By using proportions based on the concept of similar triangles, the height of the taller tree is calculated to be approximately 16.3 feet tall.
Explanation:The question asks us to compare the heights and shadows of two trees to determine the height of the taller tree given the height and shadow length of the shorter tree and the shadow length of the taller tree. Since both trees will cast shadows in the same proportions if they're under the same conditions of light, we can use similar triangles to find the height of the taller tree.
The shorter tree is 10.5 ft tall and casts a shadow that is 11.25 feet long. If the taller tree casts a 17.5 ft shadow, we can set up a proportion as follows:
Height of the shorter tree / Shadow of the shorter tree = Height of the taller tree / Shadow of the taller tree
10.5 ft / 11.25 ft = Height of the taller tree / 17.5 ft
From the proportion, we can solve for the height of the taller tree:
Height of the taller tree = (10.5 ft / 11.25 ft) × 17.5 ft
Height of the taller tree = 16.333... ft
So, the taller tree is approximately 16.3 feet tall.
Identify the variation as direct, inverse, joint or combined.
The cost of the number of the same articles purchased varying with the number purchased.
a.direct
b.inverse
c.joint
d.combined ...?
Answer:
The statements " cost of the number of the same articles purchased varying with the number purchased' shows direct variation .
Option (a) is correct .
Step-by-step explanation:
Definition of the direct variation
When two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
i.e
[tex]x \propto y[/tex]
x = ky
As the x increases than y is also increase .
As given the statement in the question
The cost of the number of the same articles purchased varying with the number purchased.
i.e
As the number of purchased article increases thus cost of the articles also increases .
Therefore the statements " cost of the number of the same articles purchased varying with the number purchased' shows direct variation .
Option (a) is correct .
Dion practiced the long jump . he jumped 3.05 meters,2.74 meters and 3.3 meters.what was the average length of dion's jumps?
A candy company used 8 gallons of syrup to make 4 batches of candy. what is the rate of syrup per batch.
Given: line DR tangent to Circle O.
If m angle C = 63°, then m angle BDR =
Answer:
m∠BDR=63°
Step-by-step explanation:
It is given that line DR tangent to Circle O and m∠BCD=63°, then the measure of the angle BDR can be determined as:
Since, angle BDR is made between the chord and the tangent, and we know that the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment, therefore
m∠BCD=m∠BDR=63°
Hence, the measure of angle BDR=63°.
Write the equation y-2=6x 3 in y mx b form
Final answer:
The equation y - 2 = 6x is rewritten in the y = mx + b form by simply adding 2 to both sides resulting in y = 6x + 2, where 6 is the slope and 2 is the y-intercept.
Explanation:
The equation y - 2 = 6x is not fully written in the y = mx + b form, which is the standard form of a linear equation where m represents the slope and b represents the y-intercept. To convert the given equation into the y = mx + b form, we need to isolate y on one side of the equation.
First, we will add 2 to both sides of the equation:
y - 2 + 2 = 6x + 2
Which simplifies to:
y = 6x + 2
Now we have written the equation in the desired form, with m = 6 and b = 2. This linear equation represents a line with a slope of 6 and a y-intercept at (0, 2). Graphically, the line can be plotted using these values, and a table of points can be created by plugging various x values into the equation.
Slingerland borrowed $8,000 on july 20, at 11% interest. if the loan was due on october 17, what was the amount of interest on the loan using the exact interest method?
I think the answer is $216.99 ?
Answer:
The amount of interest on the loan was of $214.57.
Step-by-step explanation:
Slingerland borrowed $8,000 at an 11% interest rate, thus having to pay $880 after a year.
As the loan was due on October 17, and the difference between July 20 and October 17 is of 89 days, using the exact interest method we can affirm that:
880 / 365 x 89 = X
2.41 x 89 = X
$214.57 = X
The amount of interest on the loan was of $214.57.
What can each term of the equation be multiplied by to eliminate the fractions before solving? x – 2x = x 2 6 10 12
Answer:
12
Step-by-step explanation:
I did the test
A triangle has sides of length 3 cm and 10 cm. What can you say about the length of the third side?
The inequality that represents the third side of the triangle is the third side < 13.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given, A triangle has sides of length 3 cm and 10 cm.
From the rule of the triangle, The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
thus, we can say that
third side < 10 + 3
third side < 13
Therefore, The inequality third side < 13 is used to represent the triangle's third side.
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Final answer:
Using the Triangle Inequality Theorem, the third side of a triangle with sides of 3 cm and 10 cm must be greater than 7 cm and less than 13 cm.
