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3 years ago

True or false: the diagonals of any trapezoid are congruent

Mathematics

2 answers:

Semenov [28]3 years ago

6 0

False because they intersect eachother if they were to continue

FromTheMoon [43]3 years ago

6 0

False hope it helps good luck

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Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

4 years ago

Find the solution set of the inequality

Natalija [7]

Answer: x>- 7/3

Step-by-step explanation:

Solve for x by simplifying bot sides of the equation, then isolating the variable.

5 0

3 years ago

Find the surface area of the composite solid and round to the nearest tenth. Explain your answer.

Orlov [11]

Well, notice the composite is really just 4 triangles atop sitting on top of 4 rectangles, and all of them area stacked up at the edges.

so, for the rectangle's sides,

front and back are two 6x3 rectangles

left and right are two 6x3 rectangles

the bottom part is a 6x6 rectangle

now, we don't include the 6x6 rectangle that's touching the triangles, because that's inside area, and is not SURFACE area, so we nevermind that one.

now, the triangles are just four triangles with a base of 6, and a height of 4, in red noted there.

so, just get the area of all those rectangles and the triangles, sum them up and that's the surface area of the composite,

$\bf \stackrel{lateral~rectangles}{4(6\cdot 3)}~~+~~\stackrel{bottom~rectangle}{(6\cdot 6)}~~+~~\stackrel{triangles}{4\left( \cfrac{1}{2}(6)(4) \right)}$

7 0

3 years ago

Two friends, Damian and Nicole, took summer jobs. The equation y = 15.52

Sindrei [870]

Answer:

sorry

Step-by-step explanation:

5 0

2 years ago

Anyone wanna please help it’s due at 1:30

Elan Coil [88]

The answer is D (- 4x^2 - 3x - 5)

Explanation:

- 4f(x) - 3g(x)
= - 4(x^2 + 5) - 3(x - 5)
= - 4x^2 - 20 - 3x + 15
= - 4x^2 - 3x - 5

4 0

3 years ago