How do you find the length of a missing side when you have 2 similar angles?

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

so

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

3 years ago

(02.01 LC)

denis-greek [22]

Answer:

B

Step-by-step explanation:

4 0

3 years ago

Consider the hypothesis test below.

Pavel [41]

Answer:

$Z_{H0} =1.79$

p-value: 0.0367

Decision: Reject H₀

Step-by-step explanation:

Hello!

Hypothesis to test:

H₀:ρ₁-ρ₂=0

H₁:ρ₁-ρ₂>0

The statistic to use to test the difference between two population proportions is the approximation of Z

Z= (^ρ₁-^ρ₂)-(ρ₁-ρ₂) ≈N(0;1)

√ (^ρ₁(1-^ρ₁))/n₁)+(^ρ₂(1-^ρ₂)/n₂))

Z= (0.28-0.15)-0 = 1.79

√ (0.28(1-0.28)/200)+(0.15(1-0.15)/300)

p-value

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

P(Z>1.79)= 0.0367

Conclusion:

Comparing the p-value against the significance level, you can decide to reject the null hypothesis.

I hope you have a SUPER day!

8 0

3 years ago

Taylor walks 7 miles in 2 hours. At what unite rate dose Taylor walk

IRISSAK [1]

Answer:

C

Step-by-step explanation:

Unit rate means that the denominator of the units has to be 1: units have to be miles/1 hour

Thus divide miles by hours to get the unit rate. The answer would then be 7/2 miles/1 hour

6 0

3 years ago

Write 84 as a product of primes. Use index notation where appropriate

elena-s [515]

Answer:

2 x 2 x 3 x 7

Step-by-step explanation:

2x2=4

4x3=12

12x7=84

3 0

3 years ago