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Andre45 [30]
3 years ago
7

WHY must the same operation be performed on both sides of an equation? ​

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0

Answer:When you are given a problem, the two sides are equal, so they are equally weighted. As long as you do the same thing on both sides, they remain the same weight. The only way that one side can become "more weight" on a side is if you make a math mistake, and thus the answer would not satisfy the original equation

Step-by-step explanation:looked it up... have a good day!

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Derive the equation of the parabola with the focus <br> is (-7,5) and the directrix of y=-11
Volgvan
So, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

\bf \textit{parabola vertex form with focus point distance}\\\\&#10;\begin{array}{llll}&#10;4p(x- h)=(y- k)^2&#10;\\\\&#10;\boxed{4p(y- k)=(x- h)^2}&#10;\end{array}&#10;\qquad &#10;\begin{array}{llll}&#10;vertex\ ( h, k)\\\\&#10; p=\textit{distance from vertex to }\\&#10;\qquad \textit{ focus or directrix}&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;h=-7\\&#10;k=-3\\&#10;p=8&#10;\end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2&#10;\\\\\\&#10;32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2&#10;\\\\\\&#10;y=\cfrac{1}{32}(x+7)^2-3

8 0
3 years ago
There are 1,200 students at roosevelt middle school. There are 700 boys at the school. What percentage of the students at roosev
Marat540 [252]

Answer:

100x=256.25

Step-by-step explanation:

x/1025=25/100

What is 25% of 1025

that would be 1025×25

100x=256.25

3 0
3 years ago
126,349 rounded to the hundred place
sweet [91]

Answer:

126,300.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Which sequence of transformations creates a similar, but not congruent, triangle? A. Rotation and translation B. Reflection and
Nat2105 [25]
<span><u><em>The correct answer is: </em></u>
dilation and rotation.

<u><em>Explanation</em></u><span><u><em>: </em></u>
Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.</span></span>
4 0
3 years ago
Read 2 more answers
Write an equation in standard form for a line that passes through (4,1) &amp; (5,7)
tatuchka [14]
Y = mx + b

First equation 1 = m(4) + b, bring everything to one side m(4) + b - 1 = 0
Second equation 7 = m(5) + b, bring everything to one side m(5) + b - 7 = 0

Set them equal to each other, 

m(4) + b - 1 = m(5) + b - 7

If you bring the b over to the left hand side it becomes

m(4) + b - b - 1 = m(5) - 7

m(4) - 1 = m(5) - 7

Solve for m

6 = m

Plug m = 6 into either equation from the beginning,

m(4) + b - 1 = 0

6(4) + b - 1 = 0

24 + b - 1 = 0

b = -23

Knowing m and b we can now make an equation

y = mx + b

y = 6x -23 Final answer



3 0
2 years ago
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