Mathematics, 16.07.2019 04:00 dee5896

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. the measure of the longest side of ∆abc isa)5b)6c)29^(1/2) d.34^(1/2)units. ∆abc is triangle. a. equilateralb)isosceles c. rightd)scaleneif ∆abd is formed with the point d(1, 2) as its third vertex, then ∆abd is trianglea)equilateralb)isosceles c. rightd)scalenethe length of side ad is a.3 b.5 c.8 d.10 units.

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Answer from: nathanbrockdac

The measure of the longest side of ∆ABC is:

b) 6

∆ABC is :

b) isosceles triangle.

∆ABD is :

c) right triangle

The length of side AD is :

b) 5

Step-by-step explanation:The vertices of ∆ABC are:

A(1, 7), B(-2, 2), and C(4, 2)

Length of AB is:

$AB=\sqrt{(-2-1)^2+(2-7)^2}\\\\\\AB=\sqrt{3^2+5^2}\\\\\\AB=\sqrt{9+25}\\\\\\AB=\sqrt{34}\ units$

Length of BC is:

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

Length of AC is:

$AC=\sqrt{(4-1)^2+(2-7)^2}\\\\\\AC=\sqrt{3^2+5^2}\\\\\\AC=\sqrt{34}\ units$

Since, the length of side AC=length of side AB.

Hence, we get:

The triangle is a isosceles triangle.

Also, the longest side of a triangle is: 6 units.

Now, when a new vertex D(1,2) is added.

then:

Length of AD=

$AD=\sqrt{(1-1)^2+(2-7)^2}\\\\\\AD=\sqrt{5^2}\\\\\\AD=5\ units$

Length BD

$BD=\sqrt{(1-(-2))^2+(2-2)^2}\\\\\\BD=\sqrt{3^2}\\\\\\BD=3\ units$

and Length AB is: $\sqrt{34}\ units$

Also, AD,BD and AB satisfy the Pythagorean Theorem.

Since,

$AB^2=\sqrt{AD^2+BD^2}$

Hence,

∆ABD is a right angled triangle.

and the length of side AD is 5 units

Answer from: Quest

$w\geq 14$

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

$2l+2w\geq 40$

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

$2\times 6+2w\geq 40$

now, we can solve for w

$12+2w\geq 40$

subtract both sides by 12

$12+2w-12\geq 40-12$

$2w\geq 28$

divide both sides by 2

and we get

$w\geq 14$

so,

the smallest possible measurement of the width is 14 feet

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. the measure of the longest side...

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