Eric works as a manager with an international hotel. Eric has a son who is 30 years younger than him. The product of their ages is 175 years. How old is Eric?

Answers

Answer 1

Answer: ANSWER

Eric is
$35years$

EXPLANATION

Let Eric's age be
$x \: \: years$

Then his son age will be,

$(x - 30) \: years$

The product of their ages is 175.

This implies that,

$x(x - 30) = 175$

We expand to get,

$x^2- 30x = 175$

We equate everything to zero to obtain,

${x}^(2) - 30x - 175 = 0$

We split the middle term to get,

${x}^(2) +5x- 35x - 175 = 0$

We factor to obtain,

$x(x +5)- 35(x +5) = 0$

We factor further to get,

$(x - 35)( x + 5) = 0$

This implies that,

$x = 35 \: or \: - 5$

Since age is not negative,

$x = 35years$

Therefore Eric is
$35years$

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One line passes through the points (-2, 1) and (4,9). Another line passes through points (-3, 8) and (5,2).Are the lines parallel, perpendicular, or neither?
A.Parallel
B.Perpendicular
C.Neither

Answers

The given lines are perpendicular to each other because there slope are negative reciprocals of each other.

What is the point slope form of a line ?

Point slope form is used to represent a straight line using its slope and a point on the line.

The line passes through two points which are (-2,1) and (4,9). The other line passes through points which are (-3,8) and (5,2).

We know that the equation of a linein point slope form is given by :

(y - y1) = m (x - x1)

For the first line : (x , y) = (-2 , 1) and (x1 , y1) = (4 , 9)

So ,

(1 - 9) = m (-2 - 4)

-8 = m × -6

m = 8/6

For the other line : (x , y) = (-3 , 8) and (x1 , y1) = (5 , 2)

So,

(8 - 2) = m (-3 - 5)

6 = m × -8

m = -6 / 8

We know that if two lines are perpendicular then , there slopes are negative reciprocals of each other. i.e.,

8/6 can be written as :

= -1/(8/6) = -6/8

The lines are perpendicular to each other.

Therefore , the first line and second line are perpendicular to each other because there slope are negative reciprocals of each other.

Learn more about point slope formof a line here :

brainly.com/question/22250570

#SPJ5

Answer:

Perpendicular

Step-by-step explanation:

khan academy

Write the expression as a constant , a single trigonometric function, or a power of a trigonometric function. Sin x cos x/ tan x

Answers

The expression a single Trigonometric function $(sin(x) * cos(x)) / tan(x) simplifies\ to \ 1.$

Let's express the expression $(sin(x) * cos(x)) / tan(x)$ in terms of a single trigonometric function or a power of a trigonometric function, we can simplify it as follows:

$(sin(x) * cos(x)) / tan(x)$

First, we can use the trigonometric identity: tan(x) = sin(x) / cos(x).

$(sin(x) * cos(x)) / (sin(x) / cos(x))$

Now, we can simplify by canceling out common terms in the numerator and denominator:

$(sin(x) * cos(x)) * (cos(x) / sin(x))$

Now, we can see that the sin(x) term in the numerator cancels out with the sin(x) term in the denominator, and the cos(x) term in the denominator cancels out with the cos(x) term in the numerator:

= 1

$the \ expression (sin(x) * cos(x)) / tan(x) simplifies\ to \ 1.$