Why would we start at (0,200)?

Naya [18.7K]

Firstly expand (x - 3)(ax^2 + bx + c):
ax^3 + bx^2 + cx - 3ax^2 - 3bx - 3c

Now rearrange it so that it's in the form ax^3 + bx^2 + cx + d:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c

Now we can compare both equations:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c = 2x^3 - x^2 - 19x + 12

We get:
(1) a = 2
(2) b - 3a = -1
(3) c - 3b = -19
(4) -3c = 12

If we substitute (1) into (2) we get:
b - 3*2 = -1
b - 6 = -1
b = 5

Now if we solve (4) we get:
-3c = 12
c = -4

Therefor a = 2, b = 5 and c = -4

8 0

3 years ago

(a) Find an angle between 0° and 360° that is coterminal with – 120°.

Novay_Z [31]

Answer:

a) $240\degree$

b) $\frac{15\pi}{4}$

Step-by-step explanation:

<u>Coterminal angles</u> have the same terminal sides in standard position.

a) To find an angle between $0\degree$ and $360\degree$ , that is coterminal with $-120\degree$ , we keep adding multiples of $360\degree$ until we get an angle within the specified range.

$-120\degree \implies -120\degree +360\degree=240\degree$ .

In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.

b) This time we want to find an that coterminal with $\frac{15\pi}{4}$ radians.

We keep subtracting multiples of $2\pi$ until we get an angle measure within the specified range.

$\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}$

4 0

3 years ago

The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0). Which type of triangle is ∆ABC? Select All that apply.

stepan [7]

Given:

The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0).

To find:

The type of the given triangle.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the distance formula, we get

$AB=\sqrt{(5-(-3))^2+(8-2)^2}$

$AB=\sqrt{(8)^2+(6)^2}$

$AB=\sqrt{64+36}$

$AB=\sqrt{100}$

$AB=10$

Similarly,

$BC=\sqrt{(11-5)^2+(0-8)^2}$

$BC=\sqrt{(6)^2+(8)^2}$

$BC=\sqrt{36+64}$

$BC=\sqrt{100}$

$BC=10$

And,

$AC=\sqrt{(11-(-3))^2+(0-2)^2}$

$AC=\sqrt{(14)^2+(-2)^2}$

$AC=\sqrt{196+4}$

$AC=\sqrt{200}$

$AC=10\sqrt{2}$

Two sides of the triangle are equal, i.e., $AB=BC$ . So, the triangle is an isosceles triangle.

Sum of square of two smaller side is

$AB^2+BC^2=10^2+10^2$

$AB^2+BC^2=100+100$

$AB^2+BC^2=200$

$AB^2+BC^2=AC^2$

Using the Pythagoras theorem, we can say that the given triangle is a right triangle.

Therefore, the correct options are B and F.

7 0

3 years ago

A box contains 100 balls, of which r are red. Suppose that the balls are drawn from the box one at a time, at random without rep

Eddi Din [679]

Answer:

(a) $\frac{r}{100}$

(b) $\frac{r}{100}$

(c) $\frac{r}{100}$

Step-by-step explanation:

Given,

The total number of balls = 100,

Red balls = r

So, the remaining balls = 100 - r,

(a) ∵ The probability that first ball drawn will be red

$=\frac{\text{Red balls}}{\text{Total balls}}$

$=\frac{r}{100}$

(b) Also, the probability of a ball other than red ball = $1-\frac{r}{100}$

$=\frac{100-r}{100}$

So, the probability of getting red ball in second thrawn( one is red second is red or one is not red second is red ),

$=\frac{r}{100}\times \frac{r-1}{99}+\frac{100-r}{100}\times \frac{r}{99}$

$=\frac{r}{99}[\frac{r-1}{100}+\frac{100-r}{100}]$

$=\frac{r}{99}[\frac{r-1+100-r}{100}]$

$=\frac{r}{99}[\frac{99}{100}]$

$=\frac{r}{100}$

Now, the the probability of getting red ball in third thrawn,

$=\frac{r}{100}\times \frac{r-1}{99}\times \frac{r-2}{98}+\frac{100-r}{100}\times \frac{r}{99}\times \frac{r-1}{98}+\frac{100-r}{100}\times \frac{99-r}{99}\times \frac{r}{98}$

$=\frac{r}{100}$

......so on,...

This pattern will be followed in every trials,

Hence, the probability that the 50th ball drawn will be red = $\frac{r}{100}$

(c) Similarly, the probability that the last ball drawn will be red = $\frac{r}{100}$

3 0

3 years ago

At Corner Deli, you can get 6 bagels for $6. How much does it cost per 1 bagel?

snow_lady [41]

Answer:

$1.00 per bagel

Step-by-step explanation:

To find the unit rate, you just have to divide the number of bagels by how much they cost.

In your problem, the number of bagels is 6 and the price is also 6.

Now all you have to do is divide 6 by 6 and the answer to that is 1.

Example: 6 ÷ 6 = 1

4 0

3 years ago