Brad and Wes are building a tree house. They cut a 12 and a half foot piece of wood into 5 of the same length pieces?How long is each piece of wood?

The required least common denominator for the fraction is 70.

Given that,
To determine the least common denominator for the fractions 2/7 and 9/10.

The least common denominator has defined the factor that is least common among the factors of the denominator is called the least common denominator.

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,

For the fraction, 2 / 7 and 9 / 10
the denominators are 7 and 10
Now lowest common multiple of 7 and 10 is given as ,
7 * 10 = 70

Thus, the required least common denominator for the fraction is 70.

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The amount of the original bill at johnny rockets was $32.50.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let a represent the total bill.

You and four friends split the bill equally. each person share was $6.50. Hence:

a / 5 = 6.50

a = 32.5

The amount of the original bill at johnny rockets was $32.50.

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d +q = 26

d=26-q

1d +0.25q = 17

1(26-q) +0.25q = 17

26 -q +0.25q = 17

26-0.75q = 17

-0.75q = -9

q = -9 / -0.75 = 12

 12 quarters and 14 dollars

check 12 * 0.25 = 3

3+14 = 17

The ordered pairs [tex]\left(-1, \frac{4}{25}\right)[/tex] and [tex](2,2500)[/tex] lie on the graph of the exponential function.

The quickest approach consists in evaluating the function at each value of [tex]x[/tex] to determine if the resulting value of [tex]y[/tex] coincide with the value given in statement.

x = -1

[tex]f(-1) = 4\cdot 5^{2\cdot (-1)}[/tex]

[tex]f(-1) = \frac{4}{25}[/tex]

The resulting value coincides with the value given in statement.

x = 0

[tex]f(0) = 4\cdot 5^{2\cdot (0)}[/tex]

[tex]f(0) = 4[/tex]

The resulting value does not coincide with the value given in statement.

x = 1

[tex]f(1) = 4\cdot 5^{2\cdot (1)}[/tex]

[tex]f(1) = 100[/tex]

The resulting value does not coincide with the value given in statement.

x = 2

[tex]f(2) = 4\cdot 5^{2\cdot (2)}[/tex]

[tex]f(2) = 2500[/tex]

The resulting value coincides with the value given in statement.

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The ordered pairs (-1, 4/25) and (2, 2500) lie on the graph of the exponential function f(x) = 4 × (5)^(2x), while (0, 0) and (1, 4) do not.

To determine which ordered pairs lie on the graph of the exponential function f(x) = 4 × (5)^(2x), we can substitute the given x-values into the function and check if the resulting y-values match the given coordinates.

For the point (-1, 4/25):

f(-1) = 4 × (5)^(2(-1)) = 4 × 1/25 = 4/25

This matches the given coordinate, so (-1, 4/25) is on the graph.

For the point (0, 0):

f(0) = 4 × (5)^(2 × 0) = 4 × 1 = 4

This doesn't match the given coordinate, so (0, 0) is not on the graph.

For the point (1, 4):

f(1) = 4 × (5)^(2 × 1) = 4 × 25 = 100

This doesn't match the given coordinate, so (1, 4) is not on the graph.

For the point (2, 2500):

f(2) = 4 × (5)^(2 × 2) = 4 × 625 = 2500

This matches the given coordinate, so (2, 2500) is on the graph.

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Answer:

[tex]\$60[/tex]

Step-by-step explanation:

Let

x------> the cost of the barrel of oil before the increase

we know that

[tex]100\%+20\%=120\%[/tex]

[tex]120\%=\frac{120}{100} =1.2[/tex]

so

[tex]1.2x=72[/tex]

Solve for x

[tex]x=72/1.2=\$60[/tex]

Answer:

15 texts

Step-by-step explanation:

[tex]4\dfrac{1}{3}\div\left(-\dfrac{5}{6}\right)\qquad(*)\\\\\text{Convert the mixed number to the improper fraction:}\\\\4\dfrac{1}{3}=\dfrac{4\cdot3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\(*)=\dfrac{13}{3}\div\left(-\dfrac{5}{6}\right)\\\\\text{By dividing by a fraction, we multiply by its reciprocal.}\\\\=\dfrac{13}{3}\cdot\left(-\dfrac{6}{5}\right)\qquad\text{simplify}\\\\=\dfrac{13}{3\!\!\!\!\diagup_1}\cdot\left(-\dfrac{6\!\!\!\!\diagup^2}{5}\right)=-\dfrac{13\cdot2}{1\cdot5}=-\dfrac{26}{5}=-\dfrac{25+1}{5}=-5\dfrac{1}{5}[/tex]

Answer:

the answer is 13/3  ÷ ( - 5/6 )  my luv :)

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Step-by-step explanation:

Answer:

The area of the square:

a = l²

The volume of a cube:

v = s³

the distance between the R and the T is

4 units

Answer:

Option D. 62%

Step-by-step explanation:

Net pay = $453.10

Gross pay = $734.00

We have to find the take-home percent of the gross pay.

We will divide net pay by gross pay and multiply by 100.

Percent of the gross pay =  [tex]\frac{453.10}{734}\times 100[/tex]

                                         = 0.617302452 × 100

                                         = 61.73 ≈ 62%

The take-home percent of the gross pay would be 62%.

If an apartment has  972 square feet of carpeting then from conversion we can say that it has 90 square meters.

Conversion is basically converting one unit to another because there are different quantities expressed in different units. Like in one kilogram there are 1000 grams, etc.

We have been given that an apartment has 972 square feet of carpeting and we are required to convert these 972 square units into square meters. We have been given that 1 square meter is equal to 10.8 square feet.

972 square feet=972/10.8

=90 square meters.

Hence if an apartment has  972 square feet of carpeting then from conversion we can say that it has 90 square meters.

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The answer is c.

If you have a root (a), it can also be written as (x-a).

(x+6),(x-1),(x-4)

Multiply all of them together to get the equation

(x+6)(x-1)(x-4)=

(x2-x+6x-6)(x-4)=

(x2+5x-6)(x-4)=

(x3+5x2-6x-4x2-20x+24)=

x3+x2-26x+24

To find a polynomial with given roots −6, 1, and 4, we create factors (x + 6), (x - 1), and (x - 4). Multiplying these factors, we get the polynomial x3 - 5x2 - 21x + 24.

Finding the Polynomial with Given Roots

To find a polynomial with roots of −6, 1, and 4, we need to create factors that each set to zero at these roots. A polynomial is a product of its factors, and a root is a solution to the equation where the polynomial is equal to zero. The factors corresponding to the roots −6, 1, and 4 are (x + 6), (x - 1), and (x - 4) respectively. Multiplying these factors gives us the polynomial:

(x + 6)(x - 1)(x - 4) = x3 - (1 + 4)x2 + (4 - 1 - 24)x + (6 x 1 x 4)

Let's expand and simplify:

x3 - 5x2 - 21x + 24

Therefore, the polynomial with roots of
−6, 1, and 4 is x3 - 5x2 - 21x + 24.