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Mama L [17]
3 years ago
10

Are the lines x− 2y= 4 and y= 2x − 2 parallel, perpendicular, or neither? Explain your answer. [ Select ] ; their [ Select ] [ S

elect ] the same and [ Select ] receiprocals.
Mathematics
1 answer:
erica [24]3 years ago
3 0

Answer:

Neither.

Step-by-step explanation:

First we alter the first equation to match the second.

x - 2y = 4

2y = x - 4

y = x/2 - 2.

Next we compare the slopes

2x = 2

x/2 = 1/2

Their slopes are reciprocals, but they aren't opposites. Therefore they are neither parallel nor perpendicular.

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5. Find the discriminant of 15x2 = 4x – 1 and describe
diamong [38]

Answer:

a) The discriminant of the equation =  - 44

b)The nature of the roots will be imaginary.

c) x = \frac{2 +\sqrt{11} i}{15}  or, x = \frac{2 - \sqrt{11} i}{15}

Step-by-step explanation:

Here, the given expression is 15x^{2}  = 4x -1

or, 15x^{2}  -  4x + 1   = 0

Now the discriminant (D) of a quadratic equation ax^{2}  +b x + c   = 0

D = b^{2}   -  4ac  = (-4)^{2}  -  4(15) (1)  = 16 - (60) = -44

Hence, the discriminant of the equation =  - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula : x = \frac{-b \pm \sqrt{b^{2}  - 4ac} }{2a}

So, here x = \frac{-(-4) \pm \sqrt{D} }{2a}  = \frac{4 \pm \sqrt{(-44 )} }{30}

So, either x = \frac{4 + \sqrt{(-44 )} }{30} or, x =  \frac{4 - \sqrt{(-44 )} }{30}

or, x = \frac{2 +\sqrt{11} i}{15}  or, x = \frac{2 - \sqrt{11} i}{15}

8 0
2 years ago
Explain why all squares must be rectangles but not all rectangles are squares
Neko [114]
A square is a quadrilateral with all four angles right angles and all four sides of the same length. ... Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.
5 0
2 years ago
Help fill in the blanks no
DerKrebs [107]

Answer:

Here is the full proof:

AC bisects ∠BCD      Given

∠CAB ≅ ∠CAD          Definition of angle bisector

DC ⊥ AD                    Given

∠ADC = 90°               Definition of perpendicular lines

BC ⊥ AB                    Given

∠ABC = 90°               Definition of perpendicular lines

∠ADC ≅ ∠ABC          Right angles are congruent

AC = AC                     Reflexive property

ΔCAB ≅ ΔCAD          SAA

BC = DC                     CPCTC          

7 0
2 years ago
Mode is used to ascertain what the most repeated data is in the data set. <br> True or False
Firdavs [7]

Answer:

true

Step-by-step explanation:

7 0
3 years ago
At midnight, the temperature was -8° F. At noon, the temperature was 23° F. Which expression represents the increase in temperat
Mariana [72]

Answer:

C

Step-by-step explanation:

Increase is difference between ending and begining value so 23-(-8) =23+8.

In this case its absolute value because it has to be positive

6 0
3 years ago
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