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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

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If m(x) = x+5/x-1 and n(x) = x — 3, have the same domain as (m • n) (x)

Yuri [45]

For this case we have the following functions:

$m (x) = \frac {x + 5} {x-1}\\n (x) = x-3$

By definition we have to:

$(f * g) (x) = f (x) * g (x)$

So:

$(m * n) (x) = m (x) * n (x)\\(m * n) (x) = \frac {x + 5} {x-1} (x-3)\\(m * n) (x) = \frac {(x + 5) (x-3)} {x-1}$

By definition, the domain of a function is given by the values for which the function is defined.

The domain of m(x) is given by all reals except 1.

The domain of n(x) is given by all reals.

While the domain of $(m * n) (x)$ is given by:

All reals, except the 1. With $x = 1$ , the denominator is 0 and the function is no longer defined.

Answer:

Domain of $(m * n) (x)$ is given by all reals except 1.

8 0

3 years ago

Nancy is buying a new pair of boots. The store is having a sale and all boots are 20% off.

Strike441 [17]

Can you please complete your question?

5 0

2 years ago

In a particular class, exams are worth 50% of the overall grade, quizzes are worth 30% of the overall grade, homework is worth 1

Paha777 [63]

Answer:

The student's overall grade is 85.79%

Step-by-step explanation:

Given in the question that:

Exam = 50%; Quiz = 30%, Home work = 15% and Class participation = 5%

The total giving us 100%.

A particular student scored the following;

87.9% on exams, 77.8% quiz, 90% Home work and 100% on class participation

Calculating the percentages the student had for each;

Exam total = 50*0.879 = 43.95% earned

Quiz = 30*0.778 = 23.34% earned

Home work = 15*0.9 = 13.5% earned

Class participation = 5*1 = 5% earned

Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%

3 0

3 years ago

The width of a rectangle is (x+1) and the length is (x-6). What is the length and width of the rectangle if the area is 30 squar

jolli1 [7]

Answer:

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) = 10 feet

Step-by-step explanation:

Step(i):-

Given that the width of the rectangle = (x+1) feet

Given that the length of the rectangle = ( x-6) feet

The area of the rectangle = 30 square feet

Step(ii):-

We know that the area of the rectangle

= length ×width

30 = ( x+1)(x-6)

30 = x² - 6x + x -6

⇒ x² - 5 x - 6 = 30

⇒ x² - 5 x - 6 - 30 =0

⇒ x² - 5 x - 36 =0

x² - 9 x +4x - 36 =0

x (x-9) +4 ( x-9) =0

( x+4 ) ( x-9) =0

( x+4 ) =0 and ( x-9) =0

x =-4 and x =9

Step(iii):-

we have to choose x =9

The length of the rectangle (l) = x-6 = 9-6 =3

The width of the rectangle (W) = x+1 = 9 +1 = 10

Final answer:-

The length of the rectangle (l) = 3 feet

The width of the rectangle (W) = 10 feet

5 0

2 years ago

PLZ HELP SCALE FACTOR TRIANGLE A. 10.5 cm B. 31.5 cm C. 63 cm D. 189 cm

Anarel [89]

If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².

We have the ratio:

$54:18=\dfrac{54}{18}=3:1$

Area of the smaler triangle = x

Area of the larger triangle = 567 cm²

Therefore we have the equation:

$567:x=3^2:1^2\\\\\dfrac{567}{x}=\dfrac{9}{1}\qquad|\text{cross multiply}\\\\9x=567\qquad|\text{divide both sides by 9}\\\\x=63$

<h3>Answer: C. 63 cm²</h3>

3 0

2 years ago