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3 years ago

Please help with this problem! :)

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

5 0

Answer:

∠STP = 90°

Step-by-step explanation:

The diagonals of a square are perpendicular bisectors of each other, hence

∠STP = 90°

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Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HE

inn [45]

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to $20\ units$

Part 3) The area is equal to $25\ units^{2}$

Step-by-step explanation:

we have

$A(5,0), B(2,4), C(-2,1),D(1,-3)$

Plot the points

see the attached figure

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 AB

$A(5,0),B(2,4)$

substitute in the formula

$d=\sqrt{(4-0)^{2}+(2-5)^{2}}$

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

$d=\sqrt{25}$

$AB=5\ units$

Find the distance BC

$B(2,4), C(-2,1)$

substitute in the formula

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

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

$d=\sqrt{25}$

$BC=5\ units$

Find the distance CD

$C(-2,1),D(1,-3)$

substitute in the formula

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

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

$d=\sqrt{25}$

$CD=5\ units$

Find the distance AD

$A(5,0),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-0)^{2}+(1-5)^{2}}$

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

$d=\sqrt{25}$

$AD=5\ units$

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

$B(2,4),D(1,-3)$

substitute in the formula

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

$d=\sqrt{(-7)^{2}+(-1)^{2}}$

$BD=\sqrt{50}\ units$

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

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

substitute

$(\sqrt{50})^{2}=5^{2}+5^{2}$

$50=50$ -----> is true

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

$A=b^{2}$

we have

$b=5\ units$

$A=5^{2}=25\ units^{2}$

Find the perimeter of the polygon

The perimeter of a square is equal to

$P=4b$

we have

$b=5\ units$

$P=4(5)=20\ units$

6 0

2 years ago

Solve. 164+56-[3+4+1]=

alukav5142 [94]

164+56-[3+4+1]=

= 164 + 56 - 8

= 212

Have a nice days...........

3 0

2 years ago

write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4

EastWind [94]

-------------------------------------------------------------------------------------------------------------

Answer: $\textsf{y = -1/4x - 4}$

-------------------------------------------------------------------------------------------------------------

Given: $\textsf{Slope = -1/4, Point through = (4, -5)}$

Find: $\textsf{Equation for the line that passes through the given point}$

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

$\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

$\textsf{y - (-5) = -1/4(x - 4)}$

Simplify and solve for y

$\textsf{y + 5 = -1/4(x - 4)}$

$\textsf{y + 5 = -1/4x + 1}$

$\textsf{y + 5 - 5 = -1/4x + 1 - 5}$

$\textsf{y = -1/4x - 4}$

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

5 0

2 years ago

How are the values of the 3s in 33,000 related

Ksju [112]

The first one is ten times the second one.

3 0

2 years ago

Can someone smart help me here?

V125BC [204]

The answer is 573

S is the three digit number.
h - a number of hundreds
t - a number of tens
o - a number of ones

S = 100h + 10t + o

The last two digits add to make ten: t + o = 10
The first and last digits add to make eight: h + o = 8
The first two digits add to make twelve: h + t = 12

t + o = 10 ⇒ o = 10 - t
h + o = 8 ⇒ o = 8 - h
_______
10 - t = 8 - h
h + t = 12 ⇒ h = 12 - t
_______
10 - t = 8 - (12 - t)
10 - t = 8 - 12 + t
10 - t = -4 + t
10 + 4 = t + t
2t = 14
t = 14/2 = 7
______

h = 12 - t = 12 - 7 = 5
______

o = 8 - h = 8 - 5 = 3

S = 100h + 10t + o
h = 5
t = 7
o = 3

S = 100*5 + 10*7 + 3
= 500 + 70 + 3
= 573

8 0

3 years ago