1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lianna [129]
2 years ago
10

X2–6x + 10 is to be written in the form ( x +a)2+ b Find the values of a and b.

Mathematics
1 answer:
vampirchik [111]2 years ago
8 0

Answer:

a = -3 and b = 1

Step-by-step explanation:

x² - 6x + 10

→ Half the second term and place it in the bracket

( x - 3 )²

→ Square -3

- ( 3 )² = -9

→ Place this outside the brackets along with plus 10

( x - 3 ) ² - 9 + 10

→ Simplify

( x - 3 ) ² + 1

You might be interested in
Solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8​
Ivanshal [37]

It looks like the differential equation is

\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}

Factorize the right side by grouping.

xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)

xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)

Now we can separate variables as

\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx

Integrate both sides.

\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx

\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx

\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}

You could go on to solve for y explicitly as a function of x, but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

8 0
1 year ago
​Arif's backyard is 24 by 37 meters. He wants to put a flower garden in the middle of the​ backyard, leaving a strip of grass of
Tpy6a [65]

Answer:

Length of the flower garden = 29 meters

Width of the flower garden = 16 meters

Step-by-step explanation:

I have also attached a diagram for your convenience

Now First let us see the data we are given with:

Arif's backyard length = 37 meters

Arif's backyard Width = 24 meters

Area that should be left with grass = 424 m^2

Now lets suppose the width of the stirp of grass be "a"

According the image the area of backyard will be:

Area ABCD = 24 x 37

Area ABCD = 888 m^2

The length LM will be = (37 -2a)

The Width LO will be = (24 -2a)

Area LMNO = (37 -2a) x  (24 -2a)

Area LMNO = 888 -74a -48a +4a^2

Area LMNO = 4a^2 -122a + 888

Now in order the to calculate the area of the grass strip we must subtract the area LMNO from the total area ABCD and we already know that the areas the area of grass strip should be 424 m^2

hence, A = Area ABCD - Area LMNO

424 = 888 - (4a^2 -122a + 888)

424 = 888 - 4a^2 +122a - 888

424 = -4a^2 +122a

4a^2 -122a +424=0

(We can solve this quadratic equation by breaking the middle term method)

2(2x-53)(x-4) = 0

2(2x-53) = 0

2x -53 = 0

x = 53/2

x = 26.5 (Not Possible)

x-4 = 0

x = 4

Length of the flower garden = 37 -2(4)

Length of the flower garden = 29 meters

Width of the flower garden = 24 -2(4)

Width of the flower garden = 16 meters

4 0
3 years ago
If it’s right i’ll give brainliest :)
fomenos

Answer:

x=126

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
X+y=3 3y+x=5 Substitution
jeka57 [31]
Y=1 and x=2 because 2+1=3 and 2(x) plus 3(y) is 5
3 0
3 years ago
Solve for x. Assume that lines which appear to be tangent are tangent.
Montano1993 [528]
Picture is very blurry
5 0
3 years ago
Read 2 more answers
Other questions:
  • Round 8.54 to the nearest tenth
    8·2 answers
  • IP8.4 #3b
    5·1 answer
  • Find the area of the region that lies inside the first curve and outside the second curve. r = 6 − 6 sin θ, r = 6
    15·1 answer
  • Cameron earns $7 per hour. How much does he earn in 5 hours
    10·1 answer
  • Combine the like terms to create an equivalent expression. 12p + p
    14·2 answers
  • Factor 4n 4 + n 3. n(4n3 + 1) n3(4n + 1) n3(4n)
    15·2 answers
  • What is the difference between 43.68 - 40.67
    11·1 answer
  • Help please I’ll give you brainlyst
    10·1 answer
  • Which equation can be used to represent the statement?
    11·1 answer
  • Fill in the table (image provided)
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!