All categories

2 years ago

Prove that triangle PQR is congruent to triangle QSR.

Mathematics

1 answer:

lora16 [44]2 years ago

7 0

Answer:

They are congruent to one another because both triangles have all equal sides. Therefore they are congruent.

Step-by-step explanation:

You might be interested in

(PLEASE HELP I WILL GIVE BRAINLIEST IF CORRECT (40 POINTS)

Andrews [41]

Answer:

2800 - 4000

Step-by-step explanation:

40 × 70 = 2800

50 × 80 = 4000

3 0

2 years ago

Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

2 years ago

Is (x+1) a factor off (x)=x3+x2−4x−4? <br><br> A) Yes<br> B) No

satela [25.4K]

Remainder theorem again...

$p(x)=x^3+x^2-4x-4$

$p(-1)=(-1)^3+(-1)^2-4(-1)-4=0$

So Yes, $x+1$ is a factor.

4 0

3 years ago

Read 2 more answers

What heat transfer is Christmas lights radiation or convention or conduction

Firdavs [7]

Answer:

The heat from the sun or heat released from the filament of a light bulb is the example of radiation.

7 0

2 years ago

Read 2 more answers

Can someone help me with this one math problem ? picture is below

Scorpion4ik [409]

I am not sure on how to do this however here is a link with information thst will be able to help you around this subject.i hope this helps
https://www.bbc.com/bitesize/guides/z8k887h/revision/1

4 0

3 years ago

Read 2 more answers