MATHEMATICS HIGH SCHOOL

Y= (x-1)^2 + 2

change this equation into standard form

Answers

Answer 1

Answer:

Answer:

x² - 2x + 3

Step-by-step explanation:

y = (x - 1)² + 2

= (x - 1)² + 2 [a - b]² = a²- 2ab + b²

= x²- 2x + 1 + 2

= x² - 2x + 3

Thus, the standard form of the equation isx² - 2x + 3

Related Questions

Erin and Aimee are each responsible for mowing half of their back yard. the yard is rectangular with dimensions 75 feet by 90 feet. Erin starts mowing the corner, gradually working her way towards the middle by mowing concentric bands around the outside edges. If the mower cuts a three foot wide path, at what point should Erin and Aimee stop mowing?
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F(x)=-2x+3 how do you find x if f(x) = 11
you are standing, on the horizontal ground, __ feet from the base of a cliff. Admiring your surroundings, you nite that the angle of elevation to the top of the cliff to be __ degrees. If realistic limits are imposed on your choices, what would be a reasonable distance from the cliff? What would be a reasonable angle if elevation? Explain.

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2+3x-5=5

Answers

If you would like to solve the equation x^2 + 3 * x - 5 = 5, you can calculate this using the following steps:

x^2 + 3 * x - 5 = 5
x^2 + 3 * x - 5 - 5 = 0
x^2 + 3 * x - 10 = 0
(x + 5) * (x - 2) = 0
1. x = - 5
2. x = 2

The correct result would be x = - 5, or x = 2.

Two landscapers must mow a rectangular lawn that measures 100 feet by 200 feet. Each wants to mow no more than half of the lawn. The first starts by mowing around the outside of the lawn. How wide a strip must the first landscaper mow on each of the four sides in order to mow no more than half of the lawn? The mower has a 24-inch cut. Approximate the required number of trips around the lawn.

Answers

The total area of the complete lawn is (100-ft x 200-ft) = 20,000 ft².
One half of the lawn is 10,000 ft². That's the limit that the first man
must be careful not to exceed, lest he blindly mow a couple of blades
more than his partner does, and become the laughing stock of the whole
company when the word gets around. 10,000 ft² ... no mas !

When you think about it ... massage it and roll it around in your
mind's eye, and then soon give up and make yourself a sketch ...
you realize that if he starts along the length of the field, then with
a 2-ft cut, the lengths of the strips he cuts will line up like this:

First lap:
   (200 - 0) = 200
   (100 - 2) = 98
   (200 - 2) = 198
   (100 - 4) = 96

Second lap:
   (200 - 4) = 196
   (100 - 6) = 94
   (200 - 6) = 194
   (100 - 8) = 92

Third lap:
   (200 - 8) = 192
   (100 - 10) = 90
   (200 - 10) = 190
   (100 - 12) = 88

These are the lengths of each strip. They're 2-ft wide, so the area
of each one is (2 x the length).

I expected to be able to see a pattern developing, but my brain cells
are too fatigued and I don't see it. So I'll just keep going for another
lap, then add up all the areas and see how close he is:

Fourth lap:
   (200 - 12) = 188
   (100 - 14) = 86
   (200 - 14) = 186
   (100 - 16) = 84

So far, after four laps around the yard, the 16 lengths add up to
2,272-ft, for a total area of 4,544-ft². If I kept this up, I'd need to do
at least four more laps ... probably more, because they're getting smaller
all the time, so each lap contributes less area than the last one did.

Hey ! Maybe that's the key to the approximate pattern !

Each lap around the yard mows a 2-ft strip along the length ... twice ...
and a 2-ft strip along the width ... twice. (Approximately.) So the area
that gets mowed around each lap is (2-ft) x (the perimeter of the rectangle),
(approximately), and then the NEXT lap is a rectangle with 4-ft less length
and 4-ft less width.

So now we have rectangles measuring

   (200 x 100), (196 x 96), (192 x 92), (188 x 88), (184 x 84) ... etc.

and the areas of their rectangular strips are
   1200-ft², 1168-ft², 1136-ft², 1104-ft², 1072-ft² ... etc.

==> I see that the areas are decreasing by 32-ft² each lap.
   So the next few laps are
   1040-ft², 1008-ft², 976-ft², 944-ft², 912-ft² ... etc.

How much area do we have now:

   After 9 laps,    Area =   9,648-ft²
   After 10 laps, Area = 10,560-ft².

And there you are ... Somewhere during the 10th lap, he'll need to
stop and call the company surveyor, to come out, measure up, walk
in front of the mower, and put down a yellow chalk-line exactly where
the total becomes 10,000-ft².

There must still be an easier way to do it. For now, however, I'll leave it
there, and go with my answer of: During the 10th lap.

In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science. What is the probability of randomly choosing a student who is not taking science?69%

44%

51%

49%

Answers

Answer:

Option 3 - 51%

Step-by-step explanation:

Given : In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science.

To find : What is the probability of randomly choosing a student who is not taking science?

Solution :

We can show this situation through Venn diagram,

Refer the attached figure below.

Take the Blue circle as the students taking math and Red circle as the student taking science.

Total number of student = 160

Let M be the student taking math M=90

S be the student taking math S=78

$M\cap S=B=62$

The student only take math is 90-62=28=P

The student only take science is 78-62=16=Q

Total students cover the circle is 28+62+16 = 106

Remaining students who are not in either two circles is 160-106=54

The remaining students and student taking math only is 28+54=82

So, 82 students are those who are not taking science.

The probability of student who is not taking science is

$P=(82)/(160)=(41)/(80)=0.51$

In percentage, 0.51=51%.

Therefore, Option 3 is correct.

The probability of student who is not taking science is 51%.

HELP HELP HURRY!!!!!Which point is located on ray PQ?

A. point M
B. point N
C. point O
D. point R

diagram shown below...

(((<--------M---------N---------O------P--------Q----------R--------S--------->)))

Answers

Answer:

Point R located on ray PQ.

Step-by-step explanation:

Given : Diagram

To find : Which point is located on ray PQ.

Solution : We have given <--------M---------N---------O------P--------Q----------R--------S--------->.

Ray : A part of a line with a start point but no end point (it goes to infinity).

We can see from the diagram ray PQ start from P but it has no end point.

So , point R ans S located on ray PQ but we have option R

Therefore, D. point R located on ray PQ.

If the entire ray is PQ, then all of those points lie on the ray.

Show how square root 5 can be represent on number line?

Answers

What they do is basically put it between the square root of 4 and 9, so that's 2 and 3.

In parallelogram LMNO, LM = 4.12, MN = 4, LN = 5, and OM = 6.4. Diagonals and intersect at point R. What is the length of OR?A.2
B.2.06
C.2.5
D.3.2
E.12.8