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3 years ago

In the figure, point B is the midpoint of AC . Use the figure to answer the questions.

Mathematics

1 answer:

kirza4 [7]3 years ago

4 0

Answer

Proof of (a)

Disagree with the ΔABD = ΔCBD by the SAS congruence postulate .

SAS congurence property

In this congurence property two sides and one angle of the two triangles are equal .

(1) BD = BD ( Common sides of the ΔABD and ΔCBD )

(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)

but equal angles are not given

therefore disagree with the ΔABD = ΔCBD by the SAS congurence postulate .

Proof of (b)

SSS congurence property

In this congurence property three sides of the two triangles are equal .

In the ΔABD and ΔCBD .

(1) BD = BD ( Common sides of the ΔABD and ΔCBD )

(2) AB =BC (B is the midpoint of the AC i.e it bisect AC in the two equal parts.)

(3) AD=CD (Given )

ΔABD = ΔCBD by the SSS congurence theorem

Hence proved

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in parallelogram abcd diagonals ac and bd intersect at point l . If Al= x-2 and ac =3x-16 , then which of the following represen

TiliK225 [7]

Answer:

The length of CI is 10 units.

Step-by-step explanation:

It is given that ABCD is a parallelogram and diagonals AC and BD intersect at point I.

The diagonals of a parallelogram bisect each other.

$AI=CI$

$AC=AI+CI$

$AC=AI+AI$ $[\because AI=CI]$

$AC=2AI$

$3x-16=2(x-2)$

$3x-16=2x-4$

$3x-2x=16-4$

$x=12$

The value of x is 12.

$CI=AI=x-2=12-2=10$

Therefore the length of CI is 10 units.

4 0

3 years ago

Help! ( i'll give brainlisy ) if you don't know the answer then don't type a "answer" and no sending links please.

julsineya [31]

Answer: Linear

The equation is y = 2x-5

Slope = 2

y intercept = -5

====================================================

Explanation:

Each time x goes up by 1, y increases by 2. This directly leads to a linear equation due to the same rate of change no matter where you are in the table.

The slope is rise/run = 2/1 = 2 because "y increases by 2 each time x increases by 1".

We could use the slope formula to see this. Pick on any two rows to plug in the coordinates. I'll use the last two rows

m = (y2-y1)/(x2-x1)

m = (3-1)/(4-3)

m = 2/1

m = 2

This confirms the slope is 2.

The positive slope means that the line goes uphill as you move from left to right.

---------------

The y intercept is b = -5 because the y intercept always happens when x = 0. This applies to any function, whether it's linear or not.

Together with m = 2 as the slope and b = -5 as the y intercept, we go from y = mx+b to y = 2x-5 as our linear equation

As a way to check, plug in something like x = 1 to find that...

y = 2x-5

y = 2*1-5

y = 2-5

y = -3

The table shows that x = 1 and y = -3 pair up together in the same row, so that confirms x = 1. I'll let you verify the other x values.

3 0

3 years ago

A cable car starts off with n riders. The times between successive stops of the car are independent exponential random variables

nikitadnepr [17]

Answer:

The distribution is $\frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

Solution:

As per the question:

Total no. of riders = n

Now, suppose the $T_{i}$ is the time between the departure of the rider i - 1 and i from the cable car.

where

$T_{i}$ = independent exponential random variable whose rate is $\lambda$

The general form is given by:

$T_{i} = \lambda e^{- lambda}$

(a) Now, the time distribution of the last rider is given as the sum total of the time of each rider:

$S_{n} = T_{1} + T_{2} + ........ + T_{n}$

$S_{n} = \sum_{i}^{n} T_{n}$

Now, the sum of the exponential random variable with $\lambda$ with rate $\lambda$ is given by:

$S_{n} = f(t:n, \lamda) = \frac{\lambda^{n}e^{- \lambda t}t^{n - 1}}{(n - 1)!}$

5 0

3 years ago

Complement of 70 degrees

Hitman42 [59]

Answer:

20 degrees

Step-by-step explanation:

to find the complement you subtract the angle by 90 degrees

6 0

3 years ago

What is the distance between A(-8, 4) and B(4, -1)?

Anettt [7]

Answer:

The distance between A(-8, 4) and B(4, -1) is 13 units.

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula given by:

$\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

We have the two points A(-8, 4) and B(4, -1). Let A(-8, 4) be (<em>x₁, y₁</em>) and let B(4, -1) be (<em>x₂, y₂</em>). Substitute:

$d=\sqrt{(4-(-8))^2+(-1-4)^2}$

Evaluate:

$d=\sqrt{(12)^2+(-5)^2}$

So:

$d=\sqrt{144+25}=\sqrt{169}=13\text{ units}$

The distance between A(-8, 4) and B(4, -1) is 13 units.

7 0

3 years ago

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