All categories

2 years ago

Given: PRbisects ZQPS, PQ = 12units, and PS= 12units

Mathematics

1 answer:

Ganezh [65]2 years ago

3 0

Answer:

Use SAS to show that triangles PRQ and PRS are congruent.

Step-by-step explanation:

Since PR bisects angle QPS, angles QPR and SPR are congruent. By reflexive property of congruence, PR is congruent to itself. Since PQ is congruent to PS, we can use SAS to show that the two triangles are congruent. By CPCTC, QR is congruent to SR.

You might be interested in

1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

A 500 g model train car traveling at 0.8 m/s collides with a 300 g stationary car. The cars hook up and move off down the track

sdas [7]

Answer:

$0.5ms^{-1}$

Step-by-step explanation:

Let v be the speed after the collision of both the cars.

Now, momentum is given by: mass × velocity, then by equating the total momentum before and after the collision of the two cars, we get

$500{\times}0.8+300{\times}0=(500+300)v$

⇒ $400+0=800v$

⇒ $400=800v$

⇒ $v=0.5ms^{-1}$

Thus, they are moving at the velocity of $0.5ms^{-1}$

3 0

3 years ago

Read 2 more answers

When two customers enter the store together, what is the probability that at least one of them will make a purchase?

arsen [322]

The probability is 1/2 or 50%.

Hope this helps :)

5 0

3 years ago

I need to u substitution method to solve -5x-8y=17 , 2x-7y=-17

harina [27]

Answer:

Alright well solve for the variable in one of the equation's. then substitute the result of the other equation

Point form: - 175/51, 1/51

Equation form:

x = - 175/51 y = 1/51 Hope this help's :)

Step-by-step explanation:

8 0

3 years ago

If the root of the function 4x²-6x+1=0 are a and b find the values of a and b

borishaifa [10]

Answer:

Step-by-step explanation:

We need to find 2 roots of the quadratic function given and find the greater of the two roots.

3 0

2 years ago