Mathematics, 15.12.2019 22:31 eks8252

4. determine the length across the river x to the nearest hundredth.

5. the coordinates of the vertices of a triangle are m(-4,1) , a(3,3) , and n (2,-3)

part a : determine the coordinates of j, the midpoint of ma.

part b: determine the coordinates of l, the midpoint of an.

part c: prove that jl=1/2mn

how do i solve this?

4. determine the length across the river x to the nearest hundredth. 5. the coordi

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Answer from: Nicki3729

Part 4) $x=\frac{62}{3}\ ft$

Part 5a) J(-0.5,2)

Part 5b) L(2.5,0)

Part 5c) see the explanation

Step-by-step explanation:

Part 4) we know that

The Midpoint Theorem says that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side

so in this problem

Applying the midpoint theorem

$x=\frac{124}{3}:2=\frac{124}{6}=\frac{62}{3}\ ft$

Part 5) we have

M(-4,1),A(3,3),N (2,-3)

Part a) Determine the coordinates of J, the midpoint of MA

we know that

The formula to calculate the midpoint between two points is equal to

$(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

M(-4,1),A(3,3)

substitute

$J(\frac{-4+3}{2},\frac{1+3}{2})$

J(-0.5,2)

Part b) Determine the coordinates of L, the midpoint of AN

we know that

The formula to calculate the midpoint between two points is equal to

$(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

A(3,3),N (2,-3)

substitute

$L(\frac{3+2}{2},\frac{3-3}{2})$

L(2.5,0)

Part c) Prove that JL=1/2MN

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance JL

we have

J(-0.5,2),L(2.5,0)

substitute the values in the formula

$d=\sqrt{(0-2)^{2}+(2.5+0.5)^{2}}$

$d=\sqrt{(-2)^{2}+(3)^{2}}$

$JL=\sqrt{13}\ units$

Find the distance MN

we have

M(-4,1),N (2,-3)

substitute the values in the formula

$d=\sqrt{(-3-1)^{2}+(2+4)^{2}}$

$d=\sqrt{(-4)^{2}+(6)^{2}}$

$MN=\sqrt{52}\ units$

simplify

$MN=2\sqrt{13}\ units$

Prove that

$JL=\frac{1}{2} MN$

substitute the values

$\sqrt{13}=\frac{1}{2} 2\sqrt{13}$

$\sqrt{13}=\sqrt{13}$ ---> is true

therefore

Is verified

Answer from: Quest

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )

Which is an x-intercept of the continuous function in the table

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc