Calculus

x * -2 = -2

Divide each side by -2 to get x by itself.

(x * -2)/-2 = -2/-2

x = -2/-2

x = 1

There is no rational factorisation of 6y2 + 19y - 13

The roots are [-19 +/- sqrt(673)]/12

which are -3.74519 and 0.57852

if:
y = -2x + 3

then:

if y = 0:
0 = -2x + 3
2x = 3
x = 3/2

if x = 0:
y = -2(0) + 3
y = 3

So the x-intercept is at {0, 3}, and the y-intercept is at {3/2, 0}

x - 6x = 0

-5x= 0

x = 0/-5

which equals x = 0

-6x+9 = 45

-6x = 45-9

-6x = 36

x = -6

38=1*2*19

58=1*2*29

highest common factor is 2

Let c represent cos x.

Then, we have,

4c2 - 2 = 0; whence,

4c2 = 2,

c2 = ½, and

c = ±√½ = ±½√2; that is,

cos x = ±½√2.

From this, it is evident that,

for 0 ≤ x < 360°, x = 45°, 135°, 225°, or 315°;

or, if you prefer,

for 0 ≤ x < 2π, x = ¼π, ¾π, 1¼π, or 1¾ π.

It does not. It equals volume. The weight will vary depending on the substance occupying that volume.

(3x2)2 (5x)4 = 9x4625x4 = 5625x8

It depends on what information you already have. For example, if you know the length of two sides of a triangle, you can easily find the tangent. Or, if you know the length of two angles and a side, you can find the other sides as well, using the tangent, cosine, and sine as needed.

Yes

this is not a valid equation. I assume you mean:

2X+8Y=36

in which case the graph is a line with a slope of 1/4 and a y-intercept at 9/2

or

2X+4Y+2=36

in which case the graph is still a line with a slope of 1/2 and a y-intercept at 17/2

x can be anything, if you don't have it in an equation form, can an be an infinite amount of solutions

-6x - 17 >= 8x + 25

-17 >= 14x + 25

-42 >= 14x

-3 >= x

Therefore x is less than or equal to -3.

60,000,000,000

Sixty billion.

The domain is all real numbers except when the denominator equals zero:

x2 - 4 = 0

x2 = 4

x = 2, -2

So the domain is all real numbers except 2 and -2.

-1

(2x^2-8x-42)/[(x^2-9)/(x^2-3x)]

=2(x^2-4x-21)/[(x+3)(x-3)/(x(x-3))]

=2(x-7)(x+3)/[(x+3)/x]

When we canceled out "(x-3)," it set up a domain restriction: x≠3. This is correct because we are not allowed to divide by 0 at any point, ever! Moving on...

=2(x-7)(x+3)(x)/(x+3)

=2(x-7)(x)

Now, x≠-3 for the same reason stated above. Moving on...

=2x(x-7)

=2x^2-14x

5/10

X^2 + 5X - 14

by inspection what two factors of - 14 add up to 5 ?

(X + 7)(X - 2)

X = - 7

X = 2

90+10=100+10+2=112

As the other contributor mentioned, the standard formula for the period (T) of a simple pendulum is

T = 2*pi*sqrt(L/g)

so the period is inversely proportional to the square root of acceleration 'g'. But for practical purposes (as implied by the question) we can replace 'g' with another value, the apparent acceleration due to gravity, 'ga'. This value also takes into account the rotational speed and the distance from the center of the gravitational mass

ga = GM/r**2 - (w**2)*cos(LAT)

where:

w = angular velocity of the earth's rotation

= 2*pi/(24*3600) [rad/s]

LAT = observer's latitude (0=equator, 90deg=pole)

G = universal gravitation constant

M, r = mass, radius of planet/satellite/star we are on

Thus, the period of a simple pendulum is inversely proportional to to the sqare root of 'ga'. And this value varies with latitude, mass and distance.

So then let's answer the questions!

a) as we increase the height from sea level, the radius increases, reducing the 'ga' and this increases the period, T

b) as we go to the pole, LAT = 90deg, and cos(LAT) goes to zero. We thus INCREASE 'ga' and decrease the period

c) at the equator, LAT = 0 and cos(LAT) = 1, so we have a minimum value for 'ga', this increases the period

d) on the moon, our rotational velocity is much less (1 rev per 27.3 days) and the M is much smaller, and the r is much smaller! We are told that the 'ga' will be about 1/6 of the Earth's value, so the period will increase.

e) Here the M is colossal, so if we could withstand the heat and gravitational forces, 'ga' is much larger, so period will decrease.

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