Answer:
f(x) < –x2 + x – 1
Step-by-step explanation:
The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1
. The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .
9514 1404 393
Answer:
- 125 in²
- 676 km²
- 20 square units
Step-by-step explanation:
The Pythagorean theorem tells you the square on the hypotenuse is equal to the sum of the squares on the other two sides. (This is the version you use for problem 2.)
This also means the square on one side is the difference between the square on the hypotenuse and the square on the other side. (Use this version for problems 1 and 3.)
1. ? = 200 in² -75 in² = 125 in²
2. ? = 576 km² + 100 km² = 676 km²
3. ? = 36 square units - 16 square units = 20 square units
For this case we must find an expression equivalent to:
So:
We expanded 
by moving 2 out of the logarithm:
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
Then, rewriting the expression:
We apply distributive property:
Answer:
An equivalent expression is:
Given that E is a point between Point D and F, the numerical value of segment DE is 46.
<h3>What is the numerical value of DE?</h3>
Given the data in the question;
- E is a point between point D and F.
- Segment DF = 78
- Segment DE = 5x - 9
- Segment EF = 2x + 10
- Numerical value of DE = ?
Since E is a point between point D and F.
Segment DF = Segment DE + Segment EF
78 = 5x - 9 + 2x + 10
78 = 7x + 1
7x = 78 - 1
7x = 77
x = 77/7
x = 11
Hence,
Segment DE = 5x - 9
Segment DE = 5(11) - 9
Segment DE = 55 - 9
Segment DE = 46
Given that E is a point between Point D and F, the numerical value of segment DE is 46.
Learn more about equations here: brainly.com/question/14686792
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<h2>
Answer:</h2>
y = 
x + 3
<h2>
Step-by-step explanation:</h2>
As shown in the graph, the line is a straight line. Therefore, the general equation of a straight line can be employed to derive the equation of the line.
The general equation of a straight line is given by:
y = mx + c <em>or </em>-------------(i)
y - y₁ = m(x - x₁) -----------------(ii)
Where;
y₁ is the value of a point on the y-axis
x₁ is the value of the same point on the x-axis
m is the slope of the line
c is the y-intercept of the line.
Equation (i) is the slope-intercept form of a line
Steps:
(i) Pick any two points (x₁, y₁) and (x₂, y₂) on the line.
In this case, let;
(x₁, y₁) = (0, 3)
(x₂, y₂) = (4, -2)
(ii) With the chosen points, calculate the slope <em>m</em> given by;
m = 
m = 
m =
(iii) Substitute the first point (x₁, y₁) = (0, 3) and m = into equation (ii) as follows;
y - 3 = (x - 0)
(iv) Solve for y from (iii)
y - 3 = x
y = x + 3 [This is the slope intercept form of the line]
Where the slope is and the intercept is 3
