Suppose that y varies inversely with x. Write an equation for the inverse variation. Y =4 when x =7

Answers

Answer 1

Answer: If y varies inversely as x, then we write it as:
y = k/x

where k is some constant.

If we multiply both sides of this equation by x we get an equation for k:
k = x*y

We are given that y=4 when x=7, therefore:
k = 7*4 = 28

Put this back into our original equation to get:
y = 28/x

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Suppose y varies directly with x, and y =24 when x=8. what is the value of y when x=10?

Answers

The value of y when x is equal to 10 is 30. This is because for every value of x the value of y is 3. This can be known if you divide 24 by 8 you get 3. So if x=10 then y would equal 30.

What are the key aspects of the graph of f(x) = 32 - 62, where b is a real number?

Answers

Answer:

Step-by-step explanation:

The given function is f(x) = 32 - 6x, where b is a real number.

To understand the key aspects of the graph of this function, we can analyze its equation.

1. Slope: The coefficient of x in the equation is -6. This represents the slope of the graph. A negative slope indicates that the graph is decreasing as x increases. In this case, for every unit increase in x, the graph of f(x) decreases by 6 units.

2. Y-intercept: The constant term in the equation is 32. This represents the y-intercept, which is the point where the graph intersects the y-axis. In this case, the graph intersects the y-axis at the point (0, 32).

3. X-intercept: To find the x-intercept, we set f(x) = 0 and solve for x.

32 - 6x = 0

-6x = -32

x = 32/6 = 16/3

Therefore, the x-intercept is (16/3, 0).

4. Shape: Since the coefficient of x is negative, the graph of f(x) will be a downward-sloping line.

5. Domain and Range: The domain of f(x) is all real numbers since there are no restrictions on x. The range of f(x) is also all real numbers because the graph extends infinitely in the downward direction.

To summarize, the key aspects of the graph of f(x) = 32 - 6x are:

- A negative slope of -6, indicating a decreasing graph as x increases.

- A y-intercept at (0, 32).

- An x-intercept at (16/3, 0).

- A downward-sloping line.

- A domain and range of all real numbers.

Can someone please help me solve x + 0.018 = 9

Answers

subtract .018 from 9 to get the answer

9 - .018 = 8.982

Subtract 0.018 of both sides

x + 0.018 - 0.018 = 9 - 0,018

make de operations

x = 8.982

What multiplies to be -18 and adds to be -9?

Answers

IMPORTANT:
If you're trying to factor a quadratic in Algebra I:
There are no two integers that can solve this problem!
Your quadratic is prime!

If you're trying to solve a quadratic (find x):
The factoring approach will not work for the same reasons listed above.
Try using splitting the middle or the quadratic formula instead.

Here's how you would solve it from a more advanced approach.
If you don't know what this stuff is, just ignore it.
ab = -18, a + b = -9
Find a in terms of b.
a = -9-b
Substitute this for a in the first equation.
(-9-b)b = -18
-9b-b² = -18
Multiply everything by -1 to get rid of all these negative signs.
b² + 9b = 18
Bring over that 18.
b² + 9b - 18 = 0
Apply the quadratic formula.
(a = 1, b = 9, c = -18)
$(-b\pm√(b^2-4ac))/(2a)=(-9\pm√(9^2-4(1)(-18)))/(1*2)=(-9\pm√(81+72))/(2)=(-9\pm√(153))/(2)=\boxed{(-9\pm3√(17))/(2)}$
If you need to write two distinct numbers, just write out one with a + and one with a - in place of the plus-minus sign.

El doble de un número menos su quinta parte.

Answers

Answer:

Step-by-step explanation:

2x - x/5

x is any number.

2 times any number - any number divided by 5

2 veces cualquier número - cualquier número dividido por 5

How are the two functions f(x) = 0.7(6)^x and g(x) = 0.7^-x related to each other?

Answers

to find the relationship between them, lets do some algebra:

f(x) = (7/10)^x

g(x) = (7/10)^-x

if we do:

f(x) * g(x) = 1

due to exponents multiplying addition law, therefore, the relationship, gives:

f(x) = 1 / g(x)

Answer:

We will see that g(x) is a reflection over the y-axis of f(x).

How does a reflection work?

For a given function f(x), we can define:

A reflection over the x-axis as: g(x) = -f(x)

A reflection over the y-axis as: g(x) = f(-x).

In this case we have:

f(x) = 0.7*(6)^x

g(x) = 0.7*(6)^-x = f(-x)

So is ratter easy to notice that g(x) is a reflection over the y-axis of f(x), so the correct option is:

"g(x) is the reflection of f(x) over the y-axis."

If you want to learn more about reflections, you can read: