HW1.
The vertices of a triangle ABC are A(2, 1), B(-2, 3) and C(4, 5). Find the equation of the median through the
vertex A
A
Assume D be the midpoint of BC

Answer:

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

Step-by-step explanation:

A line being perpendicular means that it has a slope that is an opposite reciprocal of the other line.

In this case:

[tex]x - 2y = 5\\-2y = -x + 5\\y = \frac{x}{2} - \frac{5}{2}[/tex]

The slope of this line is [tex]\frac{1}{2}[/tex] and so the perpendicular slope would be [tex]-2[/tex].

Using the point slope form:

[tex]y - y_1 = m(x-x_1)\\[/tex]

Substitute values:

[tex]y - y_1 = m(x-x_1)\\y - 2 = -2(x+2)\\y -2 = -2x-4\\y = -2x-2[/tex]

Answer:

  -i, 1, i, -1, 1, -1

Step-by-step explanation:

You want the simplified form of various expressions involving powers of i.

The definition of i is ...

  i = √(-1)  or  i² = -1

This value can be used to find other powers:

  i³ = (i²)(i) = -i

  i⁴ = (i²)² = (-1)² = 1

This means any power of i is equivalent to that power modulo 4.

  [tex]-i^{25}=-i^1 = \boxed{-i}\\\\i^{16}=i^0=\boxed{1}\\\\i^{17}=i^1=\boxed{i}\\\\-i^{32}=-i^0=\boxed{-1}\\\\i^{-9}\times -i^{11}=-i^{-9+11}=-i^2=-(-1)=\boxed{1}\\\\\dfrac{i^{23}}{-i^{11}}=-i^{23-11}=-i^{12}=-i^0=\boxed{-1}[/tex]

The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .

In the question ,

it is given that,

the equation of the line is  [tex]y=-\frac{4}{3}x-2[/tex] ,

we need to plot the graph of the given line ,

To sketch the graph we need minimum two points .

when we put x [tex]=[/tex] 3 in the equation , we get

y [tex]=[/tex] (-4/3)(3) - 2

y = -4 - 2

y = -6

the first point is (3,-6)  .

For second point put x [tex]=[/tex] 6 ,

we get

y = (-4/3)(6) - 2

y = -4*2 - 2

y = -8 - 2

y = -10

the second point is (6,-10) .

After plotting and joining the point  (3,-6) and (6,-10) ,

the graph is shown below .

Therefore , The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .

The given question is incomplete , the complete question is

Draw the graph which represents the equation y [tex]=[/tex] (-4/3)x - 2   ?

Learn more about Graphs here

https://brainly.com/question/27795078

#SPJ1

Answer: 177.936.....

Step-by-step explanation:but since this number is not a natural number its not possible

The required amount in the savings account=$2704.05

What is simple interest?

Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.

P=2700, r=0.3%=0.003, t= 0.5 year

A= P(1+rt)

 = 2700(1+ 0.003*0.5)

 = 2700(1+ 0.0015)

 = 2700(1.0015)

 = 2704.05

To learn more about simple interest from the link

https://brainly.com/question/25793394

#SPJ1

702, 0.91, 0.73, 0.76  shows the decimal numbers in order from smallest to largest.

What is a decimal number?

Here are four decimal numbers:

0.702, 0.76, 0.91, 0.73

the numbers in order from smallest to largest.

702, 0.91, 0.73, 0.76

Learn more about decimal number

brainly.com/question/4708407

#SPJ1

Answer:

B)  0.702, 0.73, 0.76, 0.91

Step-by-step explanation:

The given set of decimal numbers (in any order) is:

Each number has zero units.

Comparing the digits in the tenth place, all the numbers have 7 tenths except 0.91 which has 9 tenths.  Therefore, 0.91 is the largest number as 9 > 7.

Comparing the digits in the hundredths place of the other three numbers, 0.702 is the smallest number as it has zero hundredths.

As 0.73 has 3 hundredths and 0.76 has 6 hundredths, this means that 0.73 is the second smallest number as 3 < 6.

