Answer:
no
step-by-step explanation:
y=x+7
x is the slope of 1
7 is the y-intercept
because 7 is the y-intercept and the slope is positive it never touches (1,6)
<h3>Answer:</h3>
Area of DEFG = (1/2)a²
<h3>Explanation:</h3>
See the attached diagram.
Line FB ║ EG and line GA ║DF. ∆GFA ≅ ∆FGX, and ∆EXF ≅ ∆BAG. Then the area of ∆BFG is equal to the area of ∆EGF and, by symmetry, the area of ∆FDE.
This means the area of DEFG is the same as the area of ∆DFB.
The problem statement tells us ∠FDG = 45°. By symmetry, ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90° and the area of ∆DFB = (1/2)(DF)(FB) = (1/2)a².
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<em>Alternate approach</em>
Recognize that ∠EGD = ∠FDG = 45°, so ∠DXG = 90°. This means all the triangles internal to DEFG are right triangles. Designate the distance XF with the variable <em>b</em>. Then DX = (a-b) and the area of the trapezoid is ...
... Area(DEFG) = Area(DXG) + Area(DXE) + Area(GXF) + Area(FXE)
... = (1/2)(a-b)² +(1/2)(a-b)(b) +(1/2)(a-b)(b) +(1/2)b²
... = (1/2)(a² -2ab +b² +ab -b² +ab -b² +b²)
... = (1/2)(a² +ab(-2+1+1) +b²(1-1-1+1))
... Area(DEFG) = (1/2)a²
Your answer would be C and D, the domain for this function is all real numbers, and the range for this function is the set {-5}.
C is correct: The domain of a function is the amount of x values. For example, if you had a line going from an x value of 1 to an x value of 3, the domain would be {1<x<3}.
In this case, C is stating the domain of this function is all real numbers. This is true, because the straight line will continue for all values of x, so therefore the domain is all values of x, or all real numbers.
D is correct: The range is the exact opposite of a domain of a function. It is the number of y values the function covers.
In this case, D is stating the range is {-5}. This is correct, because the straight line only covers the y value of -5, so therefore that is the range.
A is therefore incorrect because the domain has already been established as all real numbers. B is incorrect because a horizontal line is a function, and one value of y can have multiple values of x. E is incorrect because the range has already been established as only one number.
Good luck!
<u>Answer</u>
1/6
<u>Explanation</u>
Probability is a chance of an event taking place.
Probability = (favorable outcome)/(total outcome)
There are 3 even sides in a dice.
P(even) = 3/6
= 1/2
There are 2 numbers that are greater than 4 in a dice.
P(x>4) = 2/6
= 1/3
P(even and x>4) = 1/2 × 1/3
= 1/6