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3 years ago

Which technique is most appropriate to solve this equation?

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

4 0

quadratic formula

Step-by-step explanation:

x(x-9)+4(x-9)

x²-9x+4x-36

x²-5x-36

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5. Line l has an equation y = 2x – 4. Write the

Vladimir [108]

Answer:

y=2x-1

Step-by-step explanation:

7 0

3 years ago

Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

3 years ago

Find the area of the figure. Round to the nearest tenth

Reika [66]

Answer:

Find the area of each triangle and then add it up. As you are aware, to find the area of a triangle the equation is B times Height divided by 2. And to make it easier do the top left triangle and the top right triangle, add them together and then divide that by 2.

Step-by-step explanation:

3 time 5 equals 15 divided by 2 equals 7.5

5 times 8 equals 40 divided by 2 equals 20

7.5 plus 20 equals 27.5

27.5 times 2 equals 55

therefor your answer should be 55m

3 0

3 years ago

there are 6 girls and 8 boys in Mr. Stevenson's class the ratio of girls to boys in the class can be expressed as the simplified

Mashcka [7]

Answer: 3

Step-by-step explanation:

7 0

2 years ago

Definicion etimologica de la palabra poliedro

lesantik [10]

Answer:

Poli (muchas) edro (caras) luego sería muchas caras lo que representas las figuras poliédricas.

Step-by-step explanation:

La palabra poliedro viene del griego clásico πολύεδρον (polyedron), de la raíz πολύς (polys), «muchas» y de ἕδρα (hedra), «base», «asiento», «cara».

6 0

2 years ago