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3 years ago

Calculate the area of triangle ABC with altitude CD, given A (6, -2), B (1, 3), C (5, 5), and D (2, 2).

Mathematics

2 answers:

pentagon [3]3 years ago

4 0

The answer is 15 square units

Flura [38]3 years ago

3 0

Answer:

15 units

Step-by-step explanation:

I just took this geometry test with the same question. Its 15

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Find the polynomial of minimum degree, with real coefficients, zeros at x=4+4i and x=2, and y-intercept at 64

Mice21 [21]

Answer:

$\displaystyle -x^3+10x^2-48x+64$

Step-by-step explanation:

We want to find the minimum-degree polynomial with real coefficients and zeros at:

$x= 4+4i\text{ and } x = 2$

As well as a y-intercept of 64.

By the Complex Root Theorem, if a + bi is a root, then a - bi is also a root.

So, a third root will be 4 - 4i.

The factored form of a polynomial is given by:

$P(x)=a(x-p)(x-q)...$

Where a is the leading coefficient and p and q are the zeros. More factors can be added if necessary.

Substitute:

$P(x)=a(x-(2))(x-(4+4i))(x-(4-4i))$

Since we want the minimum degree, we won't need to add any exponents.

Expand the second and third factors:

$\displaystyle \begin{aligned} (x-(4+4i))(x-(4-4i))&=(x-4-4i)(x-4+4i) \\ &= x(x-4-4i)-4(x-4-4i)+4i(x-4-4i)\\ &=x^2-4x-4ix-4x+16+16i+4ix-16i-16i^2\\ &= x^2-8x+32\end{aligned}$

Hence:

$P(x)=a(x-2)(x^2-8x+32)$

Lastly, we need to determine a. Since the y-intercept is y = 64, this means that when x = 0, y = 64. Thus:

$64=a(0-2)(0^2-8(0)+32)$

Solve for a:

$-64a=64\Rightarrow a=-1$

Our factored polynomial is:

$P(x)=-(x-2)(x^2-8x+32)$

Finally, expand:

$\displaystyle \begin{aligned} P(x) &=-(x^2(x-2)-8x(x-2)+32(x-2)) \\&=-(x^3-2x^2-8x^2+16x+32x-64)\\&=-(x^3-10x^2+48x-64)\\&= -x^3+10x^2-48x+64\end{aligned}$

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3 years ago

Grandma’s Guide to Cooking Measurements

Svetach [21]

Your answer is gonna be 16

3 0

3 years ago

Enter a value for x that makes the equation 7x - 2(x + 1) + 18 = 8x - 11 true.

tino4ka555 [31]

9
hope this helps :)

5 0

3 years ago

Consider a triangular prism. The triangular end has a base of 4 cm and height of 5 cm. The length of each side is 6 cm and the h

AysviL [449]

B.)10 inches
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you need to plug in 10
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thats if you don't know what to do
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the easy way

4 0

3 years ago

What is the solution of the system? Use the elimination method. 2x+y=206x−5y=12 Enter your answer in the boxes.

astraxan [27]

Answer:

The answer to your question is: x = 7; y = 6

Step-by-step explanation:

2x+y=20 ( 1 ) Multiply by 5

6x−5y=12 ( 2 )

5 (2x+y=20) = 10x + 5y = 100

10x + 5y = 100

6x − 5y = 12 Eliminate y

16 x = 112

x = 112 / 16

x = 7

2(7) + y = 20 Substitution

14 + y = 20

y = 20 - 14

y = 6

7 0

3 years ago