What is the 55th term of the sequence?
Step-by-step explanation:
Hence, the 55th term of the sequence is 161.
They now had the same amount in their accounts.
How much did they initially have altogether?
Answer:
£780 and £1300
Step-by-step explanation:
The ratio in their accounts is 3 : 5 = 3x : 5x ( x is a multiplier )
Terry put £220 into his account, then 3x + 220
Faye withdrew £300 from her account then 5x - 300
They now have the same amounts in their accounts, thus
5x - 300 = 3x + 220 ( subtract 3x from both sides )
2x - 300 = 220 ( add 300 to both sides )
2x = 520 ( divide both sides by 2 )
x = 260
Thus initial amount in their accounts
3 × £260 = £780 ← Terry's account
5 × £260 = £1300 ← Faye's account
Which function can the company use to determine its total revenue from the two products, R(x), after they have been on the market for x years, and approximately what will be the revenue generated by sales of the products after 6 years?
R(x) = 9,000[7(1.035)x + 9(1.021)x]; $635,580
R(x) = 9,000[7(1.035)x + 9(1.021)x]; $169,200
R(x) = 9,000[9(1.035)x + 7(1.021)x]; $170,936
R(x) = 9,000[9(1.035)x + 7(1.021)x]; $688,050
Answer:
a) Giving Reasons Why the Two Triangles are Similar
Similar triangles have the same shape but can be different sizes. For triangles to be similar, their matching angles must be equal, and their matching sides must have the same proportions.
In this problem, we have two triangles - one made by the tree, its shadow, and the line connecting the top of the tree to the end of the shadow. The other triangle is made the same way using the stick.
The bottom angle where the shadow meets the ground is 14 degrees for both triangles. Also, the vertical angles where the tree and stick meet the ground are both 90-degree right angles. Using those known angles, we can find the remaining top angles in each triangle, which are both 76 degrees (180 - 90 - 14 = 76).
Since the corresponding angles in the tree shadow triangle and the stick shadow triangle are all equal (14, 90, and 76 degrees), the two triangles have the same shape. This means the tree shadow triangle and stick shadow triangle are similar triangles.
b. Find the scale factor for the side lengths of the triangles.
The scale factor between two similar triangles is the ratio of their corresponding sides. In this case, you should use the length of the shadows to calculate the scale factor.
Since the shadow of the stick is 4m long and the shadow of the tree is 8m long, the scale factor from the tree's shadow to the stick's shadow is 4/8 = 0.5, or 1/2.
c. Find the height of the tree.
Given that the triangles are similar, and the scale factor is 1/2, the height of the tree would be twice the height of the stick because the stick's shadow is half the length of the tree's shadow.
So the height of the tree would be 2 * 1m = 2m.
Hope this helps! :)
(See image) thanks!
The pair of radicals that is a like pair is and
Option C is correct
For two radicals to be similar, they must contain the same number in the root operator.
Two like radicals are in the form:
and
Since and are like terms, arithmetic operations such as addition, subtraction, multiplication, and division can be carried out on them
Considering the options given, only and are in the form and because they have equal value inside the root operator.
Therefore, the pair of radicals that is a like pair is and
Learn more here: brainly.com/question/3253643
Answer:
I just finished taking this test and I just wanted to confirm for all you humans out there, that FencingParry4 is correct! (yay! wooo! celebra-ate!) the answer is indeed 7√3 and 9√3 Great job fencing!
Step-by-step explanation:
Options:
The answer is the third option "No; the data doesn't suggest a causation, and many people are healthy who don't exercise." Correlation is two data set that are linked or connected together so in this case it would be a correlation because all of the data is close and connected to each other.
Hope this helps!
Answer:
No; the data doesn't suggest a causation, and many people are healthy who don't exercise
Step-by-step explanation:
I took the quiz and this was the answer.