First: work out the difference (decrease) between the two numbers you are comparing.
Decrease = Original Number - New Number
Then: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100
If your answer is a negative number then this is a percentage increase.
Thus, the answer is a 86.7% (rounded) increase.
Final answer:
The sale of KIDZ sneakers increased by $1.3 billion, representing an 86.7% increase when rounded to the nearest tenth of a percent.
Explanation:
To find the percent of increase for the sale of KIDZ sneakers, we subtract the original amount ($1.5 billion) from the new amount ($2.8 billion) and then divide by the original amount. The difference between the two values is $2.8 billion - $1.5 billion = $1.3 billion. To calculate the percentage increase, we divide $1.3 billion by $1.5 billion, which gives us approximately 0.8667. To get the percentage, we then multiply by 100, resulting in an 86.67% increase. Finally, rounding to the nearest tenth of a percent, we get an increase of 86.7%.
determine the area of the yellow sector
Answer:
Step-by-step explanation:
To find out the area just compare the amount of green space and yellow space then calculate the numbers.
Answer:
The answer is D
Step-by-step explanation:
[tex]sector = \frac{θ}{360} \times π {r}^{2} [/tex]
Given that θ = 75° and r = 3in, so use the formula to find the shaded region :
A = (75/360)×π×3²
= (15/8)π
please help thanks ❗
Answer:
The Two Column Proof is given below.
Step-by-step explanation:
Given:
[tex]\overline{MP} \cong \overline{MN}[/tex]
[tex]\overline{PO} \cong \overline{NO}[/tex]
To Prove:
∠ P ≅ ∠ N
Proof:
In Δ MPO and Δ MNO
STATEMENT REASONS
1. MP ≅ MN 1. Given
2. PO ≅ NO 2. Given
3. MO ≅ MO 3. Reflexive property
4. ΔMPO ≅ ΔMNO 4. Side-Side-Side congruence test}
5. ∠MPO ≅∠MNO 5. Corresponding parts of congruent Triangles
i.e ∠ P ≅ ∠ N ..................Proved
Type the correct answer in the box.
The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet.
Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.\
Question:
The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.
So, the square root of what (?) equals(=) 20
Answer:
The complete equation is square root of(x + 16) = 20
Solution:
Given that Dock has a shape of square
[tex]\text{ area of square }= (side)^2[/tex]
From question, it is given that side length of new dock is 20 feet
Therefore, area of new dock is given as:
[tex]\text{ area of new dock}= (20)^2[/tex]
Taking square root on both sides,
square root of (new area ) = 20 --- eqn 1
Let "x" be the area of original dock
The area of the dock will increase by 16 square feet
New area = original area + 16
New area = x + 16 ---- eqn 2
From eqn 1,
square root of (new area ) = 20
From eqn 2
square root of(x + 16) = 20
Thus the complete equation is: square root of(x + 16) = 20
Final answer:
To find the area of the original dock, the equation x + 16 = 20^2 can be used, where x is the original area. By solving the equation, we find that x equals 384 square feet.
Explanation:
The area of the original square-shaped dock can be found using the equation for the area of a square, with the area being equal to the side length squared. Given that the new square dock has a side length of 20 feet, and the area is increased by 16 square feet, we can set up an equation to find the original area, x.
The equation is x + 16 = 20^2, where 20^2 is the area of the new, larger dock, and x is the original area of the dock before the enlargement. Therefore, the side length of the original dock is the square root of x. To find x, we can solve the equation:
x + 16 = 400
x = 400 - 16
x = 384
So the area of the original dock is 384 square feet.
I’m not good at Algebra please lend a hand
1. Is the actual equation, so this is Given
2. removing the parenthesis is the Distributive Property
3. Combining like terms.
4. They add 6x to both sides, this would be the Addition Property of Equality
5. Subtract 4 from both sides, this is the Subtraction Property of Equality.
6. Divide both sides by 8, this would be the Division Property of Equality.
Answer:
1. Given
2. Distributive property
3. Combining like Terms
4. Addition property of Equality
5. Subtraction property of equality
6. Division Property of Equality
There were 65 questions on the topic of geography on the practice test. What was the total number of questions on the practice test?
