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Radda [10]
3 years ago
10

Use y = mx + b to determine the equation of a line that passes through the point A(-1, 4) and is

Mathematics
1 answer:
Shalnov [3]3 years ago
4 0

Answer:

Step-by-step explanation:

If we are looking for a line parallel to the given line, we need to find the slope of the given line, since parallel lines have the exact same slope. That means that we need to solve this equation for y, which naturally puts the line into slope-intercept form. Solving for y:

-2y = -4x - 8 and

2y = 4x + 8 so

y = 2x + 4 and the slope, we see here, is 2. Use that slope and the given point of (-1, 4) to write the new equation we need.

In point-slope form, the line will be

y - 4 = 2(x - (-1)) which simplifies a bit to

y - 4 = 2(x + 1). That's point-slope form. Putting it into slope-intercept just requires that we solve this equation for y:

y - 4 = 2x + 2 and

y = 2x + 6. That's slope-intercept form of the same line. The last form is standard, which looks like this:

-2x + y = 6 or, if you don't like to lead with a negative,

2x - y = -6

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GenaCL600 [577]

Answer:

3.5

I,jJUiIJzuzusjdjusususuuss

8 0
2 years ago
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Let $a$ and $b$ be nonzero real numbers such that
algol [13]
<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0
1 year ago
Help me
butalik [34]

Answer:

D. Tenths

Step-by-step explanation:

Because when you go behind the decimal, it starts out with tenths, then hundredths, and then thousandths. And 6 in the 1st spot behind the decimal so it's tenths.

hope I helped.

6 0
3 years ago
Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical. 20 students have tickets. S
vlabodo [156]

Answer:

<h2>The option B and D are the equations.</h2>

Step-by-step explanation:

Let, the total number of students are x.

The number of students having the ticket is 4 + \frac{x}{2}.

It is given that the number is 20.

Hence, 4 + \frac{x}{2} = 20\\4 = 20 - \frac{x}{2}.

Option B is the equation.

Option D is also the same.

The difference is just, the variable is wriiten in the other side.

4 0
3 years ago
Please answer I would really appreciate it
quester [9]

Answer:

C. 70

Step-by-step explanation:

70/5= 14

70/7 =10

5 0
2 years ago
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