Answer:
B. 5.2%
Step-by-step explanation:
Total number of tables = 20
Number of tables next to window = 5
Number of tables next to salad bar = 5
Probability that the first customer chooses the window table = 5 out of 20 = [tex]\frac{5}{20}[/tex]
When this table is chosen, the total remaining tables are 19 out of which 4 tables are next to windows.
So, now the probability that a customer will choose a window table = 4 out of 19 = [tex]\frac{4}{19}[/tex]
Since the selection of two customers is independent of each other, the probability that two customers will chose the window table will be the product of probabilities of their individual selections.
Therefore, the probability that the next two customers will choose to sit at the window = [tex]\frac{5}{20} \times \frac{4}{19} = 0.052[/tex]
Thus, the probability that the next two customers will choose to sit at the window is 0.052 or 5.2%
A river is flowing downstream at rate of 2 km/h. Murray can swim at a rate of 3 km/h. Murray jumps in and swims downstream for a certain distance then turns around and swims upstream back to the start. In total it takes 30 minutes. How far did Murray swim downstream?
Answer:
Murray can swim 3/4 km downstream
Step-by-step explanation:
Since the current adds to his speed and
then subtracts the same amount, you can
disregard the current
d=r*t
Convert 15 min to hrs ( time to swim downstream )
15(1/60)=1/4 hours
d=3(1/4)
d=3/4 km downstream.
Hence Murray can swim 3/4 km downstream....
Final answer:
Murray swam 0.417 km downstream before turning around and swimming back upstream. The calculation involves solving a simple algebraic equation using Murray's swimming speed and the river's flow rate, within the total time frame of 30 minutes.
Explanation:
The student is asking about a problem involving rates and time, which is a common topic in algebra and physics. In this scenario, Murray is able to swim at a speed of 3 km/h in still water, and the river flow adds an extra 2 km/h when swimming downstream, making his effective downstream speed 5 km/h. When swimming upstream, Murray has to work against the river flow, reducing his effective speed to 1 km/h (3 km/h - 2 km/h). Given that the total time spent swimming is 30 minutes (0.5 hours), we need to determine the distance Murray swam downstream before turning back.
Let the distance Murray swam downstream be d kilometers. The time to swim downstream at 5 km/h is d/5 hours, and the time to swim back upstream at 1 km/h is d hours. The sum of these times equals the total time Murray was swimming:
d/5 + d = 0.5
By solving the equation, we find that d = 0.417 km. Therefore, Murray swam 0.417 kilometers downstream before turning around and swimming back upstream.
5 MINUTE TIME LIMIT LEFT Consider the polynomial expression below.
[tex]x^{3} -3x^{2} +81x-243[/tex]
Rewrite the polynomial in the form (x - d)(x - e)(x + f), where d is a real number and e and f are complex numbers of the form bi.
[tex]x^3-3x^2+81x-243=\\x^2(x-3)+81(x-3)=\\(x^2+81)(x-3)=\\(x-3)(x-9i)(x+9i)[/tex]
Which of these values cannot represent the probability of an event happening?
0.33
56%
7/8
1.2
Answer:
D.
Step-by-step explanation:
The last option, 1.2, cannot represent the probability of an event happening since it is more than 100% (120%). And event cannot have a higher probability of happening than "happening".
A. 0.33 is a valid response, since it represents 33%.
B. 56% is also a valid response.
C. 7/8 is also a valid response since it represents 0,875 or 87,5%.
Hope it helped,
BiologiaMagister
D. 1.2
Hope i Helped ❤
Suzie bought an antique jewelry box for $34.50. It originally cost $8.75 when it was made. Its value has increased $0.75 a year since it was made and it is now 83 years old. If Suzie were to sell it for what it is worth, how much money would she make? (Please show steps)
Answer:
if she would sell it for what it is worth now she would make $36.50
Step-by-step explanation:
0.75 x 83 = 62.5
62.5 + 8.75 = 71
71 is how much it is worth now
71 - 34.5 = 36.5
36.50 is how much she would make
Answer:
$36,50
Step-by-step explanation:
That is correct to me. You do those exact steps to arrive at that answer.
Pleasr help me ASAP! Thank you^-^ If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth.
Please look at picture
A: 656.2 units²
B: 400 units²
C:256.2 units²
D:456.2 units²
Answer:
D:456.2 units²
Step-by-step explanation:
Step 1: Area of all 4 sides of cuboid
Area of rectangle = 4 x length x breadth
Area of rectangle = 4 x 10 x 5
Area of rectangle = 200
Step 2: Calculate bottom of cuboid
Area = length x breadth
Area = 10 x 10
Area = 100
Step 3: Calculate slant height of pyramid
c² = a² + b²
c² is hypotenuse
a² is the base which is half of w (10/2 = 5)
b² is y which is 6
c² = a² + b²
c² = 5² + 6²
c = √61
Step 4: Calculate area of one face of the pyramid
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 10 x √61
Area of triangle = 5√61
Step 5: Calculate areas of all 4 faces of the pyramid
4 x 5√61 = 20√61
Step 6: Calculate the total surface area
Total surface area = 200 + 100 + 20√61
Total surface area = 456.2
The surface area of the figure is 456.2 units²
Option D is correct.
!!
In the drawing below, line n is a transversal that intersects two parallel lines. What is the measure of Angle 4?
40°
50°
130°
140°
Answer:
140°
Step-by-step explanation:
<3 = 40 because they are vertical angles
<3 +<4 = 180 because they are same side interior angles
40 + <4 = 180
Subtract 40 from each side
40-40 + <4 = 180-40
<4 = 140
Which values of x would make a polynomial equal to zero if the factors of the
polynomial were (x-3) and (x-7)?
