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3 years ago

Which are factors of x2 – 4x – 5?

Mathematics

1 answer:

Kitty [74]3 years ago

7 0

Answer:

(x-5)(x+1)

Step-by-step explanation:

Since the highest power of x is 2, u can assume the equation to be (x +/- A) (x +/- B), whereby A and B are unknowns.

Since the coefficient of X^2 is 1, and the number in the equation is - 5, the only possible values for A and B to get - 5 is either - 5 and 1 or 1 and - 5.

Since coefficient of x is - 4 and number in equation is - 5, imagine inserting those numbers in the equation and cross multiplying back. You would realise that the answer should be as listed above.

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I need help with it pls

Basile [38]

Answer:

Step-by-step explanation:

Step 1: What are the couch's original coordinates?

A: (-4, 2)
N: (-4, 3)
G: (-1, 3)
L: (-1, 4)
E: (-5, 4)
S: (-5, 2)

Step 2: Rotate the couch 90° counterclockwise.

Rule: (x, y) → (-y, x)

A': (-4, 2) → (-2, -4)
N': (-4, 3) → (-3, -4)
G': (-1, 3) → (-3, -1)
L': (-1, 4) → (-4, -1)
E': (-5, 4) → (-4, -5)
S': (-5, 2) → (-2, -5)

Step 3: Now reflect the "new" couch over the y-axis.

Rule: (x, y) → (-x, y)

A'': (-2, -4) → (2, -4)
N'': (-3, -4) → (3, -4)
G'': (-3, -1) → (3, -1)
L'': (-4, -1) → (4, -1)
E'': (-4, -5) → (4, -5)
S'': (-2, -5) → (2, -5)

Step 4: Finally translate the new new" couch right 1 unit and up 5 units.

Rule: (x + 1, y + 5)

A''': (2, -4) → (2 + 1, -4 + 5) → (3, 1)
N''': (3, -4) → (3 + 1, -4 + 5) → (4, 1)
G''': (3, -1) → (3 + 1, -1 + 5) → (4, 4)
L''': (4, -1) → (4 + 1, -1 + 5) → (5, 4)
E''': (4, -5) → (4 + 1, -5 + 5) → (5, 0)
S''': (2, -5) → (2 + 1, -5 + 5) → (3, 0)

Step 5: Use the distance formula to show that the length of EG is the same as the length of E'''G'''.

EG: (-5, 4)(-1, 3)
E'''G''': (5, 0)(4, 4)

Distance between E(-5, 4) and G(-1, 3)

x₁ = -5
x₂ = -1
y₁ = 4
y₂ = 3

$\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(-1-(-5))^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{(-1+5)^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{4^2+(-1)^2}$}\\\\\ \large \textsf {d = $\sqrt{16+1}$}\\\\\large \textsf {d = $\sqrt{17}$}\\\\\large \textsf {d = ${4.12}$}$

Distance between E'''(5, 0) and G'''(4, 4)

x₁ = 5
x₂ = 4
y₁ = 0
y₂ = 4

$\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(4-5)^2+(4-0)^2}$}\\\\\large \textsf {d = $\sqrt{(-1)^2+4^2}$}\\\\\large \textsf {d = $\sqrt{1+16}$}\\\\\ \large \textsf {d = $\sqrt{17}$}\\\\ \large \textsf {d = ${4.12}$}$

This means that the length of EG is the same as the length of E'''G'''.

Hope this helps!

4 0

2 years ago

Find the slope of the line that passes through (10, 8) and (1, 1).

Nana76 [90]

Answer:

2/3

Step-by-step explanation:

the formula to find slope is y1-y2/x1-x2.

The ordered pairs are (10,8) and (1,1)

(x, y). (x, y)

So it would be: 8-1 OVER 10-1

=6/9 which simplifies to 2/3

so your slope would be 2/3

5 0

3 years ago

in a round robin tennis tournament involving 7 players, each player will play every other player twice. How many total matches w

baherus [9]

Total number of ways to make a pair:

The first player can be any one of 7 . For each of those . . .
The opponent can be any one of the remaining 6 .

Total ways to make a pair = 7 x 6 = 42 ways .

BUT ... every pair can be made in two ways ... A vs B or B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.

If every pair plays 2 matches, then (21 x 2) = <em><u>42 total matches</u></em> will be played.

Now, is that an elegant solution or what !

8 0

3 years ago

6. Jenny needs to build a box that has a square base and a volume of 900 cm°. The height of the box is related to the length of

LiRa [457]

Answer:

Step-by-step explanation:

Its 43567 bc I searched it up

3 0

3 years ago

I need help with all of them

olga nikolaevna [1]

7. Is 45
10. is 15
8.32