2 sin x cos x – sin x = 0

Answer:

x=-4  and y=2  Those 2 equations when graphed give a vertical line and a horizontal line that intersect at the point (-4,2)

x+4=0 and y-2=0  are the same two lines.

or if you want more complicated systems of equations, with the same solution:

x+y=-2 and x-y=-6

in standard form, that's y=-x-2 and y=x+6  Graph those two lines and they intersect at (-4,2)

Those 2 lines are with slopes of -1 and +1.  Those 2 equations are a system of equations

whose solution is x=-4 and y=2.

Rotate two perpendicular lines around the point (-4,2) and you get more systems of  

equations with the same solution.

They don't have to be perpendicular though.  x+y=-2 and x=-4 are two lines forming

a 45 degree angle, with the same solution (-4,2)

They don't have to be linear either.  Take a parabola with the vertex (-4,2) and the line x=-4.

They intersect at the point (-4,2).  That parabola could be the simple y=x2 shifted up and

to the left, to y-2 = (x+4)2  or y=x2+8x+18   or it could be any one of a family of parabolas with

the same vertex.

You could have 2 circles tangent at the point (-4,2) Endless circles could have that point

as a tangent and their equations having that same solution (-4,2)

Step-by-step explanation:

Hope this helps <3

Answer:

36

Step-by-step explanation:

4(11 + 7) ÷ (7 – 5)

4 * 18 ÷ 2

=36

Answer:

In my opinion the limit is equal to 1 not 0, sorry.

Step-by-step explanation:     6  25  13  43

lim n ⇒∞ ((2n - 1)/2n)

lim n ⇒∞ (2n/2n) - 1)/2n)        2n/2n = 1    1/∞  = 0

              =   1  - 0

              =    1

when I graphed the function I also got 1

Answer:

The value of the z-test statistic is [tex]z = 0.68[/tex]

Step-by-step explanation:

An article claims that 12% of trees are infested by a bark beetle.

At the null hypothesis, we test if the proportion is of 12%, that is:

[tex]H_0: p = 0.12[/tex]

At the alternative hypothesis, we test if the proportion is different of 12%, that is:

[tex]H_1: p \neq 0.12[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.12 is tested at the null hypothesis:

This means that [tex]\mu = 0.12, \sigma = \sqrt{0.12*0.88}[/tex]

A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.

This means that [tex]n = 1000, X = \frac{127}{1000} = 0.127[/tex]

What is the value of the z-test statistic?

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.127 - 0.12}{\frac{\sqrt{0.12*0.88}}{\sqrt{1000}}}[/tex]

[tex]z = 0.68[/tex]

The value of the z-test statistic is [tex]z = 0.68[/tex]

Answer:

They need to survey 4145 residents.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?

This is n for which [tex]M = 0.02[/tex]. As we have no estimate for the proportion, we use [tex]\pi = 0.5[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.02})^2[/tex]

[tex]n = 4144.1[/tex]

Rounding up:

They need to survey 4145 residents.

Answer:

c.the mean of each data set

Answer:

A

Step-by-step explanation:

Answer:

ur ans is here...

Answer:

75

Step-by-step explanation:

∠K and ∠ R are congruent (equal)

Triangle Sum Theory - angles of all triangles add to 180

180 - 79 - 26 = 75

Answer:

Exponential Function

Step-by-step explanation:

y values increase by x4

Answer:

exponential function

the ans is b

Answer:

here is your answer

Step-by-step explanation:

b

c

a answer

Answer:

$1281.1

Explanation:

Unit selling price is total cost plus markup(percentage profit on total cost price)

Assuming overhead is already apportioned to each product at $585 each

Total cost:

Labor 15hrs at $26/hr=15×26=$390

Overhead 150% of labor=150%×390=$585

Material Costs= $89

Packing Costs= 10%×390= $39

Subcontract Cost= $11

Sales Commission= 5% of selling price=$55.7

Total cost = $1169.7

Profit =10% of selling price= $111.4

Selling price =total cost + profit

= $1281.1

Answer:

53*15*12=9540

Step-by-step explanation:

its just 53 times 15 times 12 for all the possibilities.

Say the first football player was picked, same with the first baseball player, and the first basketball player were all picked, then another possiblity would be the first football player, the second baseball player, and the first basketball player, here is a numerical example.

Football            Baseball             Basketball

     1                         1                             1  

     1                         2                            1

     1                         2                            2

     1                         2                            3

     1                         2                            4

and so on including all the patterns it would be 9540 possibilities

The total number of ways of forming a committee by selecting one representative from each team is 9540.

A combination is a mathematical technique that determines the number of possible arrangements or the number of ways  in a collection of items where the order of the selection does not matter.

[tex]nC_{r}= \frac{n!}{r!(n-r)!}[/tex]

Where,

[tex]nC_{r}[/tex] is a number of combination.

n is total number of objects in the set.

r is the number of choosing objects from the set.

According to the multiplication rule in combination if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions.

According to the given question

Total number of football players = 53

Total number of baseball players = 15

Total number of basket ball players = 12

Therefore,

Number of ways of selecting one representative from football team is given by  

[tex]53C_{1} =\frac{53!}{1!52!} = 53[/tex]

Number of ways of selecting one representative from baseball team is given by

[tex]15C_{1} =\frac{15!}{1!14!}=15[/tex]

Number of ways of selecting one representative from basketball team is given by

[tex]12C_{1} =\frac{12!}{1!11!} =12[/tex]

So, the total number of ways of forming a committee by selecting one representative from each team = 53 × 15 × 12 =9540.

Hence,  total number of ways of forming a committee by selecting one representative from each team 9540.

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The answers are as follows part A = 30m+15  part B =3m+15+27m

and partC = 30m+15

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.

Part A:- Two expressions that are equivalent to the given expressions are:-

3m   +   15   +   27m

30m  +   15

Part B:  Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.

3  (  m   +   5    +   9m   )

Open the bracket by multiplying 3 by what is in the bracket

3m   +   15   +   27m

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.

3   (  m    +   5   +   9m  )

Open the bracket by multiplying 3 by what is in the bracket

3m    +    15    +     27m

Collect like terms together

3m    +     27m  +   15

=   30m   +    15

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Answer:

30 loads

Step-by-step explanation:

You simply divide 40 by 1 1/3 which gives you 30 meaning you can wash 30 loads.

Answer:

30

Step-by-step explanation:

To solve this, you want to do 40÷[tex]1\frac{1}{3}[/tex], or [tex]\frac{40}{1}[/tex]÷[tex]\frac{4}{3}[/tex], which is the same as  [tex]\frac{40}{1}[/tex]×[tex]\frac{3}{4}[/tex].

This can be solved to [tex]\frac{120}{4}[/tex] and simplifies to 30.

**This content involves writing expressions from worded questions and operations with fractions, which you may wish to revise. I'm always happy to help!

Answer:

20%

Step-by-step explanation:

6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.

Answer:

x = 1 , y = - 1 , z = 2

Step-by-step explanation:

[tex]\begin{pmatrix}1&1&-1&-2\\ 2&-1&3&9\\ 1&-1&-2&1\end{pmatrix}\\\\\\= \begin{pmatrix}2&-1&3&9\\ 1&1&-1&-2\\ 1&-1&-2&1\end{pmatrix}[/tex]                          [tex][ \ swap \ R_1 \ and \ R_2 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 1&-4&-2&1\end{pmatrix}[/tex]                        [tex][ \ R_2 = R_2 - \frac{1}{2} R_1 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\end{pmatrix}[/tex]                        [tex][ \ R_3 = R_3 - \frac{1}{2} R_1 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\end{pmatrix}[/tex]                      [tex][ \ swap \ R_2 \ and \ R_3 \ ][/tex]

[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&0&-4&-8\end{pmatrix}[/tex]                        [tex][ \ R_3 = R_3 + \frac{3}{7}R_2 \ ][/tex]

Therefore,

           [tex]-4z = - 8\\\\z = 2[/tex]

        [tex]-\frac{7}{2} y - \frac{7}{2}z = -\frac{7}{2}\\\\y + z = 1\\\\y + 2 = 1 \\\\y = 1 - 2 = - 1[/tex]

      [tex]2x - 1y + 3z = 9\\\\2x -1(-1) + 3(2) = 9\\\\2x + 1 + 6 = 9\\\\2x = 9 - 7\\\\2x = 2 \\\\x = 1[/tex]

Answer:

Step-by-step explanation:

D ANSWER D

Answer:

d

Step-by-step explanation:

The graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a graph of f(x) is shown in the picture.

