Answer:
The pair of triangles that are congruent by the ASA criterion isΔ ABC and Δ XYZ.
The pair of triangles that are congruent by the SAS criterion is Δ BAC and ΔRQP.
Step-by-step explanation:
Two triangles are congruent by ASA property if any two angles and their included side are equal in both triangles .In triangles Δ ABC and Δ XYZ the equal side 5 is between the two equal angles. So these triangles are congruent by ASA criterion.
Two triangles are congruent by SAS if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle .In triangles Δ BAC and ΔRQP. the included angles A and Q are equal and hence the triangles are congruent by SAS criterion.
Answer:
Part A:
Part B:
and 
Step-by-step explanation:
Part A:
The inicial concentration of the lemonade is 50%, and the volume is 4 quarts, and we will add x quarts of a lemonade with a concentration of 100%, so the total volume will be y, and the concentration will be 0.7, so we have that:
Using the value of y from the first equation in the second one, we have:
Part B:
If he shoots a total of ten targets, we can write the equation:
Each stationary target is 2 points, and each moving target is 3 points, so if the total points is 23, we have:
If we subtract the second equation by two times the first one, we have:
⇒
He did this then that plus to this and that =334.2
You need to isolate the variable my dividing each side by factors that don’t contain the variable
x=-5
Answer:
The rock formation is approximately 7 feet tall.
Step-by-step explanation:
<em>We can visualize this situation as a triangle and know that the bottom side is </em><em>10</em><em> and the angle of elevation (the angle created by Mike and the ground, looking to the top of a rock). With this information, we can use tangent to solve.</em>
<em>x = the height of the rock formation</em>
tan(22°) = x/10
10 tan(22°) = x
x = ~4.04 feet
<em>We also have to add the </em><em>3 feet</em><em> to it because it is being measured 3 feet above the floor.</em>
x + 3 = 7.04 feet
