What is the value of x? ​

It looks like the equation is

[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]

Right away, we notice that any solution to this equation must be positive, so x > 0.

For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to

[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that

[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]

[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that

[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]

For x ≠ 0, we have [tex]\frac xx=1[/tex], so that

[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]

Take the antilogarithm of both sides:

[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]

[tex]\dfrac{2x}5 = 30[/tex]

Solve for x :

[tex]2x = 150[/tex]

[tex]\boxed{x=75}[/tex]

Answer:

quneotentendeiporoqenouteetendxdin

Step-by-step explanation:

Answer:

329 miles

Step-by-step explanation:

Create a proportion where x is the distance the car can travel on 14 gallons of gas:

[tex]\frac{70.5}{3}[/tex] = [tex]\frac{x}{14}[/tex]

Cross multiply and solve for x:

3x = 987

x = 329

So, the car can travel 329 miles on 14 gallons of gas

Answer:

329 miles

Step-by-step explanation:

We can write a ratio to solve

70.5 miles      x miles

--------------- = ------------

3 gallons          14 gallons

Using cross products

70.5 * 14 = 3x

987=3x

Divide each side by 3

987/3 = 3x/3

329=x

329 miles

Answer:

6

Step-by-step explanation:

You have 2 conditions.

1. The digits must be different.

2. The digits must add to 7.

There aren't very many

124

142

214

241

412

421

That's it. That's your answer. There are 6 of them

Answer:

-3x^2 +7x -4

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

(x-3)(x-2)(x+3)

Step-by-step explanation:

2              3x

--------   - ----------

X^2-9    x^2 -5x+6

Factor

2                 3x

--------   -      ----------

(x-3)(x+3)   (x-3)(x-2)

Get a common denominator

2  (x-2)               3x(x+3)

--------   -             ----------

(x-3)(x+3)(x-2)   (x-3)(x-2)(x+3)

2x-4  - (3x^2 -9x)

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

(x-3)(x-2)(x+3)

Distribute

2x-4  - 3x^2 +9x

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

(x-3)(x-2)(x+3)

Combine like terms

-3x^2 +7x -4

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

(x-3)(x-2)(x+3)

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Given:

The function is:

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

To find:

The graph of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

It can be written as:

[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]

[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]

[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]

Putting [tex]x=0[/tex] to find the y-intercept.

[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]

[tex]f(0)=\dfrac{-5}{3}[/tex]

So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].

Putting [tex]f(x)=0[/tex] to find the x-intercept.

[tex]0=\dfrac{-2x-5}{x+3}[/tex]

[tex]0=-2x-5[/tex]

[tex]2x=-5[/tex]

[tex]x=\dfrac{-5}{2}[/tex]

[tex]x=-2.5[/tex]

So, the x-intercept is [tex]-2.5[/tex].

For vertical asymptote, equate the denominator and 0.

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

So, the vertical asymptote is [tex]x=-3[/tex].

The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.

[tex]y=\dfrac{-2}{1}[/tex]

[tex]y=-2[/tex]

So, the horizontal asymptote is [tex]y=-2[/tex].

End behavior of the given function:

[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]

[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]

Using all these key features, draw the graph of given function as shown below.

Answer:

The Answer Is A.

Step-by-step explanation:

Answer

248.3712

Step-by-step explanation:

2(H*W)+2(H*L)

2(5.78*6.72)+2(6.72*12.7)= 248.3712                                                                                                                  

Answer:

[tex]g(x) = 5|x|[/tex]

Step-by-step explanation:

Given

[tex]f(x) = |x|[/tex]

[tex]b =5[/tex] --- vertically stretch

Required

The new function

The rule for vertical stretch is:

[tex]g(x) = bf(x)[/tex]

So, we have:

[tex]g(x) = 5 * |x|[/tex]

[tex]g(x) = 5|x|[/tex]

Step-by-step explanation:

I think something went wrong with the answer options you provided. and maybe with the problem statement itself.

I see 3 function definitions.

I can tell you what they are and use the provided option phrasing as closely as possible :

h(x) = 0 is a horizontal line (in fact the x-axis)

k(x) = 4x² + 312 is a parabola with the opening upwards

f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)

Answer:

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on

Answer:

401.92 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = (3.14) (4)^2 *8

V= 401.92

Answer:

x=12

Step-by-step explanation:

each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle

ex: 8*4=32 and 17*4=68

so we can assume that 15*4= 4x+12

60=4x+12

48=4x

x=12

Answer:

x = 12

Step-by-step explanation:

The triangles are similar so we can use ratios

4x+12      32

-------  = ------------

15             8

Using cross products

(4x+12) *8 = 15 * 32

(4x+12) *8 = 480

Divide each side by 8

(4x+12) *8/8 = 480/8

4x+12 = 60

Subtract 12 from each side

4x+12 -12 = 60-12

4x = 48

Divide by 4

4x/4 = 48/4

x = 12

Answer:

[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]

Step-by-step explanation:

One is given the following equation, and the problem asks one to identify the rational roots of the equation:

[tex]x^4-3x^2+6=0[/tex]

The rational root theorem states that the list of positive and negative factors of the constant term over the factors of the coefficients of the term to the highest degree will yield a list of the rational roots of the equation. Use this theorem to generate a list of all possible ration roots of the equation.