Explanation:
To determine the possible length of the third side of a triangle given two side lengths of 3 cm and 10 cm, we use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the third side must be longer than 7 cm (10 cm - 3 cm) but shorter than 13 cm (10 cm + 3 cm).
which expression equivalent to k^1/4 · cubed root of k^2
If
f (n)(0) = (n + 1)!
for
n = 0, 1, 2, ,
find the Maclaurin series for f.
The Maclaurin series for f(n) is 1.
Explanation:The Maclaurin series for a function can be found using the formula: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...
In this case, f(0) = (0+1)! = 1, f'(0) = d/dx((0+1)!) = d/dx(1) = 0, f''(0) = d^2/dx^2((0+1)!) = d^2/dx^2(1) = 0, and so on.
Using these values, the Maclaurin series for f(n) is: f(n)(x) = 1 + 0x + 0x^2/2! + 0x^3/3! + ... = 1.
How do the CHNOPS elements create macromolecules?
plzzzz helppppp
The sides of the cubes are numbered 1 through 6. If they are both tossed, what is the probability that they will both be a 2?
Answer:
The answer is 1/36
Step-by-step explanation:
number is a factor of 51?
At president bush's inauguration in 2005, the newspaper headline stated there were about 400,000 people in attendance at the newspaper rounded to the nearest 10,000 what is the largest number and smallest number of people who could have been there
Answer:
At president bush's inauguration in 2005, the newspaper headline stated there were about 400,000 people in attendance.
Now, rounding to nearest ten thousand the greatest number will be: 404999.
And the smallest number will be : 395000
So, the largest number of people who could have been here is 404999.
And the smallest number of people who could have been here is 395000.
What is the average rate of change for the sequence shown below?
coordinate plane showing the points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5
−2
−one half
1
2
Answer:
1
Step-by-step explanation:
Step 1: Select 2 points
(0,3) (0.5, 3.5)
x1,y1 x2,y2
Step 2: use average rate of change formula
[tex]\frac{y2-y1}{x2-x1}[/tex] = average rate of change
[tex]\frac{3.5-3}{0.5-0} =\frac{0.5}{0.5} =1[/tex]
Nick has 3.90 in quarters and dimes total number of coins is 27how many quarters and dimes
Answer:
8 quarters; 19 dimes trust me i checked
Step-by-step explanation:
simplify completely ((x2-4x+4)/(x2+10x+25)) x ((x+5)/(x2+3x-10)) ...?
Factorize the given complex expression first into simpler terms (x-2)^2, (x+5)^2 and (x-2)(x+5). After canceling the matching terms, you simplify to get (x-2)/(x+5)
Explanation:This mathematical question involves the simplification of a fractional expression. The problem can be solved with factoring and canceling out matching terms found in both the numerator and denominator. Step by step solution would be:
((x2-4x+4) can be factored into (x-2)^2.
(x^2+10x+25) can be factored into (x+5)^2.
(x^2+3x-10) can be factored into (x-2)(x+5).
Thus, the whole equation will be converted into
((x-2)^2 / (x+5)^2) x ((x+5) / (x-2)(x+5)).
Cancel (x+5) and (x-2) from the numerator and denominator, which leaves:
(x-2)/(x+5).
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Which set of line segments with the given lengths can be formed into a right triangle?
24,30,35
12,18,30
18,24,30
18,24,35 ...?
Answer:
there right
Step-by-step explanation:
93 /100 converted to percent equals? ...?
What is 39 percent of 120?
What is the range of y = sin θ ?
Name the property of equality that justifies: (I have to put question into an equation below because I can't get it in this question without it being confusing)
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplication Property of Equality
D. Division Property of Equality
If:
m
then
5×m
What are the factors of 86?
What is the length of the hypotenuse of the right triangle that has a base of 5 inches and a height of 12 inches?
Find the sum or difference write the answer in simplest form 3/10 4/10=
Factorise 6p^2-5pq-6q^2
translate the following into interval notation: "The union of all numbers greater than eight, and less than or equal to negative four".
Help needed :/
(1/2^-2) + 1/2
A. 2
B. 2 1/2
C. 4
D. 4 1/2
which value satisfies the inequality -2x + 8 + 5x > 2x + 1
The values which are greater than -7, satisfies the inequality -2x + 8 + 5x > 2x + 1.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
-2x + 8 + 5x > 2x + 1.
To find the value of x,
Simplify the inequality by using mathematical operations,
3x + 8 > 2x + 1
3x - 2x > 1 - 8
x > -7
The required solution for the given inequality is x > -7.
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What is the slope of a line perpendicular to the line with equation y = 4x + 5?
-1/4
–4
4
–5