A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 45 cm
The prism is filled with cubes that have edge lengths of
cm.
How many cubes are needed to fill the rectangular prism?
​

Answer:

The solutions to the equation are -3,-2,2

Step-by-step explanation:

x^3+3x^2=4x+12

Subtract 4x +12 from each side

x^3+3x^2-4x-12=4x+12-4x-12

x^3+3x^2-4x-12=0

I will use factoring by grouping

x^3+3x^2     -4x-12=0

I will factor out x^2 from the first group and -4 from the second group

x^2 (x+3) -4(x+3) =0

Now we can factor out (x+3)

(x+3) (x^2-4) =0

We can use the zero product principle since the right hand side is equal to 0

x+3 =0            x^2-4 =0

x+3-3=0-3        x^2 -4+4=0+4

x=-3                    x^2=4

                           Take the square root of each side

                            sqrt(x^2) = sqrt(4)

                                      x=±2

The solutions to the equation are -3,-2,2

Answer:

Estimate the surface area of a cube with side length 9.9 in.

A) 100 in²  

B) 400 in²  

C) 600 in²

D) 1000 in²

Step-by-step explanation:

9.9 to the nearest whole number is 10

We know the side length of the cube is 10

We work out the area of face and multiply by 6.

10 x 10 = 100

100 x 6 = 600 in²

Answer:

600 is the answer

Step-by-step explanation:

We can round each side length to 10 in. Therefore, the area of one face is 100 in2. Since there are 6 congruent faces in a cube, the total estimated surface area of 600 in2.

Answer:

The units price is [tex]\$0.28[/tex] per pencil

Step-by-step explanation:

we know that

To find the unit price divide the total cost by the total number of pencils

so

[tex]\frac{2.24}{8}\frac{\$}{pencils}=0.28\frac{\$}{pencil}[/tex]

3^3 + 2^7

Step-by-step explanation:

There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.

"taken from MrScienceguy"

Answer:

3^3 + 2^7

Step-by-step explanation:

There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.

To add the fractions of cheese Alana bought (3/8 and 1/4), you cannot use fractions with a common denominator, for instance, 6/16 and 4/16.

The question asked by the student is about adding fractions, and in the context given, the fractions represent pounds of cheese Alana bought. The two fractions in question are 3/8 and 1/4. To find out the total amount of cheese Alana bought, you need to add these fractions. Given that the two fractions have different denominators, you cannot use any pair of fractions with a common denominator to find the total. Hence, a pair of fractions like 6/16 and 4/16 (these fractions are equivalent to 3/8 and 1/4) cannot be used to determine the total cheese Alana bought.

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The fractions cannot be used to find the total weight of cheese if they do not have a common denominator. For example, 1/3 and 1/5 cannot be used to find the total weight of cheese because their LCM is 15, and neither fraction can be converted to have a denominator of 15.

To determine which pair of fractions cannot be used to find the total weight of cheese, we need to consider the concept of least common multiples (LCM). The LCM is the smallest positive integer that is a multiple of both denominators.

In this case, the denominators of the two fractions are 8 and 4. The LCM of 8 and 4 is 8.

If we can convert both fractions to have the same denominator of 8, then we can add the numerators to find the total weight of cheese. However, if the fractions cannot be converted to have the same denominator of 8, then we cannot use them to find the total weight of cheese.

Let's convert the first fraction, 3/8, to have a denominator of 8. We can do this by multiplying the numerator and denominator by 1:

3/8 * 1/1 = 3/8

Now let's convert the second fraction, 1/4, to have a denominator of 8. We can do this by multiplying the numerator and denominator by 2:

1/4 * 2/2 = 2/8

Since we were able to convert both fractions to have the same denominator of 8, we can use them to find the total weight of cheese. The total weight of cheese is 3/8 + 2/8 = 5/8.

Therefore, the pair of fractions that cannot be used to find the total weight of cheese is any pair that does not have a common denominator. For example, the fractions 1/3 and 1/5 cannot be used to find the total weight of cheese because their LCM is 15, and neither fraction can be converted to have a denominator of 15.

The diameter of circle is  288.84 units

As we know

Circumference of circle = 2*pi*r

where r is radius of the circle

Arranging the equation

C = 2 π r

r = C / 2 π

r = 907.46 / 2 π

r= 144.42

Since Diameter is double of radius so diameter is 2 x 144.42 = 288.84 units

The approximate percent increase in the price of the movie ticket is 18.52%.

To find the approximate percent increase in the price of the movie ticket, we can use the formula:

Percent increase = ((New price - Old price) / Old price) * 100

Plugging in the given values:

Percent increase = ((8.00 - 6.75) / 6.75) * 100 = 18.52%

Therefore, the approximate percent increase in the price of the movie ticket is 18.52%.

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Answer:

c. 1 13/15

Step-by-step explanation:

The best way to find out how much more Tristan rode his bike would be to subtract both of his distances together.