The total number of questions on the practice test is at least 66.
Since the number of geography questions is 65, and geography was one of the topics on the practice test, the total number of questions on the practice test must be greater than 65.
One option is that there were 66 questions on the practice test, with the remaining question being on a different topic.
Another option is that there were more than 66 questions on the practice test, with geography being one of multiple topics.
Therefore, the total number of questions on the practice test is at least 66.
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A number n is multiplied by -5/8. The product is -0.4. What is the value of n?
Answer:
n=0.64
Step-by-step explanation:
-5/8n=-0.4
n=-0.4/(-5/8)
n=-0.4(-8/5)
n=3.2/5
n=0.64
Determine whether the equation represents a direct variation. If it does, find the constant of variation:
1. 2y=5x+1
A. Not a direct variation
B. Direct Variation, constant of variation is 5/2
C. Direct Variation, constant of variation is 2/5
D. Direct Variation, constant of variation is 1 -2/5
2. -12x=6y
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2
3. 0.7x-1.4y=0
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2
Answer:
1) A. Not a direct variation 2) D. Direct Variation, constant of variation is -2 C) B. Direct Variation, constant of variation is ½
Step-by-step explanation:
Direct Variation requires that [tex]y=kx[/tex] with k≠0. K its constant of variation and its slope. It is a linear function with b =0
1) Examining 2y =5x + 1. Rewriting it as standard form:
[tex]2y =5x + 1\\\\y=\frac{5}{2}x+\frac{1}{2} \\\\[/tex]
Since this function cannot be written as y=kx as b ≠ 0 (b=1) then we can say that this is not a direct variation.
A. Not a direct variation
2) [tex]2). -12x=6y \Rightarrow y=-2x[/tex]
This linear function has no linear parameter. And its line goes through the origin varying directly. The constant k is equal to -2. So,
D. Direct Variation, constant of variation is -2
3) [tex]0.7x-1.4y=0\\\\-1.4y=-0.7x* (-1)\\y=0.5 \:or\,y=\frac{1}{2}[/tex]
The Constant of Variation is 1/2 and K>0. There is a direct variation between x and y of 1/2. So it's B.
B. Direct Variation, constant of variation is ½
The equation 2y = 5x + 1 represents a direct variation with a constant of variation of 5/2. The equation -12x = 6y represents a direct variation with a constant of variation of -2. The equation 0.7x - 1.4y = 0 represents a direct variation with a constant of variation of 0.5.
Explanation:For the equation 2y = 5x + 1, we need to determine if it represents a direct variation. In a direct variation, y is directly proportional to x, meaning that when x increases, y also increases or when x decreases, y also decreases. To check if it's a direct variation, we can rearrange the equation to y = mx + b form, where m is the constant of variation. In this case, rearranging the equation gives us y = (5/2)x + 1/2, so the constant of variation is 5/2. Therefore, the equation represents a direct variation and the constant of variation is 5/2.
For the equation -12x = 6y, we can rearrange it to y = (-12/6)x = -2x. Since the constant of variation is -2, the equation represents a direct variation.
For the equation 0.7x - 1.4y = 0, we can rearrange it to y = (0.7/1.4)x = 0.5x. Since the constant of variation is 0.5, the equation represents a direct variation.
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(Score for Question 2: ___ of 5 points)
2. Write in complete sentences how to tell the difference between a proportional relationship and a
nonproportional relationship.
Explanation:
All proportional relationships have a common ratio. In a set of data, if the ratio between terms are not the same, the relationship is non-proportional. The common ratio is found by dividing a term value by the previous term value. On a graph, proportional relationships form a straight line and non-proportional relationships do not.
The coordinates of a triangle are P(1, 4), Q(3, 6), and R(5, 2). The triangle is reflected over a line and its image coordinates are P'(–1, 4), Q'(–3, 6), and R'(–5, Find the equation of the reflection line.
1. x = –1
2. y = –1
3. y = 0
4. x = 0
Answer:
Option 4. x = 0
Step-by-step explanation:
we know that
The rule of the reflection of a point across the y-axis is equal to
(x,y) -----> (-x,y)
The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y-value the same
The coordinates of triangle PQR are
P(1, 4), Q(3, 6), and R(5, 2)
Applying the rule of the reflection across the y-axis we have
P(1, 4) -----> P'(-1, 4)
Q(3, 6) ----> Q'(-3, 6)
R(5, 2)----> R'(-5, 2)
The reflection line is the y-axis
Remember that the equation of the y-axis is x=0
therefore
The equation of the reflection line is x=0
Answer: The correct answer is (x = 0)
Step-by-step explanation: Took the assignment.
Find the sum of -2 and -5. Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.
please help
Answer:
The sum of - 2 and - 5 is - 7.
[tex]1\frac{2}{3} + 3\frac{1}{2} = 5\frac{1}{6}[/tex]
Step-by-step explanation:
The sum of - 2 and - 5 is [- 2 + (- 5)] = - 2 - 5 = - 7. (Answer)
Let two mixed fractions are [tex]1\frac{2}{3}[/tex] and [tex]3\frac{1}{2}[/tex] that we have to add with steps.
Now, we have to sum the mixed numbers after converting then into improper fractions.
So, [tex]1\frac{2}{3} = \frac{5}{3}[/tex] and
[tex]3\frac{1}{2} = \frac{7}{2}[/tex]
Hence, [tex]1\frac{2}{3} + 3\frac{1}{2}[/tex]
= [tex]\frac{5}{3} + \frac{7}{2}[/tex]
= [tex]\frac{5\times 2 + 7 \times 3}{6}[/tex] {Because the L.C.M. of 2 and 3 is 6}
= [tex]\frac{ 10 + 21}{6}[/tex]
= [tex]\frac{31}{6}[/tex]
= [tex]5\frac{1}{6}[/tex] (Answer)
Answer:
Hi im on odyssey ware and i had this question too, Just remember that the fractions are pictures, so they wont go on the question. Another way to write fractions is like this 4/8 so the actual question is, find the sum of -2 9/10 and -5 4/15. Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.
Step-by-step explanation:
78 thousands = 7,800 ones. True or false
Answer:
FALSE
Step-by-step explanation:
78 thousands = 78 x 1000 = 78,000
Answer:false
Step-by-step explanation:
78,000 is 78 thousands
7,800 is only 7 thousand and 8 hundred
Which expression is equivalent to StartFraction (5 a b) cubed Over 30 a Superscript negative 6 Baseline b Superscript negative 7 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.
Answer: [tex]\frac{25}{6} a^{9} b^{10}[/tex]
Step-by-step explanation:
Assuming the described expression is:
[tex]\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}[/tex]
And knowing the condition [tex]a \neq 0[/tex] and [tex]b \neq 0[/tex]
We cansimplify it following the rules related to the exponents with the same base:
[tex]\frac{25}{6} a^{3} b^{3} a^{6} b^{7}[/tex]
Finally:
[tex]\frac{25}{6} a^{9} b^{10}[/tex]
Answer:
Answer: \frac{25}{6} a^{9} b^{10}
Step-by-step explanation:
100% on ed
[Answer For Brainliest]
Solve for d.
[tex]0.5(7d+4)=7-1.5d[/tex]
question 14. Select the correct answer. If f(x)=x^2/x+3, find f(x+h)
In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:
1. Write down the original function:
\( f(x) = \fraction{x²}{x+3} \)
2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
\( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)
3. Now expand the numerator and simplify the expression:
\( (x+h)² = x² + 2xh + h² \)
Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)
That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).
A summer camp cookout is planned for the campers and their families. There is room for 525 people. Each adult costs $9, and each camper costs $5. There is a maximum budget of $1,200. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.
