Write the ratio 2/11 to 7/11 as a fraction in the lowest terms.
Answers
Final answer:
The ratio of 2/11 to 7/11 simplified as a fraction in the lowest terms is 2/7. This was done by canceling out the like terms in both fractions, essentially dividing both numbers in the ratio by the common factor of 11.
Explanation:
To write the ratio 2/11 to 7/11 as a fraction in the lowestterms, you are essentially finding the ratio of these two fractions. Starting from the fractions 2/11 and 7/11, we 'cancel out' the like terms in both fractions. Remember, a ratio is simply a way of comparing two or more numbers. So the ratio of 2/11 to 7/11 simplifies to:
2/11 : 7/11 = 2/7
So, the ratio 2/11 to 7/11 as a fraction in the lowest terms is 2/7. This was achieved by dividing both numbers in the ratio by the common factor of 11.
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To convert into decimal, move the decimal to the left by 6 positions.
It will be 0.00000563
Answer is A.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answers
u = t² + 6t - 20
+ 20 + 20
u + 20 = t² + 6t
u + 20 + 9 = t² + 6t + 9
u + 29 = t² + 3t + 3t + 9
u + 29 = t(t) + t(3) + 3(t) + 3(3)
u + 29 = t(t + 3) + 3(t + 3)
u + 29 = (t + 3)(t + 3)
u + 29 = (t + 3)²
- 29 - 29
u = (t + 3)² - 29
Part B: The vertex is (-3, -29). The graph shows that it is a minimum because it shows that there is a positive sign before the x²-term, making the parabola open up and has a minimum vertex of (-3, -29).
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Part A: g(t) = 48.8t + 28 h(t) = -16t² + 90t + 50
| t | g(t) | | t | h(t) |
|-4|-167.2| | -4 | -566 |
|-3|-118.4| | -3 | -364 |
|-2| -69.6 | | -2 | -194 |
|-1| -20.8 | | -1 | -56 |
|0 | -28 | | 0 | 50 |
|1 | 76.8 | | 1 | 124 |
|2 | 125.6| | 2 | 166 |
|3 | 174.4| | 3 | 176 |
|4 | 223.2| | 4 | 154 |
The two seconds that the solution of g(t) and h(t) is located is between -1 and 4 seconds because it shows that they have two solutions, making it between -1 and 4 seconds.
Part B: The solution from Part A means that you have to find two solutions in order to know where the solutions of the two functions are located at.
The correct answers are:
Question 1 - Part A: f(t)=(t+3)²-29; Part B: (-3, -29), minimum; Question 2 - Part A: H(1) = 124, g(1) = 76.8; H(2) = 166, g(2) = 125.6; H(3) = 176, g(3) = 174.4; H(4) = 154, g(4) = 223.2; Part B: Between 3 and 4 seconds, because that is where the values of g(t) catch up with H(t).
Explanation:
Our quadratic function is in the form f(x)=ax²+bx+c. Our value of a is 1, b is 6, and c is -20.
To write a quadratic in vertex form, first take half of the b value and square it: (6/2)² = 3² = 9. This is what we will add and subtract to the function:
f(t) = t²+6t+9-20-9
The squared portion will be (t+b/2)²:
f(t) = (t+3)²-20-9
f(t) = (t+3)²-29
Vertex form is f(x) = a(x-h)²+k, where (h, k) is the vertex; in our function, (h, k) is (-3, -29).
Since the value of a was a positive, this parabola opens upward; this makes the vertex a minimum.
For Question 2 Part A, substitute the values 1, 2, 3 and 4 in H(t) and g(t).
For Part B, we can see that the values of g(t) are much less than that of H(t) until 3 seconds. From there, we can see that g(t) passes H(t). This means that the solution point, where they intersect, is between 3 and 4 seconds.
Answers
Answer:
m = -1/3
Step-by-step explanation:
Answers
-3(4) - 3(-1) + 3(9) - 2(-1)
-12 + 3 + 27 + 2
-9 + 27 + 2
18 + 2
20
Answers
Answer: Jordan worked for 10 hours and Sydney worked for 6 hours.
Step-by-step explanation:
Let x represent the number of hours
that Jordan worked.
Let x represent the number of hours that Sydney worked.
Jordan can iron 20 shirts per hour, and Sydney can iron 25 shirts per hour. They ironed 350 shirts between them. It means that
20x + 25y = 350- - - - - - - - - - - 1
Jordan worked 4 more hours than Sydney. It means that
x = y + 4
Substituting x = y + 4 into equation 1, it becomes
20(y + 4) + 25y = 350
20y + 80 + 25y = 350
20y + 25y = 350 - 80
45y = 270
y = 270/45
y = 6
x = y + 4 = 6 + 4
x = 10