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finlep [7]
3 years ago
6

For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.

Mathematics
1 answer:
jasenka [17]3 years ago
7 0

Answer:

The the vertex is: (2, 4)

Domain: all real numbers

Range: [4 \infty)

Step-by-step explanation:

Quadratic functions can be written vertically as follows

f(x) = a(x-h)^2 +k

Quadratic functions can be written vertically as follows

Where the point (h, k) represents the vertex of the quadratic function.

For this type of functions the domain is always all real numbers and the range is [k, \infty) or if a then the range is (-\infty, k]

In this case the function is:

f(x) = (x - 2)^2 + 4

So

h = 2\\k=4

The the vertex is: (2, 4)

Domain: all real numbers

Range: [4, \infty)

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PLS HELP 50 POINTS
PtichkaEL [24]

Answer:

\text{Volume of prism made by }\Delta XYZ=2304\text{ in}^3  

Step-by-step explanation:

Let us assume that both prisms are similar, so we can use proportions to solve for the volume of prism made by triangle XYZ.

Let us find the proportion between the sides of both triangles.

\frac{\text{Side of triangle XYZ}}{\text{Side of triangle PQR}}=\frac{24}{36}

\frac{\text{Side of triangle XYZ}}{\text{Side of triangle PQR}}=\frac{12*2}{12*3}

\frac{\text{Side of triangle XYZ}}{\text{Side of triangle PQR}}=\frac{2}{3}

Since for volume of triangular prism we multiply base area and height of the prism, this means we will have to multiply the proportion of each side length 3 times to find the proportion of volumes between our both prism.

So we can set proportion for volume of both prisms as:

\frac{\text{Volume of prism made by triangle XYZ}}{\text{Volume of prism made by triangle PQR}}=(\frac{2}{3})^3  

\frac{\text{Volume of prism made by triangle XYZ}}{\text{Volume of prism made by triangle PQR}}=\frac{8}{27}

Upon substituting volume of prism made by triangle PQR we will get,

\frac{\text{Volume of prism made by triangle XYZ}}{7776\text{in}^3}=\frac{8}{27}    

Let us multiply both sides of our equation by 7776 cubic inches.

\frac{\text{Volume of prism made by triangle XYZ}}{7776\text{ in}^3}*7776\text{ in}^3=\frac{8}{27}*7776\text{ in}^3

\text{Volume of prism made by triangle XYZ}=8*288\text{ in}^3

\text{Volume of prism made by triangle XYZ}=2304\text{ in}^3  

Therefore, the volume of prism made by triangle XYZ is 2304 cubic inches.

7 0
3 years ago
Which expression is equivalent to x^6y^8/x²y²
Kipish [7]

Answer:

For this case we have the following expression:

  (x ^ 6y ^ 8) ^ 3 / x ^ 2y ^ 2

Rewriting and for power properties we have:

  (x ^ 18y ^ 24) / x ^ 2y ^ 2

  (x ^ (18-2) y ^ (24-2))

  (x ^ 16y ^ 22)

Answer:

The equivalent expression is given by:

  (x ^ 16y ^ 22)

8 0
2 years ago
What is the product of 14,560x 10?
vampirchik [111]
The product of 14560 × 10 is 145600
3 0
2 years ago
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Use the expression 5(6 + 4x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: Ho
Nikolay [14]

Answer:

Part A: The two factors are 6 and 4x. Part B: Question is confusing Part C: The coefficient of the variable is 4.

Step-by-step explanation:

Factors are what gets multiplied to give a product, therefore, 6 and 4x are the products as they are both being multiplied by 5. I don't understand what you are asking for part b. Part C, the coefficient is any number that is multiplied with the variable next to in. For example, in 16x, 16 is the coefficient and x is the variable. In 9y, 9 is the coefficient and y is the variable.

7 0
2 years ago
The diameter of a circle is 7 ft. Find its area to the nearest tenth.
Mumz [18]

Answer:

38.5ft²

Step-by-step explanation:

we know the formula for Area is

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A=38.5

6 0
2 years ago
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