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3 years ago

10. GradPoint

Mathematics

1 answer:

katovenus [111]3 years ago

4 0

Answer:

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Step-by-step explanation:

You can test this by using the Pythagorean theorem, which states a^2+b^2=c^2

with 7,40 and 41

7^2+40^2 does not equal to 41^2

but with 12,16, and 20

12^2+16^2=20^2

therefore, the last statement is correct.

You might be interested in

Find all solutions for a triangle with a = 14, b= 12, and B = 90°.

ziro4ka [17]

Answer:

No solution.

Step-by-step explanation:

Given

$a = 14; b= 12; B = 90^\circ$

Required

Find all possible solutions

If $B = 90^\circ$ , then the triangle is right-angled and the hypotenuse is at b

Given that $a = 14; b= 12;$

This implies that a > b

In a right-angled triangle, the hypotenuse (side b) is the longest.

Since this is not true for the given sides, then the triangle has no solution.

5 0

3 years ago

Describe the solution set for the equation below.

zheka24 [161]

Pretty sure it’s infinitely many solutions

5 0

2 years ago

Find the distance between P1(4,16degrees) and P2(-2,177degrees) on the polar plane.

bazaltina [42]

Polar coordinates give the distance from the origin and the angle from the positive x axis. Cartesian coordinates give the distance from the x and y axes.

You can draw a right triangle with these values. (see attached)
If you know the r value and theta of that triangle below, you can use trig to find x and y.

Let's convert (4, 16°) to Cartesian coordinates.

Note that since our angle is acute, (in Quadrant I) our sine and cosine will both be positive, as you should be able to derive from the unit circle, where cosine is represented as an x value and sine is represented as a y value.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(16°) = x/4
4cos(16°) = x ≈ 3.84504678375

sine = oppsite / hypotenuse
sinθ = y/r
sin(16°) = y/4
4sin(16°) = y ≈ 1.10254942327<span>

So (4, 16°) </span>⇒ (3.84504678375, 1.10254942327).

Let's convert (-2, 177°) to Cartesian coordinates.
Whenever you have a negative radius, that means to put the point opposite where it would have been if it had a positive radius. (see attached)

In that case, we can essentially add 180° to our current 177° to the same effect. That means that (-2, 177°) = (2, 357°).

Note that since our angle is in Quadrant IV, our cosine will be positive, but our sine will be negative. (as derived from the unit circle) We don't have to worry about this since our calculator figures this for us, but you should pay attention to it if you are converting from Cartesian to polar.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(357°) = x/2
2cos(357°) = x ≈ 1.99725906951

sine = opposite / hypotenuse
sinθ = y/r
sin(357°) = y/2
2sin(357°) = y ≈ -0.10467191248

So (-2, 177°) ⇒ (1.99725906951, -0.10467191248).

Now we must use the distance formula with our two points.
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d\approx\sqrt{(1.99725906951-3.84504678375)^2+(-0.10467191248-1.10254942327)^2}$
$d\approx\sqrt{-1.84778771^2+-1.20722134^2}$
$d\approx\sqrt{3.41431942+1.45738336}$
$d\approx\sqrt{4.87170278}$
$\boxed{d\approx2.20719342}$

7 0

3 years ago

Terica is dissolving a substance in a solution for a chemistry experiment. Terica measured the amount of substance remains in gr

vfiekz [6]

Answer: -1 1/3

She asked me where I was from

I said "Somewhere you never been to"

Little town outside of Knoxville

Hidden by some dogwood trees

She tried talkin' with my accent

We held hands and waded into

That blue water

She left her flip-flops by my Red Wings on the beach

[Chorus]

Yeah but, now I'm dodging potholes in my sunburnt Silverado

Like a heart-broke Desperado, headin' right back to my roots

Somethin' 'bout the way she kissed mе tells me she'd lovе Eastern Tennessee

Yeah, but all I brought back with me was some sand in my boots

[Verse 2]

I said "Let's go shoot tequila"

So we walked back to that beach bar

She said "Don't cowboys drink whiskey?" (huh)

So we drank bottom shelf

She said ", that sky looks perfect"

I said "Girl, you've never seen stars like the ones back home"

And she said "Maybe I should, see 'em for myself"

[Chorus]

Yeah, but now I'm dodging potholes in my sunburnt Silverado

Like a heart-broke Desperado, headin' right back to my roots

Somethin' 'bout the way she kissed me tells me she'd love Eastern Tennessee

Yeah, but all I brought back with me was some sand in my boots

[Bridge]

I said meet me in the mornin'

And she told me I was crazy

Yeah, but I still thought that maybe she'd show up

[Chorus]

Oh, but now I'm dodging potholes in my sunburnt Silverado

Like a heart-broke Desperado, headin' right back to my roots

Somethin' 'bout the way she kissed me tells me she'd love Eastern Tennessee

Yeah, but all I brought back with me was some sand in my boots

Step-by-step explanation:

7 0

2 years ago

Write as a unit rate. $300 per 6 hours. A 50 hours per dollar B $50 per hour C $0.20 per hour D 0.2 hours per dollar

jonny [76]

The correct answer is B) $50 per hour. Hope this helps!

4 0

3 years ago