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3 years ago

Express x2-8x+5 in the form (x-a)2 -b where a and b are intergers

Mathematics

1 answer:

Soloha48 [4]3 years ago

3 0

(x-4)^2-11

How?

$\\ \sf\longmapsto (x-4)^2-11$

$\\ \sf\longmapsto x^2-8x+16-11$

$\\ \sf\longmapsto x^2-8x+5$

Verified

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Categorize these samples as representative or not representative of the given populations.

yuradex [85]

Representatives: This means that a certain amount of people would constitute what the majority would think too.

1) Tina interviews the school's soccer team about the exercise habits of the students at her school. (implying all the students). This means that Tina only goes to the soccer team instead of the whole school to find out the whole school's exercise habit.
2) Alana also counts as representatives, because she did not interview ALL of the teachers, rather just a selected majority (in this case)
5) For Jeremy, he only interviews 5 students from each class rather than all students
Not Representatives: Each person is given a choice of opinion and does not affect other people.
3) Joe talks to fathers of high school students, which could be larger than just 'representatives', and implies a larger group of people, and is not as selective as having representatives
4) Social Media constitutes of a large group of people, generally larger than a school, and if people take time to take the survey, it will generate a larger test-group. Also, everybody answering the survey would take time to think about themselves, and only represent themselves, and not others.

hope this helps

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4 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed

jekas [21]

Answer:

sorry it's late but the answer should be 20 meters cubed

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the x and y intercepts of the line 2y = 4x - 5

OLga [1]

Divide by 2

Y = 2x - 2.5

x intercept: when y = 0

0 = 2x - 2.5

2.5 = 2x, x = 1.25

y intercept: when x = 0

Y = 2(0) - 2.5, y = -2.5

Solution: (1.25, 0) and (0, -2.5)

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3 years ago

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Find the point on the plane ax + by + cz = d at minimum distance from the origin using the method of lagrange multipliers.

kupik [55]

The distance between some point $(x,y,z)$ and the origin is given by

$f(x,y,z)=\sqrt{x^2+y^2+z^2}$

so this is the function we're trying to minimize. But notice that $f(x,y,z)$ and $f(x,y,z)^2$ attain their critical points at the same $(x,y,z)$ , so we can solve the same problem by minimizing $x^2+y^2+z^2$ instead.

So let's take the Lagrangian to be

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(ax+by+cz-d)$

with partial derivatives (set equal to 0)

$L_x=2x+a\lambda=0$
$L_y=2y+b\lambda=0$
$L_z=2z+c\lambda=0$
$L_\lambda=ax+by+cz-d=0$

Now, notice that

$aL_x+bL_y+cL_z=2(ax+by+cz)+(a^2+b^c+c^2)\lambda=0$
$\implies\lambda=-\dfrac{2d}{a^2+b^2+c^2}$

and we can use this to solve for $x,y,z$ . We get

$x=\dfrac{ad}{a^2+b^2+c^2}$
$y=\dfrac{bd}{a^2+b^2+c^2}$
$z=\dfrac{cd}{a^2+b^2+c^2}$

At this critical point, we get a minimum distance of

$\sqrt{\left(\dfrac{ad}{a^2+b^2+c^2}\right)^2+\left(\dfrac{bd}{a^2+b^2+c^2}\right)^2+\left(\dfrac{cd}{a^2+b^2+c^2}\right)^2}=\sqrt{\dfrac{d^2}{a^2+b^2+c^2}}$

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3 years ago

Create a system of linear equations with one solution. In your final answer, include the system of equations and the graphs of t

GrogVix [38]

Answer:

System of equations

$x + y = 5$