how many solutions doss the equation 4x+2(x-5)=3(2x-4)

Answer:

2 hours

Step-by-step explanation:

12:30 + 1 hour = 1:30

1:30 + 1 hour = 2:30

She was at the dog park with her dog for 2 hours.

Answer:

Answer. Step-by-step explanation: The answer is 0.8 because if something is 10 x of something in decimal terms it would be the number after the decimal getting smaller.

Answer:

See below

Step-by-step explanation:

It has something to do with the Weierstrass substitution, where we have

\($\int\, f(\sin(x), \cos(x))dx = \int\, \dfrac{2}{1+t^2}f\left(\dfrac{2t}{1+t^2}, \dfrac{1-t^2}{1+t^2} \right)dt$\)

First, consider the double angle formula for tangent:

\(\tan(2x)= \dfrac{2\tan(x)}{1-\tan^2(x)}\)

Therefore,

\(\tan\left(2 \cdot\dfrac{x}{2}\right)= \dfrac{2\tan(x/2)}{1-\tan^2(x/2)} = \tan(x)=\dfrac{2t}{1-t^2}\)

Once the double angle identity for sine is

\(\sin(2x)= \dfrac{2\tan(x)}{1+\tan^2(x)}\)

we know \(\sin(x)=\dfrac{2t}{1+t^2}\), but sure,  we can derive this formula considering the double angle identity

\(\sin(x)= 2\sin\left(\dfrac{x}{2}\right)\cos\left(\dfrac{x}{2}\right)\)

Recall

\(\sin \arctan t = \dfrac{t}{\sqrt{1 + t^2}} \text{ and } \cos \arctan t = \dfrac{1}{\sqrt{1 + t^2}}\)

Thus,

\(\sin(x)= 2 \left(\dfrac{t}{\sqrt{1 + t^2}}\right) \left(\dfrac{1}{\sqrt{1 + t^2}}\right) = \dfrac{2t}{1 + t^2}\)

Similarly for cosine, consider the double angle identity

Thus,

\(\cos(x)= \left(\dfrac{1}{\sqrt{1 + t^2}}\right)^2- \left(\dfrac{t}{\sqrt{1 + t^2}}\right)^2 = \dfrac{1}{t^2+1}-\dfrac{t^2}{t^2+1} =\dfrac{1-t^2}{1+t^2}\)

Hence, we showed \(\sin(x) \text { and } \cos(x)\)

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

\(5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]\)

Solving

\(5\,\overbrace{\frac{1-t^2}{1+t^2}}^{\cos(x)} = 12\,\overbrace{\frac{2t}{1+t^2}}^{\sin(x)}+3\)

\(\implies \dfrac{5-5t^2}{1+t^2}= \dfrac{24t}{1+t^2}+3 \implies \dfrac{5-5t^2 -24t}{1+t^2}= 3\)

\(\implies 5-5t^2-24t=3\left(1+t^2\right) \implies -8t^2-24t+2=0\)

\(t = \dfrac{-(-24)\pm \sqrt{(-24)^2-4(-8)\cdot 2}}{2(-8)} = \dfrac{24\pm 8\sqrt{10}}{-16} = \dfrac{3\pm \sqrt{10}}{-2}\)

\(t=-\dfrac{3+\sqrt{10}}{2}\\t=\dfrac{\sqrt{10}-3}{2}\)

Just note that

\(\tan\left(\dfrac{x}{2}\right) = \dfrac{3\pm 8\sqrt{10}}{-2}\)

and  \(\tan\left(\dfrac{x}{2}\right)\) is not defined for \(x=k\pi , k\in\mathbb{Z}\)

Answer:

Its

Step-by-step explanation:

slope: 2.5

y intercept: 3

Step-by-step explanation:

6 customers per hour \(=1\( customer per 10 minutes

\(X \sim \operatorname{Exp}(\beta=10) \quad\) (given mean)

Pdf is given by: \(f(x)=\frac{1}{\beta} e^{-x / \beta}, 0<x\)

Pdf: \(f(x)=\frac{1}{10} e^{-x / 10}, \quad 0<x,\( and zero otherwise.

Cdf: \(P(X \leq x)=1-e^{-x / \beta}\)

\(P(X \leq x)=1-e^{(-x / 10)} \quad\) for \(x>0 \Longrightarrow P(X>x)=e^{-x / 10}\)

a)\( \begin{array}{c}

P(X<12)=1-\exp (-12 / \beta)=1-e^{-1.2}=1-0.301194=0.698806 \approx 0.699 \\

P(X<12)=0.699 \end{array}\)

\(\begin{aligned}

&\begin{array}{c}

P(X>20)=\exp (-20 / \beta)=e^{-2} \approx 0.135335 \approx 0.1353 \\

P(X>20)=0.1353

\end{array}\\\)

&\text { c) }\\

&P(8<X<15)\\

&\begin{array}{l}

=P(X<15)-P(X<8) \\

=(1-\exp (-15 / \beta))-(1-\exp (-8 / \beta)) \\

=\exp (-8 / \beta)-\exp (-15 / \beta) \\

=e^{-0.8}-e^{-1.5} \\

=0.449329-0.22313 \approx 0.226199 \approx 0.2262 \\

\quad P(8<X<15)=0.2262

\end{array}

\end{aligned}

\begin{aligned}

&\text { d) }\\

&\begin{array}{l}

P(14<X<22) \\

=P(X<22)-P(X<14) \\

=(1-\exp (-22 / \beta))-(1-\exp (-14 / \beta)) \\

=\exp (-14 / \beta)-\exp (-22 / \beta) \\

=e^{-1.4}-e^{-2.2} \\

=0.246597-0.110803 \approx 0.135794 \approx 0.1358 \\

P(X<14 \cup X>22)=1-P(14<X<22)=1-0.1358=0.8642 \\

P(X<14 \cup X>22)=0.8642

\end{array}

\end{aligned}

Answer:

Step-by-step explanation:

x=100 (vertically opposite angle)

Answer:

the answer is -b³ - b² + 8b + 12

divide $3.20 to get the cost per ounce, and multiply it by 6 to get the price for 6 ounces.

6 ounces = $1.92

hope this helps!! :)

Answer:

  x ≥ 5

Step-by-step explanation:

You want the domain of the equation y = √(x -5) -1.

The domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...

  x -5 ≥ 0

  x ≥ 5 . . . . . . the domain of this function

__

Additional comment

The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.

<95141404393>

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer:

B is the correct answer

Step-by-step explanation:

there y intercept are the same which is 4

The graph of x=2(y-4) has greater slope than the graph of x=5(y-4), the correct option is B.

The standard equation of a line is given by

y = mx+c

Here m is the slope and c is the y intercept

The slope can be determined by

m = (y₂ -y₁)/(x₂ -x₁)

The equation of the line is

x=2(y-4)

x=5(y-4)

y =  (1/2)x +4  

y = (1/5)x +4

The slope is (1/2) and (1/5),

(1/2) > (1/5)

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The following conditions for inference should be met are

i) The seeds should be randomly assigned to be treatment.

iii) The number of successful and unsuccessful seeds in each group/sample should be atleast ten. So, the correct answer is option(D), i.e., I and III only.

Confidence interval (C.I.) for a difference in proportions is defined as a range of values that is likely to contain the true difference between two population proportions with a certain level of confidence. We have, a gardener who, wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. Confidence interval for difference in proportion = 95%

Seeds soaked before planting :

Sample size, n₁ = 50

Seeds soaked after planting :

Sample size, n₂ = 50

After two weeks, the gardener will record how many seeds in each group germinated. So, we have to determine the conditions should be needed for construct confidence interval for difference in proportion :

i) The seeds should be randomly assigned to a treatment is a necessary condition in statistics.

ii) The group sizes should be less than 10 percent of the population sizes, this applies only for one sample not for two samples.

Hence, required conditions are I and III only.

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12 students play defense. 1st step.  6/9 of 27 is 18.  2nd. the ratio of the students playing offense to the total number of students playing soccer is 1 to 3 which means the total amount of students is '3', in the ratio it's 3 because it's simplified (i like to think of it as 'groups'). since we know that there are a total of 18 students and there's 3 total 'groups' we divide 18 into 3 which is 6. so there's 6 students in each group. we subtract 6 (1 group) from 18 ( the total number of students) which is 12, so there are 12 students playing defense. if you wrote the ratio again without simplifying it would be  6:18

Answer:

Answer will be 55898.

Step-by-step explanation:

Answer:

I cant draw it perfectly so please dont judje if it not helpful

Step-by-step explanation:

x<------------------------------------->infinity

So put a dot at the arrow pointing to X and then trace the line and the arrow to infinity dark.

