Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?
Answers
Answer:
Vertex form of the function will be f(x) = (x - 1)² + 3.
Step-by-step explanation:
Vertex form of a quadratic function is given by f(x) = a(x - h)² + k
where (h, k) is the vertex of the given parabola.
Now we will convert the function in the vertex form.
f(x) = x² - 2x + 1 + 3
= (x - 1)² + 3
Therefore, the vertex form of the function will be f(x) = (x - 1)² + 3
and the vertex will be (1, 3).
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2 sq. units
8 sq. units
4 sq. units
16 sq. units
Answers
Answer:
4 sq. units
Step-by-step explanation:
Since the polygon has 4 vertices, hence the polygon is a quadrilateral with four sides and four angles.
We can see that for this polygon, opposite sides are parallel and equal to each other.
To find the area of the polygon, we have to first get the length of the polygon and then the width of the polygon, hence:
The length is the distance between (1, 2) and (3, 2):
The breadth is the distance between (3, 2) and (3, 0):
Since length = breadth, hence this is a square.
Area= length * breadth = 2 * 2 = 4 sq. units
Answers
Answers
Answer:
35.34 and 16.66
Step-by-step explanation:
Given data
let the numbers be x and y
the smaller number = x
the larger number = y
x+y=52--------1
The larger number is 2 less than twice the smaller number
y=2x-2-------2
put y= 2x-2 in eqn 1
x+2x-2=52
3x-2=52
3x=52-2
3x=50
x= 50/3
x= 16.66
put x=16.66 in eqn 1 to find y
x+y=52
16.66+y= 52
y=52-16.66
y= 35.34
Hence the numbers are
35.34 and 16.66
Check
35.34+16.66= 52
Answers
In every triangle, the sum of the interior angles is 180°. The sum of the angles of this triangle is
and we want this sum to be 180, so we can write the following equation:
subtract 12 from both sides:
divide both sides by 3:
Now we can plug this value for x in the expressions for the two unknown angle to get their value:
Answers
ok so
1 part almods
2 parts walnuts
3 part rasins
multiply them
almonds=12 per pound
walnuts=9 per pound
rasins=5 per pound
therefor
12 times 1+9 times 2+5 times 3=cost of ratio=45
45=a ratio with 1lb almond, 2lb walnuts, 3lb rasins
we need it to get down to 15
45/x=15
x=3
$45=1a+2w+3r
divide both sides by 3
$15=1/3a+2/3w+1r
we need to find total so add them
1/3+2/3+1=2
answer is 2lb
41.
repair
so he has to pay the employees so that is a minus from his income
therefor
8600-22x
8600 is his income
-22x is the amount he has to pay his employees
they are paid 22 dollars an hour and that is taken from his income so
-22 times number of hour=amoont to pay employee
therefor x=number of hours worked per week
answer is 2
40. 2lb
41. no. 2 'hours worked per week'
Answers
ASSUME that the time he drives only depends on the distance he covers,
and has nothing to do with his speed or how he drives.
The race rules say he has to cover at least 50 km,
so the minimum time he can drive is the solution to
[ 50 = 3t + 47 ]
Subtract 47 from each side:
3 = 3t
Divide each side by 3 :
1 = t minimum
He has fuel for exactly 53 km, so the maximum time
he can drive is the solution to
[ 53 = 3t + 47 ]
Subtract 47 from each side :
6 = 3t
Divide each side by 3 :
2 = tmaximum