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3 years ago

What is an equation of the line that is perpendicular to -x+2y=4 and passes through the point (-2, 1)

Mathematics

1 answer:

Nana76 [90]3 years ago

5 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

x + 2y = 4

2y = - x + 4

y = -x/2 + 4/2

y = - x/2 + 2

Comparing with the slope intercept form, slope = - 1/2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (- 2, 1) is 2

To determine the intercept, we would substitute m = 2, x = - 2 and y = 1 into y = mx + c. It becomes

1 = 2 × - 2 + c = - 4 + c

c = 1 + 4 = 5

The equation becomes

y = 2x + 5

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The Japanese 5 yen coin has a hole in the middle. If the diameter of the coin is 22 mm and the diameter of the hole is 5 mm, how

Yanka [14]

Answer:

4.4mm

Step-by-step explanation:

Circumference of circle

2 Pi r

Diameter of coin = 22mm

Therefore the radius = 11mm

Therfroe the outer edge (circumference)

= 2 Pi r

= 2 x Pi x 11

=69.11mm

For the inner edge

Diameter = 5

Radius = 2.5

Therefroe inner edge (circumference)

= 2 Pi r

= 2 x Pi x 2.5

= 15.7mm

The difference is

69.11 - 15.7

=4.4mm

7 0

3 years ago

A sandwich decrease from $8 to $6 what is the percentage decrease

kati45 [8]

Answer:

25%

Step-by-step explanation:

First find the difference in price= $8-$6 = $2

Now, find percentage decrease in the price of sandwich.

Percentage decrease= (difference in price/ original price) *100

= $\frac{2}{8}$ *100

= $\frac{200}{8}$

Percentage decrease=25%

4 0

3 years ago

Find the area of the shaded segment of the circle.

vredina [299]

Answer:

Around 5.5 square meters

Step-by-step explanation:

You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula $\frac{1}{3} \pi r^2 =3\pi$ square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is $\sqrt{3}$ times larger than the smaller leg. In this case, these dimensions are a base of $\frac{3}{2}$ for the smaller leg and $\frac{3\sqrt{3}}{2}$ for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get $\frac{9\sqrt{3}}{4}$ square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!