Answer:
type 2 in the first box,
13/4 in the second box, and
-9/8 in the third one
Step-by-step explanation:Notice that you are asked to write the following quadratic expression in vertex form, so you need to find the "x" value of the vertex, and then the "y" value of the vertex:
Which in our case is: -13/4
and the value of the y for the vertex is obtained using the functional expression when x equals -13/4:
Then your expression for this quadratic should be:
Then type 2 in the first box, 13/4 in the second box, and -9/8 in the third one
Answer:
Step-by-step explanation:
3(7t - 5) - 2t = 4
3*7t - 3*5 - 2t = 4
21t - 15 - 2t = 4 {combine like terms}
21t - 2t - 15 = 4
19t - 15 = 4 {Add 15 to both sides}
19t = 4 + 15
19t = 19 {Divide both sides by 19}
t = 19/19
t = 1
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
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To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).
Answer:
the supplementary angle to 313 would be 49.
Step-by-step explanation:
the supplement of an angle is when tow angles add up to equal 180 degrees. therefore, if you subtract 131 from 180, you would get the answer of 49 degrees.
