simplify.
3 - 2(4 - 7) ÷ 9
i don't know what to do after i subtract 4 and 7 which is -3 then multiply 2 which is -6 then i don't know what to do afterwards, i know pemdas so -6 divided by 9 cannot be so please help on that.
the integers from -3 to +3 can be used in the blanks below. which of these integers produces a positive, even integer for the expression ? show your work for those that do. i don't know what to do for the following questions so please explain on that.
4. -8/2 + 4 (____) - 2
5. (____)+ 3/2
4
6. ____ ÷ 2/-3
7.( -1 )
---- ÷ -1/2
(____) this was meant to be together with the fraction in a big parenthesis
9. the surface temperature of a deep, spring-fed lake is 70 F. the lake temperature drops 2 F for each yard below the lake surface until a temperature is constant. from 15 yards down to the spring source, the temperature increases 3 F per foot until the spring source is reached at 20 yards below the surface. i forgotten how to convert feet and yard so give me the conversion please. im still somewhat confused about this so please help me on this as well.
a. what is the temperature at 10 yards below the surface? i don't know since i don't understand the given information.
b. what is the temperature at 50 feet below the surface ? like i said before, don't understand the information given
c. write an expression for finding the lake temperature at the spring source. whats the spring source ?
i have one more question and i need you to check it.
8. in a sports competition, alyssa was penalized -16 points. she received the same number of penalty points in each of 4 events. how many points was she penalized in each event. -4 points she was penalized in each event. i divided -16 by 4 which is -4
#4.
-8/2 + 4 (____) - 2
-4 + 4x - 2
-6 + 4x
that will always be even, so you just want
-6 + 4x > 0
4x > 6
x > 6/4
So, any integer greater than 2 will work.
#5-7 can be done similarly
#8. yes. -16/4 = -4
#9.
surely you could easily find out that 3 ft = 1 yd. Geez.
So, with x given in feet, the temperature t(x) is
t(x) = 70-(2/3)x for x in [0,45]
at t(45)=40, so
t(x) = 40+3x for x in [45,60]
tank you very much steve, but i still don't understand because i wasn't taught of this in my class since we were just reviewing. so, i don't know how you did number 9 and thanks for that conversion hehe and i have a question for #9, so from 6 yards to 15 yards deep, the temperature is the same ? since it says the temperature is constant. also, from 5 through 7 i still don't understand, but for 5 i got 1 because i substituted at first 'cause i don't know how to do it without substitution butt i will check on other integers that will work out for 5. tank you very much steve, and i may forget about this since i posted this yesterday and the homework is due today and i might learn about this butt lets just see.
Where did the 6 yards come from? If the temperature is constant from 6 to 15 yards, then we have to modify things. We then have
at x=18 ft (6 yds), t(x) = 52.
t(x) = 70-(2/3)x for x in [0,18]
t(x) = 52 for x in [18,45]
t(x) = 40+3x for x in [45,60]
#5. Clearly you meant (x+3)/2 since adding 3/2 will never produce an integer.
1 will work, since all you need is a multiple of 4 for 1/2 that to be an even number (a multiple of 2).
#6
x ÷ (2/-3)
x * (-3/2)
-3x/2
Try x = 2 and you have
(-3)(2)/(-2) = 3
To simplify the expression 3 - 2(4 - 7) ÷ 9, we need to follow the order of operations (PEMDAS).
First, simplify within parentheses:
4 - 7 = -3
Next, perform multiplication:
-3 * 2 = -6
Finally, perform division:
-6 ÷ 9 = -2/3
Therefore, the simplified expression is 3 - 2(4 - 7) ÷ 9 = -2/3.
For question 4: -8/2 + 4 (____) - 2
Since multiplication and division should be done before addition and subtraction, the expression can be simplified as follows:
First, divide -8 by 2: -8/2 = -4
Next, multiply 4 by the blank: -4 + 4(____) - 2
Finally, perform the addition and subtraction based on the given integers.
Apply the same approach to questions 5, 6, and 7, and replace the blank with each integer from -3 to +3. Evaluate the expression using each integer and identify the positive, even integer.
For question 9: The conversion between feet and yards is as follows:
1 yard = 3 feet
a. To find the temperature at 10 yards below the surface, follow the given information step by step. Starting at the surface, you go down 15 yards, where the temperature drops by 2°F per yard. So, the temperature at 10 yards below the surface can be found by subtracting (15 - 10) * 2 from the starting temperature of 70°F.
b. To find the temperature at 50 feet below the surface, convert feet to yards: 50 feet ÷ 3 feet/yard = 16.67 yards. Then, follow the given information to determine the temperature at 16.67 yards below the surface.
c. The spring source refers to the point where the drop in temperature stops and becomes constant. The expression for finding the lake temperature at the spring source will depend on the information given.
As for question 8, your answer of -4 points penalized in each event is correct. You correctly divided -16 by 4 to find the penalty points in each event.