How many isosceles triangles appear in this figure? Given: ca=ce 1 2 3 4

Find the value of k

Sholpan [36]

9514 1404 393

Answer:

k = -2

Step-by-step explanation:

The determinant can be formed by subtracting up-diagonal products from down-diagonal products:

(x)(x+y)(y) +(y)(x)(x+y) +(x+y)(y)(x) -(x+y)^3 -x^3 -y^3

= 3xy(x+y) -(x^3 +3x^2y +3xy^2 +y^3) -x^3 -y^3

= -2(x^3 +y^3)

The value of k is -2.

4 0

3 years ago

caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe. Two caps are drawn wothout replacement from the wardrobe.

Hitman42 [59]

Answer:

18/95

Step-by-step explanation:

What is probability?

Probability is simply the chances of something occuring.

As a formula, I like to say that formula = # of favorable outcomes / total # of outcomes

Where favorable outcomes is what we want to happen and total # of outcomes is the total number of possibilities.

In order to find the probability of the occurrence of something in a row, we multiply the individual probabilities of each action

Understanding the question

Here we are given that caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe and given this we want to find the probability of Caleb randomly selecting 2 blue caps without replacing it the first being drawn.

So here # of favorable outcomes = # of blue caps = 9

and

total number of outcomes = total # of caps = 7 + 4 + 9 = 20

Finding the probability

For first draw

First let's find the probability that caleb will select a blue cap the first time.

We know that probability = # of favorable outcomes / total # of outcomes

We also know that # of favorable outcomes = 9 and total # of outcomes = 20

Plugging this in, we get that the probability of Caleb randomly selecting a blue cap on the first draw is 9/20

For second draw

Because it says that caleb will not replace the cap when drawn it's important to subtract 1 from both the # of caps and # of blue caps

This results us in having # of favorable outcomes as 8 and total # of outcomes as 19

Plugging this in we get that the probability of Caleb drawing a blue cap the second time is 8/19

Finally to find the total probability of him selecting two blue caps in a row without replacing the first cap, we multiply the individual probabilities

From doing so we acquire 9/20 * 8/19 = 18/95

4 0

2 years ago

Read 2 more answers

In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen t

zheka24 [161]

Answer:

B. F:S = 17 to 19; S:F = 19 to 17

Step-by-step explanation:

Put the corresponding numbers in the corresponding parts of the ratio you want to write:

freshmen to sophomores (F:S)

17 to 19

___

sophomores to freshmen (S:F)

19 to 17

These pairs of numbers match choice B.

5 0

3 years ago

Use the distributive property to remove the parentheses. -8(-v^[2]-3+6x^[3])

Kruka [31]

Answer:

8v^2+24-48x^3

Distribute the -8 to each term to get your answer.

Hope I helped!

6 0

3 years ago

ABCD is a trapezoid. What is the area of trapezoid?

lana [24]

Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
Area = (1/2)(AB + AB/4)·h = (5/8)AB·h

The given dimensions let us determine the area of ∆BCE to be
Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²

The total area of the trapezoid is also the sum of the areas ...
Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h

Putting all of the above into the equation for the total area of the trapezoid, we have
Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
(5/8 -1/6 -1/12)AB·h = 30 cm²
AB·h = (30 cm²)/(3/8) = 80 cm²

Then the area of the trapezoid is
Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²

6 0

3 years ago