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1 year ago

Bentley's rectangular desktop measures 39 1/2in long and 24 3/4in wide what is the area of his desktop

Mathematics

1 answer:

Galina-37 [17]1 year ago

5 0

Answer:

95,013

Step-by-step explanation:

If you use the formula A=L*W You multiply the width, 24 3/4, by how long it is, 39, 1/2. And you should get a rounded answer of 95,013!

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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

*******************************************************************************************

2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$

4 0

2 years ago

7.34 in scientific notation

Allushta [10]

Answer:

7.34×10⁰

Unless you're missing something in your question then that'd be it I guess... There isn't really a reason to put 7.34 in scientific notation though, so I'm assuming something isn't loading for me (or the question was changed).

6 0

2 years ago

Find the area, in square meters, of an equilateral triangle with a perimeter of 36 m.

Citrus2011 [14]

I hope it helps you!!!

6 0

2 years ago

What Difference between hundreds and hundredths?

nordsb [41]

hundred means 100 or 200. Like I have 100 cats.

Hundredth means you have 1/100 of something. I have a peice of pie that is 1/100 of the pie. That means there are 100 pieces of the pie but I only have one out the hundred pieces.

hundred=100

hundredth = 1/100 = 0.01

tenth= 1/10 = 0.1

7 0

2 years ago

Read 2 more answers

In each case, determine if the function can be differentiated using the rules developed so far (sections 3.1 and 3.2). (a) y = 2

Alex_Xolod [135]

The rule for differentiation for variable with exponents has the formula:

d/dx (xⁿ) = nxⁿ⁻¹
where n is the exponent

Thus, for the given equation, the solution is as follows:
y = 2x²
dy/dx = 2(2)x²⁻¹ = <em>4x

Thus, the derived equation of the given would now be 4x.</em>

3 0

2 years ago