Saturday = [tex]3\dfrac{2}{3}[/tex]

Sunday = [tex]1\dfrac{4}{5}[/tex]

Now we actually have two different fractions with different denominators.

We can solve this first by converting the mixed numbers into improper fractions.

[tex]3\dfrac{2}{3}=\dfrac{9+2}{3}[/tex]

[tex]3\dfrac{2}{3}=\dfrac{11}{3}[/tex]

Now how did I do that?

First we take the denominator and multiply it to our whole number, then add the product to the numerator.

Let's proceed to the next mixed fraction.

[tex]1\dfrac{4}{5}=\dfrac{5+4}{5}[/tex]

[tex]1\dfrac{4}{5}=\dfrac{9}{5}[/tex]

We are then left with:

[tex]\dfrac{11}{3}-\dfrac{9}{5}[/tex]

Since we cannot subtract them directly because they have different denominators, we need to find the LCD of both denominators.

[tex](\dfrac{5}{5}) \dfrac{11}{3}-\dfrac{9}{5}(\dfrac{3}{3})[/tex]

[tex]\dfrac{55}{15}-\dfrac{27}{15}[/tex]

Now that they have similar denominators, we can then proceed to subtract them to each other.

[tex]\dfrac{55}{15}-\dfrac{27}{15}=\dfrac{28}{15}or1\dfrac{13}{15}[/tex]

Answer:

There is no solution.

0^-1 = 1/0

You can't divide by 0; therefore, there is no solution because the solution is undefined.

Zero to the power of negative one can be rewritten as one over zero. This fraction is technically equal to infinity, though it is also undefined.

X = number of correct answers

Y = number of incorrect answers

School A has 174 points and school B has 102 points.

A = 174

B = 102

School A has the same number of correct and incorrect answers during the final round.

A = 174 + 10X - 6Y

School B gives no incorrect answers and the same number of correct answers as school A.

B = 102 + 10X

The contest ends with the two schools tied.

Score = 174 + 10X - 6Y = 102 + 10X

174 + 10X - 6Y = 102 + 10X

Answer:

60 i think

Step-by-step explanation:

Hope this helped :)

Answer:

84.7058824 %

Step-by-step explanation:

Of means multiply and is means equals

P *85 = 72

Divide each side by 85

P *85/85 = 72/85

P = .847058824

Change from decimal form to percent form by multiplying by 100

P =  .847058824 * 100

P = 84.7058824 %

Answer:

84.7058824 %

This is the correct answer.

i believe the answer is B but im not sure

Answer:

582 ft²

Step-by-step explanation:

2(6x15)= 180

2(9x9)=  162

  (9x4)=   36

  (6x4)=   24

3(15x4)= 180  

            582 ft²

             648 ft²

Answer:

Step-by-step explanation: the answer is true

The given statement is true. Both functions and relations can be represented by mapping diagrams is true statement.

Mapping diagrams: A mapping diagram is a visual representation that shows the relationship between the elements of a domain and the corresponding elements in a co-domain or range.

Functions: A function is a specific type of relation where each element in the domain is mapped to exactly one element in the co-domain. In a mapping diagram for a function, each element in the domain is represented by an arrow pointing to its corresponding element in the co-domain.

Representing functions with mapping diagrams: To represent a function using a mapping diagram, follow these steps:

Identify the elements in the domain and co-domain of the function.

Draw a set of arrows from each element in the domain to its corresponding element in the co-domain.

Make sure that each element in the domain has only one arrow pointing to it from the co-domain, indicating the one-to-one mapping characteristic of functions.

Relations: A is a more general concept that describes any set of ordered pairs consisting of elements from a domain and co-domain. A relation can have multiple outputs for a single input, unlike a function.

Representing relations with mapping diagrams: To represent a relation using a mapping diagram, follow these steps:

Identify the elements in the domain and co-domain of the relation.

Draw arrows from each element in the domain to all the corresponding elements in the co-domain, representing the multiple outputs or mappings.

In summary, mapping diagrams can be used to represent both functions and relations. Functions have a one-to-one mapping, whereas relations can have multiple mappings for a single input. Mapping diagrams provide a visual way to understand and represent the relationships between the elements of a domain and co-domain.

Therefore, the given statement is true. Both functions and relations can be represented by mapping diagrams is true statement.

Learn more about mapping diagrams here:

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120°

hope you are having a good day :)

Answer:

Final answer is [tex]3x^2-4x+15[/tex]

Step-by-step explanation:

Given expression is [tex](5x^2+3)-(2x^2+4x-12)[/tex].

Now we need to subtract them.

We are allowed to subtract like terms only that has same variable with same exponent.

