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3 years ago

What is the equation of a line that is perpendicular to 2x+3y=9 and passes through the point (8,5)

2 answers:

7 0

For
ax+by=c
slope=-a/b

perpendiculare lines have slopes that multiply to -1

so

2x+3y=9
slope=-2/3
-2/3 times what=-1
what=3/2

point slope form
the equation of a line that passes through the point (x1,y1) and the slope is m is
y-y1=m(x-x1)
slope=3/2
point i (8,5)

equation is
y-5=3/2(x-8)
converted to standard form
2y-10=3x-24
-3x+2y=-14
3x-2y=14

Ipatiy [6.2K]3 years ago

7 0

2x+3y=9
3y = -2x + 9
y = -2/3x + 3
slope = -2/3 so perpendicular slope = 3/2

y - 5 = 3/2 (x - 8)
y - 5 = 3/2x -12
y = 3/2x - 12 + 5
y = 3/2x - 7

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Can anyone help with the answers to all these questions with an explanation please?

saveliy_v [14]

ANSWER:

1) 25.70 cm 2) 30.84 cm 3) 10.71 km 4) 1.07 km 5) 6.71 cm 6) 10.07 mm

EXPLANATION:

1. Know that the circumference formula for a full circle is:

$C = 2\pi r$

The value of pi ( $\pi$ ) = 3.14

The radius ( $r$ ) will be given in the diagrams.

2. Now we can figure out the perimeters.

Shape One: Semi-circle

C = 2 x 3.14 x 5

C = 31.4 cm

Divide the circumference by 2 because it is a semi-circle. Then add 10 cm to this (because the flat side is 10 cm).

P = $\frac{31.4}{2} +10$

P = 25.7 cm ≈ 25.70 cm

Shape Two: Semi-circle

C = 2 x 3.14 x 6 (the picture shows the diameter so we need to half that to get the radius)

C = 37.68 cm

Divide the circumference by 2 because it is a semi-circle. Then add 12 cm to this (because the flat side is 12 cm).

P = $\frac{37.68}{2}+12$

P = 30.84 cm

Shape Three: Quadrant

C = 2 x 3.14 x 3

C = 18.84 km

Divide the circumference by 4 because it is a quadrant. Then add 6 km to this (because the two flat sides are 3 km each and so it is 6 km total).

P = $\frac{18.84}{4} +6$

P = 10.71 km

Shape Four: Quadrant

C = 2 x 3.14 x 0.3

C = 1.884 km

Divide the circumference by 4 because it is a quadrant. Then add 0.6 to this (because the two flat sides are 0.3 km each and so it is 0.6 km total).

P = $\frac{1.884}{4} + 0.6$

P = 1.071 km ≈ 1.07 km

Shape Five

C = 2 x 3.14 x 1

C = 6.28 cm

For this shape, we need to subtract the circumference of the missing sector from the circumference of the full circle to obtain the circumference for this shape. So, the circumference for the shape would be:

C = $6.28 - \frac{6.28}{4}$

C = 6.28 - 1.57

C = 4.71 cm

Then add the flat sides (1 cm + 1 cm = 2 cm) to this circumference to get the perimeter.

P = 4.71 + 2

P = 6.71 cm

Shape Six

C = 2 x 3.14 x 1.5 (Divide the 3 mm diameter by 2 to get the radius)

C = 9.42 cm

Do the same thing you did for Shape 5.

C = $9.42 - \frac{9.42}{4}$

C = 7.065 mm

Then add the flat sides (1.5 + 1.5 = 3) to this circumference.

P = 7.065 + 3

P = 10.065 mm ≈ 10.07 mm

7 0

3 years ago

A student determined that the area of shown above is A= 137.71ft² . the students work is shown below. Evaluate the students answ

MArishka [77]

Where is the students work?

6 0

3 years ago

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4 0

3 years ago

What is the probability of having 53 Mondays in a leap year?

Ronch [10]

Answer:

1/7

Step-by-step explanation:

There are 52 weeks in a year. Each have one Monday. Leap years have a total of 366 days. There are 7 days of the week. Monday is one of them, so it'll be a 1/7 chance.

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3 years ago

Ryan is buying batteries for his remote control cars. Charge Zone batteries cost $15.80 for 20 batteries. Electrocell batteries

Montano1993 [528]

Answer:

Charge Zone

Step-by-step explanation:

If Charge Zone (CZ) costs 15.80 for 20, and Electrocell batteries (EB) costs 8.10 for 10 batteries, you would find the price and quantity amount by multiplying by two. 8.10x2= 16.20, which is more than CZ.

Therefore, CZ is of better value.

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3 years ago