inches on Tuesday. Then, it rained 2 inches on Wednesday.
B.It snowed 4 inches last week. Then, 8 inches of snow melted during this week.
C.I put 5 pounds of birdseed in the feeder. Then, birds ate 5 pounds of birdseed.
D.A farmer sold 3 bushels of apples last week. Then, she sold 6 bushels of apples this week.
E.3 feet of growth was cut from a tree branch last year. Then, the tree branch grew 3 feet this year.
F.My family painted a 300 square foot barn on Saturday. Then on Sunday, we painted a 300 square foot garage.

Answers

Answer: C

Explanation:
C is the only answer that gives answer of 0.
+5lbs then -5lbs = 0lbs

All others don’t give same amount.
Option E is a trick,
-3 puts at 0 growth then add 3feet

Based on the graph, estimate (to one decimal place) the average rate of change f

Answers

The estimate (to one decimal place) of the average rate of change f is 1.7

How to estimate (to one decimal place) the average rate of change f?

The interval is given as

x = 1 to x = 4

This can be represented as

(a, b) = (1, 4)

From the attached graph, we have

f(1) = 2

f(4) = 7

The estimate (to one decimal place) of the average rate of change f is

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(4) - f(1)]/[4 - 1]

So, we have

Rate = [7 - 2]/[4 - 1]

Evaluate

Rate = 1.7

Hence, the estimate (to one decimal place) of the average rate of change f is 1.7

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A ship’s sonar detects a submarine 440 feet below a point on the ocean’s surface 600 ft dead ahead of the ship. To the nearest degree, find the angle x. hurryy!!!

Answers

The angle x to the nearest degree is 40°

Given,

The depth of submarine that a ship's sonar detects = 440 feet

The distance from submarine to ship in oceans surface = 600 feet

We have to find the angle x.

The figure is given below:

Here, we have to use the tangents definition:

That is,

tan θ = opposite side / adjacent side

Here,

tan x = 440 / 600

We want to find x,

So,

x = tan⁻¹ (440 / 600)

x = tan⁻¹ (0.73333)

x = 40.28°

By taking nearest angle, we get x as 40°

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Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks,

bonds, and CDs. CDs pay 3.75 % interest, bonds pay 4.8 % interest, and stocks pay 7.2 % interest.

Maricopa Success invests $ 45000 more in bonds than in CDs. If the annual income from the

investments is $ 6322.5, how much was invested in each account?


stock=
bonds=
cds=

Answers

The value invested in each security will be:

stock= $38000 ,

bonds= $46000

cds= $3000

How to calculate the value?

Let the money invested in stocks be 'x', bonds be 'y' and CDs be 'z'.

Total money received as fund = x+y+z = $115000 -(Eqn 1)

$15000 more is invesed in bonds as compared to CDs i.e y = z + $15000 - (Eqn2)

Stocks pay 6.8%, bonds pay 3.6% and CDs pay 4% interest

Interest earned from stocks = 6.8% of x = 0.068x

Interest earned from bonds = 3.6% of x = 0.036x

Interest earned from CDs = 4% of x = 0.04x

Total interest earned = 0.068x + 0.036y + 0.04z = $5840 - (Eqn 3)

x + y + z =$115000 ----(1)

y = z + $15000 -----(2)

0.068x + 0.036y + 0.04z = $5840 ------(3)

Putting y = z+$15000 in Eqn 1 gives us:

x + (z+$15000) + z = $115000 ==> x = $100000 - 2z ----(Eqn 4)

Similarly,

Putting y = z+$15000 in Eqn 3 gives us:

0.068x + 0.036(z+$15000) + 0.04z = $5480 ==> 0.068x + 0.076z = $4940 ----(Eqn 5)

Putting Eqn 4 in Eqn 5,

0.068($100000 - 2z) + 0.076z = $4940

Hence, 0.06z = $1860

z = $31000

Put z = $31000 in Eqn 4 and get x = $100000 - 2z = $38000

Put z = $31000 in Eqn 2 and get y = z + $15000 = $46000

Hence final answer: x = $38000 , y = $46000, z = $31000

where x is the money invested in stocks, y in bonds and z in CDs.

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For the function f(x) = (2e)5, find
ƒ−¹(x).

Answers

Answer:

no

Step-by-step explanation:

89382

Geometry please answer quickly I will give brainliest

Answers

Answer:

20 +2x+1=7, hope this is the answer

simply the following
2(2x+2y)-14x+7

Answers

Answer:

4 y + -10 x + 7

Step-by-step explanation:

Simplify the following:

2 (2 x + 2 y) - 14 x + 7

2 (2 y + 2 x) = 4 y + 4 x:

(4 y + 4 x) - 14 x + 7

Grouping like terms, 4 y + 4 x - 14 x + 7 = 4 y + (4 x - 14 x) + 7:

4 y + (4 x - 14 x) + 7

4 x - 14 x = -10 x:

Answer: 4 y + -10 x + 7

construct a triangle ABC with line AB= 10cm BC=6cm and AC=11cm. Hence measure the values of the angle

Answers

Hence , the construction of the triangle is given below.

