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Montano1993 [528]
3 years ago
5

Write the equation of a line perpendicular to y=3x+1and goes through the point ( 6,2) y=−13x+4 y=−13x−4 y=3x+4 y=3x−4

Mathematics
1 answer:
Korolek [52]3 years ago
6 0

Answer:

y=-\frac{1}{3}x+4

Step-by-step explanation:

step 1

Find the slope of the perpendicular line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal

(the product of their slopes is equal to -1)

In this problem

we have

y=3x+1

The equation of the given line is m=3

so

the slope of the perpendicular line to the given line is

m=-\frac{1}{3}

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-\frac{1}{3}

(x1,y1)=(6,2)

substitute

y-2=-\frac{1}{3}(x-6)

Convert to slope intercept form

y=mx+b

Distribute right side

y-2=-\frac{1}{3}x+2

y=-\frac{1}{3}x+2+2

y=-\frac{1}{3}x+4

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3 years ago
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find the length of AC.
Oxana [17]

Answer:

AC=16 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.  It was given that diagonals AC and BD intersect at point E.

This implies that: AE=CE.

We substitute the expression for x, we get:

11x-3=12-4x.

Group similar terms to get:

11x+4x=12+3.

15x=15.

x=1

AC = 2(12-4x)

AC=2(12-4(1))

AC=2(8)

AC=16

8 0
3 years ago
In only three days the temperature dropped by 24 degrees.How many degrees per day did the temperature drop?
yan [13]

Answer: 8° per day.

Step-by-step explanation:

Based on the information above, since we are informed that in three days, the temperature dropped by 24 degrees, the number of degrees per day that the temperature dropped will be go by dividing 24° by 3 days. This will be:

= 24° / 3 days

= 8° per day

6 0
3 years ago
Help!! Find missing value for each quadratic function
Svetllana [295]

I'll do the first one to get you started. The answer is -3

=================================================

Explanation:

When x = -1, y = 0 as shown in the first column. The second column says that (x,y) = (0,1) and the third column says (x,y) = (1,0)

We'll use these three points to determine the quadratic function that goes through them all.

The general template we'll use is y = ax^2 + bx + c

------------

Plug in (x,y) = (0,1). Simplify

y = ax^2 + bx + c

1 = a*0^2 + b*0 + c

1 = 0a + 0b + c

1 = c

c = 1

------------

Plug in (x,y) = (-1,0) and c = 1

y = ax^2 + bx + c

0 = a*(-1)^2 + b(-1) + 1

0 = 1a - 1b + 1

a-b+1 = 0

a-b = -1

a = b-1

------------

Plug in (x,y) = (1,0), c = 1, and a = b-1

y = ax^2 + bx + c

0 = a(1)^2 + b(1) + 1 ... replace x with 1, y with 0, c with 1

0 = a + b + 1

0 = b-1 + b + 1 ... replace 'a' with b-1

0 = 2b

2b = 0

b = 0/2

b = 0

------------

If b = 0, then 'a' is...

a = b-1

a = 0-1

a = -1

------------

In summary so far, we found: a = -1, b = 0, c = 1

Therefore, y = ax^2 + bx + c turns into y = -1x^2 + 0x + 1 which simplifies to y = -x^2 + 1

------------

The last thing to do is plug x = 2 into this equation and simplify

y = -x^2 + 1

y = -2^2 + 1

y = -4 + 1

y = -3


3 0
3 years ago
Work out the shaded area of this shape.
Yuri [45]

Answer:

look at the picture .................

8 0
2 years ago
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