Which fraction shows 32/48 in simplest form

Answers

Answer 1

Answer: 32÷16=2
48÷16=3

so 2/3

Answer 2

Answer: 32 / 8 = 4
48 / 8 = 6
4/6 can be reduced by two
2/3 is the final answer.

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192 rounded to nearest tenth?

Answers

There is no TENTH in 192 so 192 rounded to the nearest TENTH is 192.

If you meant TEN then 192 rounded to the nearest TEN is 190.

Good Luck!

The next larger tenth is 192.1

The next smaller tenth is 191.9

But 192 is closer to 192 than it is to 192.1 or 191.9, so 192 is ALREADY rounded to the nearest tenth.

Which of the following is a solution to the equation 2/3 x + 16 = -14?-45
-30
20
-3

Answers

It's -45
-14-16=-30
-30÷2/3= -45

Answer: -45

Step-by-step explanation:

How do you solve a quadratic equation

Answers

$- \beta +- √( \beta ) {2} -4ac (all divided by)/2a$

You should already know how to factor quadratics. (If not, review Factoring Quadratics.) The new thing here is that the quadratic is part of an equation, and you're told to solve for the values of x that make the equation true. Here's how it works: Solve (x – 3)(x – 4) = 0. Okay, this one is already factored for me. But how do I solve this?Think: If I multiply two things together and the result is zero, what can I say about those two things? I can say that at least one of them must also be zero. That is, the only way to multiply and get zero is to multiply by zero. (This is sometimes called "The Zero Factor Property" or "Rule" or "Principle".) Warning: You cannot make this statement about any other number! You can only make the conclusion about the factors ("one of them must equal zero") if the product itself equals zero. If the above product of factors had been equal to, say, 4, then we would still have no idea what was the value of either of the factors; we would not have been able (we would not have been mathematically "justified") in makingany claim about the values of the factors. Because you can only make the conclusion ("one of the factors must have equaled zero") if the product equals zero, you must always have the equation in the form "(quadratic) equals (zero)" before you can attempt to solve it. The Zero Factor Principle tells me that at least one of the factors must be equal to zero. Since at least one of the factors must be zero, I'll set them eachequal to zero:x – 3 = 0   or   x – 4 = 0This gives me simple linear equations, and they're easy to solve:x = 3 or  x = 4And this is the solution they're looking for:  x = 3, 4Note that "x = 3, 4" means the same thing as "x = 3 or  x = 4"; the only difference is the formatting. The "x = 3, 4" format is more-typically used.One important issue should be mentioned at this point: Just as with linear equations, the solutions to quadratic equations may be verified by plugging them back into the original equation, and making sure that they work, that they result in a true statement. For the above example, we would do the following: Checking x = 3 in (x – 3)(x – 4) = 0:([3] – 3)([3] – 4) ?=? 0
     (3 – 3)(3 – 4) ?=? 0
               (0)(–1) ?=? 0
                       0   =   0Checking x = 4 in (x – 3)(x – 4) = 0:([4] – 3)([4] – 4) ?=? 0
     (4 – 3)(4 – 4) ?=? 0
                 (1)(0) ?=? 0
                       0   =   0So both solutions "check" and are thus verified as being correct.Solve x2 + 5x + 6 = 0.This equation is already in the form "(quadratic) equals (zero)" but, unlike the previous example, this isn't yet factored. The quadratic must first be factored, because it is only when you MULTIPLY and get zero that you can say anything about the factors and solutions. You can't conclude anything about the individual terms of the unfactored quadratic (like the 5x or the 6), because you can add lots of stuff that totals zero.So the first thing I have to do is factor:x2 + 5x + 6 = (x + 2)(x + 3)Set this equal to zero:(x + 2)(x + 3) = 0Solve each factor: Copyright © Elizabeth Stapel 2002-2011 All Rights Reservedx + 2 = 0  or  x + 3 = 0
x = –2 or  x = – 3The solution to x2 + 5x + 6 = 0 is x = –3, –2Checking x = –3 and x = –2 in x2 + 5x + 6 = 0:[–3]2 + 5[–3] + 6 ?=? 0
           9 – 15 + 6 ?=? 0
           9 + 6 – 15 ?=? 0
               15 – 15 ?=? 0
                        0   =   0[–2]2 + 5[–2] + 6 ?=? 0
           4 – 10 + 6 ?=? 0
           4 + 6 – 10 ?=? 0
               10 – 10 ?=? 0
                        0   =   0So both solutions "check".Solve x2 – 3 = 2x.This equation is not in "(quadratic) equals (zero)" form, so I can't try to solve it yet. The first thing I need to do is get all the terms over on one side, with zero on the other side. Only then can I factor and solve:x2 – 3 = 2x
x2 – 2x – 3 = 0
(x – 3)(x + 1) = 0
x – 3 = 0  or  x + 1 = 0
x = 3  or  x = –1Then the solution to x2 – 3 = 2x is x = –1, 3Solve (x + 2)(x + 3) = 12.It is very common for students to see this type of problem, and say:"Cool! It's already factored! So I'll set the factors equal to 12 and
solve to get x = 10 and x = 9. That was easy!"Yeah, it was easy; it was also (warning!) wrong. Besides the fact that (10 + 2)(9 + 3) does not equal 12, you should never forget that you must have "(quadratic) equals (zero)" before you can solve.So, tempting though it may be, I cannot set each of the factors above equal to the other side of the equation and "solve". Instead, I first have to multiply out and simplify the left-hand side, then subtract the 12 over to the left-hand side, and re-factor. Only then can I solve.(x + 2)(x + 3) = 12
x2 + 5x + 6 = 12
x2 + 5x – 6 = 0
(x + 6)(x – 1) = 0
x + 6 = 0  or   x – 1 = 0
x = –6  or   x = 1Then the solution to (x + 2)(x + 3) = 12 is x = –6, 1

