Elroy's Balloon Emporium sells boxes of balloons. There are 500 balloons in a box. In January, they sell 3 boxes.In February they sell 6 boxes .If they started with 10 boxes, how many balloons do they have left to sell?

Answer:

AB=5

Step-by-step explanation:

the steps are on top

Answer:

True

Step-by-step explanation:

(2) (3+4) = (2) (3) + (2) (4)

(2) (3+4)=2(7)=14

(2) (3) + (2) (4)=6+8=14

14=14 √

Answer:

  a.  Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2

  b.  Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5

Step-by-step explanation:

Given two tables of values, you want to find the explicit and recursive formulas for those values.

When the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.

When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.

The constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).

The attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...

  f(x) = 2x² +3

The attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.

The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...

  an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term

Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...

  g(x) = 3x² +(-10 +(-2)(x -5))

 g(x) = 3x² -2x

A recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.

The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.

The applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...

  d(x) = -10 +4(x -(-2)) = 4x -2

Then the recursion relation is

  f(x) = f(x -1) +d(x) = f(x -1) +4x -2

And the recursive formula is ...

  f(-3) = 21; f(x) = f(x -1) +4x -2

The applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...

  d(x) = 31 +6(x -6) = 6x -5

Then the recursive formula is ...

  g(5) = 65; g(x) = g(x -1) +6x -5

Answer:

There are 16 cups in a gallon.

Step-by-step explanation:

Not sure what you're asking but there are 16 cups in a gallon.

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer: A conditional statement (also called an if-then statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.

Step-by-step explanation:

Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

We can conclude that no value of 'a' will make the equation an identity.

So, to get 0 = 0 to make the equation an identity, we have to get such a value of a that makes the LHS 8x - 16 which will be similar to RHS 8x - 16.

If we take a = 1 then the LHS will be less than the RHS as:

If we take a = 2 then:

If we take a = 3 then the LHS will be greater than the RHS as:

So, we can conclude that no value of 'a' will make the equation an identity.

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The circumference is 150.72 millimeters and the area is 1808.64 square millimeters

The radius of the coin is given as

r = 12 millimeters

The diameter of the coin is calculated as

Diameter = 2 * r

So, we have

Diameter = 2 * 12 millimeters

Evaluate

Diameter = 24 millimeters

The circumference of the coin is calculated as

C = 2πr

So, we have

C = 2 * 3.14 * 24

Evaluate

C = 150.72 millimeters

The area of the coin is calculated as

A = πr²

So, we have

A = 3.14 * 24²

Evaluate

A = 1808.64 square millimeters

Hence, the circumference is 150.72 millimeters and the area is 1808.64 square millimeters

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The way a flow proof shows logical steps in the proof of a conditional statement is; A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

A flow proof uses a diagram to show each statement leading to the conclusion. Arrows are drawn to represent the sequence of the proof. The layout of the diagram is not important, but the arrows should clearly show how one statement leads to the next. The explanation for each statement is written below the statement.

A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

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Answer:

exact form= 1/49

and the decimal form= 0.02040816

Step-by-step explanation:

Answer:

1. True

2. True

3. True

4. False

5. False

6. False

7. True

8. False

9. True

10. False

Step-by-step explanation:

∈ means "is an element of"

⊂ means "only contains some, but not all, the elements of"

⊆ means "only contains some, possibly all, the elements of"

If one of those symbols is strickenthrough, it simply means the opposite, e.g. "it's not true that it's an element of" or "it's not true that it only contains some, (...) the elements of"

∅ is an empty set

{ something } is a set containing everything inside the curly brackets. Thus, { } is an empty set.

