Simplify this expression.

A parabola has its vertex at (-6, 5) and focus at (-6.25, 5). Which of the following is an equation for this parabola?

Pavlova-9 [17]

Answer:

Step-by-step explanation:

vertex and focus are horizontally aligned, so parabola is horizontal.

focal length p = distance between focus and vertex = 0.25

focus lies to the left of vertex, so the parabola opens to the left.

x = a(y-k)² + h,

vertex (h,k)

a = -1/(4p)

vertex (-6,5)

h = -6

k = 5

p = 0.25

a = -1/(4·0.25) = -1

x = -(y-5)² - 6

6 0

3 years ago

Which graph represents an exponential function?

geniusboy [140]

Answer:The function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

What are exponential functions?

The exponential functions are written in the form of y = aeᵇˣ, where the output y increases exponentially for the input x.

In order to find the graph that represents an exponential function, we will discuss each of the following graphs,

For the 1st graph, (Black),

In the first graph, the graph is of a parabola, and the function which represents this kind of graph is a quadratic equation, therefore, this graph represents a parabolic equation. It is given by the function,

y=ax²+bx+c or y=a(x-h)²+k

For the 2nd graph, (Red),

In the second graph, the graph represented is the graph of a reciprocal function, the function that can be represented by the graph,

y=a/x + b

For the 3rd graph, (Blue),

In the third graph, the graph represented is the graph of root function, it can be modeled as,

y = a+√(x+b)

For the 4th graph, (Green),

In the fourth graph, the graph represented is the graph of an exponential function, and it can be modeled as,

y = aeᵇˣ

Hence, the function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

Step-by-step explanation:

7 0

2 years ago

Whats 150-x-2x=120+2x

Stels [109]

Answer:

X=6

Step-by-step explanation:

4 0

3 years ago

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Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume

aalyn [17]

Answer : The correct option is, (A) $54\pi cm^3$

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder = $\pi r^2h$

where,

r = radius = 3 cm

h = height = 18 cm (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)

Volume of cylinder = $\pi (3cm)^2\times (18cm)$

Volume of cylinder = $162\pi cm^3$

Now we have to calculate the volume of 3 solid spheres.

Formula used:

Volume of 3 spheres = $3\times \frac{4}{3}\pi r^3$

Volume of 3 spheres = $4\pi r^3$

Volume of 3 spheres = $4\pi (3)^3$

Volume of 3 spheres = $108\pi cm^3$

Now we have to calculate the amount of empty space within a cylinder.

Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres

Amount of empty space within a cylinder = $162\pi cm^3-108\pi cm^3$

Amount of empty space within a cylinder = $54\pi cm^3$

Therefore, the amount of empty space within a cylinder is, $54\pi cm^3$

5 0

4 years ago

Help please... dont answer if u dont know bc this is for a grade

guapka [62]

Answer: The answer is 14

Step-by-step explanation:

For 2.5 they multiplied by 10 so you'd do that for 1.4 and the answer would be 14

7 0

4 years ago

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