Therefore, the given set of decimals in order from smallest to largest is:

Answer:

the first one

Step-by-step explanation:

one because 13+7= 20 and 20 is a bigger than 5 so there for it i one

Answer: 4 + (2*3)^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

you'll need to know  L'Hôpital's Rule.  Obviously this problem goes to zero in the denominator if you let x go to zero, which is a big problem :P  sooo use L'Hopital's rule to solve this messy problem.  

L'Hoptial's rule takes the advantage that you can find the derivative of something but still find it's limit just like you didn't take a derivative.  soo

take derivative of numerator and denominator  separately

remember how to take derivative of  sin^2(3x) ??

pull the two down,   then chain rule

d/dx (sin^2(3x) =   2sin(3x) * cos(3x) * 3    = 6*sin(3x)*cos(3x)

d/dx (4x^2)  = 8x

we still have the same issue if we take the limit if x goes to zero :0

but it's okay... just take L'Hopitals' again :P

d/dx (6*sin(3x)*cos(3x)) =  6*cos(3x) *3 *(-sin(3x)*3 = 54*cos(3x)*(-sin(3x))

d/dx (8x) = 8

now we can let the limit go to zero

lim ( x ->0)[54*cos(3x)*(-sin(3x)) / 8]

we can see that sin(x) will get closer and closer to zero so we have 0/8

so we can fairly say,  without guessing, that yes... this limit goes to zero as X goes to zero.  :)  nice

Answer:

Time 2 540 years

Step-by-step explanation:

T = 5 600 yares - Half-life

73% - Carbon content

N = 0.73·N₀

Decay constant:

λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124  (years)⁻¹

Law of radioactive decay:

N = N₀·e^(-λ·t)

0.73·N₀ = N₀·e^(-λ·t)

0.73 = e^(-λ·t)

ln (0.73) = -λ·t

t = ln (0.73) / (-λ)  = ln (0.73) / (- 0.000124)  ≈ 2 540 years

The area of lengthwise pathway is 610 m²

The area of breadthwise pathway is 360 m²

The total area of the two pathways is 985 m²

Given,

The side of square field = 125 m

The width of the lengthwise path = 3 m

The width of the breadthwise path = 5 m

We have to find the area of the two pathways.

Here,

Area of path on length wise = (125 - 3) × 5 = 610 m².

Area of path on breadth wise = (125 - 5 ) × 3 = 360 m²

Area of rectangle at intersection of paths = 5 × 3 = 15 m².

Thus the Total area of two pathways = 610 + 360+15 = 985 m²

Learn more about area here;

https://brainly.com/question/14882802

#SPJ1

Answer

0.8 ft/hr

Explanation

2 4/5 ÷ 3 1/2 = 2.8 ÷ 3.5 = 0.8

Terry should mix 29 gallons of the 25%  acid solution and 11 gallons of the 80%  acid solution

Given: 40% acid and 80% acid solutions

Terry needs 40 gal of a 40% acid solution

Let x represent the amount of the 25%  acid solution required in gal

Thus, the amount of the 80% acid solution required will be (40-x) gal

The amount of acid in these solutions is 0.25x + 0.8(40-x)

Since Terry wants exactly 40% or 0.4 of 40 gallons i.e. 0.4×40 gallons

The amount  of acid in these solutions will be:

0.25x + 0.8(40-x) = 0.4×40      Solve for x

0.25x + 32-0.8x  = 16

0.8x-0.25x = 32-16

0.55x = 16

x = 16/0.55 = 29 gallons

40-x = 40 -29 = 11 gallons

Therefore, the amount of the 25%  acid solution required is 29 gallons

and the amount of the 80%  acid solution required is 11 gallons. So she should mix 29 gallons and 11 gallons respectively

Learn more about percentages on:

https://brainly.com/question/843074

#SPJ1

71.849 feet of fencing are required.

Given:

In a rectangle two sides are 13 feet and 12 feet.

In right angled triangle sides are 15 feet and 13 feet.

Let x be the hypotenuse of the triangle.

From rectangle opposite sides are equal so the other two sides are equal to 12 feet and 13 feet.

According to pythagorean theorem:

[tex]15^{2} +13^{2} =x^{2}[/tex]

x = [tex]\sqrt{225+169}[/tex]

x = 19.849

The perimeter of the pool = 15 + 12 + 13 + 12 + 19.849

= 27 + 13 + 12 + 19.849

= 52+19.849

= 71.849 feet.

Therefore 71.849 feet of fencing are required.

Learn more about the fencing here:

https://brainly.com/question/13953358

#SPJ1

The equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.

Given equation is -x+2y = 30

and passing through the point (3,6).

If two lines are parallel, their slopes will be equal.

We know that equation for parallel lines is y = 3x+c

Now, -x + 2y = 30

= 2y = 30 + x

[tex]= y = \frac{30+x}{2}[/tex]

[tex]= y = \frac{30}{2} +\frac{x}{2} \\\\= y = 15 + \frac{x}{2}[/tex]

Therefore slope = [tex]\frac{1}{2}[/tex]

Equation of line with slope and passing through (3,6)

[tex]y-y_{1} = m(x-x_{1}) \\\\y - 6 = \frac{1}{2} (x-3)\\\\[/tex]

2(y-6) = 1(x-3)

2y - 12 = x - 3

x - 2y + 9 = 0

Hence the answer is the equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.

To learn more about equations click here https://brainly.com/question/25678139

#SPJ9

The arrow first reach an altitude of 60 meters is 13 seconds.

A General Rule for Solving Equations

h (t) = -2.1t² +32t-0.03 ---(i)

The arrow first reach an altitude of 60 meters:

h(t) = 60 -- (ii)

Equate the (i) and (ii)

60 = -2.1t² +32t-0.03

2.1t² - 32t + 0.03 + 60 = 0

2.1t² - 32t + 600.3 + = 0

t = -13, 13

Hence, The arrow first reach an altitude of 60 meters is 13 seconds.

To know more about equations check the below link:

https://brainly.com/question/22688504

#SPJ1

In the right-angled triangle ABC, CA is 4.2cm.

What is a right-angled triangle? How to identify it?

Any angle that is a right angle or has one of its interior angles equal to 90 degrees is considered to be in a right-angled triangle. This triangle is also known as the right triangle or the 90-degree triangle for this reason. Trigonometry heavily utilizes the right triangle. In this article, let's learn more about this triangle.

By applying Pythagoras' theorem, one can determine whether a triangle has a right angle. If the squares of the triangle's two shorter sides equal the square of the hypotenuse, a right angle is present.

Solution explained:

A/Q, we have

BC = 9.2cm and m∠A = 63°

Using the tangent ratio formula (ratio of a side that is not the hypotenuse to a side that is near to an angle), we get

[tex]tanA = \frac{BC}{CA}[/tex]

tan 63° = [tex]\frac{9.2}{CA}[/tex]

CA = [tex]\frac{9.2}{1.96}[/tex]     (tan 63° = 1.96)

CA = 4.687 ≅ 4.7cm

To learn more about right-angle triangles, use the link given
https://brainly.com/question/25016594
#SPJ1

The value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].

The coefficient of restitution is the ratio of the final to initial speed between two bodies after the collision. While a value of 1 indicates a perfectly elastic collision, a value of 0 indicates a perfectly inelastic collision.

The first option is

We can find the displacement by using the area under the graph, which is equal to the displacement. The area of the triangle can be found using the formula below.

[tex]Area = \frac{1}{2} . base . length[/tex]

[tex]Area = 0.5m.50m.50. = 1250 m^{3}[/tex]

The other option is

We use the conservation of energy. So, we equate the potential energy and the kinetic energy.

[tex]E_{pot} = E_{kin}\\ \\ m.g.h = \frac{1}{2}.m.v^{2}[/tex]

The mass is cancelled out in the above equation, and we re-arrange with respect to velocity.

[tex]v^{2} = 2.g.h\\ \\v = \sqrt{2.9.81\frac{m}{s^{2} }.3m } = 7.67\frac{m}{s}[/tex]

Hence the answer is the value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].