Let's rewrite the statements:

1. 5 is an element of {1, 3, 5, 7, 9}

TRUE

2. 4 is not an element of {1, 3, 9}

TRUE

3. {5, 6, 7} only contains some, possibly all, the elements of {5, 6, 7}

TRUE

4. {1, 2, 3} only contains some, but not all, the elements of {1, 2, 3}

FALSE (it contains all)

5. it's not true that {9} only contains some, possibly all, the elements of {9, 10}

FALSE (it does only contain elements of {9, 10} )

6. it's not true that 8 is an element of {2,4,6,8,10}

FALSE (because it is an element of that set)

7. empty set only contains some, possibly all, the elements of empty set

TRUE (it contains only elements of empty set - all of them, namely none)

8. 0 is an element of empty set

FALSE (empty set is empty, so it cannot contain 0)

9. {13, 11} only contains some, but not all, the elements of {11, 12, 13}

TRUE (order is irrelevant)

10. {7, 8}  only contains some, possibly all, the elements of {8}

FALSE (7 is not an element of {8} )

the awnser: is 960 inches

Answer:

3w - 4 1/2

Step-by-step explanation:

6(1/2w- 3/4)

distributing gives you

6/2w- 18/4

simplifying it gives you

3w-4 1/2

Answer:

1/5, 1:5, 1 to 5

Step-by-step explanation:

The ratio is 3/15, but simplest form is 1/5.

The number of boards it would take to cover the floor is 48

From the question, we are to determine how many boards it would take to cover the floor

From the given information,

The width of the floor is 248 in.

and

The width of the board is 5 1/6 in.

Thus,

The number of boards it would take to cover the floor is

248 ÷ 5 1/6

= 248 ÷ 31/6

= 248 × 6/31

= 1488/31

= 48

Hence, the number of boards it would take to cover the floor is 48

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Answer: False

Step-by-step explanation: If you multiply a fraction between 0 and 1 by another fraction between 0 and 1, the result would be smaller than 1.

For example,  [tex]\frac{3}{5} * \frac{1}{2} = \frac{3}{10}[/tex]

Answer:

r=30

Step-by-step explanation:

first expand:

4r+60+4r=300

8r+60=300

8r=300-60

8r=240

r=30

hope this works:)

Answer:

  (c)  55°, 90°, and 35°

Step-by-step explanation:

Given lists of angle measures, you want to know which could be the interior angles of a triangle.

The angle sum theorem tells you the sum of interior angles of a triangle is 180°. To find the angles that could be those of a triangle, check to see if their sum is 180°.

a) 60 +45 +70 = 175 ≠ 180

b) 30 +85 +25 = 140 ≠ 180

c) 55 +90 +35 = 180 . . . . . . . could form a triangle

d) 110 +15 +45 = 170 ≠ 180

The angle measures 55°, 90°, and 35° could be the interior angles of a triangle.

Answer: 2⁴

Step-by-step explanation:

The factors of 16 are 1, 2, 4, 8, and 16. The prime factors of 16 as a product can be written as 2 × 2 × 2 x 2 or 2^4, where 2 is the prime number.

Answer:

20

Step-by-step explanation:

The common factors for 60,40,20,80 60 , 40 , 20 , 80 are 1,2,4,5,10,20 1 , 2 , 4 , 5 , 10 , 20 . The GCF for the numerical part is 20 .

The simplified fraction is -2 1/4

From the question, we are to evaluate the given fractions

The given fraction is

[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

Evaluating the fraction

[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

First, convert the mixed fraction to an improper fraction

[tex]-\frac{9}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

Now, clear the parentheses
[tex]-\frac{9}{5} -\frac{1}{4}- \frac{1}{5}[/tex]

Find the LCM of the denominators

The LCM is 20

Thus,

[tex]\frac{-36 - 5 - 4}{20}[/tex]

= [tex]\frac{-45}{20}[/tex]

= [tex]-2\frac{5}{20}[/tex]

= [tex]-2\frac{1}{4}[/tex]

Hence, the simplified fraction is - 2 1/4

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Answer:624

Step-by-step explanation:

Answer:

624

Step-by-step explanation:

Answer:

C. No, because the graph is technically correct.

Step-by-step explanation:

19.8 is greater than 5.5 by a lot, so 19.8 will look much bigger than 5.5.

Answer:

An animal shelter needs to buy 6 pounds of cat food for every cat they have. Complete the following table of cats to pounds of cat food. Cats. Lbs of cat food

0

Step-by-step explanation:

Answer:

an animal shelter needs to buy 6 pound of cat food for every cat they have . The following table of cat to pounds of cat food

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

3−11−(−6)=

3-11= -8

-8-(-6)

the two minus become plus so

-8+6= -2