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Illusion [34]
3 years ago
7

Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

Mathematics
1 answer:
weeeeeb [17]3 years ago
5 0

Answer:

\[y = (-1/2) * x + 6\]

Step-by-step explanation:

Equation of the given line: y=2x+2

Hence the slope of the line is given by 2

Any line which is perpendicular to the given line will have a slope m such that m*2 = -1

Or, \[m = \frac{-1}{2}\]

Only options 2 and 3 satisfy this condition.

The line is also supposed to pass through the point (6,3).

Substituting these values in the option 2:

\[3 = (-1/2) * 6 + 3\]

Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.

Now substituting (6,3) in option 3:

\[3 = (-1/2) * 6 + 6\]

Or, \[ 3 =3 \] which is true . Hence option 3 is the required equation of the line.

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Z wants to buy five shirts worth 34 dollars each and three baseball caps worth 31
ella [17]

Answer:

$199.50

Step-by-step explanation:

10% discount of $34 = 10/100*34 = $3.40

so, a single shirt costs $34-$3.40 = $30.60

half off = 50% discount of $31 = 50/100*31 = $15.50

so, a single cap costs $31-$15.50 = $15.50

so, 5 shirts and 3 caps cost now

5*$30.60 + 3*$15.50 = $153 + $46.50 = $199.50

but careful - can this be a trick question ?

the phrasing of the problem description can also suggest that the discounts are only listed to confuse us and are already included in the mentioned prices ("worth" $34 - what does that mean ? because including the discounts they are currently "worth" their prices).

then it would just plainly be

5*$34 + 3*$31 = $170 + $93 = $263

4 0
3 years ago
Solve the equation 4=t/2.5
larisa [96]

the answer would be 10 because you have to times by 2.5 on both sides to get t on its own.

4 × 2.5 is 10

6 0
3 years ago
Read 2 more answers
What does this equal? 3(x+5)=7-x
True [87]
3(x+5)=7-x3x+15=7-x4x=-8x=-2
3 0
3 years ago
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Vector has x, y, and z components of 4.00, 4.00, and 1.00 units, respectively. calculate the magnitude of .
Molodets [167]
Magnitude  = sqrt (4^2 + 4^2 + 1^2)  = sqrt 33  Answer
5 0
3 years ago
The population of kansas city, missouri was 435,000 in 1990 and 482,300 in 2005. if the population is changing linearly, write a
Jlenok [28]
Find the slope of the line connecting (1990,435000) and (2005,482300):

        482300-435000        47300
m = ----------------------- = ---------------- = 3153/yr (approx)
          2005 - 1990                15 yr

Use the point-slope formula to find the equation of this str. line:

y-435000 = (3153/yr)(x-1990)

The year 2020 is 30 years after 1990.  Thus, the expected pop in 2020 is

given by     y-435000 = 3153(30) = 94590, so that y = 529590.
4 0
3 years ago
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