The figure gives a dimension for the hypotenuse of 19
the height is given as 17, using the Pythagorean theorem we can find the base of the triangle:
19^2 = 17^2 + base^2
Simplify:
361 = 289 + base^2
Subtract 289 from both sides:
72 = base^2
Take the square root of both sides:
Base = 8.49 Round to 8.5
There are two identical triangles on each sides, so 8.5 x 2 = 17
The length of the two triangle bases is 17
The total base of the object is 31, so the length of the rectangular part in the middle would be 31 - 17 = 14
And X would be the same length as the bottom rectangle.
Therefore x = 14
Answer:
a[n] = a[n-1]×(4/3)
a[1] = 1/2
Step-by-step explanation:
The terms of a geometric sequence have an initial term and a common ratio. The common ratio multiplies the previous term to get the next one. That sentence describes the recursive relation.
The general explicit term of a geometric sequence is ...
a[n] = a[1]×r^(n-1) . . . . . where a[1] is the first term and r is the common ratio
Comparing this to the expression you are given, you see that ...
a[1] = 1/2
r = 4/3
(You also see that parenthses are missing around the exponent expression, n-1.)
A recursive rule is defined by two things:
- the starting value(s) for the recursive relation
- the recursive relation relating the next term to previous terms
The definition of a geometric sequence tells you the recursive relation is:
<em>the next term is the previous one multiplied by the common ratio</em>.
In math terms, this looks like
a[n] = a[n-1]×r
Using the value of r from above, this becomes ...
a[n] = a[n-1]×(4/3)
Of course, the starting values are the same for the explicit rule and the recursive rule:
a[1] = 1/2
Answer:
GCF-12
Step-by-step explanation:
Find the prime factorization of 84
84 = 2 × 2 × 3 × 7
Find the prime factorization of 120
120 = 2 × 2 × 2 × 3 × 5
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 2 × 3
GCF = 12
Reflection over the y-axis = change 
Compress by a factor of k = multiply by k
So, in your case, we first change the sign of the argument. Note that this has no effect, because f(x) is symmetric with respect to the y-axis:
Then, we compress the function, multiplying it by the scaling factor:
Find 75% of 150
First, let's convert 75% to decimal by dividing by 100:
Now, we will multiply 0.75 with 150 to find out answer:
Answer112.5