A
x + y ≤ 525
5x + 9y ≤ 1,200
B
x + y ≤ 1,200
5x + 9y ≤ 525
C
x + y ≤ 525
9x + 5y ≤ 1,200
C
x + y ≤ 1,200
9x + 5y ≤ 525
Need help ASAP.
x+y≤525 and 9x+5y≤1200 represents the scenario.
Step-by-step explanation:
Given,
Room for people at summer camp = 525 people
Maximum budget = $1200
Cost per adult = $9
Cost per camper = $5
It means that there cannot be spent more than $1200.
x represents the number of adults.
y represents the number of campers.
x+y≤525
9x+5y≤1200
x+y≤525 and 9x+5y≤1200 represents the scenario.
Keywords: inequality, budget
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Answer:
x+y≤525
9x+5y≤1200
Step-by-step explanation:
Rectangle FGHJ shown below, is translated 6 unit up to produce rectangle F’G’H’J
Answer:
The correct option is (a).
Step-by-step explanation:
See the diagram attached.
Whatever be the translation done on a figure the dimensions of the figure will remain unchanged and only the coordinates of the vertices will change according to the rule of translation.
Therefore, if a rectangle FGHJ is translated by 6 units right and one unit up to produce a rectangle F'G'H'J', then the length F'G' = FG = 3 units and G'H' = GH = 5 units.
So, the correct option is (a). (Answer)
Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.
Given to us,
Rectangle FGHJ, with sides, FG = JH = 3 units, and, FJ=GH=6 units.
Now, as given to us, Rectangle FGHJ has translated 6 units up to produce rectangle F’G’H’J', but even if the rectangle is translated it will still be a rectangle making no changes in its sides.
Therefore, Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.
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When 90 is added to a number it equals 30 less than 3 times the number.
Answer:
90+x=30-3[x]
Step-by-step explanation:
collect like terms
x+3x=30-90
4x=-260
divide both sides by 4
x=-60/4
x=-4*3*5/4
x=-[3*5/1]
x=-[3*5]
x=-15
Answer:
The number is 60.
Step-by-step explanation:
Let x = unknown number.
Now we translate the sentence into an equation, one piece at a time.
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90
When 90 is added to a number it equals 30 less than 3 times the number.
x + 90 = 3x - 30
We now solve the equation for x.
Subtract 3x from both sides.
-2x + 90 = -30
Subtract 90 from both sides.
-2x = -120
Divide both sides by -2.
x = 60
The number is 60.
Check:
When 90 is added to a number it equals 30 less than 3 times the number.
Add 90 to 60:
90 + 60 = 150
We get 150.
When 90 is added to a number it equals 30 less than 3 times the number.
Now multiply 60 by 3 and subtract 30.
3(60) - 30 = 180 - 30 = 150
We also get 150.
That means our answer of 60 is correct.
Answer: 60
Solve each equation by using the zero product property
(B-4)(3b-1)=0
Answer:
Step-by-step explanation:
(b - 4)(3b - 1) is the factored form of some second degree polynomial. Once you factor to this point, you can solve for the values of b using the Zero Product Property, which says that one of the those factors has to equal 0 for the product to equal 0 (cuz any number times 0 is equal to 0). The first expression is b - 4. If we set b - 4 equal to 0, we can solve for b:
b - 4 = 0 so
b = 4
Likewise with the second factor, 3b - 1. Set it equal to 0 and solve for b:
3b - 1 = 0 and
3b = 1 so
b = 1/3
To solve the equation (B-4)(3b-1)=0 using the zero product property, set each factor equal to zero and solve for the variable. The solutions are B = 4 and b = 1/3.
Explanation:To solve the equation (B-4)(3b-1)=0 using the zero product property, we set each factor equal to zero and solve for the variable:
First factor: B-4 = 0
Second factor: 3b-1 = 0
Solving each equation separately:
B-4 = 0So the solutions to the equation (B-4)(3b-1)=0 are B = 4 and b = 1/3.
