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1 year ago

Find the remaining factors of x^3+6x^2-4x+3 given (x+2)

Mathematics

1 answer:

satela [25.4K]1 year ago

4 0

Answer:

y=(x+6)(x−2)(x+2)

Step-by-step explanation:

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Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

Gnesinka [82]

Answer:

Step-by-step explanation:

Suppose we a point $P(x,y,z)$ such that its distance from either the point $A(3,4,-5)$ or $B(-2,1,4)$ is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

$r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}$

$AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}$

similarly, we can find the distance BP

$BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

since both distances are exactly the same we can equate them

$AP = BP$

$\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

$(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2$

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

3 0

2 years ago

8x^(2)+16x=42 completeing the square

Yuri [45]

16
x
2
+
16
x
=
42
Step 2: Subtract 42 from both sides.
16
x
2
+
16
x
−
42
=
42
−
42
16
x
2
+
16
x
−
42
=
0
For this equation: a=16, b=16, c=-42
16
x
2
+
16
x
+
−
42
=
0
Step 3: Use quadratic formula with a=16, b=16, c=-42.
x
=
−
b
±
b
2
−
4
a
c
2
a
x
=
−
(
16
)
±
(
16
)
2
−
4
(
16
)
(
−
42
)
2
(
16
)
x
=
−
16
±
2944
32
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46
Answer:
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46

7 0

3 years ago

Promise Easy Points

Harman [31]

$420+$350+$432=kelsey's monthly expenses

$700+$800=Micheal's Monthly expenses

8 0

2 years ago

Weak battery is considered to be a part of routine

grandymaker [24]

Answer:

A. wear and tear

Step-by-step explanation:

A battery is generally expected to become weaker over time, as a consequence of the normal use of equipment. The presence of a weak battery would be found by a routine check, and replaced by routine maintenance.

The fact that a battery is weak would be considered the result of routine wear and tear

3 0

3 years ago

For her birthday party, Dina wants to invite at least 8 guests but not more than 12 guests. How many guests might she have? Name

natulia [17]

This can be represented by the inequality 8 $\leq$ x $\leq$ 12
As Dina wants at least 8, and no more than 12, that means 8, 9, 10,11, and 12, are applicable

4 0

3 years ago