Answer:
413.03
Step-by-step explanation:
405 increased by 8.3 is 405+8.3.
Problem 2
Midpoint: Think 1/2. A midpoint cuts a line segment in 1/2 (in this question). That means that the left segment = the right segment. Remember: midpoint means 1/2.
LN is given as 14.
LM is 1/2 the distance of 14
LM = 1/2 * 14
LM = 7
Problem 3
If the midpoint = the 1/2 way point, the two halves are equal. Remember a midpoint divides the 2 parts into 2 EQUAL parts.
4a - 2 = 18 Add 2 to both sides
4a = 18 + 2
4a = 20
a = 20 /4
a = 5
Problem 4
Remember that midpoint means 1/2. That a midpoint cuts a segment into 2 equal segments
Equation
2n + 2 = 5n - 4
Solve
2n + 2 = 5n - 4 Add 4 to both sides
2n + 2 + 4 = 5n Subtract 2n from both sides.
6 = 5n - 2n
6 = 3n Divide both sides by 3
6/3 = n
n = 2
<u>Answer:</u> B
Problem 5
And again the whole line segment is divided into 2 equal parts.
<u>Equation</u>
6p - 12 = 4p Add 12 to both sides
6p = 12 + 4p Subtract 4p from both sides.
6p - 4p = 12
2p = 12 Divide by 2
p = 12/2
p = 6 <<<<< Answer
The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
<h3>What is the instantaneous rate of change of the function at the given point?</h3>
The instantaneous rate of change is simply the change in the derivative value at a specific point.
Given the data in the question;
- f(x) = −4x² − 3x + 1
- Point x = -3
To determine the instantaneous rate of change of the function, first find the derivative of the function.
f(x) = −4x² − 3x + 1
Applying sum rule, with respect to x
d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]
[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]
[ -8x ] + [ -3 ] + d/dx[ 1 ]
-8x - 3 + d/dx[ 1 ]
Differentiate using constant rule
-8x - 3 + [ 0 ]
-8x - 3
f'(x) = -8x - 3
Next, plug x = -3 into the derivative and simplify.
f'(x) = -8x - 3
f'(-3) = -8(-3) - 3
f'(-3) = 24 - 3
f'(-3) = 21
Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
Learn more about instantaneous rate of change here: brainly.com/question/28122560
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10.5 or 10 1/2 basically ten and a half
The answer is 9
12 ounces x
--------------- = ----------------
10 pounds of soil 120 pounds of soil
Set the equation up as a proportion and solve for x:
10x = 1440
---- -----
10 10
x = 144 ounces
The question asks for the answer in pounds, and 16 ounces = 1 pound.
144/16 = 9
