The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.
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What is the Angle Bisector Theorem?</h3>
The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.
Note that the angle that has been dissected here is ∠CBD. Thus,
= 
See the link below for more about Angle Bisector Theorem of the Triangle:
brainly.com/question/21475560
Answer:
If Kristen were to make 4 batches, and each batch requires 2 cups of flour, how many cups of flour would she need? To solve this question, we would just multiply 4 by 2, which gives us a final product of 8.
Similarly, in this question, if one batch requires 1 3/4 cups of flour and Kristen wants to bake 3 1/2 batches, she would need 1 3/4 x 3 1/2 cups of flour.
1 3/4 can be rewritten as an improper fraction- 7/4.
3 1/2 can also be rewritten as an improper fraction- 7/2.
Multiplying 7/4 and 7/2, we obtain a final product of 49/8, or 6 1/8.
This means, Kristen will need 6 1/8 cups of flour to make 3 1/2 batches, and her belief that she needs 3 3/8 cups of flour is wrong, as she needs a lot more than that.
Hope this helps!
Answer:
A
Step-by-step explanation:
For finding the value of b, we must consider that Line MN passes through points M(4, 3) and N(7, 12). With this condition y = mx + b, can be written 3=4m+ b (because line passes through M(4,3) ) and 12=7m+b, b ( because line passes through M(7,12)).
We have a system of equation
4m+ b=3
7m+b=12
For solving this, 4m+b- (7m+b)= 3-12, it is equivalent to -3m= -9 and then m=3, if m=3 so
4x3 +b =3 implies b= 3 -12= -9, so the value of b= -9
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is a quadratic function, so its graph is a parabola.
Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.
That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.
for x=0, y=-1. So the vertex is (0, -1)
The coefficient of
is negative. This means that the parabola opens downwards, so the vertex is a maximum.
Answer: (0, -1) , maximum (none of the choices)
