MATHEMATICS HIGH SCHOOL

The end points of one side of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the pentagon?(1) the square root of 10
(2) 5 times the square root of 10
(3) 5 times the square root of 2
(4) 25 times the square root of 2
The end points of one side of a regular pentagon - 1

Answers

Answer 1
Answer: To determine the perimeter of the pentagon, you must first calculate a side length of it. Let's name the coordinates A(-1,4) and B(2,3).

To figure out how far the points are from each other, you have to use the distance formula:
D_(AB) = \sqrt{( x_(2)-x_(1))^2+{(y_(2)-y_(1))^2}
x_(1) =1, x_(2) =-2, y_(1) =2, y_(2) =3
D_(AB)= \sqrt{(2--1)^2+{(3-4)^2}
D_{AB}= \sqrt{(2--1)^2+{(3-4)^2} 
D_(AB)= \sqrt{(2+1)^2+{(3-4)^2}
D_(AB)= √((3)^2+(-1)^2)
D_(AB)= √(9+1)
D_(AB)= √(10)

Now, the formula for the perimeter of a pentagon is 
P = 5×side length
 
So...
Perimeter = 5×√(10)

The answer is (2)
Answer 2
Answer:

the answer is (2) because using the distance formula which can be found on your browser, it will lead us to the answer 5 radical 10

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(08.01, 08.02, 08.03, 08.05, 08.06 MC)Part A: Factor x2y2 + 6xy2 + 8y2. Show your work. (4 points)

Part B: Factor x2 + 8x + 16. Show your work. (3 points)

Part C: Factor x2 − 16. Show your work. (3 points)

Answers

Answer: The factorization of all the parts are :

Part A : x^2y^2+6xy^2+8y^2=y^2(x+2)(x+4).

Part B :  x^2+8x+16=(x+4)(x+4).

Part C :  x^2-16=(x+4)(x-4).

Step-by-step explanation:  We are given to factorize the following quadratic polynomials :

Part A : Factor x²y² + 6xy² + 8y².  

Part B : Factor x² + 8x + 16.

Part C: Factor x² − 16.

We will be using the following factorization formulas :

(i)~x^2+ax+bx+ab=(x+a)(x+b),\n\n(ii)~x^2+2xa+a^2=(x+a)^2=(x+a)(x+a),\n\n(iii)~x^2-a^2=(x+a)(x-a).

The factorization of all the parts area as follows :

Part A :

We have

x^2y^2+6xy^2+8y^2\n\n=y^2(x^2+6x+8)\n\n=y^2(x^2+4x+2x+8)\n\n=y^2(x(x+4)+2(x+4))\n\n=y^2(x+2)(x+4).

So,x^2y^2+6xy^2+8y^2=y^2(x+2)(x+4).

Part B :

We have

x^2+8x+16\n\n=x^2+2* x*4+4^2\n\n=(x+4)^2\n\n=(x+4)(x+4).

So, x^2+8x+16=(x+4)(x+4).

Part C :

We have

x^2-16\n\n=x^2-4^2\n\n=(x+4)(x-4).

So,x^2-16=(x+4)(x-4).

Thus, all the parts are factorized.
is it x times 2 times y times 2? is that what it is asking or is it meaning squared

Between 1998 and 2018, inflation for prices of goods and services has been about 51%. Suppose a salon charged $18 for a basic haircut in 1998 and has been raising prices by a steady percentage each year to keep up with inflation.What is the price of a haircut at the salon in 2008? Explain or show your reasoning.

In 2003, the salon charged $19.95 for a basic haircut. Find the cost of the basic haircut in 2013. Explain your reasoning.

Answers

9514 1404 393

Answer:

  • $22.12
  • $24.51

Step-by-step explanation:

For some growth factor f each year, the growth factor over 20 years is given as ...

  f^20 = 1 +0.51 = 1.51

Then the growth factor in 10 years is ...

  f^10 = (f^20)^(1/2) = √1.51 ≈ 1.22882

__

a) In the 10 years between 1998 and 2008, the price of a basic haircut would rise to ...

  $18 × 1.22882 ≈ $22.12 . . . price in 2008

__

b) In the 10 years between 2003 and 2013, the price of a basic haircut would rise to ...

  $19.95 × 1.22882 ≈ $24.51 . . . price in 2013

F(x) = 3x + 2 g(x) = 2x^2 - 4x
h(x) = x^2 - x + 7

Find f[g(5)]

A. 92
B. 2
C. 30
D. 242

Answers

Answer:

A

Step-by-step explanation:

Evaluate g(5), then use the value obtained to evaluate f(x) , that is

g(5) = 2(5)² - 4(5) = 2(25) - 20 = 50 - 20 = 30, then

f(30) = 3(30) + 2 = 90 + 2 = 92

Jackson has a credit card with a 15% interest rate. His dad has a credit card with a 5% interest rate. If they both charge $1,000, how much more will Jackson end up paying?

Answers

Jackson's credit card charges 15% interest.
His dad's credit card charges 5% interest.
NOw, they both soend 1000 dollars. Let's find out the difference between their interests.
Jackson => 1000 * .15 = 150 dollars
Dad of Jackson => 1000 * .05 = 50 dollars.
THus, their difference is about 100 dollars

Answer: Their difference is 100 dollars!

Have a great day! <3

13. Find the exact value of sin 30 ° - sin 45 ° cos 45 ° .a. 0
b. 1/2
c. 1
d. 2

Answers

sin30^o-sin45^ocos45^o\n\nsin30^o=(1)/(2)\n\nsin45^o=cos45^o=(\sqrt2)/(2)\n\nsin30^o-sin45^ocos45^o=(1)/(2)-(\sqrt2)/(2)\cdot(\sqrt2)/(2)=(1)/(2)-(2)/(4)=(1)/(2)-(1)/(2)=0\n\nAnswer:a.
sin30  1/2
sin45*cos45=1/2
=>  1/2  -  1/2 = 0

When you use the distance formula, does the order in which you subtract the x- and y- coordinates matter? Explain please

Answers

lets say ur points are (1,2)(3,4)

d = sqrt (x2 - x1)^2 + (y2 - y1)^2

u would label ur points
set 1 (1,2)...x1 = 1 and y1 = 2
set 2 (3,4)...x2 = 3 and y2 = 4

or u could label them this way..
set 1 (3,4)...x1 = 3 and y1 = 4
set 2 (1,2)...x2 = 1 and y2 = 2

u have to do (x2 - x1)^2 and (y2- y1)^2....but u can label ur sets of points different. Just make sure u keep ur sets together. Does that make sense ?
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