MATHEMATICS HIGH SCHOOL

Multiply and simplify
(x-3y) (x + 3y)

Answers

Answer 1
Answer: (x-3y) (x + 3y)=x^2-9y^2\n\n (a-b)(a+b)=a^2-b^2
Answer 2
Answer: (x-3y)(x+3y) \n =x^2+3xy-3xy-9y^2 \n =x^2-9y^2

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Which of the following are solutions to the equation below?check all that apply. x^2+6x+9=6 A. x=3+√6 B. x=3-√6 C. x=3 D. x=0 E. x=-3+√6 F. x= -3-√6
A line segment is drawn from (+6, +4) to (+9, +4) on a coordinate grid.Which explains one way that the length of this line segment can be determined? A. Add 9 + 6. B. Add 6 + 6. C. Subtract 9 – 6. D. Subtract 6 – 6.
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Anita has $300 in her savings account that earns 5% annually. The interest is not compounded. How much interest will she earn in 1 year?

Answers

Answer:

$15

Step-by-step explanation:

We are given that

Anita has money in her saving account=$300

She earns annually=5%

We have to find the value of interest she will earn in 1 year when the interest is not compounded.

P=300, r=5%,t=1

To find the value of interest we will use the formula of simple interest.

Simple interest,I=(P* r* t)/(100)

Substitute the values in the formula then, we get

Interest=(300* 5* 1)/(100)=15

Hence, she will earns interest in 1 year=$15
300 x 0.05 = 15

So she will earn $15 of interest in 1 year

A triangle ABC with vertices A (6, 8), B (6, 12), and C (10, 12) is rotated 90 degrees What are the coordinates of B'?

Answers

i think it would be (2,8)

Let $A = (5,12)$, $B = (0,0)$, and $C = (14,0)$. For a point $P$ in the plane, the minimum value of $PA^2 + PB^2 + PC^2$ can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

Answers

Answer:

45

Step-by-step explanation:

do it

To find the minimum value of the sum of the squares of distances, we can use calculus. The minimum value can be expressed as $233/9$.

To find the minimum value of $PA^2 + PB^2 + PC^2$, we need to find the point $P$ that minimizes the sum of the squares of the distances from $P$ to $A$, $B$, and $C$. Let's denote the coordinates of $P$ as $(x, y)$. Using the distance formula, we can find the expressions for the squares of the distances:




  2.  
  3. $PA^2 = (x - 5)^2 + (y - 12)^2$

  5.  
  6. $PB^2 = x^2 + y^2$

  8.  
  9. $PC^2 = (x - 14)^2 + y^2$



The sum of these expressions is $PA^2 + PB^2 + PC^2$:



$PA^2 + PB^2 + PC^2 = (x - 5)^2 + (y - 12)^2 + x^2 + y^2 + (x - 14)^2 + y^2$



Simplifying the expression:



$PA^2 + PB^2 + PC^2 = 3x^2 + 3y^2 - 38x - 24y + 365$



To find the minimum value, we can use calculus. Taking the partial derivatives of this expression with respect to $x$ and $y$ and setting them to zero, we can find the critical points. The coordinates of the point $P$ that minimizes the sum of the squares of the distances are $(x, y) = (13/3, 8/3)$. Plugging these values into the expression, we get:



$PA^2 + PB^2 + PC^2 = (13/3)^2 + (8/3)^2 = 233/9$



Therefore, the minimum value can be expressed as $233/9$, and $m + n = 233 + 9 = 242$.

Learn more about Sum of squares of distances here:

brainly.com/question/34148489

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Factor the following polynomial completely. -x^2y^2 + x^4 + 9y^2 - 9x^2

Answers

move the pure terms to outside

x^4-9x^2-x^2y^2+9y^2
grop
(x^4-x^2y^2)+(-9x^2+9y^2)
undistribute common factors
(x^2)(x^2-y^2)+(-9)(x^2-y^2)
reverse distributive
(x^2-y^2)(x^2-9)
factor perfect squares
(x-y)(x+y)(x-3)(x+3)

Multiply and simplify.
(a - 2b) (2a - b) (a + 2b)

Answers

(a - 2b) (2a - b) (a + 2b)=\n (2a-b)(a^2-4b^2)=\n 2a^3-8ab^2-a^2b+4b^3=\n 2a^3-a^2b-8ab^2+4b^3

Civil engineer wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He assumes that each car is 14 feet long, travels at speed S, and follows the car in front of it at a safe distance for that speed. He finds that the number N of cars that can pass a given spot per minute is modeled by the function N=(89s)/(14+14(s/17)^2))

At what speed can the greatest number of cars travel safely on that road? Assume that the maximum possible speed of a car is less than 300.

Answers

N(s)= (89s)/(14+14( (s)/(17))^2 )\n\nN'(s)= ((89s)/(14+14( (s)/(17))^2 ) )'= (89* 14(1+( (s)/(17))^2)-89s* (28)/(17) )/(14^2(1+( (s)/(17))^2)) \n\nN'(s)=0\n\n89* 14(1+( (s)/(17))^2)-89s* (28)/(17)=0\n\n1+( (s)/(17))^2- (2s)/(17) =0\n\n289+s^2-34s=0\n\ns^2-34s+289=0\n\n(s-17)^2=0\n\ns=17
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