By using percentage, the deductible amount is $103.73 for each paycheck. So, option b is correct.
We are provided by some percentage here. A percentage is a part of a whole that is expressed in hundredths.
Sally paid 38% of her annual health insurance premium of $4,350.00 and left with the 62%.
62% of $4,350.00 is equal to $2697
62/100 x 4,350.00 = 2697
So, the net amount that Sally has to pay is $2697 in equal distribution from her 26 paychecks throughout the calendar year.
Therefore, each paycheck will be deducted as = $2697/26
= $103.73
Hence, $103.73 will be deducted from her paycheck.
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following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in.
The probabilities from this problem are given as follows:
a) The probability that a student participates in exactly three activities is 0.23.
b) The probability that a student participates in less than three activities is 0.68.
c) The probability that a student participates in at least two activities is 0.82.
Item aThe event associated with exactly three activities is given by:
X = 3.
Hence, from the table on the image at the end of the answer, the probability is:
P(X = 3) = 0.23.
Item bThe events associated with less than three activities are given by:
X = 0, X = 1 and X = 2.
Hence, from the table on the image at the end of the answer, the probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.05 + 0.13 + 0.45 = 0.68.
Item cThe events associated with at least two activities are given by:
X = 2, X = 3, X = 4.
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.45 + 0.23 + 0.14 = 0.82.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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Complete the point-slope equation of the line through (-1,-10)(−1,−10)left parenthesis, minus, 1, comma, minus, 10, right parenthesis and (5,2)(5,2)left parenthesis, 5, comma, 2, right parenthesis.
Answer:
y + 10 =2( x +1)
or
y -2 + 2( x -5)
These both name the same line.
Step-by-step explanation:
First we need to find the slope. The slope is the change in y over the change in x. In the point (-1,-10)
-1 is the x and -10 is the y.
In the point (5,2)
5 is the x and 2 is the y.
[tex]\frac{2- -10)}{5 - -1)}[/tex] Subtracting a negative is the same as adding a positive.
[tex]\frac{2+ 10}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2
We know know the slope. We will use the form
y - [tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex]) we will plug in the numbers that we know.
If we use point (-1, -10)
y -- -10 = 2(x - -1)
y + 10 = 2( x+1)
If we use the point (5,2)
y -2 = 2(x -5)
Both equations mean the same thing.
Giải phương trình lượng giác sau
sin2x+cos2x+sin4x=1
Answer:
2
Step-by-step explanation:
Given, cosx+cos
2
x=1
⇒cosx=1−cos
2
x
⇒cosx=sin
2
x
Squaring both sides we get
⇒cos
2
x=sin
4
x .....(1)
⇒sin
4
x−cos
2
x=0
Adding both side 1, we get
⇒sin
4
x+1−cos
2
x=1
∴sin
2
x+sin
4
x=1 Proved.
In a survey 34% of population was found to know hindi 46% to know english and 23% to know both languages.What is the percentage of those knowing neither hindi nor english
The percentage of population of those knowing neither Hindi nor English is 43%.
What is percentage?The outcome of multiplying a given number by a percentage is the percentage. Since a percentage is a portion of a number or quantity, they are typically smaller than the actual number. There are instances, though, where the percentage exceeds the number. If the percentage is greater than 100%, this would occur.
A percentage is simply a certain proportion of a number.
Typically, the phrase "percent of" comes after the quantity.
So, 70% of 50 is 35, for instance.
50 is the quantity, 35 is the percentage, and 70% is the percent in this sentence.
The total percentage of population is represented by 100%, so let the population be 100
No. of population that knows only Hindi = 34 - 23
= 11
No. of population that knows only English = 46 - 23
= 23
No. of population that knows both = 23
The sum = 11 + 23 + 23
= 57
No. of population that knows neither Hindi nor English = 100 - 57
= 43
And percentage = 43%
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|2b + 2| = 6
please help put
Answer:
b is -4
Step-by-step explanation:
we're given:
|2b + 2| = 6
substituting b for -4 :
|2(-4) + 2| = 6
|-8 + 2| = 6
|-6| = 6
any negative number between absolute value becomes positive.
Hence b is -4
Completely factor 4s4 +8s3 - 60s².
O 45² (s - 5)(s + 3)
O This polynomial does not factor.
4s² (s 15)(s + 4)
4s² (s + 5)(s − 3)
Answer:
4s² (s + 5)(s − 3)
Step-by-step explanation:
Factor [tex]4s^{4} +8s^{3}-60s^{2}[/tex]
45² (s - 5)(s + 3)
This polynomial does not factor.
4s² (s 15)(s + 4)
4s² (s + 5)(s − 3)
The common term is [tex]4s^{2}[/tex] so:
[tex]4s^{2} (s^{2} +2s-15)[/tex]
assume:
a = 1
b = 2
c = -15
Find two numbers that sum to 2 and multiply to -15:
-3+5 = 2
-3 × 5 = -15
so [tex](s^{2} +2s-15) = (s-3)(s+5)[/tex]
Plug in to [tex]4s^{2} (s^{2} +2s-15)[/tex]
to get: [tex]4s^{2} (s-3)(s+5)[/tex]
Lesley wants to be a soccer star. To be scouted by a professional team, she needs to score an average of at least 4 goals per game. Her current stats are 6 goals, 1 goal, no goals, and 3 goals. 1. How many goals does she need to score in her next game to get scouted? 2. When this inequality is graphed will the limit be an open or closed circle?
If we define x as the number of goals that she needs to do, we can write the inequality:
x ≥ 10.
And to graph that we need to use a closed dot at x = 10.
How many goals does she need to score on the next game?
We know that Lesley wants to have an average of 4 games per day.
Until now she played:
Game 1: → 6 goals.Game 2: → 1 goals.Game 3: → 0 goals.Game 4: → 3 goals.Now we assume that on game 5 she does x goals, and if we want the average to be 4 or larger, then we can write:
(6 + 1 + 0 + 3 + x)/5 ≥ 4
Now we need to solve that inequality, we can rewrite:
(6 + 1 + 0 + 3 + x)/5 ≥ 4
(10 + x)/5 ≥ 4
(10 + x) ≥ 4*5
(10 + x) ≥ 20
x ≥ 20 - 10
x ≥ 10
So she needs to do at least 10 goals on the next game.
Now, when graphed we will have an open or a closed circle? In the inequality we have the symbol " ≥ " so x = 10 is a solution, then we need to use a closed circle.
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The formula t= represents the time t in seconds that it takes an object
4
to fall from a height of h feet. If a rock falls from 125 feet, estimate how long
it will take the rock to hit the ground. Estimate the square root to the nearest
integer.
Answer: 3 seconds
Step-by-step explanation:
t = √h / 4
t = (√125) / 4
t = (5√5) / 4
t = 2.795 seconds
Because integer numbers can't be decimals so we round it to 3.
Algebra 2.6 2.7
Helpmeeeeeeeee
a)Percentage increase is 23.07%.
b)Percentage increase is 28.5%.
What is percentage?Percentage is a relative value that represents hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is
([tex]\frac{value}{total value}[/tex])100%.
Given Data
Percentage increase = [tex]\frac{final value - starting value}{starting value}[/tex]× 100
a) Cost = $65
New cost = $70
Difference = 5
Equating,
Percentage increase = [tex]\frac{70-65}{65}[/tex] × 100
Percentage increase = [tex]\frac{15}{65}[/tex] × 100
Percentage increase = 23.07%
Percentage increase is 23.07%.
b) Cost = $45
New cost = $35
Equating,
Percentage increase = [tex]\frac{45-35}{35}[/tex] × 100
Percentage increase = [tex]\frac{10}{35}[/tex] × 100
Percentage increase = 28.5%
Percentage increase is 28.5%.
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Solve the simultaneous equations 3 x + 2 y = 7
2 x − 3 y = − 4
Pls pls pls help me
On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2 .
In the question,
it is given that the simultaneous equations are
3x+2y=7 ....(i)
and
2x-3y=-4 ...(ii)
to solve these equations ,
we multiply equation(i) with 2 and
multiply equation(ii) with 3 .
So , the equations become
6x+4y=14 ...(iii)
and
6x-9y=-12 ....(iv)
we subtract equation (iv) from (iii) ,
So,
(6x+4y)-(6x-9y)=14-(-12)
Solving further ,
6x+4y-6x+9y = 14+12
4y+9y = 26
13y = 26
y = 26/13
y = 2
Substituting the value of y as 2 in equation (iii) , we get
6x+4(2) = 14
6x + 8 = 14
6x = 14-8
6x = 6
x=6/6
x=1
hence x=1 and y=2 .
