Step-by-step explanation:
just think - what does it mean to translate (shift) a graph upward by 5 units ?
does the graph change in its content ? no. all the functional result value (= y values or coordinates) are still calculated as before, BUT before marking them on the chart the y values are moved up by 5 units. that means they are increased by 5 (that is the only way to move something "up" on a coordinate grid).
so, in other words, f(x) is nothing else but h(x), but it increases the results of h(x) consistently by 5.
h(x) = 2x² + 4
f(x) = h(x) + 5 = 2x² + 4 + 5 = 2x² + 9
It is given that the triangles ITH and APG are congruent.
When the two triangles are congruent, then the corresponding angles and sides are congruent to each other.
By being congruent, the corresponding angles which are congruent are:
Therefore, 
SO, Option 2 is the correct answer.
Answer:
Step-by-step explanation:
Since the cost for border paper is given in terms of feet and the dimensions of the gym are given in meters, we want to convert them to the same unit. Let's choose to convert feet to meters since that would be only one conversion:
Therefore, the cost of border paper is $6.99 pet 15 feet or $6.99 pet 4.572 meters.
Since the gym is rectangular, the gym's perimeter is equal to:
Therefore, the cost of the total border paper for the gym is equal to:
Answer:
The correct option is B.
Step-by-step explanation:
Given information: AB\parallel DCAB∥DC and BC\parallel ADBC∥AD .
Draw a diagonal AC.
In triangle BCA and DAC,
AC\cong ACAC≅AC (Reflexive Property of Equality)
\angle BAC\cong \angle DCA∠BAC≅∠DCA ( Alternate Interior Angles Theorem)
\angle BCA\cong \angle DAC∠BCA≅∠DAC ( Alternate Interior Angles Theorem)
The ASA (Angle-Side-Angle) postulate states that two triangles are congruent if two corresponding angles and the included side of are congruent.
By ASA postulate,
\triangle BCA\cong \triangle DAC△BCA≅△DAC
Therefore option B is correct
