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3 years ago

Which system below has no solution?

Mathematics

1 answer:

Art [367]3 years ago

4 0

Answer:

None of the above.

If that isn't a choice, make sure you have written the equations correctly in your question. This is what I'm seeing:

y = 4x and y = 2x - 3

y = -4x and y = 2x - 3

y = -4x and y = 2x + 3

y = -4-x and y = 2x - 3

Step-by-step explanation:

We are looking for a system that has the same slope and a different y-intercept (the lines will be parallel in this case and never cross)

None of your pairs have the same same slope.

The first pair have slopes of 4 and 2 respectively.

The second pair have slopes of -4 and 2 respectively.

The third pair have slopes of -4 and 2 respectively.

The fourth pair have slopes of -1 and 2 respectively.

So all of these pairs will have one solution.

You might be interested in

Simplify to create an equivalent expression. 2(3r+7)−(2+r)

tamaranim1 [39]

2(3r+7)−(2+r)

Use distributive property:

6r + 14 - 2 - r

Simplify by combining like terms:

5r +12

7 0

3 years ago

Find the measure of the reference angle for an 11 radian<br> radian angle.

Vesnalui [34]

Answer:

about 1.56637 radians ≈ 89.746°

Step-by-step explanation:

The reference angle in radians can be found by the formula ...

ref angle = min(mod(θ, π), π -mod(θ, π))

Equivalently, it is ...

ref angle = min(ceiling(θ/π) -θ/π, θ/π -floor(θ/π))×π

<h3>Application</h3>

When we divide 11 radians by π, the result is about 3.501409. The fractional part of this quotient is more than 1/2, so the reference angle will be ...

ref angle = (1 -0.501409)π radians ≈ 1.56637 radians ≈ 89.746°

<em>Additional comment</em>

For calculations such as this, you need to use the most accurate value of pi available. The approximations 22/7 or 3.14 are not sufficiently accurate to give good results.

4 0

1 year ago

How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?

BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

$\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}$

Where n = 8 and r = 0,1....8

When r = 0

$\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1$

When r = 1

$\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 2

$\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8$

When r = 3

$\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 4

$\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70$

When r = 5

$\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$