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2 years ago

The slope of two lines are - 3/2 and 18/a. Determine the value of α that will make the lines:

Mathematics

1 answer:

Yuliya22 [10]2 years ago

5 0

Answer:

a) a=-12

b) a=27

Step-by-step explanation:

a) parallel lines have = slopes SO

-3/2 = -3/2

-3/2 = 18/a

-3a/2 = 18

-3a = 18 * 2 = 36

a = -12

b) perpendicular lines have negative inverse slopes SO

- 3/2 ---> 2/3

2/3 = 18/a

2a/3 = 18

2a = 18 * 3 = 54

a = 54/2 = 27

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The figure below shows a shaded rectangular region inside a large rectangle: (pic)

mariarad [96]

Answer:

Step-by-step explanation:

Probability of falling NOT in the shaded region is "area of white region" divided by "area of whole rectangle (big one)".

Area of whole rectangle:

Area of rectangle = length * width = 10 * 5 = 50

Area of White Region:

First, area of shaded region = length * width = 4 * 2 = 8

Now,

Area of white region = area of whole rectangle - area of shaded rectangle

Area of white region = 50 - 8 = 42

Hence, probability is $\frac{42}{50}=0.84$

0.84 = 84%

Answer choice D is right.

8 0

2 years ago

Find the slope of the line whose equation is 4x - 6y = 8.

ss7ja [257]

Answer:

$Slope=\frac{2}{3}$

Step-by-step explanation:

4x - 6y = 8 ⇔ - 6y = -4x + 8 ⇔ y = 4/6x - 8/6 ⇔ y = 2/3x - 4/3

4 0

3 years ago

Read 2 more answers

A student solved 6x+4=2(x−8) in four steps as shown:

mr_godi [17]

The first thing you should do is solve the equation yourself.

1) Distribute the 2.
6x + 4 = 2x – 16

2) Next, you'll want to get the x's on one side. So add -2x to both sides.
6x + 4 + -2x = 2x + -2x - 16
4x + 4 = -16

3) Now subtract 4 from both sides
4x + 4 – 4 = -16 – 4
4x = -12

4) Finally, divide both sides by 4
4x/4 = -12/4
x = –3

To solve this problem all you need to do is look back out you work, and figure out the correct solution. The answer the question is The student made an error in Step 1.

7 0

3 years ago

4 a + 5 b when a = 4 and b = - 1.2

Firdavs [7]

The answer is 10.

4 a + 5 b when a = 4 and b = - 1.2

8 0

3 years ago

Read 2 more answers

An oval track is made by erecting semicircles on each end of a 60m by 120m rectangle. Find the length of the track and the area

vodomira [7]

Refer to the figure shown below.

Because the question states that the semi circles are at the ends of the rectangle, each semicircle has a radius of 30 m.

The circumference of the oval is
2π(30) + 2*120 = 60π + 240 m = 428.5 m

The area of the oval is
π(30²) + 60*120 = 900π + 7200 m² = 1.0027 x 10⁴ m²

Note:
If the semi circles are placed on the 120-m sides of the rectangle, then similar calculations yield:
Circumference = 120π + 120 m = 497 m
Area = 3600π + 7200 m² = 1.851 x 10⁴ m²

Answer:
If the semi circles are placed on the 60-m sides of the rectangle, then
Circumference = 60π + 240 m, or 428.5 m
Area = 900π + 7200 m², or 1.0027 x 10⁴ m²

if the semi circles are placed on the 120-m sides of the rectangle, then
Circumference = 120π + 120 m, or 497 m
Area = 3600π + 7500 m², or 1.851 x 10⁴ m²

3 0

3 years ago