Using the algebraic expression 4n + 6, what is the greatest whole-# value of n that will give you a result less than 100? A- 22
B- 23
C- 24
D- 25

Answer:

• f(x): vertical, x = -4; horizontal, y = 3
• g(x): vertical, x = 2; horizontal, y = -4
• g(x) is shifted right 6 and down 7 from f(x)

Step-by-step explanation:

The vertical asymptote is the vertical dashed line in each graph. Its equation is x = constant, where the constant can be read from the graph where the line crosses the x-axis.

The horizontal asymptote is the horizontal dashed line in each graph. Its equation is y = constant, where the constant can be read from the graph where the line crosses the y-axis.

f(x)

The vertical asymptote is x = -4. The horizontal asymptote is y = 3.

g(x)

The vertical asymptote is x = 2. The horizontal asymptote is y = -4.

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The vertical asymptote of g(x) is 2-(-4) = 6 units to the right of that of f(x). The horizontal asymptote of g(x) is -4-3 = -7 units up from that of f(x). The graph of g(x) matches that of f(x) shifted right 6 units and down 7 units.

To find the intersection points of two graphs, set f(x) equals to g(x) and solve for 'x'. Substituting the x-value into either function gives the y-coordinate. The intersection point is the (x, y) pair.

In the subject of Mathematics, to find the specific points where function f(x) and function g(x) intersect, we need to set them equal to each other and solve for the variable x.

The formula we use is f(x) = g(x).

If f(x) is a linear equation such as y = 2x + 3 and g(x) is also a linear equation such as y = -3x + 7, setting them equal gives 2x + 3 = -3x + 7.

Solving for x ends up with x = 0.8. This x value is where the two functions intersect on a graph.

Another step can be taken to find the y coordinate by substituting the x value into either function.

So, if we substitute 0.8 into the function f(x), f(0.8) = 2(0.8) + 3 = 4.6. So the intersection point is (0.8, 4.6).

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Answer:

Step 1 instruction is incorrect.

Step-by-step explanation:

The given equation is

In step 1, Deepak rearranged the terms in order to simplify like terms together that is followed in step 2.

So, rearranging of the terms of an expression is commutative property and not distributive property.

Distributive property is generally applicable to multiplication and is given as:

Commutative property is given as:

.

Therefore, adding terms by changing their order is commutative property of addition and not distributive property.Step 1 instruction is wrong.

Answer: The answer is A

Step-by-step explanation: Because I took the test

The spheres are similar as their radius will be in the ratio

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the first sphere be represented as A

Now , the radius of the sphere A = r₁

Let the first sphere be represented as B

Now , the radius of the sphere B = r₂

And , the volume of sphere A , V₁ = ( 4/3 ) πr₁³

The volume of sphere B , V₂  = ( 4/3 ) πr₂³

The ratio of V₁ / V₂ is given by

V₁ / V₂ = ( 4/3 ) πr₁³ / ( 4/3 ) πr₂³

On simplifying , we get

V₁ / V₂ = r₁³ / r₂³

So , the spheres are similar by their ratio of radius

Hence , all the spheres are similar in ratios

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Answer:

True

Step-by-step explanation: