-36x<8 divide both sides by -36 (reversing the direction of the inequality sign because of division by a negative number)
x>-8/36 the largest common factor of 8 and 36 is 4 so divide numerator and denominator by this factor, 8 to simplify the fraction
x>-2/9 or in proper notation, x=(-2/9, +oo)
That is an arithmetic sequence of the form:
a(n)=2n-1
Now the sum of an arithmetic sequence is just the average of the first and last terms times the number of terms...
We know the first term is 1, let's find the last term...
a(1000)=2(1000)-1=1999
So the sum of that sequence is:
1000(1999+1)/2
1,000,000
Answer:
Part 1) The ratio of the sides is 1.5
Part 2) see the explanation
Step-by-step explanation:
Part 1) we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
If Δdef and Δxyz are similar (given problem)
then
substitute the values
solve for FY
When two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
The scale factor is equal to
Part 2) How you could verify that these two triangles are indeed similar.
Remember that
In similar figures the corresponding angles are congruent
so
If
m∠D≅m∠X
m∠W≅m∠Y
m∠F≅m∠Z
then
Triangles are similar
We can use PEMDAS to help us:
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
PEMDAS states what occurs first in order of which letter pertains to which mathematical operation and how you are suppose to do it from left to right. Since multiplication and division comes before addition and subtraction, we know C isn't the answer since it is subtraction. This leaves us with A, B, and D. They all happen to be either multiplication and division. Although multiplication SEEMS to come before division, multiplication and division are actually paired together (just like addition and subtraction) meaning that if either a multiplication or division comes before a division and multiplication operation, you do it left to right. For example, 2 x 2/2. You do 2 x 2 first equaling 4 and then divide by 2 to get 2. Another example is 10/2 x 5. You DO NOT do multiplication first since multiplication and division are paired together meaning you do 10/2 equaling 5 and then do 5 x 5 equaling 25. Enough explanation for that part. Since 20/4 is the first multiplication/division operation, that is what you do first. The answer is A.