 AB = 10 cm           BC = 6 cm           AC = 11 cm

We have to find ∠A, ∠B, and ∠C.

To construct a triangle,

Firstly draw a line segment AB = 10 cm

From A we need a point C at a distance of 6 cm. So with A as the center, draw an arc of 6cm in length from point A.

From B we need a point C at a distance of 11 cm. So with B as the center, draw an arc of 11cm in length from point B.

Mark the point of intersection of the arcs as C.

Meet points C to A and B respectively.

By using a protractor measure the angles of A, B, and C.

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Find an equation for the line graphed below:

Answers

Answer: y = -1/5x -3

Step-by-step explanation:

Answer:

Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct

I am simply providing an explanation in case you need it

Step-by-step explanation:

The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b

where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis

Given two points (x₁, y₁) and (x₂, y₂)  on the straight line, we can compute the slope as follows

m = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]

Two distinct points on the line are at (0, -3) and (5,-4)

[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]

So we know the equation to be

[tex]y = - \frac{1}{5}x + b[/tex]

To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b

However, looking at the graph we see that the line crosses the y axis at

y = -3. So this is the value for the y intercept i.e. b

The equation of the line is therefore

[tex]y = - \frac{1}{5}x - 3[/tex]

g(x)=−5x+1, find g(1)

Answers

Answer:

-4

Step-by-step explanation:

keep value of x as 1 in 5x+1

g(1)=-5×1+1

=-4

Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.

Answers

The time it would take from when you threw the ball until it lands on the ground below is equal to 2.16 seconds.

Given the following data:

Height of building =  (42.0+A) m =  (42.0+9) m = 51 m.

Initial speed of ball = (14.5+B) m/s = (14.5+8) m/s = 22.5 m/s.

Scientific data:

Acceleration due to gravity = 9.8 m/s²

How to determine the time?

Generally speaking, when this ball is thrown straight up at a certain speed, it begins to slow down as a result of the effect of downward gravitational acceleration. Consequently, the ball reaches a maximum height where it can't go higher anymore and then starts to fall down due to gravity.

In order to determine the time it would take from when you threw the ball until it lands on the ground below, we would apply the second equation of motion:

S = ut + ½gt²

½gt² + ut - S = 0

Substituting the given parameters into the formula, we have;

0.5(9.8)t + 22.5t - 51 = 0.

4.9t + 22.5t - 51 = 0.

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]t = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-22.5\; \pm \;\sqrt{22.5^2 - 4(0.5)(-51)}}{2 \times 0.5}\\\\t = \frac{-22.5\; \pm \;\sqrt{506.25 + 102}}{2}\\\\t = \frac{-22.5\; \pm \;\sqrt{608.25}}{2}[/tex]

t = 2.16 or -47.16

Since the time cannot be negative, the value of t to three significant figures is equal to 2.16 seconds.

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Complete Question:

Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from when you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.

A=9, B=8

SLOVE FOR X , really need help it’s due tmrw thanks

Answers

Answer:

3.5

Step-by-step explanation:

21x+6

21/21    6/21

x=3.5

The functions fand g are defined as follows.
g(x)=2x³ +6
f(x)=-4x-1
Find f(7) and g (-3).
Simplify your answers as much as possible.

f(7)=

g(-3)=

Answers

f ( x ) = - 4x - 1
f ( 7 ) = - 4 ( 7 ) - 1
= -28 - 1
= - 29
g ( x ) = 2x^3 + 6
g ( -3 ) = 2 (-3)^3 + 6
= 2 ( -27 ) + 6
= - 54 + 6
= - 48

(PLEASE ANSWER A, B, AND C)
Give each probability as a simplified fraction, decimal, and percent.
If the spinner below is spun once, find each probability.
A. P (4)
B. P (a number less than 10)
C. P (a prime number)

Answers

The probability of P(4) is 1/8. 12.5%, 0.125.

The probability of a number less than 10 is 8/8. 1 , 100%

The probability of a prime number is 1/2. 0.5. 50%.

What is the probability?

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

Probability of spinning 4 = number of possible outcomes / number of sections

1/8 = 0.125 = 12.5%

Probability of spinning a number less than 8 = possible outcomes / total sections

8/8 = 1 = 100%

Probability of spinning a prime number = number of possible outcomes / total sections

Prime numbers between 1 and 8 = : 2, 3, 5, 7

4/8 = 0.5 = 50%

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