Two samples of carbon come into contact. A heat transfer will occur between sample A and sample B. What must be true for

Q.2

Katen [24]

Answer:

Q2. (16,8)

Q3. $k=\frac{2}{3}$ , ratio=5:1

Q4. Ratio=2:1

Q5. Ratio=1:1

Step-by-step explanation:

Q2. Let (2a,a) be the coordinates of P.

Since P is equidistant from Q (2,-5) and R (-3, 6), we have

$|PQ|=|PR|$

This gives us:

$\sqrt{(2a-2)^2+(a+5)^2}=\sqrt{(2a+3)^2+(6-a)^2}$

$\implies (2a-2)^2+(a+5)^2=(2a+3)^2+(6-a)^2$

Expand:

$4a^2-8a+4+a^2+10a+25=4a^2+12a+9+a^2 -12a+36$

$2a=16$

$a=8$

The coordinates of P are $(16,8)$

Q.3 The equation of the line segment joining the points

A (5.-6) and B (-1,-4) is $x+3y=-13$ .

The x-coordinate of the point that divides AB in the ratio m:n is

$x=\frac{mx_2+nx_1}{m+n}$

The y-axis meets this line at $(0,-\frac{13}{3})$

We substitute $x_2=-1,x_1=5,x=0$ into this equation and solve for m and n.

$0=\frac{-m+5n}{m+n}$

$m=5n$

$\frac{m}{n}=\frac{5}{1}$

Therefore the ratio is m:n=5:1

Q.4 The equation of the line segment joining

the points (-5,-4) and (-2,3) is $-7x+3y=23$ .

The point (-3, k) must satisfy this line because it lies on it.

$-7(-3)+3k=23$ .

$\implies k=\frac{2}{3}$

We again use the equation $x=\frac{mx_2+nx_1}{m+n}$ to find the given ratio.

Substitute: $x_2=-2,x_1=-5$

$4=\frac{-2m+-5n}{m+n}$

$\implies m=2n$

$\frac{m}{n}= \frac{2}{1}$

The ratio is m:n=2:1

Q. 5 The equation of the line joining A (2,3) and B(6,-3) is $3x+2y=12$ .

We substitute (4,m) to get:

12+4m=12

4m=0

m=0

It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).

Hence the ratio is 1:1

5 0

3 years ago

Two numbers add to 251 and the second is 41 bigger then the first. what are the two numbers?

PIT_PIT [208]

$\left\{\begin{array}{ccc}x+y=251\\y=x+41\end{array}\right\\\\substitute:\\\\x+x+41=251\\2x+41=251\ \ \ \ /-41\\2x=210\ \ \ /:2\\x=105\\\\y=105+41=146\\\\Answer:105\ and\ 146.$

6 0

3 years ago

Read 2 more answers

Which is the graph of LaTeX: y=x^2-4x+4y = x 2 − 4 x + 4?

Nat2105 [25]

Answer:

Step-by-step explanation:

Since we will be "completing the square" we will isolate the x2 and x terms ... so move the + 5 to the other side of the equal sign. y - 5 = 2x2 - 4x. We need a leading coefficient of 1 for completing the square ..

6 0

3 years ago

Gina takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit

Kipish [7]

Answer: second option.

Step-by-step explanation:

Let be "w" the credit hours at Westside Gina is taking.

You know that class fees are $98 per credit hour at Westside, then the expression for the dollar amount she paid for her class fees at Westside is:

$98w$

Since she is taking a combined total of 13 credit hours at the two schools, the credit hours at Pinewood Gina is taking can be represented by this expression:

$13-w$

You know that class fees are $115 per credit hour at Pinewood, then the dollar amount she paid for her class fees at Pinewood can be expressed as:

$115(13-w)$

Therefore, the expression for the combined total dollar amount she paid for her class fees is:

$total\ paid=98w+115(13-w)\\\\total\ paid= -17w + 1495$

6 0

3 years ago

Read 2 more answers

Find the X COORDINATE OF THE intersection of 9x - 6y = 12 and 3x + 2y =8

yaroslaw [1]

Answer: $x=2$

Step-by-step explanation:

Given a System of linear equations, the solution of the system is the point $(x,y)$ in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.

Having the following System of equations:

$\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.$

You can use the Elimination method to find the value of "x":

-Multiply the second equation by 3.

- Add the equations.

- Solve for "x".

Then, you get:

$\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2$

8 0

3 years ago