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3 years ago

Factor completely: x^3 - x^2 - 6x

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

4 0

Answer:

$x(x-3)(x+2)$

Step-by-step explanation:

1. Find the GCF (Greatest Common Factor)

$GCF=x$

2. Factor out the GCF and simplify.

$x(x^{2} -x-6)$

3. Factor $x^{2} -x-6.$

Which two numbers add up to -1 and multiply to -6?

-3 and 2

Rewrite the expression using the numbers above.

$(x-3)(x+2)$

4. Done!

$x(x-3)(x+2)$

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A thermometer is taken from a room where the temperature is 24oc to the outdoors, where the temperature is −15oc. After one minu

kap26 [50]

Solution:

Use Newton's Law of Cooling.

T = T_s + (T_0 - T_s)*e^(-kt)

where

T = temperature at any instant

T_s = temperature of surroundings

T_0 = original temperature

t = elapsed time

k = constant

Now, we need to find this constant. We are given that after one hour, the temperature drops to 13° C in a 7°C Environment.

T = 14, T_0 = 24, T_s = -15, t = 1, k = ?

T = T_s + (T_0 - T_s)*e^(-kt)

==> 14 = -15 + (24 - 7)*e^(-k)

==> 14 = 7 + 17*e^(-k)

==> 7 = 17*e^(-k)

==> 7/13 = e^(-k)

==> -k = ln(7/17)

==> k = -ln(7/17) ≈ 0.774

Now,

Let's calculate temperatures!

T = ?, T_0 = 24, T_s = -15, k = 0.773, t = 3

T = T_s + (T_0 - T_s)*e^(-kt)

==> T = -15 + (24 –(-15))*e^[ -(0.774)(2) ]

==> T = -15 + 39*e^(-1.548)

==> T ≈ 15.72° C

This the required answer.

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3 years ago

What is the LCM of 95 and 14

kicyunya [14]

Answer:

LCM of 95 and 14 is 1330

Step-by-step explanation:

refer to the picture for explanation

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Find the value of X. Write your answer in simplest form. What does X equal?

drek231 [11]

Given:

Given that the figure of similar triangles.

The altitude of the triangle is x.

The length of the left part is 30.

The length of the right part is 15.

We need to determine the value of x.

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The value of x can be determined using the geometric mean theorem.

Thus, we have;

$\frac{\text { left }}{\text { altitude }}=\frac{\text { altitude }}{\text { right }}$

Substituting the values, we have;

$\frac{30}{x}=\frac{x}{15}$

Cross multiplying, we get;

$30 \times 15= x^2$

$450=x^2$

Taking square root on both sides, we have;

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