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2 years ago

Question 5Multiple Choice Worth 1 points)

Mathematics

1 answer:

kolbaska11 [484]2 years ago

8 0

It would be y=x+3 because you have a slope of 1 and a y-intercept at 3

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Please help me with this question with full solutions!!!

Novay_Z [31]

Answer: Choice C

x/w and z/(y+v)

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Explanation:

All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.

Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).

So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w

x/w is one of the answers

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Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z

Therefore,

sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)

z/(y+v) is the other answer

Side note: triangle ACD is not used at all.

5 0

3 years ago

Read 2 more answers

PLEASE HELP I WILL GIVE A LOT OF POINTS!

vazorg [7]

9514 1404 393

Answer:

(2.27, 0.96)

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.

For example, the line perpendicular to side AC can be found as ...

(∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)

∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)

For side AC, we want the point to be B(4, 5), so the equation is ...

7(x -4) -3(y -5) = 0

7x -3y -13 = 0

Similarly, the altitude to side AB can be written as ...

(∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)

8(x -3) +3(y +1) = 0

8x +3y -21 = 0

By the "cross multiplication method", the solution to these equations is ...

x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27

y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96

The orthocenter is near (2.27, 0.96).

A graphing application confirms this result.

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Additional information about the cross multiplication method

For the general form equations ...

ax +by +c = 0
dx +ey +g = 0

The "cross multiplication method" has you write the array ...

$\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}$

and form the "cross products" in groups of four coefficients:

D = ae -db, X = bg -ec, Y = cd -ga

Then the solution to the set of equations is ...

1/D = x/X = y/Y ⇒ x = X/D, y = Y/D

Additional note

Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.