Let k = 5. What is the value of 27 – k · 2?
A.
11
B.
17
C.
24
D.
44
Answers
Solution: 27-5 ·2 = n
22 · 2 = n
Answer: 44 option D
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What is the volume, in cubic cm, of a cylinder with the height of 16cm and a base radius of 3 cm, to the nearest tenths place?
Mandy and Jordan each bought some of the same notebooks and the same three-ring binder. Mandy paid $5.85 for 3 notebooks and 1 binder. Jordan paid $4.65 for2 notebooks and 1 binder. What is the price of one ofthe notebooks?
Solve the inequality. |3x + 6| < 12A. –6 > x > 2 B. –2 < x < 2 C. –6 < x < 2 D. –21 < x < 3
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).
------------------------------------------------------------------------------------------------------------------
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:
c
Step-by-step explanation:
Slope intercept form:
The equation of straight line is given by:
....[1]
where, m is the rate or slope and b is the initial value of y-intercept.
As per the statement:
A certain species of tree grows an average of 3.1 cm per week.
Let x be the number of week and y represents the weekly height of the tree.
then;
" tree grows an average of 3.1 cm per week." translated to 3.1 x
It is also given that:
the measurements begin when the tree is 400 centimeters tall.
⇒y(0) =b = 400 cm
Substitute the given values in [1] we have;
Therefore, an equation for the sequence that represents the weekly height of this tree in centimeters is,
X for the number of weeks
Y for total CM
Hope this helps...
box to the tower. How tall is the tower now? Give your answer
in centimetres (cm).
Answers
Answer:
126 cm
Step-by-step explanation:
each block is 112/8 cm tall=14cm
112cm is the current tower
add one more block +14cm is 126 cm total
Answers
Answer:
97.50
Step-by-step explanation:
9.75(3) + 9.75(7);
9.75(3+7); 97.50
Answers
The sum of the geometric progression up to the 6th term is 512/7
To find the sum of a geometric series, you can use the formula for the sum of a finite geometric series:
Where:
- Sₙ is the sum of the first n terms of the series.
- a is the first term of the series.
- r is the common ratio.
- n is the number of terms in the series.
In your case, you have the geometric series: 16, 2, 1/4, ...
1. Identify the values for the formula:
- The first term (a) is 16.
- The common ratio (r) is found by dividing the second term by the first term: 2/16 = 1/8.
- You want to find the sum of the first 6 terms (n = 6).
2. Plug these values into the formula and calculate S₆:
S₆ = (16(1 - (1/8)⁶))/(1 - 1/8)
Now, calculate the individual terms in the formula:
S₆ = (16(1 - 1/262144))/(7/8)
S₆ = (16(262143/262144))/(7/8)
S₆ = ((4194288/262144)/(7/8)
Now, perform the division:
S₆ = (4194288/262144) \* (8)/(7)
S₆ = 64 * 8/7
Now, multiply:
S₆ = 512/7
So, the sum of the geometric progression up to the 6th term is 512/7
Learn more about geometric series here
#SPJ1
Answers
f (9) = 5 - 2 (9)
f (9) = 5 - 18
f (9) = - 13
f (9) + 3 = - 13 + 3
f (9) + 3 = - 10
Answer:
the answer is -10
Step-by-step explanation: