Step-by-step explanation:
If mUTV < mUTS < mSTR, which statement is true? VU < US < SR by the hinge theorem. VU = US = SR by the hinge theorem
. mUTV = mUST = mSTR by the converse of the hinge theorem. mUTV > mUTS > mSTR by the converse of the hinge theorem.
2 answers:
Answer:
True statement is VU < US < SR by the hinge theorem.
Step-by-step explanation:
It is given that ∠UTV < ∠UTS < ∠STR.
According to Hinge theorem "if 2 sides of two triangles are congruent and the included angle of the 1st triangle is larger than the included angle of the 2nd triangle, then the third side of the 1st triangle is longer than the third side of the 2nd triangle."
since ∠UTV < ∠UTS < ∠STR.
So, by hinge theorem sides opposite to these angle are also is this inequality order,
So, according to fig. and by using hinge theorem, we can say that
VU < US < SR.
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Answer:
The vertex of the function is at (1,-25)
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one.
<em>Part of the graph of the function f(x) = (x + 4)(x-6) is shown below. </em>
<em>Which statements about the function are true? Select two </em>
<em>options. </em>
<em>The vertex of the function is at (1,-25). </em>
<em>The vertex of the function is at (1,-24). </em>
<em>The graph is increasing only on the interval -4< x < 6. </em>
<em>The graph is positive only on one interval, where x <-4. </em>
<em>The graph is negative on the entire interval </em>
My answer:
Given the factored form of the function:
f(x) = (x + 4)(x-6)
<=> f(x) =
We will convert to vertex form
<=> f(x) = () - 25
<=> f(x) =
=> the vertex of the function is: (1,-25)
We choose: a. The vertex of the function is at (1,-25)
Let analyse other possible answers:
<u>c. The graph is increasing only on the interval -4< x < 6.</u>
Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.
So the graph is increasing in the domain (1, +∞)
=> C is wrong
<u>d. The graph is positive only on one interval, where x <-4</u>
Wrong, The graph is positive only on one interval, where x > 6
<u>e. The graph is negative on the entire interval</u>
Wrong, The graph is negative only on one interval, where -4< x < 6.
