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2 years ago

What is the equation of the line through (−2, −2) and (4, −5)?

Mathematics

1 answer:

Liono4ka [1.6K]2 years ago

7 0

Answer:

y = -1/2x - 3

Step-by-step explanation:

slope: (y2-y1) / (x2-x1)

(-5 - -2) / (4 - -2)

(-5 + 2) / (4 + 2)

-3 / 6

- 1 / 2

y-intercept: y = mx + b

-5 = -1/2(4) + b

-5 = -2 + b

-3 = b

You might be interested in

If r(X)=2-x^2 and w(X)=X-2, what is the range of (w*r)(X)

slega [8]

The given function are
r(x) = 2 - x² and w(x) = x - 2
(w*r)(x) can be obtained by multiplying the both function together

So, (w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)
(w*r)(x) = x (2-x²) - 2(2-x²)
= 2x - x³ - 4 + 2x²

∴ (w*r)(x) = -x³ + 2x² + 2x - 4


It is a polynomial function with a domain equal to R

The range of (w*r)(x) can be obtained by graphing the function

To graph (w*r)(x), we need to make a table between x and (w*r)(x)

See the attached figure which represents the table and the graph of (w*r)(x)


As shown in the graph the range of (w*r)(x) is (-∞,∞)

8 0

3 years ago

Read 2 more answers

bezimeni [28]

Answer:

260 stickers

Step-by-step explanation:

Let Gareth's stickers be x.

Hence Cheryl sticker is 160+x;

If Cheryl gave 185 stickers

to Gareth, it means:

Cheryl has at the moment;

160 + x - 185 = x - 25

At this time when Gareth receives 185 he now has:

x+ 185

Also when he receives x +185, he has 3 times Cherry's meaning:

x+185 =3(x-25)

x + 185 = 3x -75

185 + 75 = 3x-2x

260= x

x = 260.

Hence Gareth has 260 stickers

5 0

3 years ago

Create a one step equation using the numbers 4 and 6. One you create the

Nataly [62]

Answer:

x=1.5

Step-by-step explanation:

4x=6

6/4=1.5

5 0

3 years ago

You are planning to hire a full-time electrician who will work 40 hours per week. If you plan on giving this new hire three week

tresset_1 [31]

Option b) 1960 is the total number of hours the electrician worked.

Step-by-step explanation:

It is given that, the full-time electrician will work 40 hours per week.

So, we need to know the total number of hours he could work in twelve months which is one year.

Therefore, one year has a total of 365 days.

To find the number of weeks in twelve months :

Number of weeks = Total days in one year / 7 days of week

⇒ 365 / 7

⇒ 52.14 (approximately 52 weeks)

The number of weeks in twelve months is 52 weeks.

Now, of this 52 weeks, the three weeks are given as vacation.

The total number of weeks the electrician worked = 52 weeks - 3 weeks

⇒ 49 weeks.

The electrician worked for 49 weeks.

To calculate the total number of hours he worked = 49 weeks × 40 hours

⇒ 1960 hours.

Therefore, the total number of hours the electrician worked is 1960 hours which is option b).

5 0

3 years ago

Question 2 of 5

AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$

$f(n)=5+3(n-1)$

Therefore, the correct option is D, i.e., $f(n)=5+3(n-1)$ .

6 0

3 years ago

Read 2 more answers