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3 years ago

Remainder theorem

1 answer:

8 0

The remainder theorem lets you find the remainder when a polynomial is divided by a linear function like the above, without actually doing the division.

It states that when the polynomial f(x) is divided by x - a then the remainder is f(a)

Applying it to the items in your question x - a = x + 2 so -a = 2 and so a = -2 :-
f(-2) = 2(-2)^3 - 3(-2)^2 - 5(-2) + 23 = 5 so the remainder will be 5.

Note if the remainder had been 0 then x + 2 would have been a factor of f(x). This process can be used to find if x - a is a factor.

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12. Volume of a cube is 648V3 cm³. Find its total surface<br>area.

AleksAgata [21]

Answer:

area= 449.2984 cm^2 if I understand correctly that the volume is 648 cm^3

Step-by-step explanation:

side length=the cube root of 648

side length=8.6535 cm

area=8.6536x8.6535x6=449.2984 cm^2

7 0

3 years ago

Molly's basic cell phone plan charges $35.99 for service plus $0.21 per minute beyond the included 250 minutes in the plan. How

Ilia_Sergeevich [38]

The answer is $84.29

Let the number of minutes be x.
$35.99 is fixed price and does not depend on the number of minutes x. Each minute costs $0.21 so it depends on x and we have 0.21x in the function. However, 250 minutes are already included and should not be included in x. Therefore, the function that represents the monthly cost looks like this:
f(x) = 35.99 + 0.21 * (x - 250)

Now, let's calculate for x = 480 minutes:
f(480) = 35.99 + 0.21 * (480 - 250)
f(480) = 35.99 + 0.21 * 230
f(480) = 35.99 + 48.30
f(480) = 84.29

6 0

3 years ago

Please help whilst I try to solve this as well.

lidiya [134]

Answer:

420

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

The distance between two cities on a map is 3.25 centimeters. The map used a scale in which 1 centimeter represents 20 kilometer

____ [38]

Answer:

Step-by-step explanation:

Step one:

given

we are told that the distance is 3.25cm on the map

the scale is 1cm to represent 20km

Required

the actual distance

Step two

if 1cm represent 20km

then 3.25cm will represent x km

cross multiply we have

x=2.35*20

x= 65km

Hence, the actual distance between these two cities in kilometers 65km

6 0

3 years ago

Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.

Hunter-Best [27]

Answer:

The answer is 25 :)

Step-by-step explanation:

Ok, this explanation will probably be super confusing so sorry about that but you get two statements about each aquarium. Aquarium 1 starts with 4.6 gallons and will INCREASE by 1.2 gallons every minute. So now you have statement one, so let's plug it into the y=mx+b formula. y is the result/ the answer you get, m is the slope/how much your points INCREASE or DECREASE. x is the variable you use to plug and b is your starting point. So you are trying to find the y which means we cannot plug it in yet so right now we have y=mx+b. your next letter to switch out is m. Like I said, M is how much each point increases or decreases and if you go back, the statement says "will increase by 1.2 gallons every minute." so your m is 1.2 and will be positive because of the keyword INCREASE. now we have y=1.2x+b. B is your starting point so let's go back to the statement to find the starting point/ number, it states "Aquarium 1 contains 4.6 gallons" meaning aquarium 1 starts with 4.6 gallons, so let's plug it into the equation. you should have y=1.2x+4.6, which is your first equation. Your next equation will be a bit more tricky. we start with y=mx+b and we start with finding m, how much each point will increase or decrease. "Isaac will begin DRAINING aquarium 2 at a rate of 0.8 gallon per every minute." so M will be .8 but notice the keywords DRAINING, meaning decreasing. So because Isaac isn't filling and increasing, but he is decreasing, you will make .8 negative. so you should currently have y=-.8x+b. Now let's find the starting point, or B. "Aquarium 2 contains 54.6 gallons of water." making your m 54.6 gallons of water. Let's plug it in. y=-.8x+54.6. Now that you have to equations, this is how you will find when both equations have a point intercepting, or in other words, the answer you are looking for. you will remove the "y=" on both equations, and place an "=" between them. You should have something looking like this on your paper. "1.2x+4.6 = -.8x+54.6". Now you are going to combine like terms, so look on both sides of the equation and look for the 2 numbers with no "x" next to them. You should find "4.6" on your left and "54.6" on your right side of the equal sign. you are going to equal out "4.6" with itself by writing "-4.6" underneath it but because you did this on one side of the equal sign, you have to do it on the other side but before you do so you should have "1.2x = -.8x+54.6". now let's subtract "4.6" to "54.6" you will write "-4.6" underneath "54.6" to get your new number, "50". your problem should look like "1.2x = -.8x + 50". now we are going to do the same for your number's with an "x" by it. on the right side of the equation, you will cancel out "-.8x". notice it's NEGATIVE so, in order to cancel out a negative number, you just make the number positive. so you will ADD ".8x" to "-.8" to get 0 but because you added ".8x" to one side, you have to do it to the other side. Let's check what we have first, you should have "1.2x = 50". so now let's ADD ".8x" to "1.2x". you will get "2x" so now you should have both equations simplified like this, "2x = 50" and now we are going to make x one so we will divide "2x" by "2" to get "x", but because you did this to one side, you have to do it to the other. so now you divide "50" by "2" to get 25. now you should have written down "x = 25". Thank you so much for reading this and please let me know if this was helpful or confusing. :)))

6 0

4 years ago