Therefore , On solving the simultaneous equations 3x+2y=7 and 2x-3y=-4 , the value of x is 1 and the value of y is 2 .
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Which is an equation of the line through (0, 0) and (2, –3)?A.y=−23xy=− 32 xB.y=32xy= 23 xC.y=−32xy=− 23 xD.y=23xy= 32 x
The equation of the line passing through (0, 0) and (2, –3) is y = - 3 / 2 x
How to find the equation of a line?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, 0)(2, -3)
m = y₂ - y₁ / x₂ - x₁
m = -3 - 0 / 2 - 0
m = - 3 / 2
Therefore, the y-intercept is 0.
The equation of the line is y = - 3 / 2 x
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GJ = 4x - 8, and GH = 120
The value of x if H is the midpoint of GJ is 31 units.
How to find value of x using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points.
Therefore, H is the midpoint of GJ
Hence,
GJ = GH + HJ
GJ = 4x - 8
GH = 120
Therefore, GH and HJ are congruent because H is the midpoint of GJ
GH = HJ
Hence,
4x - 8 = 120 + 120
4x - 8 = 240
4x = 240 + 8
4x = 248
x = 248 / 4
x = 31
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Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given equation.
5x+2y=10 and passes through (-6, 7)
y = -5/2x-8 is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.
Given that, the line 5x+2y = 10 passes through the point (-6,7) and is parallel to the given equation. Now, we have to write an equation in the slope-intercept form.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as: y = mx + b.
where, m is the slope of the line and b is the y-intercept of the line.
Let's proceed to find the equation.
5x+2y = 10
2y = -5x+10
y = -5/2x+10/2
y = -5/2x+5
Now, comparing with y = mx+b (slope-intercept form)
m = -5/2 and b = 5
As the two lines are parallel with each other then the slope of other line will also be same as m = -5/2
Now, the line passing through the point (-6,7)
⇒ x₁ = -6 and y₁ = 7
y-y₁ = m(x-x₁) ..........(1)
putting values in equation (1), we get
y-7 = -5/2(x-(-6))
⇒ y-7 = -5/2(x+6)
⇒ y = -5/2x-15+7
⇒ y = -5/2x-8
This is the slope-intercept form for the lines that passes through the point (-6,7) and parallel to 5x+2y = 10.
Hence, y = -5/2x-8 is the required answer.
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Find P on NM that is the given fractional distance from N to M. Such that, 1/5 is the fractional distance from N to M, and N(-3,-2),M(1,1)
please help
The point P is ( -2.2 , -1.4) on the line segment NM, which represents the fractional distance from N to M.
Given:
Fractional Distance from n to m is 1/5 and
points are N (-3, -2), M (1, 1).
From the graph we can see that the distance from M to R is 4,
And the distance between N to R is 3.
So, 1/5 MR = 1/5 (4)
=4/5
And, 1/5 NR=1/5 (3)
=3/5
By substituting these values in N (-3, -2),
We get a point p on MN.
-3 + 4/5 = -2.2
and -2 + 3/5 = -1.4
Hence p(-2.2, -1.4) is the point on line segment NM.
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To enroll in lessons to learn about pottery wheel throwing, you must pay an enrollment of $20 for each lesson. The pottery studio also charges you $2. 99 per pound for the amount of clay used.
Write an expression for the total cost of a person using c pounds of clay during a lesson. Use the expression to calculate the cost of a lesson where Sam uses 3. 5 pounds of clay
The expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.
What are expressions?Using the operations +, -, ×, or ÷, a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that only contain numbers and mathematical operators.So, the expression for the total cost of the person using c pounds of clay:
2.99c + 20 = Total costTotal cost when Sam uses 3.5 pounds of clay:
2.99c + 20 = Total cost2.99(3.5) + 20 = Total cost10.465 + 20 = Total cost$30.465 = Total costTherefore, the expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.
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I beg for help please!
What is the equation of the line in slope-intercept form?
Answer:
The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.
Answer:
y = x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line
m = [tex]\frac{10-6}{4-0}[/tex] = [tex]\frac{4}{4}[/tex] = 1
the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = x + 6 ← equation of line
Write an equation that represents the line. *Use exact numbers*
The equation that represents the line is,
y+3 = 3/4(x-2)
We are asked to find the equation that represents the line shown in the figure.