What does input and output mean

Answers

Step-by-step explanation:

In mathematics, input and output are terms that relate to functions. Both the input and output of a function are variables, which means that they change. ... A simple example is y = x2 (which you can also write f(x) = x2). In such cases, x is the input and y is the output.

Grandma Edith uses her big punch bowl at family gatherings. The bowl is half of a sphere, with a diameter of 30 cm. Her ladle is also half of a sphere, with a diameter of 8 cm. How many ladles can Grandma Edith scoop from the punch bowl? use 3.14 to approximate pi and express your answer as a whole number. show your work.

Answers

Our first instinct is to go through every step ...

-- calculate the volume of the bowl
-- calculate the volume of the ladle
-- divide the volume of the bowl by the volume of the ladle

and we may even start down that path. But we soon realize that
it's going to be painful and take a lot of time. So we stop right
where we are, and consider our options.
We have two options:
      #1). Give up, quit, and walk away.
      #2). Find a smarter way to do it.

Look at the formula for the volume of a sphere:

   Volume = (4/3 π) (radius³) .

Do you see that ? The radius³ is a factor in the volume of
everysphere. That means that if you multiplythe radius
of a sphere by (a number),the volume of the sphere gets
multiplied by (the same number)³ !

How does that help us with this problem ? Well, it alsomeans
that the ratio of the volumes of two spheres is

   (the ratio of their radii)³.

Radius of the bowl = 15 inches
Radius of the ladle = 4 inches
Ratio of their radii = (15/4) = 3.75

   So the bowl holds (3.75)³ as much as the ladle holds.

   (3.75)³ = 52.73 ...

   The bowl holds 52.73 ... times as much as the ladle.

   After Grandma Edith scoops 52 ladle-fulls from the bowl,
there will be less than 1 ladle-full remaining in there.

And we did it all without even knowing π .

1) we calculate the volume of the big punch bowl
Volume (half sphere)=(1/2)(4/3)πr³=2/3πr³
radius=30 cm / 2=15 cm

Volume=(2/3)π(15 cm)³=2250π cm³

2) we calculate the volume of the ladle:
radius=8 cm/2=4 cm
Volume=(2/3)π(4 cm)³=128π/3 cm³

3) we calculate the number of ladles by the rule of three.
1 ladle----------------------128π/3 cm³
x------------------------------2250π cm³

x=(1 ladle * 2250π cm³) / (128π/3 cm³)=52.73 ladles≈52 ladles

Answer: 52 ladles.

The graph shows the relationship between pounds of dog food and total cost, in dollars, for the dog food. Which statement(s) about the graph is/are true? A. Point (0, 0) shows the cost is $0 for 0 pound of dog food. B. Point (1, 0.5) shows the cost is $1 for 0.5 pound of dog food. C. Point (2, 1) shows that 2 pounds of dog food cost $1. D. Point (4, 2) shows the cost is $4 for 2 pounds of dog food. E. Point (10, 5) shows that 10 pounds of dog food costs $5.sorry there is a graph, I cant paste it

Answers

we know that x-axis represents weight of dog food in pounds

and y-axis represents total cost in dollars

and a line connects (0,0) and (10,5)

based on the information we can plot a graph that can be seen in the attached image. the line represents y = $(x)/(2)$

now, let's look at each of the statements to see which is true and which is false:

a) point (0, 0) shows the cost is $0 for 0 pound of dog food.

(0,0) indicates that the cost for 0 pound dog food is $0. hence, this statement is true.

b) point (1, 0.5) shows the cost is $1.00 for 0.5 pound of dog food.

(1,0.5) indicates that the cost for 1 pound dog food is $0.5. hence, this statement is false.

c) point (2, 1) shows that 2 pounds of dog food cost $1.

(2,1) indicates that the cost for 2 pounds dog food is $1. hence, this statement is true.

d) point (4, 2) shows the cost is $4 for 2 pounds of dog food.

(4,2) indicates that the cost for 4 pounds dog food is $2. hence, this is false.

e) point (10, 5) shows that 10 pounds of dog food costs $5

(10,5) indicates the cost for 10 pounds dog food is $5. hence, this is true.

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