Identify the vertex, axis of symmetry, maximum orminimum, and domain and range of the function
2x² – 5x + 3 = m(x)
Answers
Answer:
- vertex: (1.25, -0.125)
- axis of symmetry: x = 1.25
- minimum: -0.125
- domain: all real numbers
- range: y ≥ -0.125
Step-by-step explanation:
For quadratic ax² +bx +c, the axis of symmetry is x = -b/(2a). For your function, a=2, b=-5, c=3 and the axis of symmetry is ...
x = -(-5)/(2(2)) = 5/4 = 1.25
The vertex is on the axis of symmetry. The y-value there is ...
m(5/4) = (2(5/4) -5)(5/4) +3 = (-5/2)(5/4) +3 = -25/8 +24/8 = -1/8
The vertex is (5/4, -1/8).
The axis of symmetry is x = 5/4.
The leading coefficient is positive, so the parabola opens upward. The vertex is a minimum.
The minimum is -1/8.
The function is defined for all values of x, so ...
the domain is all real numbers.
Values of y can only be -1/8 or greater, so ...
the range is y ≥ -1/8.
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Answers
Step-by-step explanation:
higher
Answers
We have then:
We now look for the amount of watermelons that people ate.
We have then:
Therefore, the amount of watermelon remaining is:
We note that the amount of watermelon remaining is equal to 8.5 pounds.
Answer:
the amount of leftover watermelon is: equal to 8.5 pounds
The amount of leftover watermelon is equal to 8.5 pounds
Explanation:
1- getting the total weight of the watermelon:
The total weight of the watermelon will be the summation of the weights of the 5 watermelons he bought.
This means that:
Total weight = 8.25 + 9.25 + 8.875 + 9.625 + 10.75
Total weight = 46.75 pounds
2- getting the weight of the eaten watermelon:
We know that at the party, there were 153 people and each ate 0.25 of a pound of watermelon.
This means that:
amount eaten = 153 * 0.25
amount eaten = 38.25 pounds
3- getting the weight of the leftover:
weight of leftover = total weight - amount eaten
We have:
Total weight = 46.75 pounds
amount eaten = 38.25 pounds
Therefore:
weight of leftover = 46.75 - 38.25
weight of leftover = 8.5 pounds
Hope this helps :)
Answers
Answer:
12 pieces
Step-by-step explanation:
80 pieces of candy
1/4 is 25% or 20 pieces of candy
10% would be 8 pieces of candy
subtract the two. Your answer is 12
Answer:
He had 14 more pieces
Step-by-step explanation:
So 80/4 is 20 pieces. So we know John has 20. Now she has 60 left since 80-20 is 60. Now 10 percent of 60 would be 6 pieces. We can subtract 6 from 20 to find out how many more pieces John had. 20-6 is 14. So John had 14 more than Lisa
Answers
sin⁻¹[sin(α)] = sin⁻¹(⁻⁵/₁₃)
α ≈ 1.1256π
cos(β) = ²/₅
cos⁻¹[cos(β)] = cos⁻¹(²/₅)
β ≈ 1.6311π
sin(α - β) = sin(1.1256π - 1.6311π)
sin(α - β) = sin(-0.5055π)
sin(α - β) = -sin(0.5055π)
sin(α - β) = -sin(90.99)
sin(α - β) ≈ -0.116
Answers
Answer:
1. Line g
2. Line j (not sure)
3. Plane S
4. 3 ( QT, QR, TR )
Step-by-step explanation:
Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.
Answers
The volume of the cube can be expressed as a function of m, the number of minutes elapsed as V(m) = (3 + 4m)³ feet³.
What do we mean by volume?
The volume of an object is the total space occupied by the object in the three-dimensional space.
How do we solve the given question?
In the question, we are asked to express the volume of a cube as a function of m, the number of minutes elapsed. We are given that the initial length of the edge of the cube was 3 feet, and it increases at a rate of 4 feet per minute.
∴ We can say that the length of the edge after m minutes = 3 + 4m
As 4 feet is the increase per minute and m minutes have elapsed.
We know, that the volume of a cube is the cube of the length of the edge.
∴ The volume = (3 + 4m)³.
Hence, the function of the volume of the cube in m can be written as,
V(m) = (3 + 4m)³ feet³.
Learn more about volumes at
#SPJ2
Answer:
so it increases by 4 per minute
the volume of a cube is v=side^3
so the side length be 5+4m where m is the number of minutes
therefor the volume can be expressed as V(m)=(5+4m)³
Step-by-step explanation: