Chan rows at a rate of 8 mph in still water. It takes him three hours to row upstream from his house to the park. He rows back home, and it takes him 2 hours. What is the speed of the current?

[tex]\left(\dfrac{1}{3}\right)^2\cdot\left(\dfrac{1}{3}\right)^x=\dfrac{1}{729}\\\\\left(\dfrac{1}{3}\right)^{2+x}=\left(\dfrac{1}{3}\right)^6\iff2+x=6\ \ \ \ |-2\\\\\boxed{x=4}\\\\\text{used:}\\\\a^n\cdot a^m=a^{n+m}[/tex]

Answer:

Domain =R-{6}

Range =R-[-2,0)

Step-by-step explanation:

edge 2021

Answer : option A

To find the range of scores that represents the middle 50 % of the student who took the test , we find inter quartile

Inter quartile range is the middle 50% of the given range of scores.

The difference between the upper quartile and lower quartile is the inter quartile that is middle 50%

From the diagram , we can see that

Upper quartile = 89

lower quartile = 65

So range is 65%  to 89%

Here we will use the formula of compound interest which is as follows:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

A=amount

P=principal

r=rate of interest

n=number of times interest is compounded in a year

t=time

We are given,

r=2% or 0.02

t= 5 years

n =4( compounded quarterly)

A= $300

Let us plug these in the formula to find Principal

[tex]300=P(1+\frac{0.02}{4})^{4*5}[/tex]

[tex]300=P(\frac{4.02}{4})^{4*5}[/tex]

[tex]300=P(1.005)^{20}[/tex]

[tex]300=P(1.105)[/tex]

Principal = $271.49

Answer: Mark earned $271.49 during odd jobs.

To calculate the original amount Mark earned, the compound interest formula is used with the given interest rate, compounding frequency, future amount, and time period. After solving for the principal amount, it's determined that Mark originally earned approximately $271.73.

In order to determine how much Mark originally earned, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

Given that the final amount A is $300.00, the annual interest rate r is 2%, the interest is compounded quarterly (so n is 4), and the time t is 5 years, we can plug these values into the formula and solve for P:

300 = P(1 + 0.02/4)⁴*⁵

300 = P(1 + 0.005)²⁰

300 = P(1.005)²⁰

To find P, we divide both sides by (1.005)²⁰:

P = 300 / (1.005)²⁰

Using a calculator, we can find that:

P ≈ 300 / 1.10408

P ≈ 271.73

Therefore, Mark originally earned approximately $271.73 doing odd jobs last summer.

We are given sides of the triangle by expression

First side : n

Second side : m = 5n-5.

Third side : l = 5/4 m - n.

Perimeter is 90.

Therefore, first equation could be set :

n +m +l = 90   --------------equation(1)

Second equation would be

m = 5n-5        --------------equation(2)

Third equation would be

l = 5/4 m - n   --------------equation(3)

Let us solve the system of equations by substitution.

Substituting m = 5n-5 and l = 5/4 m - n in first equation.

We get

n +5n-5 +5/4 m - n= 90

Now, substituting m = 5n-5 in above equation we get

n +5n-5 +5/4 (5n-5) - n= 90

5n + 25n/4 -5 - 25/4 =90

5n + 6.25n -5-6.25 = 90.

11.25n-11.25 = 90

Adding 11.25 on both sides, we get

11.25n-11.25+11.25 = 90+11.25

11.25n = 101.25.

Dividing both sides by 11.25, we get

n=9.

Plugging n=9 in 2nd equation.

m = 5(9)-5 = 45 -5 = 40.

Plugging n=9 and m=40 in first equation, we get

9 +40 +l = 90

49 +l = 90.

Subtracting 49 from both sides, we get

49-49 +l = 90-49

l = 41.

Therefore, sides are of lengths l = 41, m= 40 and n=9.

To determine how many bottles of soda are needed for 12 bowls of punch, we use the given ratio of 7 bowls to 5 bottles and set up a proportion. We find that 9 bottles of soda are needed for 12 bowls of punch.

The question asks us to figure out how many bottles of soda we need to make a larger amount of punch based on a known ratio. Since it is given that 7 bowls of punch require 5 bottles of soda, we can set up a proportion to find out how many bottles of soda we need for 12 bowls of punch. To do this, we use the initial ratio (7 bowls/5 bottles) and set it equal to the desired ratio (12 bowls/x bottles), where x represents the unknown number of bottles needed for 12 bowls.

We can solve for x by cross-multiplying and dividing:

Set up the proportion: (7 bowls / 5 bottles) = (12 bowls / x bottles)

Cross-multiply: 7 * x = 5 * 12

Simplify: 7x = 60

Divide both sides by 7: x = 60 / 7

Since 60 divided by 7 is not a whole number, we round up, because you can't have a fraction of a bottle in this context. Therefore, x
= 9 bottles (rounded up from 8.57)

So, we would need 9 bottles of soda to make 12 bowls of punch.

-2x + 6y = -38   ⇒   3(-2x + 6y = -38)   ⇒   -6x + 18y = -114

3x  - 4y  = 32   ⇒    2(3x  - 4y  = 32)   ⇒    6x - 18y =   64

                                                                              0   =   50

                                                                                 FALSE

False statement means there are no solutions.

Answer: No Solution

We will solve this system with method of opposing coefficients - Gaussian algorithm

-2x+6y= -38

3x-4y= 32

We will divide first equation with number 2 and get

-x+3y = - 19

then we will multiply the same equation with number 3 and get

-3x+9y = - 57

We will overwrite the second equation below the last one and get next equivalent system

-3x+9y = - 57

 3x-4y = 32

We add first equation to the second and get

5y = -25 => y= -25/5 => y= -5

Now we will replace variable y= -5 in the equation -x+3y = - 19 and get

-x+3(-5) = -19 => -x-15 = -19 => x- 19-15=4 => x=4

The correct answer is (x,y) = (4,-5)

We can check in the first equation and get

-2*4+6*(-5) = -38

-8-30 = -38

-38 = -38  We get equality, the solutions are correct.

This system have one real solution.

Good luck!!!

y² - 4y - 2x - 4 = 0

           +2x +4   +2x + 4

y² - 4y              = 2x + 4

            +4                 +4      

 (y - 2)²          = 2x + 8

             -8              -8

 (y - 2)²  - 8   = 2x

[tex]\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}[/tex]

[tex]\frac{1}{2}[/tex](y - 2)² - 4 = x

x = [tex]\frac{1}{2}[/tex](y - 2)² - 4

Note: this is a parabola whose axis of symmetry is y = 2 and vertex is (-4, 2)

Answer: B) 122 and 58

Supplementary angles add to 180 degrees. In other words, they form a straight angle or a straight line when you combine them together (make sure they don't overlap and that there isn't any gap between them).

Choice B is the only pair of angles where they add to 180 since 122+58 = 180. The values in choice A and choice D add to 90; the values in choice C adds to 270.

Note: complementary angles add to 90 degrees. One way to remember "supplementary" vs "complementary" is to think "S for straight, C for corner". By "corner", I mean a 90 degree corner.

What's the equation?

Without knowing the specific equation, it's difficult to definitively judge the student's conclusion. Assuming the equation is correctly simplified, if both sides of the equation are identical, then it has infinitely many solutions.

The student's claim about the equation having infinitely many solutions is valid only if, upon reducing the equation to its simplest form, both sides are completely identical. Unfortunately, without knowing the specific equation in question, it's impossible to precisely identify whether the conclusion is correct or not.  However, if we assume the student has correctly simplified the equation and found that both sides match exactly, then we can say that statement C: 'The conclusion is correct because when simplified, both sides of the equation are equivalent' is valid.

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The slope is [tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

We have slope m = 3.

[tex]m=3=\dfrac{3}{1}[/tex]

3 > 0 - up 3 units

1 > 0 - right 1 unit

Answer in attachment.

ANSWER

[tex]x=-6y-\frac{21}{2} [/tex]

EXPLANATION

We have

[tex]\frac{2}{3}x +4y=-7[/tex].

Expressing  [tex]x[/tex]  in terms of  [tex]y[/tex] means we should rewrite the relation such that  [tex]x[/tex]  will remain on one side of the equation while  [tex]y[/tex]  and any other constant will be at the other side.

To make [tex]x[/tex] the subject, we add [tex]-4y[/tex] to both sides of the equation.

[tex]\frac{2}{3}x =-4y-7[/tex].

we now multiply the whole equation by the reciprocal of the coefficient of [tex]x[/tex], which is [tex]\frac{3}{2}[/tex].

This implies that;

[tex]\frac{3}{2} \times \frac{2}{3} x=\frac{3}{2} \times (-4y)-\frac{3}{2} \times 7[/tex]

This simplifies to;

[tex]x=-6y-\frac{21}{2} [/tex]

Answer:

the answer is y=1/2

Step-by-step explanation:

Answer:the answer is y=1/2

Step-by-step explanation:

Answer:

Your answer choice is appropriate

Step-by-step explanation:

The orientation is vertical, so the parent function is

... y² - x² = 1

The vertical offset is -3 and the horizontal offset is positive, so the variables will be of the form (y+3)² and (x-something)². At this point, you're able to choose the correct answer.

The distance center to vertex is 13, so we know the y-term denominator is 13². We cannot tell from this graph what the x-term denominator should be, but all the answer choices are in agreement that it should be 81.

The appropriate choice is ...

... (y+3)²/169 - (x-2)²/81 = 1

Answer:

If you are looking for the answer to a graph that looks similar but slightly different, the answer is C.

This graph looks like the one above, but it is inverted, the top hyperbola reaches 15, and the bottom reaches 10. This is correct for A.P.E.X

Hope this helps I couldn't find it anywhere else on brainly.

The given condition is- A bottle contains 20% milk and the rest water. The bottle has 1 liter of water.

Part A:

Let the amount of mixture in the bottle be = x ; mixture will be amount of water plus milk

Given is- the bottle has 1 liter of water and 20% is milk. 20% is 0.2

Hence equation will be:

[tex]0.2x+1 =x[/tex]

Part B:

Solving the equation

[tex]x-0.2x=1[/tex]

[tex]0.8x=1[/tex]

[tex]x=\frac{1}{0.8}[/tex] = 1.25

Hence, total mixture is 1.25 liters.

Water is 1 liter so milk will be = [tex]1.25-1=0.25[/tex]

Or it can also be solved using milk percentage of 0.2%

[tex]0.2*1.25=0.25[/tex]

Hence, milk is 0.25 liter

For the graph of given function ,

At x=2, the graph crosses x axis

At x=-6, the graph touches x axis

At x=-12, the graph crosses x axis

Given :

Equation of a function  [tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:[/tex]

Lets find out the roots and analyze

lets set each factor =0 and solve for x

Exponent in each factor tell us the multiplicity . Using multiplicity we check whether crosses or touches x axis

When multiplicity is odd then graph crosses x axis .

when multiplicity is even then graph touches x axis.

[tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:\\(x-2)^3= 0\\x-2=0\\x=2[/tex]

Root is x=2  with multiplicity 3. 3 is odd

At x=2, the graph crosses x axis

[tex](x+6)^2=0\\x+6=0\\x=-6[/tex]

At x=-6, multiplicity is 2 that is even .

At x=-6, the graph touches x axis

[tex]x+12=0\\x=-12[/tex]

x=-12  with multiplicity 1. 1 is odd

At x=-12, the graph crosses x axis

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To answer this, you will first need to simply the expressions.

[tex]4\sqrt{27} = 12\sqrt{3}[/tex]

[tex]6\sqrt{75} = 30\sqrt{3}[/tex]

Now with the expressions simplified, you'll add the two together getting [tex]42\sqrt{3}[/tex]

So firstly, we have to simplify the radicals. Using the product rule of radicals, simplify these radicals as such:

4√27 = 4 × √9 × √3 = 4 × 3 × √3 = 12√3

6√75 = 6 × √5 × √15 = 6 × √5 × √5 × √3 = 6 × 5 × √3 = 30√3

Now, add these two simplified radicals as such:

12√3 + 30√3 = 42√3

42√3 is your final answer.

(a) 32 orange marbles

the ratio of red : blue = 18 : 48 = 3 : 8 ( in simplest form )

the ratio of green : orange = 3 : 8 ( equal ratio )

divide green by 3 to obtain 1 part of ratio then multiply this value by 8 to obtain the amount of orange marbles

3 parts → 12

8 parts → 12 × [tex]\frac{8}{3}[/tex] = 32 orange marbles

1. If the intersection of two lines is a point, then they intersect. = Converse

2. If two lines do not intersect, then their intersection is not one point. = Inverse

3. If the intersection of two lines is not one point, then the two lines do not intersect. = Contrapositive

I did the assignment already, it's correct.

The conditional statement 'If two lines intersect, then their intersection is one point' is matched with three possible related statements.

The conditional statement 'If two lines intersect, then their intersection is one point' can be matched with the following:

If the intersection of two lines is a point, then they intersect

If two lines do not intersect, then their intersection is not one point

If the intersection of two lines is not one point, then the two lines do not intersect

Explanation:

This question is about conditional statements related to the geometric properties of lines. The given statement is that if two lines intersect, their intersection is exactly one point. Statement 1 is the converse, meaning if their intersection is a point, then the lines must intersect. Statement 2 is the contrapositive, asserting that if two lines do not intersect, they can't have a single intersection point. Statement 3 reason that if the intersection is not exactly one point, then they do not intersect at all.

A 7th grade student will be absent approximately 0.4 times during the month.

To find out how many times a 7th grade student will be absent during the month, we first need to determine the average number of absent students per day for each grade. The total number of absent students across all grades is 5 + 8 + 9 = 22. Since there are 20 school days in a month, the average number of absent students per day is 22 / 20 = 1.1.

Next, we need to determine the proportion of absent students that are 7th graders. The 7th graders had 8 absent students, so their proportion of absent students is 8 / 22 = 0.3636 (rounded to four decimal places).

Finally, to find out how many times a 7th grade student will be absent during the month, we multiply the average number of absent students per day (1.1) by the proportion of absent students that are 7th graders (0.3636). This gives us the final answer of approximately 0.39996 (rounded to five decimal places) or about 0.4 times.

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I believe the answer would be 46 students

> 46 Students in Tom's school are Left-Handed

Answer:

[tex]x=3\sqrt{3i} \\or\\x=-3\sqrt{3i}[/tex]

Step-by-step explanation:

What is the solution of the equation when solved over the complex numbers?

x2+27=0

Enter your answers, as exact values, in the boxes.

x =  [tex]3\sqrt{3i}[/tex]  or x =[tex]-3\sqrt{3i}[/tex]