Least to greatest .5 1/5 .35 12/25 4/5

A forest ranger spots a fire from a 115 meter tall tower. The angle of depression from the forest ranger to the fire is 28o. Wha

nikklg [1K]

Answer:

61.15 m

Step-by-step explanation:

From trigonometry :

Tan x = opposite / Adjacent

x = 28°

Tan 28 = distance from base to fire / height

0.5317094 = distance from base to fire / 115

distance from base to fire = 115 * 0.5317094

distance from base to fire = 61.15 m

4 0

2 years ago

Write the expression for when you translate the graph of y = | 1/2 x−2 |+3 a) one unit up, b) one unit down, c) one unit to the

alukav5142 [94]

Answer:

a) y = |x/2 -2| +4

b) y = |x/2 -2| +2

c) y = |(x+1)/2 -2| +3

d) y = |(x-1)/2 -2| +3

Step-by-step explanation:

To translate the function f(x) by (h, k) in the (right, up) direction, you transform it to ...

g(x) = f(x -h) +k

a) one unit up

Add 1 to the function value.

$y=\left|\dfrac{x}{2}-2\right|+3+1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+4}$

b) one unit down

Subtract 1 from the function value.

$y=\left|\dfrac{x}{2}-2\right|+3-1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+2}$

c) one unit left

Replace x with x-(-1).

$y=\left|\dfrac{x-(-1)}{2}-2\right|+3\\\\\boxed{y=\left|\dfrac{x+1}{2}-2\right|+3}$

d) one unit right

Replace x with x-1.

$\boxed{y=\left|\dfrac{x-1}{2}-2\right|+3}$

7 0

3 years ago

What does the quotiant 35/x represent?

Bumek [7]

When 35 ÷ 7, the quotient would be 5, while 35 would be called the dividend, and 7, the divisor. I hope this helps

5 0

3 years ago

A bag of 15 apples was shared among five boys equally.How many apples did each boy get

andreyandreev [35.5K]

Answer:

3 apples

Step-by-step explanation:

15 / 5 = 3

3 0

2 years ago

Read 2 more answers

Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6

Oksi-84 [34.3K]

Answer:

$-1/3$

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

$9x^2-15x$

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

$9x^2-15x=6$

Subtract 6 from both sides:

$9x^2-15x-6=0$

Divide everything by 3:

$3x^2-5x-2=0$

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

$3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0$

Find the x using the Zero Product Property:

$3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2$

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

$x=-1/3$

Assume that the correct symbol is >. Thus,

$x>-1/3$

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

$9x^2-15x$

0 is indeed less than six, so our first correct solution is:

$x>-1/3$

For the second one, do the same thing. We have:

$x=2$

Assume that the correct symbol is <. Thus:

$x$

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

$9x^2-15x$

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

$x>-1/3 \text{ and } x$

Together, we can write them as:

$-1/3$

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0

3 years ago