Add 5 2/7+ 19 1/3+ 14 1/8= . Simplify the answer and write as a reduced mixed number.

Which expressions represent rational numbers? Select all the apply.

RUDIKE [14]

Answer:

the answers are A, B, C, and F

Step-by-step explanation:

just took the quiz

8 0

3 years ago

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Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

3241004551 [841]

First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(8--5)^2+(-3-4)^2} \\ \\ =\sqrt{(13)^2+(-7)^2} \\ \\ =\sqrt{169+49} \\ \\ =\sqrt{218} \\ \\ \approx14.7648... \end{gathered}$

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

5 0

11 months ago

This is a geometry question, i need something quickly :)

Marysya12 [62]

Answer:

hope it helps mark me brainlieast!

Step-by-step explanation:

For triangle ABC with sides a,b,c labeled in the usual way,

c2=a2+b2−2abcosC

We can easily solve for angle C .

2abcosC=a2+b2−c2

cosC=a2+b2−c22ab

C=arccosa2+b2−c22ab

That’s the formula for getting the angle of a triangle from its sides.

The Law of Cosines has no exceptions and ambiguities, unlike many other trig formulas. Each possible value for a cosine maps uniquely to a triangle angle, and vice versa, a true bijection between cosines and triangle angles. Increasing cosines corresponds to smaller angles.

−1≤cosC≤1

0∘≤C≤180∘

We needed to include the degenerate triangle angles, 0∘ and 180∘, among the triangle angles to capture the full range of the cosine. Degenerate triangles aren’t triangles, but they do correspond to a valid configuration of three points, namely three collinear points.

The Law of Cosines, together with sin2θ+cos2θ=1 , is all we need to derive most of trigonometry. C=90∘ gives the Pythagorean Theorem; C=0 and C=180∘ give the foundational but often unnamed Segment Addition Theorem, and the Law of Sines is in there as well, which I’ll leave for you to find, just a few steps from cosC= … above. (Hint: the Law of Cosines applies to all three angles in a triangle.)

The Triangle Angle Sum Theorem, A+B+C=180∘ , is a bit hard to tease out. Substituting the Law of Sines into the Law of Cosines we get the very cool

2sinAsinBcosC=sin2A+sin2B−sin2C

Showing that’s the same as A+B+C=180∘ is a challenge I’ll leave for you.

In Rational Trigonometry instead of angle we use spreads, squared sines, and the squared form of the formula we just found is the Triple Spread Formula,

4sin2Asin2B(1−sin2C)=(sin2A+sin2B−sin2C)2

true precisely when ±A±B±C=180∘k , integer k, for some k and combination of signs.

This is written in RT in an inverted notation, for triangle abc with vertices little a,b,c which we conflate with spreads a,b,c,

(a+b−c)2=4ab(1−c)

Very tidy. It’s an often challenging third degree equation to find the spreads corresponding to angles that add to 180∘ or zero, but it’s a whole lot cleaner than the trip through the transcendental tunnel and back, which almost inevitably forces approximation.

6 0

2 years ago

Six friends share 2 pizzas equally. How much of a pizza does each friend get?

GarryVolchara [31]

each one gets 2 and their will be 4 slices left

6 0

3 years ago

If the measure of arc GH = 110 and the measure of arc EF =55 calculate m angleGDH

natulia [17]

If I remember My geometry correctly
you add GH AND EF then divide 2

3 0

3 years ago

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