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3 years ago

Write an equation of the line containing the given point and perpendicular to the given line:

Mathematics

2 answers:

Maru [420]3 years ago

6 0

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

9x+7y=4

7y = - 9x + 4

y = -9x/7 + 4/7

Comparing with the slope intercept form, slope = - 9/7

If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (7,-4) is 7/9

To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes

- 4 = 7/9×7 + c = 49/9 + c

c = - 4 - 49/9 = -85/9

The equation becomes

y = 7x/9 - 85/9

yulyashka [42]3 years ago

6 0

Answer:

Step-by-step explanation:

any eq. of line perpendicular to 9x+7y=4 is

7x-9y=a

it passes through (7,-4)

7(7)-9(-4)=a

49+36=a

a=85

reqd. eq. is 7x-9y=85

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a roller coaster train with 6 passenger cars and the front decoration has a mass of 3500 kg. when the train has the front decora

irinina [24]

Answer: The mass of each passenger is 550 kg.

The mass of front decoration = 200 Kg.

Step-by-step explanation:

Let the mass of each passenger be 'x'.

Let the mass of front decoration be 'y'.

So, Number of passenger = 6

Mass of 6 passengers and front decoration = 3500 kg.

Number of passengers = 4

Mass of 4 passengers and front decoration = 2400 kg.

According to question, it becomes,

$6x+y=3500\\\\\implies y=3500-6x----------------(1)\\\\4x+y=2400\\\\\implies y=2400-4x---------------(2)$

so, From Eq(1) and Eq(2), we have,

$3500-6x=y=2400-4x\\\\3500-6x=2400-4x\\\\3500-2400=-4x+6x\\\\1100=2x\\\\x=\frac{1100}{2}=550$

Hence, the mass of each passenger is 550 kg.

The mass of front decoration = 3500-550(6)=200 Kg.

6 0

3 years ago

Tickets to a concert cost $50 for each orchestra seat and $40 for each

Vsevolod [243]

Answer:

H. the number of orchestra seat is 900

Step-by-step explanation:

Step one:

let the number of orchestra seat be x

and balcony seat be y

cost of orchestra= $50 each

cost of balcony =$40 each

total tickets= 1500

x+y= 1500----------1

amount earned= $69000

50x+40y=69000--------2

The system of equation for the situation is

x+y= 1500----------1

50x+40y=69000--------2

from 1, x=1500-y

put this in equation 2

50(1500-y)+40y=69000

75000-50y+40y=69000

-10y=69000-75000

-10y=-6000

divide both sides by -10

y=-6000/-10

y=600

put y= 600 in equation 1

x+600= 1500

x=1500-600

x=900

6 0

3 years ago

If you chose a 3 letter password from the letters A,B,C, and D the password cannot have the same letter repeated in it. How many

ozzi

There are 4 possible passwords

6 0

3 years ago

If you had dollars, how

solong [7]

Answer:

Just how much dollars?

Step-by-step explanation:

If a whole number, then rounded would be the exact same thing. If a decimal, example, $12.28 then round it to $12.30. Hope this helps!

8 0

3 years ago

The school choir is going on a trip. They plan on bringing 100 total bottles of water and juice with them. Each bottle of water

jarptica [38.1K]

Answer:

40 bottles of juice

60 bottles of water

Step-by-step explanation:

let w represent water, let j represent juice. set up a system of equations:

w+2j=140

w+j=100

isolate the w by itself on the bottom equation:

w=100-j

solve the top equation by substitution, substituting 100-j for w:

w+2j=140

100-j+2j=140

100+j=140

j=40

this means that they bought 40 bottles of juice.

to find the amount of bottles of water the bought, substitute 40 for j in either of the equations (i did it in the bottom one, because it's easier):

w=100-j

w=100-40

w=60

so, they bought 60 bottles of water.

5 0

3 years ago