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WILL MARK BRAINLIEST!!! I need the answer. please help!!!!
Answer:
Step-by-step explanation:
Later area of Pyramid = 2 * 1/2 * 9 * 12.3 + 2*1/2*11*11.9
= 9*12.3 + 11*11.9
= 110.7 +130.9
= 241.60 sq.feet
20 pts and brainiest if correct. Please and Thank You
Answer:
1. 24 2. 21:15 3. 36:21
Step-by-step explanation:
18:27 is 2:3 and 24 is 16/2*3
7:5 is also 21:15
36:21 fully simplified is 12:7 not 9:7
Answer:
1:24 2: 21:15 3: 36:21
Step-by-step explanation:
Simplify the ratio, then find the equivalent one.find the multiple that matches both.Find the one that is oddHope this helps!!!
PLZ HELPPP PLZZZZ
Dev has 9 shells. Zoe has 55 shells, Zoe gives some shells to Dev. Now zoe has 3 times as many shells as dev. How many shells does Zoe give to Dev.
Help please please help!!!!!
Answer:
I have no idea
Step-by-step explanation:
Which statements accurately describe the function f(x) = 3(16) Superscript three-fourths x? Select three options.
The initial value is 3.
The domain is x > 0.
The range is y >0.
The simplified base is 12.
The simplified base is 8.
Answer:
The initial value of the function is 3.
The range of the function is y > 0.
The simplified base value of the function is 8.
Step-by-step explanation:
The given function is [tex]f(x) = 3(16)^{\frac{3}{4}x }[/tex]
Therefore, the simplified function will be [tex]f(x) = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}[/tex] ........ (1)
Now, at x = 0, f(x) = 3.
Hence, the initial value of the function is 3. (Answer)
The value of x in the equation (1) can be any real value but for any value of x, the f(x) value will be greater than 0.
Hence, y > 0 that is the range that the function has. (Answer)
Again, from equation (1) we get the simplified base value of the function is 8. (Answer)
Answer:
A, C, E
Step-by-step explanation:
Egde 2020
1. A school booster club is selling
T-shirts. The silk-screening company
is selling shirts to the boosters for
$3 each, plus a one-time fee of $150
to cover supply costs. If the boosters
want to make at least $300 in profits
and they sell a shirt for $12, how
many shirts do they need to sell?
Answer:
Step-by-step explanation:
sales - expenses = profit
lets x represent number of shirts sold
12x - (3x + 150) > = 300
12x - 3x - 150 > = 300
9x - 150 > = 300
9x > = 300 + 150
9x > = 450
x > = 450/9
x > = 50 <== they would need to sell at least 50 shirts
If triangle pqr is and equilateral triangle, pq = 18x+1, qr = 24x-17, and pr = 15x+10, find x and the measure of each side.
Answer:
The value of x is 3 ,
The measure of each side is 55 units .
Step-by-step explanation:
Given as :
The sides of the equilateral Triangle are pq , qr , pr
The measure of side pq = 18 x + 1
The measure of side qr = 24 x - 17
The measure of side pr = 15 x + 10
∵ The triangle is equilateral then all sides are equal
i.e pq = qr = pr
So, 18 x + 1 = 24 x - 17
Or, 24 x - 18 x = 17 + 1
Or, 6 x = 18
∴ x = [tex]\dfrac{18}{6}[/tex]
i.e x = 3
So, Putting the value of x
The measure of side pq = 18 × 3 + 1 = 55 unit
The measure of side qr = 24 × 3 - 17 = 55 unit
The measure of side pr = 15 × 3 + 10 = 55 unit
Hence The value of x is 3 ,
And The measure of each side is 55 units . Answer
Answer:
x = 3.
Measure of each side is 55 units.
Step-by-step explanation:
In an equilateral triangle, the length of all the three sides are equal.
Therefore, Side PQ = QR = PR.