[tex](+-)\frac{6,3,2,1}{1}[/tex]

Now rewrite this list in a numerical format:

[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]

This is the list of the possible rational roots. One has to synthetically divide each of these numbers by the given polynomial equation to find the actual rational roots. However, the problem only asks for the possible rational roots, not the actual rational roots, thus, this is not included.

Answer:

Step-by-step explanation:

The most repeated value is:

There are 4 of them.

Correct choice is A

Answer:

It is the last one.

Step-by-step explanation:

You must factor out the top expression, and then factor the bottom expression. Then, cancel out all of the terms that are equivalent to get one expression on the left side of the inequality sign. Then, subtract the answers to the "0" side and divide to find the coordinates.

Answer:

Last option

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

Answer:

Length of all 3 sides: 7, 7, and 9

Length of the two sides that have the same length: 7

Step-by-step explanation:

Let the two sides with equal lengths have a length of [tex]x[/tex]. We can write the third side as [tex]2x-5[/tex].

The perimeter of a polygon is equal to the sum of all its sides. Since the perimeter of the triangle is 23 meters, we have the following equation:

[tex]x+x+2x-5=23[/tex]

Combine like terms:

[tex]4x-5=23[/tex]

Add 5 to both sides:

[tex]4x=28[/tex]

Divide both sides by 4:

[tex]x=\frac{28}{4}=\boxed{7}[/tex]

Therefore, the three sides of the triangle are 7, 7, and 9 and the length of the two sides that have the same length is 7.

Answer: A. (-1, -6)

Step-by-step explanation:

Use the midpoint formula:

[tex]midpoint = (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}) \\\\(6, -4) = (\frac{13+x_{2}}{2}, \frac{-2+y_{2}}{2})\\\\\frac{13+x_{2}}{2} =6\\\\13+x_{2}=6*2\\\\x_{2}=12-13=-1\\\\ \\ \frac{-2+y_{2}}{2}=-4\\\\-2+y_{2}=(-4)*2\\\\y_{2}=-8+2=-6\\\\\\\left \{ {{x_{2}=-1} \atop {y_{2}=-6}} \right.[/tex]

The shapes are the same size. Match the sides.

3x -1 = 17

Add 1 to both sides:

3x = 18

Divide both sides by 3:

X = 6

2y = 16

Divide both sides by 2

Y = 8

Answer: x = 6, y = 8

Answer:

Survey

Step-by-step explanation:

During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.

Answer:

3/ 7

Step-by-step explanation:

We know that it is an even ball

2,4,6,8,10,12,14 are even balls

2,4,6,8 are red and 10,12,14 are white

P ( white) = white even / total even

              = 3/ 7

Answer:

0.054

Step-by-step explanation:

9 3/5% as a decimal is 0.054 (already to 3 decimal places)

Answer from Gauthmath

9 are just, well..., 9

3/5 are 0.6

because 1/5 is 0.2

so it's 9.6%, not so complicated I guess

Answer:

Minimum = 0

Maximum = 15

Step-by-step explanation:

Given

Optimization Equation: [tex]z = 2x + 5y[/tex]

Constraints:

[tex]2x- y \le 12[/tex]

[tex]4x + 2y \ge 0[/tex]

[tex]x + 2y \le 6[/tex]

[tex]x,y\ge 0[/tex]

Required

The maximum and the minimum values of z

To do this, we make use of graphical method.

Plot the constraints on a graph (see attachment)

Get the corner points from the points.

These are the points where [tex]x,y\ge 0[/tex]

So, we have:

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (0,3)[/tex]

[tex](x_3,y_3) = (6,0)[/tex]

Substitute these points in the optimization equation:

[tex](x_1,y_1) = (0,0)[/tex]

[tex]z = 2x + 5y[/tex]

[tex]z = 2 * 0 + 5 * 0 = 0[/tex]

[tex](x_2,y_2) = (0,3)[/tex]

[tex]z = 2 * 0 + 5 * 3 = 15[/tex]

[tex](x_3,y_3) = (6,0)[/tex]

[tex]z = 2 * 6 + 5 * 0 = 12[/tex]

So, the values are:

Minimum = 0

Maximum = 15

Answer:

max= 16 min= -24

Step-by-step explanation:

Answer:

They are equal

Step-by-step explanation:

4.5% is 0.045 in decimal form

Answer: They are equal

Step-by-step explanation:

I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent  (move it two spots to the right).

Answer:

f(x) is compressed horizontally

Step-by-step explanation:

Given

[tex]f(x) = \log(4x)[/tex]

[tex]g(x) = f(13x)[/tex]

Required

The effect on f(x)

[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.

So, we have:

[tex]f(13) = \log(4 * 13x)[/tex]

[tex]f(13) = \log(52x)[/tex]

So:

[tex]g(13) = \log(52x)[/tex]

eueuhhbee×€×&÷;#;;#

shehdjdjjrnsns

shehehensndneee

nejeje

Answer:

it's 91.027%

Step-by-step explanation:

I hope i helped

Answer:

4/5

Step-by-step explanation:

I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.

Answer:

3 students

Step-by-step explanation:

since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.

7+5+10+x=25

x=25-22

=3

I hope this helps

Answer:

Answered March 20, 2021

This is a right angle triangle where the hypotenuse a^2 = b^2 + c^2

= 15^2 + 8^2 = 225+64= 289

289= 17^2

17 = hypotenuse

The sine of an angle is the ratio of the shortest side to the hypotenuse

= 8/17= 0.4705

sine^-1 0.4705 = 28°