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2 years ago

Which shortcut proves these triangles are congruent?

Mathematics

1 answer:

vekshin12 years ago

7 0

The SAS or side angle side proves the triangle is congruent to each other

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The point F(5, 5) is translated 7 units left.

QveST [7]

5 - 7 = -2. Therefore, the answer is (-2, 5).

6 0

2 years ago

The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t

wolverine [178]

Answer:

a) The implied differential equation is $\frac{dN}{725 - N} = kdt$

b) The general equation is $N = 725 - C e^{-kt}$

c) The particular equation is $N = 725 - 325 e^{-0.49t}$

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, $\frac{dN}{dt} \alpha (725 - N(t))$

$\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt$

Integrating both sides of the equation

$\int {\frac{1 }{725 - N}} \, dN = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}$

When t = 0, N = 400

$400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325$

When t = 3, N = 650

$650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49$

The equation for the population becomes:

$N = 725 - 325 e^{-0.49t}$

At t = 5, the population becomes:

$N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697$

N(5) = 700 ( to the nearest 50)

6 0

2 years ago

11 divided by 634 long division

Kazeer [188]

11 / 634

Decimal form: 0.017350158...(there are probably more digits, but these are all that fit on my calculator screen)

Fraction form: 11/634

634 / 11

I have attached an image of this problem completely worked out.

5 0

3 years ago

1/5 (5x-15) -2x What is the question ?? How do I solve the problem ??

Ksenya-84 [330]

Answer:

$-x-3$

Step-by-step explanation:

They want you to simplify the expression.

Step 1: Apply the distributive property.

$\frac{1}{5} (5x)+\frac{1}{5} (-15-2x)$

Step 2: Cancel the common factor of 5.

$x+\frac{1}{5} (-15-2x)$

Step 3: Cancel the common factor of 5.

$x-3-2x$

Step 4: Subtract 2x from x.

$-x-3$

8 0

2 years ago

Find the solutions to the equation below.

yanalaym [24]

Answer:

X=1/2. X=4/3

Step-by-step explanation:

6x2+5X-4=0

6X2+8X-3X-4=0

2x(3x+4) - 1(3x+4)=0

2x-1) (3X-4)

X=1/2. X=4/3

4 0

2 years ago