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Solnce55 [7]
3 years ago
12

Write an equation or inequality that best represents each statement below

Mathematics
1 answer:
frez [133]3 years ago
4 0
Let the number be x 

6 times the number = 6x

<em>at least 22 (it be 22 or more}</em>
6x ≥ 22
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Solve equation. Verify answer 14=-2w
notka56 [123]

Answer:

w = -7

Step-by-step explanation:

Isolate the variable, w. Note the equal sign, what you do to one side, you do to the other.

Divide -2 from both sides:

(14)/-2 = (-2w)/-2

(14)/-2 = w

Note that when you are dividing:

  • 1 negative & 1 positive sign will result in a negative answer
  • 2 negative sign will result in a positive
  • 2 positive sign will result in a positive

In this case:

(14)/-2 = -7

-7 is your answer for w.

~

8 0
3 years ago
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
The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SR Prove: ΔQPT ≅ ΔQRT
DiKsa [7]
Dude triangle is qpt and qrt where did the side s come from ,at least provide the fig
8 0
3 years ago
Read 2 more answers
The volume of the trapezoidal prism is m?.
Lubov Fominskaja [6]

Answer:

hello

Step-by-step explanation:

I'm new I'm just figuring this out

8 0
3 years ago
HELP NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Umnica [9.8K]
I think that it is B because I'm pretty sure it has to be log of 50,000. But I forgot how to get the rest of it but B is the only one with log of 50k.
6 0
3 years ago
Read 2 more answers
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