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.
Step-by-step explanation:
By substituting x = 0.4 in equation 7 + (-3x^2)
= 7 - 3 (0.4)^2
First solving o.4^2 as per the rule of BODMAS
= 7- 3 (0.16)
Now multiplying -3 with 0.16
= 7 - 0.48
= 6.52 THIS IS THE ANSWER
The point (1,5) is:
Like it is shown this means that we have to move one unit in the right direction and 5 units up.
Answer:
The workers will need 10 days to finish the job.
Step-by-step explanation:
To solve this question we can use a compound rule of three. We have:
10 road workers -> 5 days -> 2h/day
2 road workers -> x days -> 5h/days
The first thing we should do is analyze how the proportions between the variables work, if they're inversely or directly proportional. If we raise the number of workers we expect that the amount of days needed to finish the job lowers and if we raise the number of hours worked in a day we expect that the workers would need less days to finish the job. So we need to invert the fractions that are inversely proportional to the amount of days worked, then we have:
2 -> 5 -> 5
10-> x -> 2
x = (5*2*10)/(2*5) = 100/10 = 10 days
Answer:
a. $24,512.32
b. $712.32
Step-by-step explanation:
a. A price of car $15,300, Tony made a down payment of $3900 so car has $11,400 left of a price and took out a loan.
He paid monthly payments of $252.34 for 4 years. Which mean $252.34 is paid for 48 months, multiplication $252.34 and 48 are $12,112.32. So we have monthly payments is $12,112.32
The total amount Tony ended up for the car is $11,400 + $12,112.32 = $24,512.32
b. The interest Tony pay on the loan is $12,112.32 - $11,400 = $712.32