We need the slope of the line and a point on the line to find the equation of the line.
The equation of a line can be written in the slope-intercept form given below as,
y-y₁ = m(x-x₁),
where m is the slope of the line and (x₁, y₁) is a point on the line.
From the figure we can find two points on the line which are (x₁ ,y₁) = (2, -3) and (x₂, y₂) = (-2, -6).
Hence slope, m = (y₂-y₁)/(x₂-x₁)
= (-6- -3)/(-2-2)
= 3/4
So the equation that represents the line is
y - -3 = 3/4(x-2)
⇒ y+3 = 3/4(x-2)
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21. If x: y = 3: 4, find (3x + 4y): (5x + 6y).
Correct option is B)
Put x=3y=4
(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)
=(9+16):(15+24)
=25:39
suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per hour. what is the rate of change of the surface area s when the radius is 4?
When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr
As the radius r is shrinking at the rate of two inches per hour, it can be represented as;
dr/dt = -2 in / hr
Here, the negative sign represents the shrinking of the snowball with time t.
The surface area of a sphere can be represented by the formula;
S = 4πr²
Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;
dS/dt = d/dt (4πr²)
dS/dt = 4π (d/dt) (r²)
dS/dt = 4π × 2r (dr/dt)
Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;
dS/dt = 4π × 2(4)(-2)
dS/dt = -64π
Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.
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Evaluate the function below for the given value of x
Answer:
Step-by-step explanation:
- 4 ≤ 3 , then f(- 4) = [tex]\frac{1}{2}[/tex] ( - 4) + 1 = - 1
2 ≤ 3 , then f(2) = [tex]\frac{1}{2}[/tex] (2) + 1 = 2
3 ≤ 3 , then f(3) = [tex]\frac{1}{2}[/tex] (3) + 1 = 2.5
5 > 3 , then f(5) = 9×5 - 4 = 41
HELP HELP ME ASAP!!!
At LEAST ONE value of x MUST be 7 (x = 7 or x = ?)
My teacher said that a, b, and c ALL have to be greater than 0 and b has to be greater than 1
At LEAST ONE extraneous solution
Part a
Let [tex]a=2[/tex]. Then, we have that
[tex]7+2=\sqrt{7b+c}\\\\81=7b+c[/tex]
We can let [tex]b=11[/tex] and [tex]c=4[/tex], meaning the equation is [tex]x+2=\sqrt{11x+4}[/tex].
Part b
[tex]x+2=\sqrt{11x+4}\\\\x^2 +4x+4=11x+4\\\\x^2 -7x=0\\\\x(x-7)=0\\ \\ x=0, 7[/tex]
Substituting both of these values into the equation, we see they are both solutions.
Part c
[tex]x+10=\sqrt{10x+219}[/tex]
find the value of x and y.
(8x-31) (5y+35) (6x+3)
Answer: 8x + -31 + 5y + 35 + 6x + 3 = 180. Reorder the terms: -31 + 35 + 3 + 8x + 6x + 5y = 180.
Which Of the Following Is not a regular polygon
A) Square B) Equilateral Triangle C) Rectangle D) Regular Hexagon
Answer:
Rectangle
Step-by-step explanation:
It is because the length and breadth are not equal
4. On her way to work each morning, Alexia purchases a small cup of coffee for $6.50 from the coffee
shop.
Independent Quantity:
Dependent Quantity:
Units:
Units:
On her way to work each morning, Alexia purchases a small cup of coffee for $6.50 from the coffee shop. So the
Independent Quantity: time, Units: days
Dependent Quantity: cost, Units: dollar($)
What is Independent and Dependent Quantity?The dependent and independent quantity or variable are the two main factors in an experiment.
In a scientific experiment, the variable that is altered or controlled to examine the effects on the dependent variable is referred to as an independent quantity.
In a scientific experiment, the variable under test and the measurement is the dependent quantity.
On the independent quantity, the dependent quantity is said to be "dependent." The impact on the dependent quantity is seen as the experimenter modifies the independent quantity, and this effect is noted.
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A person driving her car at 12.5 m/s approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning red, and she is 28 m away from the beginning of the intersection, which is 15 m wide, as shown below. Using the gas pedal she can accelerate at 3.5 m/s2 and using the brake pedal she can accelerate at –5.8 m/s2. Ignoring reaction time and car length, determine whether she should try to stop or speed up to be a legal driver.
