Solve the equation algebraically.

2lnx + 7 = ln(4x) + 10

Round your final answers to two decimal places.

Answers

Answer 1

Answer:

x = 80.34 (2 dp)

Step-by-step explanation:

[tex]2\ln(x)+7=\ln(4x)+10[/tex]

[tex]\implies \ln(x^2)+7=\ln(4x)+10[/tex]

[tex]\implies \ln(x^2)-\ln(4x)=10-7[/tex]

[tex]\implies \ln\left(\dfrac{x^2}{4x}\right)=3[/tex]

[tex]\implies \ln\left(\dfrac{x}{4}\right)=3[/tex]

[tex]\implies e^{\ln\left(\dfrac{x}{4}\right)}=e^3[/tex]

[tex]\implies \dfrac{x}{4}=e^3[/tex]

[tex]\implies x=4e^3[/tex]

[tex]\implies x=80.34 \textsf{ (2 dp)}[/tex]


Related Questions

What time does the first train get to oakengates

Answers

Answer:

a) 0815

b) 22 minutes

Hope this helps!

Look at the image. (calculus)

Answers

Answer: Choice H)  2

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

Explanation:

Recall that the pythagorean trig identity is [tex]\sin^2 x + \cos^2x = 1[/tex]

If we were to isolate sine, then,

[tex]\sin^2 x + \cos^2x = 1\\\\\sin^2 x = 1-\cos^2x\\\\\sin x = \sqrt{1-\cos^2x}\\\\[/tex]

We don't have to worry about the plus minus because sine is positive when 0 < x < pi/2.

Through similar calculations, [tex]\cos x = \sqrt{1-\sin^2x}\\\\[/tex]

Cosine is also positive in this quadrant.

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

So,

[tex]\frac{\sqrt{1-\cos^2x}}{\sin x}+\frac{\sqrt{1-\sin^2x}}{\cos x}\\\\\frac{\sin x}{\sin x}+\frac{\cos x}{\cos x}\\\\1+1\\\\2[/tex]

Therefore,

[tex]\frac{\sqrt{1-\cos^2x}}{\sin x}+\frac{\sqrt{1-\sin^2x}}{\cos x}=2[/tex]

is an identity as long as 0 < x < pi/2

Answer:

2

Step-by-step explanation:

[tex]=\frac{\sqrt{1-cos^{2}x }}{sinx} +\frac{\sqrt{1-sin^{2}x } }{cosx} \\\\When \:0 < x < \frac{\pi }{2} \\\\=\frac{\sqrt{sin^{2}x } }{sinx} +\frac{\sqrt{cos^{2}x } }{cosx} \\\\=\frac{sinx}{sinx} +\frac{cosx}{cosx} \\\\=1+1\\\\=2[/tex]

Here we use the formula sin²x=1-cos²x and cos²x=1-sin²x.

En la misma papelería, a Julián le cobraron $40 por 4 lápices y 8 plumas, mientras que a Estefanía le cobraron $25 por 6 lápices y 2 plumas. ¿Cuántos pesos costó cada pluma?

Answers

The cost of a pen is $3.5 while the cost of a pencil is $7

Simultaneous equation

Let the price of pen  be x

Let the price of pencil be y

If Julian was charged $40 for 4 pencils and 8 pens, then;

4y + 8x = 40

y + 2x = 10

y = 10 - 2x .............. 1

Similarly, if Estefania was charged $25 for 6 pencils and 2 pens, then;

6y + 2x = 25

Substitute 1 into 2 to have:

6(10-2x)+ 2x = 25

60 - 12x + 2x = 25

60-10x = 25

10x = 35

x = 3.5

Since y = 10 - 2x

y = 10 - 7

y = 3

Hence the cost of a pen is $3.5 while the cost of a pencil is $7

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What is the value of 2y + 3 when y +4 ?

Answers

Answer:

substitute y = 4 into the expression⇒(2×4)+3=8+3=11

Step-by-step explanation:

please help me please

Answers

Answer:

g(x) has the greater value when x = 2, g(2) is 7 greater than f(2)

Step-by-step explanation:

From the graph, f(2) = 1

g(2) = 0.5(4)² = 8

So g(x) has the greater value when x = 2, g(2) is 7 greater than f(2)

What additional information is needed to prove the triangles are congruent by the SAS postulate

Answers

Answer:

Step-by-step explanation:

The additional information needed to prove the triangles are congruent by the SAS postulate:

If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are congruent.

Pls help I’m confused

Answers

Answer:

3 3/8= 8×3+3=27/8

ans:27/8

2 4/1=4×2+1=9/4

ans:9/4

9 2/3=9×3+2=29/3

ans:29/3

What is the area of this triangle ?

Answers

Answer:

8

Step-by-step explanation:

The formula for aera of a triangle is Square =1/2*base*height.

