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2 years ago

Complete a two-column proof for each problem.

Mathematics

1 answer:

attashe74 [19]2 years ago

3 0

Answer:

D is the midpoint of AC Given

∠BDC ≅ ∠BDA Given

BD ≅ BD Reflexive Property

AD ≅ DC Definition of line segment bisector

ΔADB ≅ ΔCBD CPCTC (Congruent Parts of Congruent Triangles are Congruent)

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If f(x) and its inverse function, f^-1(x), are both plotted on the same coordinate plane, what is their point of intersection?

Romashka-Z-Leto [24]

Answer:

(a, a)

Step-by-step explanation:

actually there are two cases, don't have intersection and have. if have intersection, then they intersect at line y = x or point (a, a) by definition of inverse function.

8 0

2 years ago

Read 2 more answers

What is the length side of a triangle that has vertices at (-5, -1), (-5, 5), and (3, -1)?

Rasek [7]

The side lengths of triangle are 6 units, 8 units and 10 units.

<u>SOLUTION: </u>

Given that, we have to find what is the length side of a triangle that has vertices at (-5, -1), (-5, 5), and (3, -1)

We know that, distance between two points $P\left(x_{1}, y_{1}\right) \text { and } Q\left(x_{2}, y_{2}\right)$ is given by

$P Q=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Now,

$\begin{array}{l}{\text { Distance between }(-5,-1) \text { and }(-5,5)=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {\qquad \begin{array}{l}{=\sqrt{(-5-(-5))^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(0)^{2}+(5+1)^{2}}=\sqrt{(6)^{2}}=6} \\\\ {=\sqrt{(-5)^{2}+(5+1)^{2}+(5-(-1))^{2}}} \\\\ {=\sqrt{(-8)^{2}+(5+1)^{2}}=\sqrt{64+36}=\sqrt{100}=10} \\\\ {=\sqrt{(3-1)^{2}+(-1-(-1))^{2}}} \\\\ {=\sqrt{(5+3)^{2}+(0)^{2}}=\sqrt{(8)^{2}}=8}\end{array}}\end{array}$

8 0

2 years ago

Solve the system of equations below by graphing. Y=-5x and y=x-6

11Alexandr11 [23.1K]

9514 1404 393

Answer:

(x, y) = (1, -5)

Step-by-step explanation:

Using a graphing calculator to solve equations such as these is quick and easy. It is one of my favorite methods. The attached graph shows the solution is ...

(x, y) = (1, -5)

5 0

2 years ago

The size of the largest angle in a triangle is 3 times the size of the smallest angle.

prohojiy [21]

Answer:

a = 29

b = 64

c = 87

Step-by-step explanation:

Let the angles be a (smallest), b, and c (largest).

We know that a triangle's angles must add up to 180 degrees, so we can construct the following equations.

a + b + c = 180

c = 3a

b = a +35

With some solving and substitution...

a + (a + 35) + c = 180

2a + c = 145

2a + (3a) = 145

5a = 145

a = 29

and therefore,

b = 29 + 35 = 64

c = 3(29) = 87

6 0

2 years ago

Read 2 more answers

A playground has the shape of a trapezoid.

Dmitrij [34]

Answer:

short base: 6 yards
long base: 8 yards

Step-by-step explanation:

Our understanding of your figure is shown below.

The question says the "shortest side" and the "width" have the same dimension. If the "width" is a reference to "height 6 yards", then it seems the "shortest side" is 6 yards. Since the slant sides are longer than the height, the "shortest side" is also the "short base."

The short base is 6 yards.

The long base overhangs the short base by 1 yard on either end, so it is a total of 2 yards longer than the short base. It it 6+2 = 8 yards long.

The long base is 8 yards.

6 0

2 years ago