1. 3x - 5< 19 3x - 5+<19+ 38 < 3x : x<

Mazyrski [523]

28% of 1.00 = 28
To get your answer, multiply .28 * 100.
28% of $1.00 = 28 cents.

8 0

3 years ago

Mikheal wanted to rewrite the conversion factor "1 yard = 0.914 meters" to create a conversion factor to convert meters to yards

Levart [38]

Divide both 1 yard and 0.914 meters by 1. 1x = 0.914y
Now, since you want 1 meter = "variable"
1 meter times 1 yard divided by 0.914 meters.
1 meter = 1.094 yards

7 0

3 years ago

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by: P(x)=-12x^2 +12

Minchanka [31]

Given:

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

$P(x)=-12x^2+120x$

To find:

The current that will produce the maximum power.

Solution:

We have,

$P(x)=-12x^2+120x$

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is $f(x)=ax^2+bx+c$ , then

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

In the given function, a=-12 and b=120. So,

$-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}$

$-\dfrac{b}{2a}=-\dfrac{120}{-24}$

$-\dfrac{b}{2a}=5$

Putting x=5 in the given function, we get

$P(5)=-12(5)^2+120(5)$

$P(5)=-12(25)+600$

$P(5)=-300+600$

$P(5)=300$

Therefore, 5 watt current will produce the maximum power of 300 amperes.

6 0

3 years ago

Mrs. Solar is remodeling a house and is looking for a contractor to do the work. She is getting quotes from 3 different contract

andrezito [222]

#b. The equation y = 50x + 200 represents the total cost that the contractor will charge for x hours of work.
#c. (1, 250); (2, 300); (3, 350)

6 0

3 years ago

4 hours 30 minutes = ? Minutes

tigry1 [53]

The answer is: " 270 minutes " .
__________________________________________________________
→ There are "270 minutes" in "4 hours and 30 minutes" .
__________________________________________________________
Explanation:
__________________________________________________________
Method 1):
__________________________________________________________
Note: 60 minutes = 1 hour (exactly);

30 minutes = ? hr ? ;

→ (30 minutes) * (1 hr/ 60 minutes) ;

= (30/60) hr = (3/6) hr = (3÷3)/(6÷3) hr ;

= " $\frac{1}{2}$ hr " ;

or; write as: " 0.5 hr " .
_________________________________________________________

So "4 hours & 30 minutes" = 4 hours + 0.5 hours = 4.5 hours.

→ 4.5 hours = ? minutes ;

The answer is: " 270 minutes" . 4.5 hours * $\frac{60 min}{1 hr}$ ;

= (4.5 * 60) minutes = " 270 minutes " .

→ The answer is: " 270 minutes ".
___________________________________________________________
Method 2)
___________________________________________________________

"4 hours and 30 minutes" =  ?  minutes " .
___________________________________________________________

→ " 4 hours =  ?  minutes " ;

→ 4 hr . * $\frac{60 min}{1 hr}$ = (4 * 60) minutes = 240 min. ;

→ There are " 240 minutes in 4 hours" .

→ To find the number of "minutes" in "4 hours and 30 minutes" ;

→ we takes the number of minutes in 4 hours—which is "240 minutes"—and add "30 minutes" to that number; as follows:

→ " 240 minutes + 30 minutes " ;

to get: " 270 minutes " .
_______________________________________________________

 → There are "270 minutes" in "4 hours and 30 minutes" .
_______________________________________________________

The answer is: " 270 minutes " .
_______________________________________________________

4 0

3 years ago