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sergij07 [2.7K]

4 years ago

8

WHAT IS THE LENGTH OF THE SECOND BASE OF A TRAPEZOID IF THE LENGTH OF ONE BASE IS 27 AND THE LENGTH OF THE MIDSEGMENT IS 19 SHOW

YOUR WORK

1 answer:

timama [110]4 years ago

6 0

Answer:

1/2 * (27 + x) = 19

27 + x = 38

x = 11

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Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

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

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

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

p is the distance from the vertex to the focus

1)

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

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

2)

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

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

3)

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

3 years ago

What is 400 percent as a mixed number?

prohojiy [21]

You can put 400/100 to get the fraction 4/1 or 4, it is not a mixed number though. So the final answer is 4

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%28%20%5Cfrac%7B8%7D%7B11%7D%29%20%7B%7D%5E%7B7%20-%202%20%5Ctimes%203%20-%201%7D%20" id="TexF

Darya [45]

Answer:

1

Step-by-step explanation:

$(\frac{8}{11})^{7- 2*3 - 1} = (\frac{8}{11})^{7- 6 - 1}\\\\=(\frac{8}{11})^{7- 7}\\\\=(\frac{8}{11})^{0}\\\\=1$

6 0

3 years ago

-2x + 5y=12 for y helpp plsss

icang [17]

Y=12/5 + 2x/5

Explanation:

4 0

3 years ago

Read 2 more answers

What is x in this Math problem 2/3x=27

jek_recluse [69]

Answer: x = 40.5

Step-by-step explanation:

Simply divide 27/(2/3) to get 40.5

<em>Hope it helps <3</em>

4 0

3 years ago

Read 2 more answers