[tex](5x^2+3)-(2x^2+4x-12)[/tex]

[tex]=5x^2+3-2x^2-4x+12[/tex]

[tex]=5x^2-2x^2-4x+3+12[/tex]

[tex]=(5-2)x^2-4x+(3+12)[/tex]

[tex]=(3)x^2-4x+(15)[/tex]

[tex]=3x^2-4x+15[/tex]

Hence final answer is [tex]3x^2-4x+15[/tex]

Answer:

(5x² + 3) - ( 2x² + 4x - 12) = 3x² - 4x + 15

Step-by-step explanation:

The given expression is

(5x² + 3) - ( 2x² + 4x - 12)

To find the subtraction result

(5x² + 3) - ( 2x² + 4x - 12) = 5x² + 3 - 2x² - 4x + 12

= 5x² - 2x² - 4x + 3 + 12

= 3x² - 4x + 15

Therefore the correct answer is

(5x² + 3) - ( 2x² + 4x - 12) = 3x² - 4x + 15

Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

Let's solve your equation step-by-step.

−3(2−5w)=9w+66

Step 1: Simplify both sides of the equation.

−3(2−5w)=9w+66

(−3)(2)+(−3)(−5w)=9w+66(Distribute)

−6+15w=9w+66

15w−6=9w+66

Step 2: Subtract 9w from both sides.

15w−6−9w=9w+66−9w

6w−6=66

Step 3: Add 6 to both sides.

6w−6+6=66+6

6w=72

Step 4: Divide both sides by 6.

   6w

    6

=    72

     6

w=12

Answer:

w=12

77.5 answer

Step-by-step explanation:

The Planet Diner, being halfway between Lutherville and Otisburg, is 115 miles away from Clark.

To answer this question, we need to find out how far the Planet Diner is from Clark. Given that the Planet Diner is halfway between Lutherville and Otis burg, it is about half of the distance from Otis burg to Lutherville, which is 155 miles - 75 miles = 80 miles.

So, the distance from Lutherville to the Planet Diner is 80 miles / 2 = 40 miles. Since Lutherville is 75 miles away from Clark, the distance from Clark to the Planet Diner would be 75 miles + 40 miles = 115 miles.

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Answer:

[tex]\$77,000[/tex] and the graph would fall at a slower rate to the right

Step-by-step explanation:

we have

[tex]y=Ao(0.79)^{x}[/tex]

Observing the graph

The initial value Ao of the truck is equal to the y-coordinate of the y-intercept of the graph

so

[tex]Ao=\$77,000[/tex]

If the depreciation rate was 15% per year, the new formula would be

[tex]y=Ao(1-0.15)^{x}[/tex]

[tex]y=Ao(0.85)^{x}[/tex]

[tex]y=77,000(0.85)^{x}[/tex] ----> the graph would fall at a slower rate to the right

using a graphing tool

compare the graphs

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-3, -1) and (-6, 8). Substitute:

[tex]m=\dfrac{8-(-1)}{-6-(-3)}=\dfrac{9}{-3}=-3\\\\y-8=-3(x-(-6))\\\\y-8=-3(x+6)[/tex]

Answer:

P(x) = x³ - 3x² - 5x + 15

Step-by-step explanation:

∵ The roots of the polynomial are -√5 , √5 , 3

∴ The polynomial has 3 factors:

  (x - √5) , (x + √5) , (x - 3)

∴ P(x) = (x - √5)(x + √5)(x - 3)

          = (x² + √5x - √5x - 5)(x - 3)

          = (x² - 5)(x - 3) = x³ - 3x² - 5x + 15

∴ P(x) = x³ - 3x² - 5x + 15

Answer:

4 hours

Step-by-step explanation:

3 x 12 = 36

36/9 = 4

Answer:

4 hours

Step-by-step explanation:

3 x 12 = 36

36/9 = 4

Answer:

x³ + 3x² - 46

Step-by-step explanation:

note that (f + g)(x) = f(x) + g(x)

f(x) + g(x)

= x² - 36 + x³ + 2x² - 10 ← collect like terms

= x³ + 3x² - 46

Answer:

1/4 lb

Step-by-step explanation:                                  

                                                                                9

Multiply:  (3/9) times (3/4).  This comes out to --------- = 1/4

                                                                            9(4)

On Tuesday Ned picked up 1/4 lb of cans.

Answer:

Step-by-step explanation:

it easy tim will get 20 and sam will also get 20 so the ratio is 20;20 jope this helps you

Answer:

-0.14 * 0.12 = -0.0168

Step-by-step explanation:

You could multiply both numbers by 100 to make them whole integers.

-0.14 * 100 = -14

0.12 * 100 = 12

-14 * 12 = -168

Now divide by 100 twice.

-168 / 100 = -1.68 / 100 = -0.0168

Answer:

Step-by-step explanation:

First you wanna put the numbers in from least too greatest,

3

3

3

4

4

5

6

now cross out one by one from both sides and that will leave you with your answer, 4

To find the total distance, multiply the speed by the number of hours.

The equation would be d = 49t

First we need to simplify:

(-2x^2-4x+13 + (12x^2+2x-25) to get (−2x+12x​​ )+(−4x+2x)+(13−25).

Simplify to get [tex]10x^2 - 2x - 12[/tex]

There is your answer^

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