PLZ HELP ASAP!!

A triangle has side lengths of 14, 23, and 27. Is it a right angle ?

shusha [124]

Answer:

No, it is not

Step-by-step explanation:

Here, we want to check if the lenghts given is that of a right angle triangle

For a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides

The hypotenuse represents the longest side

So 27^2 = 14^2 + 23^2

The difference between these is 4, and as such the triangle is not a right angled

6 0

3 years ago

What is the area of a 120 degree sector of a circle with the radius of 15 cm? Round to the nearest square cm.

Delvig [45]

Answer:

236 cm^2

Step-by-step explanation:

Formula

Area = sector angle/360 * pi * r^2

Givens

Sector angle = 120

r = 15

Solution

Area = 120/360 * 3.14 * 15 * 15

Area = 1/3 * 3.14 * 225

Area = 235.5

Area = 236 cm^2

8 0

3 years ago

PLS HELP ASAP

Contact [7]

Answers:

Equation is $(x+1)^2 + (y+2)^2 = 25$

Center is (-1, -2)

Radius = 5

===========================================

Work Shown:

$x^2+2x+y^2+4y=20\\\\(x^2+2x)+(y^2+4y)=20\\\\(x^2+2x+1)+(y^2+4y)=20+1\\\\(x^2+2x+1)+(y^2+4y+4)=20+1+4\\\\(x+1)^2 + (y+2)^2 = 25\\\\$

center = (h,k) = (-1,-2)

radius = 5

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

Explanation:

I grouped up the x and y terms separately. Then I added 1 to both sides to complete the square for the x terms. I cut the 2 from 2x in half, then squared it to get 1. In the next step, I cut the 4 from 4y in half to get 2, which squares to 4. So that's why I added 4 to both sides to complete the square for the y terms.

Each piece is factored using the perfect squares factoring rule which is a^2+2ab+b^2 = (a+b)^2

The last equation is in the form (x-h)^2 + (y-k)^2 = r^2

We can think of x+1 as x - (-1) to show that h = -1

Similarly, y+2 = y-(-2) = y-k to show that k = -2

The center is (h,k) = (-1,-2)

The radius is r = 5 because r^2 = 5^2 = 25 is on the right hand side in the last equation above.

3 0

3 years ago

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable

notsponge [240]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) $Z=2.45$