A tree and a one metre vertical stick cast their shadows at a particular time in the day.The shadow lengths are shown in the diagram below (not drawn to scale).B)Find the scale factor for the side lengths of the triangles.
Answers
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! :)
Related Questions
Complete the inequality statement. (help)5/11___7/11
What is the 44th decimal digit in the decimal representation of 1/11?
Solve for z. w(−4+z)=mz+17
How would you solve this??
−3xy(2x2 + 3xy − 4y2)
−3xy(2x2 − 3xy + 4y2)
−3(2x3y − 3x2y2 + 4xy3
Answers
Answer:
Option C is the answer.
Step-by-step explanation:
We have to factor the GCF of the given expression:
-6x³y + 9x²y² - 12xy³
To get the GCF of the given expression we will find the factors of each term first.
Factors of 6x³y = 2 × 3 × (x) × (x) (x) (y)
Factors of 9x²y² = 3 × 3 × (x) (x) (y) (y)
Factors of 12xy³ = 2 × 2 × 3 × (x) (y) (y) (y)
So the common factor is 3 × (x) (y)
Now we will take out the GCF as a factor of the given expression = 3xy (-2x² + 3xy - 4y² )
= -3xy ( 2x² - 3xy + 4y² )
Option C is the answer.
-3xy(2x^2) - 3xy(-3xy) - 3xy(4y^2)
-3xy(2x^2 - 3xy + 4y^2)
The answer is C.
b. It is wider and shifted 3 units to the right.
c. It is narrower and shifted 3 units to the left.
d It is narrower and shifted 3 units to the right.
Answers
Transformation involves changing the position of a function.
The true statement is: (b) It is wider and shifted 3 units to the right.
The function is given as:
First, the function is translated right by 3 units.
So, we have:
Next, the function is enlarged horizontally by a factor of 0.1.
So, we have:
The above highlights mean that:
will be wider than
Hence, the correct option is (b)
Read more about function transformations at:
For f(x) u would be moving to the right being that it is a decimal times to a negative number so the answer would be B
f(a)=5(a+1)-6
Answers
Answer:
To find the value of f(5) for the given function f(a) = 5(a + 1) - 6, you simply need to substitute the value a = 5 into the function and then solve for f(5).
Step-by-step explanation:
Given the function:
f(a) = 5(a + 1) - 6
To find f(5), you need to substitute the value a = 5 into the function.
Start with the original function:
f(a) = 5(a + 1) - 6
Replace 'a' with 5:
f(5) = 5(5 + 1) - 6
Simplify the expression inside the parentheses:
f(5) = 5(6) - 6
Now, perform the multiplication:
f(5) = 30 - 6
Finally, subtract 6 from 30:
f(5) = 24
So, the value of the function f(5) is 24. This means that when the input value is 5, the function evaluates to 24.
hope this helps you!
A.9/120=x/100
B.120/x=100/9
C.x/120=100/9
D.120/9=100/x
Answers
$120*.09+$120=$130.80
$10.80 in Tax
B.120/x=100/9
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The number of hours that it will take for both Hannah and Destiny to paint the room when they are working together is 9 8/9 hours.
Based on the information given, the fraction that can be painted by Hannah in an hour will be 1/20.
The fraction that can be painted by Destiny in an hour will be 1/16.
Therefore, the formula to solve the question will be:
1/20x + 1/16x = 1/1
4x + 5x = 80
9x = 80
Divide both side by 9
9x/9 = 80/9
x = 8 8/9 hours.
Therefore, it'll take them 8 8/9 hours to paint the room.
Read related link on:
amount of room destiny can paint in an hour = 1/16
number of hours = x
1/20x + 1/16x = 1
the reason why this formula is true is, the amount of the room painted in the end should be 1 (the whole room)
4/80x + 5/80x = 1
9/80x = 1
9x = 80
x = 80/9 hours
x = 8.89 hours
Answers
Answer:
35
Step-by-step explanation:
the two angles are equvalient because they are same side exterior angles.
105/3 = 35