⇒ 18X + 1 = 24X - 17
⇒ 24X - 18X = 18
⇒ 6X = 18
⇒ X = 3
Substituting the value of X, we get:
PQ = 18(3) + 1 = 55 Units.
QR = 24(3) - 17 = 55 units.
PR = 15(3) + 10 = 55 units.
We see the length of all the sides are equal.
Need some help boyss
Answer: 0
Step-by-step explanation: The answer would be 0 since if y = -4, the graph of the line would just be a horizontal line through the point (0,-4). This would be like saying that y = 0x-4. Hope this helped!
Answer:
slope = 0
Step-by-step explanation:
The equation of a horizontal line parallel to the x- axis is
y = c
where c is the value of the y- coordinates the line passes through.
y = - 4 ← is therefore a horizontal line
with slope = 0
Round each number to the nearest 10 and 1000
What numbers??? You need to either add a picture or just write the numbers
Ming took a cab across town. His fare was
$22 sign, and he leaves an 18% percent tip.
Question:
Ming took a cab across town. His fare was $22 and he leaves an 18%, percent tip. What is the total amount Ming pays the cab driver?
Answer:
Ming pays the $25.96 to cab driver
Step-by-step explanation:
Given:
the fare of the car = $22
Percentage of tip paid by the Ming = 18%
To Find:
Total amount Ming pays the cab driver=?
Solution:
The total amount of the tip paid by the Ming to the cab driver be x
then
x = car fare + 18% of cab fare
substituting the values we get
x = 22 + 18% of 22
x = 22 + [tex]\frac{18}{100} \times 22[/tex]
x = 22 + [tex]\frac{18}{100} \times 22[/tex]
x = 22 + [tex]0.18 \times 22[/tex]
x = 22 + 3.96
x = 25.96
Write the value of 17 tens three different ways. Use the largest unit possible. Standard form. Expanded form. Unit form
Final answer:
The value of 17 tens can be written in standard form as 170, in expanded form as (1 × 10²) + (7 × 10¹), and in unit form as '1 hundred 7 tens 0 ones'.
Explanation:
When asked to write the value of 17 tens three different ways, we first recognize that '17 tens' is essentially the number 170, since 17 tens are 17 multiplied by 10.
Standard Form
The standard form is simply writing the number as it is, so in this case, it would be 170.
Expanded Form
The expanded form breaks down the number into its place value components. Since 170 comprises 1 hundred, 7 tens, and 0 ones, it can be written as:
(1 × 10²) + (7 × 10¹) + (0 × 10°)
Unit Form
Last, the unit form expresses each digit's value according to its place value, which for 170 is '1 hundred 7 tens 0 ones'.
Problem: you must find the horizontal distance between two towers (points a and b) at the same elevation on opposite sides of a wide canyon running east and west. The towers lie directly north and south of each other. You mark off an east/west line CD running perpendicular to AB.
A) From C you measure the angle between the two towers (angle ACB) as 88.60 degrees. Given the distance from C to B is 389 feet, write an equation and solve it to find an expression for the distance AB to the nearest whole foot. (Note: AB is perpendicular to CD)
B) You want to check your work to make sure it’s right. You should be able to both measure and compute the angle at D. Knowing the distance between the two towers from above and the distance BD is 459 feet, what is the angle at D to the nearest hundredth degree?
C) What is angle CAD in radians? Give your answer rounded correctly to 4 decimal places.
The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.
Step-by-step explanation:
Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.
Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length
tan 88.60°=O/A
tan 88.60°=AB/389
AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)
B.
Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.
tan Ф=O/A where Ф=∠D
tan ∠D =15917/459
tan ∠D =34.6772834701
tan⁻(34.6772834701) =88.35°
C.
Finding angle ∠A in radians will be;
Applying the sum of angles in a triangle theorem
∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°
Changing degrees to radians, multiply value of degrees by π/180°
3.05×π/180 =0.05323254 ⇒ 0.0532 rad
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Tangent of an angle formula :https://brainly.com/question/12003325
Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth
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