All categories

3 years ago

Can someone help me with this two column proofs? -this one is confusing to me

Mathematics

1 answer:

Shalnov [3]3 years ago

6 0

Perpendicular bisectors have a particular property: if AB is a perpendicular bisector of CD, then every point lying on AB has the same distance from C and D.

In your case, we have that every point lying on AC has the same distance from B and D.

So, in particular, we have EB=ED, because E lies on AC.

Moreover, since AC is a perpendicular bisector, it is the height of the triangle (if we choose BD as base), and it bisects BD: this means that the triangle is isosceles, so AD=AB.

This means that triangles ABE and ADE have:

AD=AB because ABD is isosceles
EB=ED because AC is the perpendicular bisector of BD
AE in common

So, their sides are all equal, and thus they are congruent.

You might be interested in

Solve -2(x+13)+37<5x-17

katovenus [111]

-2(x+13) + 37 < 5x -17
-2x - 26 + 37 < 5x -17
-2x + 11 < 5x - 17
28 < 7x
x > 4

3 0

3 years ago

The vertices of parallelogram ABCD are A(2,1),B(3,4),C(5,3), and D(4,0). ABCD is reflected over the x-axis to create parallelogr

Scorpion4ik [409]

So, coordinates of QRST will be:

Q(2,−1),R(3,−4),S(5,−3),T(4,0)

Option D is correct.

Step-by-step explanation:

The vertices of given parallelogram ABCD are A(2,1),B(3,4),C(5,3), and D(4,0).

ABCD is reflected over the x-axis to create parallelogram QRST

We need to find coordinates of QRST.

When the graph is reflected across x-axis, the x-coordinate remains the same, while y-coordinate becomes opposite i.e the sign is changed of the given coordinate.

So, coordinates of QRST will be:

Q(2,−1),R(3,−4),S(5,−3),T(4,0)

All the y-coordinates have been converted to their opposite signs

So, Option D is correct.

Keywords: Reflection across x-axis

Learn more about reflection across x-axis at:

brainly.com/question/11203617

brainly.com/question/4057490

brainly.com/question/5017530

#learnwithBrainly

5 0

3 years ago

f(x)= -4x^2+10x-8 what is the value of the discriminant of f how many distinct real number zeros does f have

Mazyrski [523]

Answer:

Step-by-step explanation:

The function is f(x) = -4x²+10x-8

Let Δ be our the dicriminant

Δ= b²-4ac
b = 10
a = -4
c = -8
Δ = 10²-4*(-4)(-8)
Δ = 100-128
Δ = -28

The value of the discriminant is -28 and since it is negative this function has no real zeroes

4 0

3 years ago

Angelina factored (x - 48 ) and wrote that it was equal to (x^2 - 4^2)^2(x^2 + 4^2). Use complete sentences to explain how you c

defon

(x^2 - 4^2)^2 = x^4 - 4^4
(x^4 - 4^4) (x^2 + 4^2) = x^2 - 4^6
The Angela's solution is wrong cause when you multiply you get a different answer.

7 0

3 years ago

Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service cha

max2010maxim [7]

Part A:
Company A: $7 per hour +$30 service charge =money spent
Company B: $8 per hour +$40 service charge =money spent

Part B:
Company A: $7(8)+$30 = $86
Company B: $8(8)+$40 = $104

Part C:
Company A: $7(2)+$30 = $44
Company B: $8(2)+$40 = $56
You would save $12 if you use Company A instead of Company B's truck rental.

7 0

3 years ago