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Shalnov [3]
3 years ago
5

Tell whether the lines through the given points are parallelperpendicular, or neither Line 1: (1, 0), (7, 4) Line 2: (7, 0) , (3

, 6) The slope of line 1 is The slope of line 2 is
Mathematics
1 answer:
Radda [10]3 years ago
4 0

Answer:

<h3>The lines are perpendicular</h3>

Step-by-step explanation:

We determine whether lines are parallel or perpendicular by getting their slopes

For line 1; (1, 0), (7, 4)

Slope m = 4-0/7-1

M1 = 4/6

M1 = 2/3

Hence the slope of M1 is 2/3

For Line 2; (7, 0) , (3, 6)

M2 = 6-0/3-7

M2 = 6/-4

M2 = -3/2

Take the product of the slopes

M1 * M2 = 2/3 * -3/2

M1M2 = -1

Since the product of their slope is -1, hence the lines are perpendicular

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3 years ago
Barry has 17 more than two-thirds of the number of cards in his brother’s baseball card collection. If x represents the number o
ioda

Answer:

(2/3) x + 17

Step-by-step explanation:

One way we can solve this is to start at x and to work from there.

Since x represents the number of baseball cards that Barry's brother has, and the closest phrase to it is "two-thirds of the number of cards", we can start by writing that as "2/3 of x", or (2/3) * x.

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yulyashka [42]

Answer:

8x² +36x -27=0

Step-by-step explanation:

2x²= 6x +3

Let's rewrite the equation into the form of ax²+bx+c= 0.

2x² -6x -3=0

Thus, a= 2

b= -6

c= -3

Sum of roots= -  \frac{b}{a}

Since your roots are p and q, sum of roots= p +q

p +q= - (\frac{ - 6}{2} )

p +q= 6 ÷2

p +q= 3

Product of roots= \frac{c}{a}

pq= -  \frac{3}{2}

<u>Quadratic equations</u><u>:</u>

x² -(sum of roots)x +(product of roots)= 0

Thus, we have to find the sum and the product of the new roots, p²q and pq².

p +q= 3

pq= -3/2

Product of new roots

= (p²q)(pq²)

= p³q³

= (pq)³

= ( -  \frac{3}{2} )^{3}  \\  =  -  \frac{27}{8}

sum of new roots

= p²q +pq²

= pq(p +q)

= (-3/2)(3)

= -9/2

Thus, the quadratic equation with roots p²q and pq² is

x² -(-9/2)x -27/8 = 0

x ^{2}  +  \frac{9}{2} x -  \frac{27}{8}  = 0

Multiply by 8 throughout:

8 {x}^{2}  + 36x - 27 = 0

3 0
3 years ago
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