Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?

The inverse is f⁻¹(x) = -3(x + 1)/(x + 2).

To find the inverse of the given function f(x), follow these steps:

Thus, the inverse function is f⁻¹(x) = -3(x + 1)/(x + 2).

708 millimeters of juice Mrs. Goldstein pour into the bowl.

Given that, Mrs. Goldstein pours 3 juice boxes into a bowl to make fruit punch. Each juice box holds 236 millimeters.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the quantity of juice Mrs. Goldstein pour into the bowl be x millimeters.

Now, x=236 × 3

⇒ x = 708 millimeters

Therefore, 708 millimeters of juice Mrs. Goldstein pour into the bowl.

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Answer:

[tex]0.16666666666=\frac{16666666666}{100000000000}[/tex]            

Step-by-step explanation:

Given : Expression 0.16666666666.

To find : What is expression as a simplified fraction ?

Solution :

Expression 0.16666666666.

We have to remove decimal to convert into fraction,

By multiplying and divide by 10,

[tex]0.16666666666=\frac{0.16666666666\times 10}{10}[/tex]

[tex]0.16666666666=1.6666666666[/tex]

Similar approach we get,

[tex]0.16666666666=\frac{16666666666}{100000000000}[/tex]

The unit form of 905 is 900 + 0 + 5. This represents 900 hundreds, 0 tens, and 5 ones.

The number 905 in unit form can be written as 900 + 0 + 5. In other words, it represents 900 hundreds, 0 tens, and 5 ones. Writing numbers in unit form helps you see the value of each digit. For example, in the number 905, the 9 is in the hundreds place, giving it a value of 900, the 0 is in the tens place, giving it a value of 0, and the 5 is in the ones place, giving it a value of 5. Therefore, the unit form of 905 is 900 + 0 + 5.

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Answer:

Domain of h(x) : [2,∞)

Step-by-step explanation:

Given: Two functions

[tex]f(x)=\sqrt{2-x}[/tex]

[tex]g(x)=x-1[/tex]

Composite function, [tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]

[tex]f(x)=\sqrt{2-x}[/tex], It is square root function. As we know square root function is always greater than 0.

2-x ≥ 0

  2 ≥ x

Domain of f(x) : [2,∞)

[tex]g(x)=x-1[/tex], It is straight line equation (Linear function) As we know domain of linear function is all real number.

Domain of g(x) : (-∞,∞)

[tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]

[tex]h(x)=\dfrac{\sqrt{2-x}}{x-1}[/tex] , It is rational function. Denominator can't be zero.

So, x-1 ≠ 0

        x ≠ 1

Now, we will see domain of h(x) common all three domain.

Domain of h(x): [2,∞)

Hence, The domain of h(x) is [2,∞)

The added zeros when changing a number from scientific notation to expanded notation are usually not considered significant. They primarily serve as placeholders and do not indicate precision of measurements.

In the field of Mathematics, specifically when working with numbers in scientific notation and expanded notation, the concept of significant zeros comes into play. When you convert a number from scientific notation to expanded notation, zeros that are included in this process are not considered to be significant. Rather, the concept of significant zeros mostly applies to measurements and the precision of those measurements. For example, in the measurement 300.0, the zero at the end is significant because it shows the measurement was precise to the tenth's place. However, in changing a number from scientific to expanded notation, any added zeros primarily serve as placeholders and are typically not considered significant.

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To solve for the differential equation where y is the independent variable, one must interchange x and y, do some algebraic manipulations to separate the variables, and then integrate. Additional steps may be necessary to solve for individual constants in the equation, using given points such as x=2 when y=4. Given the absence of a starting function, a definite solution cannot be provided.

To find the solution of the differential equation (6−8xy2)dy/dx=y3 where y is the independent variable, we must first formulate the differential equation such that y is the independent variable. We do this by interchanging x and y, leading to (6-8x/y^2)dx/dy= x^3. By separating the variables and integrating, we will get the function y=f(x).

However, often with differential equations, a specific solution is also required. In this case, we know that x=2 when y=4. Plugging these into the function y=f(x) we can solve for the individual constant. Since no function f(x) is given in the question as a basis, it's impossible to come up with a definite solution, but I hope this general approach helps clarify how to solve such problems.

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Answer:

Yes

No

Step-by-step explanation:

It is appropriate to eliminate parentheses as a first step. This can be done using the distributive property, resulting in either of ...

or by dividing the equation by the factor outside parentheses, resulting in ...

___

Any of the equations other than these represent violations of the equal sign. Something has been done to one side of the equation without the same thing being done to the other side.

The scientific notation of the decimal number 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].

Scientific notation is a way to express numbers in a concise form, particularly useful for very large or very small numbers.

It consists of two parts: a coefficient and an exponent of 10.

In the case of 0.0013, we can convert it to scientific notation as follows:

[tex]0.0013 \times 10^{-3}[/tex].

Hence, the scientific notation of 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].

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Answer:

We can add any rational number to 1/5 to get a rational number.

Step-by-step explanation:

Given: We have given a rational number 1/5.

To find: We need to find a number which is added to 1/5 gives a rational number.

Solution: We know that,

Rational number + Rational number = Rational Number

Rational number + Irrational Number = Irrational Number

Irrational Number  + Irrational Number  = Irrational Number.

As we know that given fraction 1/5 is a rational number.

So, when we add any rational number to 1/5 would give a rational number.

Let us we take an example,

[tex]\frac{1}{5} +\frac{2}{3} = \frac{3+10}{15}= \frac{13}{15}[/tex]

We can see in above example that a rational number 2/3 is added to 1/5 gave us 13/15 which is also a rational number.

Therefore, we can add any rational number to 1/5 to get a rational number.

Given: Angle 1 and angle 2 are supplementary.

Angle 3 and angle 4 are supplementary.

Angle 1 is congruent to angle 3.

Prove: Angle 2 is congruent to angle 4.

Answer:

The tax rate is 4%.

Step-by-step explanation:

It is given that the property in Live Oak County is assessed at $250,000,000.

The total amount of tax raised on property is $10,000,000.

Let the tax rate be x%.

Since the rate of tax is x%, therefore x% of $250,000,000 is equal to $10,000,000.

[tex]250,000,000\times \frac{x}{100}=10,000,000[/tex]

[tex]2,500,000\times x=10,000,000[/tex]

[tex]x=\frac{10,000,000}{2,500,000}[/tex]

[tex]x=\frac{100}{25}[/tex]

[tex]x=4[/tex]

Therefore the tax rate is 4%.

Final answer:

The real numbers a and b that make the equation a+bi=13+9i true are a = 13 and b = 9. We match real and imaginary parts of the complex numbers to find a and b.

Explanation:

To find the real numbers a and b such that the equation a+bi=13+9i is true, we simply match the real parts and the imaginary parts of the complex numbers on both sides of the equation. The real part of a+bi is a, and the real part of 13+9i is 13. Therefore, a = 13. Similarly, the imaginary part of a+bi is bi and the imaginary part of 13+9i is 9i. Thus, b = 9. Hence, the values we are looking for are a = 13 and b = 9.

3-2(-7) -(-7)

3-(-14)-(-7)

3+14+7 = 24