In the picture, the base of the triangle is 4, and the height of the triangle is 4, too.

Then we use the formula, the square of the triangle is 1/2*4*4=8

Determine if true:
3x12+12=48

Answers

Answer:

True

Step-by-step explanation:

3x12=36

3x12=3636+12=48

3x12=3636+12=4848=48

Hecne, the equation is true.

Answer: The left side 48 is equal to the right side 48. So this means that 3 × 12 + 12=48 is TRUE!

Step-by-step explanation:

.ok so I don't get it ​

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Answer:

5280 feet

Step-by-step explanation:

Answer:

how many feet is a mile its 5280 feet

Step-by-step explanation:

aaaaaaa help!! just tell me where the things go pls <3​

Answers

Answer:

2x then 15x then 10

Step-by-step explanation:

Answer:

variables are: (x,y)

Step-by-step explanation:

and I am sorry that is all I know

Ashley painted 1/2 of her bathroom ceiling. Alex painted 1/4 of the ceiling in the school library. Who painted the larger fraction of their ceiling? (USE A PICTURE TO DEMONSTARTE YOUR ANSWERS). ​

Answers

Answer:

you can not solve this question

Step-by-step explanation:

you don't know how big a cieling is

for example:

Challenge Tim paints ornaments for a school
play. Each ornament is as shown and is made up
of two identical cones. He uses one bottle of
paint to paint 150 in.2. How many bottles of paint
does he need in order to paint 60 ornaments?
Use 3.14 for t.
98 in
24 in
The fire in Atlanta
The surface area of one ornament is about ?inches squared

Answers

Answer:

183.9 square inches74 bottles of paint

Step-by-step explanation:

The surface area of one ornament is twice the area of a cone with radius 2.4 inches and slant height 9.8 inches. The number of bottles of paint required will be found by dividing the total area to be painted by the area covered by one bottle.

__

The area formula for a cone is ...

  A = πr(r +s) . . . . . radius r, slant height s

The area of the double cone ornament will be ...

  A = 2(3.14)(2.4 in)(2.4 +9.8 in) = 183.8784 in²

The surface area of one ornament is about 183.9 square inches.

__

The surface area of 60 ornaments is ...

  60 × 183.8784 in² = 11,032.704 in²

The number of bottles of paint required is ...

  11,032.704 in²/(150 in²/bottle) = 73.55136 bottles

Tim will need 74 bottles of paint for 60 ornaments.

Susan bought a 2-kilogram bag of grapes.On the way home,she ate 125 grams of the grapes.How many grams of grapes did Susan have left?

Answers

Answer:

2 kilograms =2000grams

2000grams - 125grams =1875grams

1875grams of grapes did Susan have left

what is the population variance for 138, 151, 169, 142, 176, 155, 132, 177

Answers

Answer:

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Step-by-step explanation:

Factor the greatest common factor (GCF) from each polynomial. 2x^4 +8x^3+2x​

Answers

Answer:

2x(x^3+4x^2+1)

Step-by-step explanation:

Answer:

2x(x³ + 4x² + 1)

Step-by-step explanation:

The coefficients are 2, 8, 2.

The GCF of the coefficients is 2

The variable parts are x^4, x^3, x

The GCF of the variable parts is x

The GCF of the entire polynomial is 2x

Now we factor out 2x:

2x^4 + 8x^3 + 2x​ = 2x(x³ + 4x² + 1)

Which function grows faster?
Twelve bacteria are placed into a petri dish. The
number of bacteria doubles every thirty minutes.
or
y = 8x + 29

Answers

y= 12x + 30 and y= 8x + 29. its y= 12x + 30 for the word equation or it might be Y= 30x + 12 either way the word equation ROC is larger so it grows faster

Amina can read 35 pages in
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Answers

Answer: Should be 157.5 pages / 2.25 hours

Step-by-step explanation:

Part C
Write an equation showing the relationship between the number of baskets (b) made from outside the three-point line and the
number of points scored (p).

Answers

The equation that shows the relationship between the number of baskets (b) made from outside the three-point line and the number of points scored (p) is p = 3b

In basket ball, If a shot is successfully scored from outside of the three-point line, three points are awarded.

The variables are b and p.

where

p = number of points scored

b = number of basket made outside the three point line.

What is Variables?

Variables are numbers represented with letters in a mathematical expression.

Therefore, the equation that shows the relationship between the number of baskets (b) made from outside the three-point line and the number of points scored (p) is as follows:

p = 3b

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Answer:

P = 3b

Step-by-step explanation:

Determine the solution for the polynomial:
14x^2 + 60x = -2(5x^2 + 3x - 9)

Answers

Answer B is correct.

5. Dana had $700. She spent 1/2 of her money on car note and 1/4 of the remainder on car
insurance. How much money is left with her?

Answers

Answer:

the answer is 87.5.