As we know, if f(x) has ordered double (x, y)

Then inverse of function g(x) must have ordered double (y, x)

From the given options graph (C) satisfy the condition.

Thus, the graph (C) represents the inverse function of f(x) if the graph of a function f(x) is given option (C) is correct.

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Answer:

the answer would be option C

x = 30

y = 2

Get the explanation from the image I have shared.

Hope it helps you

Answer:

it is a letter b

Step-by-step explanation:

that does not contain an outlet

Answer:

I hope this helps

the outcomes are the compulsory 6, and 1 or 2

Step-by-step explanation:

[tex] \frac{3}{6} \\ \frac{1}{2} or \: 0.5[/tex]

Answer:

a. [tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]

b. [tex]\frac{dx}{dt} = \frac{9}{2}[/tex]

Step-by-step explanation:

To solve this question, we apply implicit differentiation.

xy = 2

Applying the implicit differentiation:

[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = \frac{d}{dt}(2)[/tex]

[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]

a. Find dy/dt, when x = 4, given that dx/dt = 13.

x = 4

So

[tex]xy = 2[/tex]

[tex]4y = 2[/tex]

[tex]y = \frac{2}{4} = \frac{1}{2}[/tex]

Then

[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]

[tex]\frac{1}{2}(13) + 4\frac{dy}{dt} = 0[/tex]

[tex]4\frac{dy}{dt} = -\frac{13}{2}[/tex]

[tex]\frac{dy}{dt} = -\frac{13}{8}[/tex]

b. Find dx/dt, when x = 1, given that dy/dt = -9.

x = 1

So

[tex]xy = 2[/tex]

[tex]y = 2[/tex]

Then

[tex]y\frac{dx}{dt} + x\frac{dy}{dt} = 0[/tex]

[tex]2\frac{dx}{dt} - 9 = 0[/tex]

[tex]2\frac{dx}{dt} = 9[/tex]

[tex]\frac{dx}{dt} = \frac{9}{2}[/tex]

Answer:2921

Step-by-step explanation: Add the two equations together to get (x+y)+(x-y)=3500+2342. Simplify and get 2x=5842. Divide 5842 by 2 and get 2921.

Answer:

b) f(x) = x + 6

Step-by-step explanation:

The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.

Answer:

3:6:9

Step-by-step explanation:

1/1+2+3 × 90 = 15

2/1+2+3 × 90 = 30

3/1+2+3 × 90 = 45

Answer:

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

Step-by-step explanation:

Midpoint of a segment:

The coordinates of the midpoint of a segment are the mean of the coordinates of the endpoints of the segment.

Midpoint of s1:

Using the endpoints given in the exercise.

[tex]x = \frac{3 + \sqrt{2} + 4}{2} = \frac{7 + \sqrt{2}}{2}[/tex]

[tex]y = \frac{5 + 7}{2} = \frac{12}{2} = 6[/tex]

Thus:

[tex]M_{s1} = (\frac{7 + \sqrt{2}}{2},6)[/tex]

Midpoint of s2:

[tex]x = \frac{6 - \sqrt{2} + 3}{2} = \frac{9 - \sqrt{2}}{2}[/tex]

[tex]y = \frac{3 + 5}{2} = \frac{8}{2} = 4[/tex]

Thus:

[tex]M_{s2} = (\frac{9 - \sqrt{2}}{2}, 4)[/tex]

Find the midpoint of the segment with endpoints at the midpoints of s1 and s2.

Now the midpoint of the segment with endpoints [tex]M_{s1}[/tex] and [tex]M_{s2}[/tex]. So

[tex]x = \frac{\frac{7 + \sqrt{2}}{2} + \frac{9 - \sqrt{2}}{2}}{2} = \frac{16}{4} = 4[/tex]

[tex]y = \frac{6 + 4}{2} = \frac{10}{2} = 5[/tex]

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

Answer:

[tex]{ \tt{ {x}^{2} + 4x + 3 = 0}} \\ { \tt{(x + 1)(x + 3) = 0}} \\ \\ { \tt{x = - 1 \: \: and \: \: - 3}}[/tex]