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3 years ago

Find the slope of a line parallel to each given line

Mathematics

1 answer:

o-na [289]3 years ago

5 0

It’s (b) because parallel lines have equal slopes

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Complete the point-slope equation of the line through (-5,4) and (1,6)

swat32

The slope is 1/3
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3 years ago

Two rectangles are similar. Rectangle ABCD has a length of 20 inches and width of 12 inches. Rectangle ABCD is dilated 25% of it

Solnce55 [7]

FGHJ is 60 inches, because it was dilated 25%, and 25% of 240 is 60

7 0

3 years ago

How do you find the area of the shaded sector of the circle? The radius is 10in and the sector is 45 degrees

Step2247 [10]

Given:

Radius of the circle = 10 in

Central angle of the sector = 45 degrees

To find:

The area of the sector.

Solution:

Area of a sector is

$A=\dfrac{\theta}{360^\circ}\pi r^2$

Where, $\theta$ is the central angle in degrees.

Putting r=10 and $\theta=45^\circ$ , we get

$A=\dfrac{45^\circ}{360^\circ}\pi (10)^2$

$A=\dfrac{1}{8}\pi (100)$

$A=12.5\pi$

Therefore, the area of the sector is 12.5π sq. inches.

7 0

3 years ago

What is (X^3 - 4x^2 + 4x - 1) / (x-1)?

professor190 [17]

Answer:

$x^{2} -3x+1$

Step-by-step explanation:

$\frac{x^{3}-4x^{2} +4x-1}{x-1}=\frac{(x-1)(x^{2}-3x+1 )}{x-1}=x^{2}-3x+1$

8 0

3 years ago

1)a chord of length 18cm midway the radius of a circle. calculate the radius of the circle correct to 1d.p. 2)if two parallel ch

kykrilka [37]

Part 1:

Given that the length of the chord is 18 cm and the chord is midway the radius of the circle.

Thus, half the angle formed by the chord at the centre of the circle is given by:

$\cos\theta=\frac{\left( \frac{1}{2} r\right)}{r}= \frac{1}{2} \\ \\ \Rightarrow\theta=\cos^{-1}\left( \frac{1}{2} \right)=60^o$

Now,

$\sin60^o= \frac{9}{r} \\ \\ \Rightarrow r= \frac{9}{\sin60^o} =10.392$

Therefore, the radius of the circle is 10.4 cm to 1 d.p.

Part 2I:

Given that the radius of the circle is 10 cm and the length of chord AB is 8 cm. Thus, half the length of the chord is 4cm. Let the distance of the mid-point O to /AB/ be x and half the angle formed by the chord at the centre of the circle be θ, then

$\sin\theta= \frac{4}{10} = \frac{2}{5} \\ \\ \theta=\sin^{-1}\left( \frac{2}{5} \right)=23.6^o$

Now,

$\cos23.6^o= \frac{x}{10} \\ \\ \Rightarrow x=10\cos23.6^o=9.165\approx9.2cm$

Part 2II:

Given that the radius of the circle is 10cm and the angle distended is 80 degrees. Let half the length of chord CD be y, then:

$\sin40^o= \frac{y}{10} \\ \\ \\ \Rightarrow y=10\sin40^o=6.428$

Thus, the length of chord CD = 2(6.428) = 12.856 which is approximately 12.9 cm.

3 0

3 years ago