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3 years ago

The points -4. -4 -4, 4

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

3 0

Answer:

whats the question?

Step-by-step explanation:

I don't get the question so what is the question?

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A 12-foot ladder leans against the wall makes an angle of 62.87 degrees with the ground. How high up the wall does the ladder re

Alex

Answer:

10.68 ft

Step-by-step explanation:

sin(62.87)=x/12

12sin(62.87)

=10.68 ft

4 0

2 years ago

Log10 (2x + 1) - logio(3x - 2) = 1

Pavlova-9 [17]

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

(2x+1)/(3x-2)=10^1

(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

1+20=28x-20+20

21=28x

And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

3/4=x

Hence, the solution to the given equation is x=3/4 .

3 0

3 years ago

What is the value of ln e^4

sineoko [7]

Answer:

$\large\boxed{\ln e^4=4}$

Step-by-step explanation:

$Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^4=4\ln e=4(1)=4$

3 0

3 years ago

Danielle earns a 7.5% commission on everything she sells at the electronics store where she works. How much commission did she e

andrew11 [14]

Answer:

$262.5

Step-by-step explanation:

Given data

Commission earned= 7.5%

Sales for last week= $3,500

Let us find the amount of the commission

=7.5/100* 3500

=0.075*3500

=$262.5

Hence the commission earned last week is

$262.5

7 0

2 years ago

If it takes you 40 minutes to go 20 miles downstream and then 60 minutes on the way back, what is the speed of the current?

IrinaK [193]

Answer:

Speed of Current = 5 miles per hour

Step-by-step explanation:

We know distance formula,

D = RT

Where

D is distance

R is rate

T is time

If we let speed of boat (assume) to be "x" and speed of current to be "c"

Then downstream rate is (with current) = x + c

Upstream rate is (against current) = x - c

40 mins to go 20 miles downstream, that means:

D = RT

20 = (x + c)(40)

and

60 minutes to go upstream, 20 miles, that means:

D = RT

20 = (x - c)(60)

Simplifying first equation:

40x + 40c = 20

Simplifying second equation:

60x - 60c = 20

Multiplying first equation by 60, we get:

60 * [40x + 40c = 20] = 2400x + 2400c = 1200

Multiplying second equation by 40, we get:

40 * [60x - 60c = 20] = 2400x - 2400c = 800

Now we add up both these equations:

2400x + 2400c = 1200

2400x - 2400c = 800

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

4800x = 2000

x = 2000/4800 = 5/12

We need speed of current, that is "c", so we plug in the value of x into first equation and solve for c:

$40x + 40c = 20\\40(\frac{5}{12}) + 40c = 20\\\frac{50}{3}+40c=20\\40c=20-\frac{50}{3}\\40c=\frac{10}{3}\\c=\frac{1}{12}$

Speed of Current = 1/12 miles per minute

Since there is 60 minutes in an hours, that would be:

(1/12) * 60 = 5 miles per hour

Speed of Current = 5 miles per hour

3 0

3 years ago