Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.The company also discovered that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets.
How much does it cost to make 3 widgets?
Answers
Answer:
The total cost to make 3 widgets is $64.
Step-by-step explanation:
As cost is give by quadratic function such as
As it costs $29 to produce 2 widgets. So,
As it costs $115 to produce 4 widgets. So,
As it costs $757 to produce 10 widgets. So,
In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]
Subtracting Equation [A] from [B] and [B] from [C]
12a + 2b = 86 ........[D]
84a + 6b = 642 ........[E]
Multiplying Equation [D] by 3 and subtracting from [E]
84a + 6b + 3(12a + 2b) = 642 - 86
48a = 384
a = 8
Putting value of a = 8 in equation [D]
12(8) + 2b = 86
96 + 2b = 86
2b = -10
b = -5
Substituting the value of a = 8 and b = -5 in Equation [A].
29= 4a+2b+d
29 = 4(8) + 2(-5) + d
29 = 32 - 10 + d
d = 29 + 10 - 32
d = 7
The required form of equation can be obtained by substituting a = 8, b = -5 and d = 7 in the cost equation. So,
is the required form of equation.
Therefore, the total cost to make 3 widgets will be:
Putting x = 3 in
Hence, the total cost to make 3 widgets is $64.
Keywords: quadratic equation, cost
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Determine the area, in square meters, of the new rectangular garden.
Answers
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= a² + 0.25·a²
= 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(a - 3)
1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
Therefore, the equation that could be used to determine the length of a side of the original square garden is:
2a² - 6a = 1.25a²
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
Answers
Answer:
½ or 11/10
Step-by-step explanation:
3/10 = 8/10 - X
X = 8/10 - 3/10 = 5/10 = 1/2
Or,
X - 8/10 = 3/10
X = 11/10
Answer:
5/10
Step-by-step explanation:
8/10 -5/10 =3/10
y = –8x – 6 and One-halfy = –4x – 3
y = –8x – 6 and y = 8x – 6
y = –8x – 6 and –y = 8x + 6
Answers
Answer:
The given system of equations 
and
has exactly one solution
Step-by-step explanation:
Given that the system of equations and
has exactly one solution
For :
Now to show that the given system of equations has exactly one solution :
Solving the given equations (1) and (2) to get solution
Adding the equations (1) and (2) we get
______________
Therefore the value of is y=-6
Substitute the value of y in equation (1) we have
Therefore the value of x is x=0
Therefore it has exactly one solution is (0,-6)
Therefore the given system of equations and
has exactly one solutione given system of equations has exactly one solution
Answer:
y=-8x-6 and
y=8x-6 has exactly one solution
Step-by-step explanation:
Answers
Answer:
Triangle GAS = Triangle IOL by rule AAS
Step-by-step explanation:
The points must be ordered correctly so they correspond within the triangles. Point G = Point I, Point A = Point O, Point S = Point L.
A rule for determining Triangle Congruency is AAS. If two angles and a side of a triangle are equal to one of another triangle, the triangles are congruent.
2. b+0.6= -1
3. a+(-4)= -13
4. x+27= -12
5. a+(-1.2)= -5.5
Answers
2. b+0.6=-1 -1-0.6=-1.6 -1.6+0.6=-1 b=-1.6
3. a=-9
4. x=-39 I believe
5. a=-4.3
2. b = -1.6
3. a= -9
4. x = -39
5. a = -4.3