Answer:
1.) Triangle ABC is congruent to Triangle CDA because of the SAS theorem
2.) Triangle JHG is congruent to Triangle LKH because of the SSS theorem
Step-by-step explanation:
Alright. Let's start with the 1st figure. How do we prove that triangles ABC and CDA (they are named properly) are congruent? First, we can see that segments BC and AD have congruent markings, so that can help us. We also see a parallel marking for those segments as well, meaning that the diagonal AC is also a transversal for those parallel segments. That means we can say that angle CAD is congruent to angle ACB because of the alternate interior angles theorem. Then, the 2 triangles also share the side AC (reflexive property).
So, we have 2 congruent sides and 1 congruent angle for each triangle. And in the way they are listed, this makes the triangles congruent by the SAS theorem since the angle is adjacent to the 2 sides that are congruent.
The second figure is way easier. As you can clearly see by the congruent markings on the diagram, all the sides on one triangle are congruent to the other. So, since there are 3 sides congruent, we can say the triangles JHG and LKH are congruent by the SSS theorem.
Answer:
x=5, y=3
Step-by-step explanation:
1) x+3y=14,4x+5y=35
2) x+3y=14
3) x=-3y+14
4) 4(-3y+14)+5y=35
5) -12y+56+5y=35
6) -7y+56=35
7) -7y=-21
8) y=3
9) x=-3\times 3+14
10) x=-9+14
11) x=5
finale and last : x=5,y=3 ✅
9514 1404 393
Answer:
The given graph shows a function of x.
Step-by-step explanation:
Neither 1 nor 3 is a single-valued relation for some values of x. The graph shown passes the vertical line test, so does represent a function.
The graph is a relation that is a function of x.
___
The attached graph is of the equation of 3. A vertical line will intersect the graph in more than one place, so the relation is NOT a function.
Answer:
atleast 385
Step-by-step explanation:
Given that an electrical power company is looking to expand into a new market. Before they commit to supplying the new area with electricity, they would like know the mean daily power usage for homes there.
Population std deviation = 
Sample size =
STd error of sample mean = 
Margin of error for 95% would be Critical value ( std error)
Here since population std dev is known we can use Z critical value= 1.96
Sample size should be atleast 385
Answer:
17 feet
Step-by-step explanation:
A bag of lawn fertilizer covers 289 square feet
Dimensions of the largest square plot of lawn that the bag of fertilizer will cover.
Area of a square lawn = length^2
Area of the square lawn = 289 square feet
Area of a square lawn = length^2
289 = length^2
Find the square root of both sides
√289 = √length^2
17 = length
Length = 17 feet
Dimensions of the largest square plot of lawn that the bag of fertilizer will cover = 17 feet by 17 feet
