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EleoNora [17]
3 years ago
10

Calculate the area of triangle ABC with altitude AD, given A(-5, 4), B(-6, 1), C(0, 1), and D(-5, 1).

Mathematics
1 answer:
snow_lady [41]3 years ago
3 0

Answer:

the area of triangle ABC = 9

Step-by-step explanation:

Check the photo below for the details.

:)

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Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2. ​
insens350 [35]

Answer:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

Step-by-step explanation:

Given

p(x) = \frac{x^2-2x-3}{x+2} -- Missing from the question

Required

The behavior of the function around its vertical asymptote at x = -2

p(x) = \frac{x^2-2x-3}{x+2}

Expand the numerator

p(x) = \frac{x^2 + x -3x - 3}{x+2}

Factorize

p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}

Factor out x + 1

p(x) = \frac{(x -3)(x + 1)}{x+2}

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

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

As x approaches -2 implies that:

x -> -2^{-} Say x = -3

p(x) = \frac{(x -3)(x + 1)}{x+2}

p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

x->-2^{-}, p(x)->-\infty

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: x>-2

Say x = -2.1

p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

x->-2^{+}, p(x)->-\infty

So, the behavior is:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

6 0
3 years ago
WHAT TERM SHOULD BE ADDED TO CREATE A PERFECT SQUARE TRINOMIAL?
boyakko [2]
Answer: We should add the constant 81 to the expression to have a perfect square trinomial.

The perfect square trinomial that would be formed would result from (x + 9)^2.

We can use foil to prove it.

(x + 9)(x + 9)
x^2 + 9x + 9x + 81
x^2 + 18x + 81

81 is the value that must go with 18x in the middle to form the perfect square trinomial.
8 0
3 years ago
Jay sells 10 packs of apples for 80p. He wants to make £75 at the end of the year. How many packs of apples does he need to sell
ipn [44]

Answer:

937.5 packs of apples

Step-by-step explanation:

Note that:

100p = £1

80p = x

Cross Multiply

100x = 80p × £1

x = 80/100

x = £0.8

Jay sells 10 packs of apples for 80p.

Hence:

£0.8 = 10 packs of apples

£75 = x

Cross Multiply

£0.8 × x = £75 × 10 Packs

x = £75 × 10 Packs/£0.8

x = 937.5

Therefore, to make £75 at the end of the year, he has to sell 937.5 packs of apples

3 0
2 years ago
How to slove 81.45-1000 in a easy way to slove step by step
Butoxors [25]

Answer:

-918.55

Step-by-step explanation:


4 0
3 years ago
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In a population, 93% of the people are right-handed, and 7% of the people are left-handed. In each of the last 100 days, 1 perso
vfiekz [6]
The answer is 93%... Pretty sure.
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2 years ago
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