To learn more about functions of height click here https://brainly.com/question/25037584

#SPJ9

Answer:

5(d)

Step-by-step explanation:

(3.0471×10⁹)/2.4×10^-4

30471×10^9-4÷24×10^-4-1

30471×10⁵÷24×10^-5

(30471÷24)×10^5-(-5)

1269.625×10^5+5

1269.625×10¹⁰

1.269625×10^10-3

1.269625×10⁷

1.2696 to 5s.f

from the reading above, doesn't seem the boric acid has any alcohol at all, so we can say 0% alcohol.

now let's see how many liters we have hmmm 2 of hazel, 1 of alcohol and the rest in boric acid, to make a total of 5 liters, so boric acid must be 2, since 2 + 1 + 2 = 5.

how much alcohol is there in 14% of 2 liters?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{14\% of 2}}{\left( \cfrac{14}{100} \right)2}\implies 0.28[/tex]

how much alcohol is there  in 95% of 1? well, no to bore you to death, is just 0.95 liters, and we know the boric acid has no alcohol.

so in the 5 liters of the lotion, we have 0.28 liters plus 0.95 liters of alcohol total, that's 1.23 liters total.

now, if we know the 100% of the lotion is the 5 liters, how much is 1.23 liters off of it in percentage?

[tex]\begin{array}{ccll} liters&\%\\ \cline{1-2} 5 & 100\\ 1.23& x \end{array} \implies \cfrac{5}{1.23}~~=~~\cfrac{100}{x} \\\\\\ 5x=123\implies x=\cfrac{123}{5}\implies x=\stackrel{\%}{24.6}[/tex]

Step-by-step explanation:

One taco =$10.20/12=$0.85

Answer:

5 nickels and 4 dimes

Step-by-step explanation:

5 nickels = 25 (5 x 5)

4 dimes = 40 (4 x 10)

Answer:

23

Step-by-step explanation:

5^2=25

50/10 = 5

3+25-5

Answer:

40

Step-by-step explanation:

We divide 317 by 8 to see how much for each table

317/8 is 39.625

We round up for the next whole number since the last table is probably not filled all the way

So we need 40 tables

Hopes this helps please mark brainliest

Answer:

40 tables

Step-by-step explanation:

317 divided by 8 equals 39.625

Round the answer.

Since the number after the decimal is bigger than 4, round up to the nearest whole number which is 40.

P.S. this is simple math. No offense, but you should have been able to figure this out yourself. It's not that hard. Again, not trying to offend you. Just letting you know.

Answer:

D.4

Step-by-step explanation:

You can try replacing x value with the answer one by one.

A. 1(7) > 22 = 7 > 22, false, 7 smaller than 22

B. 2(7) > 22 = 14 > 22, false, 14 smaller than 22

C. 3(7) > 22 = 21 > 22, false, 21 smaller than 22

D. 4(7) > 22 = 28 > 22, true, 28 is larger than 22

The number is 11.

Lets assume that the P is the product of the number 'x' and 5, then the equation will become :

P = 5x .......i

now given that the product P is same as the 11 less than 6 times the number 'x'., therefore the equation will become :

P = 6x -11 ......ii

Now from i and ii,

5x = 6x -11 ,

11 = 6x - 5x

therefore, x = 11.

to know about more equation https://brainly.com/question/27429713

#SPJ1

Answer:

Any of the following will work: -9,-8,-7,-6,-5,-4,-3, or -2,

Step-by-step explanation:

What does < mean?

The less than sign shows that the number being compared is LESS than the other number.

Think: 9 < 100 showing that the number 9 is less than the number 100

What does > mean?

The greater than sign shows that the number being compared is GREATER than the other number.

Think: 100 > 9 showing that 100 is greater than the number 9

What is an integer?

Integers are all whole positive and negative numbers including zero.

Think: -13 and 13 are integers but 13.445 or -13.445 are not.

How can we prove these answers?

Simply looking at a number line, we can fill in what numbers would be greater than -10 but less than -1. Remember, these numbers must be whole numbers.

Answer:

Step-by-step explanation:

Given

Number of servings:

The number local extremas to the function is given as follows:

3.

They are classified as follows:

The local extremas of a function are the turning points of the graph of the function, and they are classified as follows:

The graph of the function has three turning points, and they are defined as follows:

More can be learned about the local extremas of a function at https://brainly.com/question/24367710

#SPJ1

It will take the boat going north 16.5hrs and the boat going south will take it 8.25hrs

Step-by-step explanation:

divide 66/4 for the north boat and 66/8 for the south boat