Step-by-step explanation:

If you divide 700 by 2 it equals 350. Then when you multiply 350*0.25, 87.5 or 87 1/2 is your answer

PLEASE HELP FOR BRAINLIESTTT.

A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function [tex]C(x)= 1.1x^2-638x+103,259[/tex]. What is the minimum unit cost?
Do not round your answer.

Answers

Answer:

Answer:

Minimum Unit Cost = $14,362

Minimum Unit Cost = $14,0362

Please answer the question in the picture

Will mark brainliest

Answers

I’m like 100 percent sure it goes upwards

Joseph is planting a veggie Garden he plants two tamaotos for every 5 peppers. Of Joseph plants 14 tomatos how many pepers does he plant

Answers

Answer:

The answer is 35 plants.

Step-by-step explanation:

The ratio of tomato plant to that of pepper plant = 2:5

Let x be the number of pepper plants for 14 tomato plants.

Now, according to the question:

2:5 = 14:x

14×5 = 2x

x = 70/2 = 35 plants.

Answer:

35 peppers

Step-by-step explanation:

Use cross multiplication

2 tomatoes/5 peppers = 14 tomatoes/x peppers

x peppers = (5*14) / 2 = 35

Select the point on the number line located at -3/4

Answers

Answer:

that one before -1

Step-by-step explanation:

A guitar effects pedal enthusiast is going to a gear convention where people sometimes break out their own custom pedals to show off or trade. She has 5 different pedals she's thinking about packing with her, but she's not sure whether she should bring all of them, some of them, or none of them. How many different ways are there for her to decide whether and how many pedals to pack? Use subsets to help you figure this out, and write your answer as a whole number.

Answers

There are 32 different combinations that she can select out of the 5 pedals.

How many different combinations there are?

We want to get the total number of different combinations that we can make with 5 different pedals.

Remember that for a set of N elements, the number of different sets of K elements that we can make is:

[tex]C(N, K)=\frac{N!}{(N - K)!*K!}[/tex]

In this case, the total number of different combinations that we can make with the 5 pedals is given by:

C = C(5, 0) + C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4) + C(5, 5).

Let's calculate each one of these:

[tex]C(5, 0) = \frac{5!}{(5 - 0)!*0!} = \frac{5!}{5!} = 1\\\\C(5, 1) = \frac{5!}{(5 - 1)!*1!} = \frac{5!}{4!} = 5\\\\C(5, 2) = \frac{5!}{(5 - 2)!*2!} = \frac{5!}{3!*2!} = \frac{5*4}{2} = 10\\\\C(5, 3)= \frac{5!}{(5 - 3)!*3!} = \frac{5!}{3!*2!} = \frac{5*4}{2} = 10\\\\\\C(5, 4) = \frac{5!}{(5 - 4)!*4!} = \frac{5!}{4!} = 5\\\\C(5, 5) = \frac{5!}{(5 - 5)!*5!} = 1[/tex]

So the total number of different combinations is:

C = 1 + 5 + 10 + 10 + 5 + 1 = 32

If you want to learn more about combinations, you can read:

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aisha estimates the product of 12 and 2.4 by round in 2.4 to the nearest whole

what is aishas estimate?

what is the product of 12 and 2.4

i will give brainiest

Answers

Answer:

I'm pretty sure this is the answer its 24 or 30

Step-by-step explanation:

Because first what you would do is round 2.4 to 2 then multiply it by 12 to get 24 if its not 24 it would be 28.8 then you round 28.8 to 30. Hope that helped! :)

The Jones family was one of the first to come to the U.S. They had 7 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had:

Answers

Answer:

Probability of at least 4 girls

= P(X >= 4)

= P(X=4) + P(X=5) + P(X=6)

= .2734 + .1641 + .0547 + .0078

= .5

Step-by-step explanation:

hope this helps.

How does the diagram show that x + 4 has the same value as 17

Answers

Step-by-step explanation:

We can tell that x + 4 has the value of 17 by visualization.

[tex]\boxed{ \: \: \: \: \: \: x \: \: \: \: \: \: }\boxed{4}[/tex]

x is larger in length, we can identify that x has the value of 13 when 17 and 4 subtract.

Evaluate 14(7) -d 2f when d = 2 and f = 4

Answers

Step-by-step explanation:

98 - 3 * 2 * 4 equal to 9 - 2 * 840 + 9 - 6 equal to -7

The evaluation of 14(7) -d 2f when d = 2 and f = 4 is 82.

What is an equation?

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An expression,

14(7) -d 2f.

To find the value of the expression:

Substitute the given value of d and f.

When d = 2 and f = 4,

the equation is,

14(7) -(2)2(4)

= (14 x 7) - ( 2 x 2 x 4)

= 98 - 16

= 82

The evaluation of the equation when d = 2 and f = 4 is 82.

Therefore, the solution is 82.

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#SPJ2

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