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Ugo [173]
3 years ago
15

Solve for the variable: x – 12 = 3

Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

x=15

Step-by-step explanation:

add the 12 to the other side

x-12=3

and you will get 15

x=15

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What is the equation of the quadratic graph with a focus of (-4,17/8) and a directrix of y=15/8
Temka [501]
So hmm notice the graph below

based on where the focus point is at, and the directrix, then, the parabola is opening upwards, meaning the squared variable is the "x"

\bf \begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})}\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}

now, keep in mind, the vertex is at coordinates h,k
the vertex itself is half-way between the focus and directrix
the directrix is at y=15/8 and the focus is at y=17/8
so, half-way will then be \bf \cfrac{17}{8}-\cfrac{15}{8}=\cfrac{2}{8}\iff \cfrac{1}{4}

well, so is 1/4 between the focus point and the directrix, half of that is 1/8
so, if you move from the focus point 1/8 down, you'll get the y-coordinate for the vertex, or 1/8 up from the directrix, since the vertex is equidistant to either

what's the "p" distance? well, we just found it, is just 1/8

so, the x-coordinate is obviously -4, get the y-coordinate by 17/8 - 1/8   or 15/8 + 1/8

and plug your values (x-h)² = 4p(y-k)   and then solve for "y", that's the equation of the quadratic

4 0
3 years ago
a pastry recipe calls for 3 cups of flour to make 8 serving .how many cups of flour are needed to make 6 serving
ser-zykov [4K]
If you would like to know how many cups of flour are needed to make 6 servings, you can calculate this using the following steps:

3 cups of flour ... 8 servings
x cups of flour = ? ... 6 servings

3 * 6 = 8 * x
18 = 8 * x      /8
x = 18/8
x = 9/4
x = 2 1/4 cups of flour

The correct result would be 2 1/4 cups of flour.
5 0
3 years ago
Explain how to write a function rule from the table below. Then write a function rule.
Brut [27]

To find the slope you do y1-y2/x1-x2

To find the y intercept you look at when x is zero what is y.

Equation is y=-1/2x -2

4 0
3 years ago
Read 2 more answers
What is 7+6*(15-8)+3
Rama09 [41]
Use pemdas : so do parenthesis first 15-8, then multiply the answer by 6. OR u can use distributive property & multiply 6 by 15 & 8
3 0
3 years ago
To one-one functions g and h are defined as follows.
Andreyy89

Answer:

  • 9
  • (x-8)/3
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Step-by-step explanation:

The inverse function for a set of ordered pairs can be found by swapping the x- and y-coordinates in each pair.

  g^{-1}(-1)=9\qquad\text{from the $g(x)$ ordered pair $(9, -1)$}

__

The inverse of a function expressed algebraically can be found by swapping the x- and y-variables and solving for y.

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A function of its own inverse returns the original value:

  \boxed{\left(h\circ h^{-1}\right)(-1)=-1}

6 0
3 years ago
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