Answer:
Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.
Step-by-step explanation:
For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.
In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.
To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.
9/6 = 3/2
12/8 = 3/2
15/10 = 3/2
Alternatively:
6/9 = 2/3
8/12 = 2/3
10/15 = 2/3
Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.
Given that both conditions are satisfied, then we can say these triangles are similar.
Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.
Cheers.
Answer:
x = 2/5
Step-by-step explanation:
5x=2
Divide each side by 5
5x/5 = 2/5
x = 2/5
Compound interest can be defined as the interest <em>on a deposited amount, an investment</em> that is <em>compounded based on its principal and interest rate.</em>
It will take about 3.239 years for the principal amount of $13,000 to double its initial value.
From the above question, we can deduce that we are to find the time "t"
The formula to find the time "t" in compound interest is given as:
t = ln(A/P) / r
where:
P = Principal = $13,000
R = Interest rate = 21.4%
A = Accumulated or final amount
From the question, the Amount "A" is said to be the double of the principla.
Hence,
A = $13,000 x 2
= $26,000
- Step 1: First, convert R as a percent to r as a decimal
r = R/100
r = 21.4/100
r = 0.214 per year.
- Step 2: Solve the equation for t
t = ln(A/P) / r
t = ln(26,000.00/13,000.00) / 0.214
t = 3.239 years
Therefore, it will take about 3.239 years for the principal amount of $13,000 to double its initial value.
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Answer:
It would be option two: Bill's Electric Company charges 6 dollars per hour plus a flat rate of 15 dollars for a service call. If Monica has at least 100 dollars to spend, how many hours can the service man work?
Step-by-step explanation:
6 dollars an hour means it would be 6x.
A flat rate of 15 means there would be just 15 as a number, no x's.
And the sign is less than or equal to, so she has over a hundred dollars to spend.
