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Work out the y-intercept of the line going through (1, 2) with a gradient of 3

Tasya [4]

I think we need a coordinate grid for that,,

4 0

3 years ago

a scuba diver descended at a rate of 2 1/4 per second. If 0 represents the surface of the water and distances below the surface

Shtirlitz [24]

Answer:

The location will be at $- 28\frac{1}{8}$ units.

Step-by-step explanation:

A scuba diver descended at a rate of $2\frac{1}{4}$ units per second.

Now, if 0 represents the surface of the water and distances below the surface are negative, then after $12\frac{1}{2}$ seconds the location of the diver will be given by the followings :

In one second the diver descends by 2.25 units depth.

So, in 12.5 seconds the diver will descend by $(2.25 \times 12.5) = 28.125$ units i.e. $28\frac{1}{8}$ units depth.

Therefore, the location will be at $- 28\frac{1}{8}$ units. (Answer)

6 0

3 years ago

Find the smallest non-zero whole number n such that 756n is a perfect cube.

Kitty [74]

Step-by-step explanation:

756 = 2² * 3³ * 7.

For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.

How to get from 2² to 2³: Multiply by 2.

3³ has already a power that is a multiple of 3.

How to get from 7 to 7³: Multiply by 7².

Hence n = 2 * 7² = 98.

5 0

3 years ago

Find x so that x, X +2, X'+3 are the first three terms of a geometric sequence. Then find the 5" term of the

velikii [3]

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.

So, our first term is x.

Then our second term will be our first term multiplied by the common ratio r. So:

$x+2=xr$

And our third term will be our first term multiplied by the common ratio r twice. Therefore:

$x+3=xr^2$

Solve for x. From the second term, we can divide both sides by x:

$\displaystyle r=\frac{x+2}{x}$

Substitute this into the third equation:

$\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2$

Square:

$\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)$

Simplify:

$\displaystyle x+3=\frac{(x+2)^2}{x}$

We can multiply both sides by x:

$x(x+3)=(x+2)^2$

Expand:

$x^2+3x=x^2+4x+4$

Isolate the x:

$-x=4$

Hence, our first term is:

$x=-4$

Then our common ratio r is:

$\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}$

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.

So, our fifth term is -1/4.

4 0

3 years ago

Evaluate (4)^-4 pls answer!!!

geniusboy [140]

Answer:

Fraction: 1/256 or

Decimal: 0.00390625 or 0.00391

Step-by-step explanation:

4^-4=1/4^4

4^4=256

=1/256

8 0

3 years ago