Answer:

A is -24

B is 0

C is  1

Step-by-step explanation:

Hope this helps and please give me brainlest

Answer:

y = 2x + 3

Step-by-step explanation:

Points (6,3) are x,y coordinates.

Use slope intercept form: y = mx + b

b = y intercept

m = slope

The equation that has a slope of 2 and passes through (6, 3) will be y = 2x - 9.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the equation is 2. Then the equation is given as,

y = 2x + c

The line is passing through (6, 3), then we have

3 = 2(6) + c

3 = 12 + c

c = 3 - 12

c = - 9

The equation will be given as,

y = 2x - 9

The equation that has a slope of 2 and passes through (6, 3) will be y = 2x - 9.

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Answer:

F. 6π is the correct answer

As the diameter of the 2nd circle is 2x+3, its radius will be (2x+3)/2 which is equal to x + 1.5  

But as it is identical to the 1st circle their radii will be equal.

Therefore, 2x = x + 1.5

Therefore, 2x - x = 1.5

Thus we get that x = 1.5

Therefore, r (radius) = 2x = 2*1.5 = 3

Now we can find the circumfrence by the equation circumference = 2πr

Therefore, circumference = 2*π*3 = 6π

The circumference of each circle is 6π.

The Circumference (or) perimeter of circle = 2πR

where, R is the radius of the circle. π is the mathematical constant with an approximate (up to two decimal points) value of 3.14. Again, Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.

Given:

Circle 1: radius of 2x;

Circle 2: diameter = 2x+3

radius of circle 2 = x+1.5

Now, the two circles are identical then they have equal radius

2x = x + 1.5

2x - x = 1.5

x = 1.5

Now, circumference of circle = 2πr

= 2*π*3

= 6π

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Answer:

not sure but -2

Step-by-step explanation: I did on calculator

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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Answer:

3(x+2y+1)

3x+6x+3

Step-by-step explanation:

Answer:

<ABD and <DBC are supplementary angles by Linear Pair Postulate and m<ABD + m<DBC=180 by definition of supplementary angles

Step-by-step explanation:

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

\(\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}\)

Let the no. of students be x

total cost = y

Then the first equation will be

8x + 20 = y

And the second equation will be

3x + 40 = y

A system of two equations where each equation models the total cost y to take x students on each field trip is;

8x + 20 = y

3x + 40 = y

The total cost y is 48 to take x = 4 students on each field trip.

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.

A science teacher is planning a field trip to either the aquarium or the science center.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

The science center charges $3 per student and has a class lab fee of $40.

Let the total cost y to take x students on each field trip.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

8x + 20 = y

The science center charges $3 per student and has a class lab fee of $40.

3x + 40 = y

On solving both the equation

Substitute the value of y in the equation 2

3x + 40 = y

3x + 40 = 8x+20

8x - 3x = 40-20

5x = 20

x = 20/5

x = 4

Substitute the value of x in the equation 1

3x + 40 = y

2(4) + 40 =y

8 + 40 = y

y = 48

Hence, the total cost y is 48 to take x = 4 students on each field trip.

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turn wrong

Step-by-step explanation:

A rotation turns and if it goes the wrong way it looses its coordinate points.

The rotation may get lost due to change in centrifugal force.

It is given that the two same masses are joined with cords T1 and T2 and length of T1 and T2 are equal.

It is required to explain how the rotation get lost.

It is defined as the force when object with mass rotates about a fixed axis with a string connected to it a force generated outward.

The object is moving in circular path and the force which is experienced by the object known as the centrifugal force.

When two identical masses are joined by the T1 and T2 cords with equal length, the masses are moving in circular path with w angular velocity.

The outer ball experiencing inward tension force T1 and the other ball experiencing outward tension force T2.

The radial force will be;

\(\rm F =mwr^2\)   where r is the circular path radius and m is the mass of balls and          

                  w is the angular velocity.

The tension forces is balancing with the angular force since the radius is  remain same but when the centrifugal force will change the rotation get lost.

Thus, the rotation may get lost due to change in centrifugal force.

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Answer:

2/9 = 0.222 (this is repeating) 3/8 = 0.375 -- not repeating 5/6 = 0.83333 (this is repeating) 5/4 = 1.25 -- not repeating answer is : 2/9 and 5/6

Step-by-step explanation:

Answer:

proportion of ratio will be used

Answer:

C. 1 4/10 + 9/10 + 6/10

got it right

Mr Smith looks their children 1 times 1