8. If tan + 2 = 0, find in the range 0° and 360°

What is 9 x 10-2 as an ordinary number? Give your answer as a decimal.

DochEvi [55]

Answer:

0.09

Step-by-step explanation:

8 0

3 years ago

Find the equation of the lines parallel and perpendicular to the line 5x+2y=12 through the point (-2,3)

muminat

Answer:

The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Step-by-step explanation:

Given equation of line as :

5 x + 2 y = 12

or, 2 y = - 5 x + 12

or , y = $\frac{-5}{2}$ x + $\frac{12}{2}$

Or, y = $\frac{-5}{2}$ x + 6

∵ Standard equation of line is give as

y = m x + c

Where m is the slope of line and c is the y-intercept

Now, comparing given line equation with standard eq

So, The slope of the given line = m = $\frac{-5}{2}$

Again,

The other line if passing through the points (- 2 , 3 ) And is parallel to given line

So, for parallel lines condition , the slope of both lines are equal

Let The slope of other line = M

So, M = m = $\frac{-5}{2}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M x + c

Now , satisfying the points

So, 3 = $\frac{-5}{2}$ × ( - 2 ) + c

or, 3 = $\frac{10}{2}$ + c

Or, 3 = 5 + c

∴ c = 3 - 5 = - 2

c = - 2

So, The equation of line with slope $\frac{-5}{2}$ and passing through points ( -2 , 3)

y = $\frac{-5}{2}$ x - 2

or, 2 y = - 5 x - 4

I.e 5 x + 2 y + 4 = 0

Similarly

The other line if passing through the points (- 2 , 3 ) And is perpendicular to given line

So, for perpendicular lines condition,the products of slope of both lines = - 1

Let The slope of other line = M'

So, M' × m = - 1

Or, M' × $\frac{-5}{2}$ = - 1

Or, M' = $\frac{-1}{\frac{-5}{2}}$

Or, M' = $\frac{2}{5}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M' x + c'

Now , satisfying the points

So, 3 = $\frac{2}{5}$ × ( - 2 ) + c'

or, 3 = $\frac{- 4}{5}$ + c'

Or, 3 × 5 = - 4 + 5× c'

∴ 5 c' = 15 + 4

or, 5 c' = 19

Or, c' = $\frac{19}{5}$

So, The equation of line with slope $\frac{2}{5}$ and passing through points ( -2 , 3)

y = $\frac{2}{5}$ x + $\frac{19}{5}$

y = $\frac{2 x + 19}{5}$

Or, 5 y = 2 x + 19

Or, 2 x - 5 y + 19 = 0

Hence The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

And The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Answer

4 0

3 years ago

Several thousand teens were asked one question, "What do you think are the chances you will be married in the next ten years?" T

Readme [11.4K]

Answer:

about 54% of the people surveyed were females

Step-by-step explanation:

to calculate the % of females out of everyone, you need to add everyone up, and then add up only the females.

119+150+447+735+1174+103+171+512+710+756=4877

4877 is the Total number of people surveyed

119+150+447+735+1174=2625

2625 is the total number of females surveyed

so

to convert 2625/4877 to a %, first turn it into a decimal

2625/4877=0.538

now multiply 0.538 by 100

0.538*100=53.8%

so about 54% of the people surveyed were females

7 0

4 years ago

Read 2 more answers

The vertex of this parabola is at (-4, -1). When the y-value is 0, the x-value is 2. What is the coefficient of the squared term

satela [25.4K]

$\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\
x=a(y-{{ k}})^2+{{ h}}
\end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\
y=a(x-(-4))^2-1\implies y=a(x+4)^2-1
\\\\\\
\textit{now, we also know that }
\begin{cases}
y=0\\
x=2
\end{cases}\implies \underline{0}=a(\underline{2}+4)^2-1$

solve for "a"

5 0

3 years ago

A group of tourists spends $156 to rent snorkels and fins. A total of 15 snorkels and 18 pairs of fins are rented. Renting a sno

konstantin123 [22]

There is two answers , TX$65p/hLaura L.Experienced ACT / SAT Tutor: English, Math, Reading, Science, Writing 2000+ hours 5.0 (629 Ratings) Message Laura 3 0

At any given time, the amount of money in a club's bank account will equal the starting amount plus the amount saved each week. We can set up an equation for each club that adds these two parts together to give us that total:

$ saved up by each club after X weeks = starting $ + ($ saved per week)*(X number of weeks)

For each club, here are the equations we need:

Total $ Saved by Science Club after X weeks = 20 + 10X
Total $ Saved by Music Club after X weeks = 50 + 5X
Total $ Saved by Math Club after X weeks = 0 + 15X

We can use "Y" to represent the total $ saved by each club:

Ysci = 20 + 10X

Ymus = 50 + 5X

Ymath = 15X

To find all the possible times when any two clubs will have saved the same amount of money, we just need to graph these three equations and find the points where each pair of lines intersect. After graphing the equations, we're looking for the X-values for the intersection points where:

1) Ysci = Ymus

(The point at which 20 + 10X = 50 + 5X)

2) Ysci = Ymath

(The point at which 20 + 10X = 15X)

Ymus = Ymath

(The point at which 50 + 5X = 15X)

We can check the graphing solution by solving these pairs of equations with algebra. We just combine all "X" terms on one side and all number terms on the other side to solve for X.

1) Ysci = Ymus

20 + 10X = 50 + 5X

5X = 30

X = 6

2) Ysci = Ymath

20 + 10X = 15X

20 = 5X

X = 4

Ymus = Ymath

50 + 5X = 15X

50 = 10X

X = 5

Answer Summary:
1) $ saved by Science Club = $ saved by Music Club after 6 weeks;
2) $ saved by Science Club = $ saved by Math Club after 4 weeks;
3) $ saved by Music Club = $ saved by Math Club after 5 weeks.

7 0

3 years ago