She should try to stop the car.
We will discuss the possibilities of trying to stop and trying to speed up in 2s and find the distance she travels to get into a conclusion.
If she try to stop, then the acceleration, a = -5.8 m/s²
Initial velocity, v₀ = 12.5 m/s
Final velocity, v₁ = 0 m/s [Since the car is stopped]
Let d be the distance the car travels before stopping.
Then, we have, v₁² = v₀² + 2ad
Therefore, d = v₁²-v₀²/2a
= 0-(12.5)²/2 x (-5.8)
= 156.25/11.6
= 13.47 m
So she can stop in time as she is 28m far from the beginning of the intersection.
If she try to speed up, then the acceleration of the car, a = 3.5 m/s²
Initial velocity of the car, v₀ = 12.5 m/s
Time she have, t = 2 s
Let d be the distance the car travels in 2 s.
Then, d = v₀t +(1/2)at²
= 12.5 x 2 + (1/2) x 3.5 x 2²
= 25 + 7
= 32 m
She is 28 m before the beginning of the intersection which is 15 m wide. So if she speed up she will be in the middle of the intersection when the light turns red and may have to stop.
Hence as a legal driver, she should try to stop the car.
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Solve the inequality. |x − 3| + 8 > 6
The inequality expression given has a solution of 1 < x < 5.
Solving inequalities
Inequality are expressions not separated by an equal sign. Given the inequality expression below;
|x − 3| + 8 > 6
The expression can be divided into x − 3 + 8 > 6 and -(x - 3) + 8 > 6
For the inequality x − 3 + 8 > 6
x - 3 > 6 - 8
x - 3 > -2
x > 1
For the inequality -(x - 3) + 8 > 6
-(x - 3) > 6 - 8
-(x - 3) > - 2
x - 3 < 2
x < 5
Hence the solution to the given inequality is 1 < x <5
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Geometry, which is congruent to <GFH
(it's a test and I'm not complete sure if that one's correct)
Answer:
A)
Step-by-step explanation:
vertical angle rule
If Vivian is eating pizza, then she is at Big Slice Pizza.
If Vivian is at Big Slice Pizza, then she is eating pizza.
Is the second conditional the contrapositive, converse, or inverse of the first conditional?
contrapositive
converse
inverse
The second conditional statement is the converse of the first.
A conditional statement has two phrases and each phrase starts with an 'if' and the other with a 'then'.
Symbolically, it is also expressed as 'p ⇒ q'.
The converse of such a statement is expressed as 'q ⇒ p'.
The first conditional statement given is 'If Vivian is eating pizza, then she is at Big Slice Pizza.'
The second conditional statement given is 'If Vivian is at Big Slice Pizza, then she is eating pizza.'
From the definition of the converse of a conditional statement, the second statement is clearly the converse of the first statement.
Contrapositive of the conditional statement 'p ⇒ q ' is 'not q ⇒ not p'.
Inverse of the conditional statement 'p ⇒ q ' is 'not p ⇒ not q'
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Which graph represents y=3√x+6-3?
The graph shown below represents the equation y =[tex]3\sqrt{x+6} -3[/tex]
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.
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Un árbol que mide 22 metros de altura está creciendo a un ángulo de 83° con respecto al suelo (ver la figura siguiente). Miranda se para a cierta distancia de la base del árbol, se da cuenta que el ángulo de elevación desde el suelo hasta la parte alta del árbol es 32°. ¿A qué distancia está ella de la base del árbol? Redondear la respuesta a la décima más cercana de un metro.
Answer: ≈37.8 m
Step-by-step explanation:
The sum of the angles of a triangle is equal to 180°.
⇒ х+32°+83°=180°
х+115°=180°
x+115°-115°=180°-115°
x=65°
The sine theorem goes like this: the sides of a triangle are proportional to the sines of the opposing angles.
[tex]\displaystyle\\\frac{22}{sin32^0} =\frac{S}{sin65^0} \\\\Multiply\ both \ parts\ of \ the \ equation\ by\ sin65^0:\\\\S=\frac{22(sin65^0)}{sin32^0} \\\\S\approx\frac{22(0.91)}{0.53}\\\\ S\approx37.8 \ m[/tex]