Answer:
x = 3 and x = 7
Step-by-step explanation:
Equate the product of the factors to zero, that is
(x - 3)(x - 7) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 7 = 0 ⇒ x = 7
Final answer:
To find the values of x that make a polynomial equal to zero, set each factor equal to zero and solve for x. The values of x that would make the polynomial equal to zero are x = 3, and x = 7.
Explanation:
To find the values of x that make a polynomial equal to zero, you need to set each factor equal to zero and solve for x.
Set x-3=0 and solve for x to get x=3.
Set x-7=0 and solve for x to get x=7.
Therefore, the values of x that would make the polynomial equal to zero are x = 3 and x = 7.
Find the median of the following data:
10,16, 15, 14, 8, 21, 10, 5, 19, 18, 4, 5, 16, 12, 10,9
Answer:
The median is 11.
Step-by-step explanation:
First arrange the data in ascending order:
4, 5, 5, 8, 9 , 10, 10, 10, 12, 14, 15, 16, 16, 18, 19, 21
There are 16 numbers so the median is the mean of the middle 2 numbers in the list. That is the mean of the 8th and ninth number.
Median = 10 + 12 / 2
= 11.
Answer:
answer is 12 ape x
Step-by-step explanation:
i am not sure why tho to be honest if a verified answer is 11
Write 65% as a fraction in simplest form.
Answer:
13/20
Step-by-step explanation:
This is actually pretty simple. I had trouble with this for the longest time but it makes sense to me now. A number that is a percent is equal to that number over 100.
65%=65/100
Then all you have to do is simplify! (yaaay)
65/100=13/20
If you need anymore help with this or anything else just let me know!
Write 65% as a fraction in simplest form.
13/20
65%=65/100
65/100=13/20
When is a rhombus a rectangle?
Answer: D
Step-by-step explanation:
They are rectangles when the sides are 90 degrees. :)
A rhombus is a rectangle when all its angles are right angles.
What is a rectangle?
A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.
Given is a rhombus.
A rhombus is a rectangle when all its angles are right angles. Due to this, the tilt of the vertical sides of rhombus will become 0 degrees.
Therefore, a rhombus is a rectangle when all its angles are right angles.
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Can I get some help with this question? Solve 3(x + 2) > x.
Answer:
x > -3
Step-by-step explanation:
We are given the following inequality that we are to solve:
[tex]3(x+2)>x[/tex]
Applying the distributive property of multiplication on the left side of the inequality to get:
[tex] 3 x + 6 > x [/tex]
Rearranging the inequality:
[tex] 3 x - x > - 6 [/tex]
[tex] 2 x > - 6 [/tex]
[tex] x > \frac { - 6 } { 2 } [/tex]
x > -3
Answer:
[tex]\large\boxed{x>-3\to\{x\ |\ x>-3\}\to x\in(-3,\ \infty)}[/tex]
Step-by-step explanation:
[tex]3(x+2)>x\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(2)>x\\\\3x+6>x\qquad\text{subtract 6 from both sides}\\\\3x+6-6>x-6\\\\3x>x-6\qquad\text{subtract x from both sides}\\\\3x-x>x-x-6\\\\2x>-6\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{-6}{2}\\\\x>-3[/tex]
Over what interval is the quadratic function decreasing?
I ONLT HAVE 5 min left please answer
Answer:
See below.
Step-by-step explanation:
It decreases in the interval where x > -2.
In interval notation this is (-2, ∞).
The quadratic function decreasing at x>-2.
What is a quadratic function?A quadratic polynomial is a polynomial of degree two in one or more variables.
Given is a graph,
It decreases in the interval where x > -2.
In interval notation, this is (-2, ∞).
Hence, the quadratic function decreasing at x>-2.
For more references on a quadratic function, click;
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Solve the three equations in the table by factoring. Then enter those factors and the solutions in the table.
Equations: x^2 + 10 = 0, 4x^2 + 25 = 0, x^2 + 121 = 0
Factors: _______, ________, _______
solutions: _______,________, _______
Solutions are denoted by index. Most of the equations you listed has 2 solutions.
Number one cannot be factored using whole numbers.
Number two.
[tex]
4x^2+25=0\Longrightarrow(2x+5)(2x-5)=0 \\
x_1\Longleftrightarrow\boxed{2x+5=0\Longrightarrow x=-\dfrac{5}{2}} \\
x_2\Longleftrightarrow\boxed{2x-5=0\Longrightarrow x=\dfrac{5}{2}}
[/tex]
Number three.
[tex]
x^2+121=0\Longrightarrow(x+11)(x-11)=0 \\
x_1\Longleftrightarrow\boxed{x+11=0\Longrightarrow x=-11} \\
x_2\Longleftrightarrow\boxed{x-11=0\Longrightarrow x=11}
[/tex]
Hope this helps.
Check the picture for the correct answer:
Graph the linear equation in three plots: -x+2y=11
Answer:
In the attachment.Step-by-step explanation:
Convert the given equation to the form y = mx + b:
[tex]-x+2y=11[/tex] add x to both sides
[tex]2y=x+11[/tex] divide both sides by 2
[tex]y=\dfrac{1}{2}x+\dfrac{11}{2}[/tex]
It's a linear function.
We need only two points to plot the graph. Select any two x values, insert into the equation and calculate y values.
for x = 1
[tex]y=\dfrac{1}{2}(1)+\dfrac{11}{2}=\dfrac{1}{2}+\dfrac{11}{2}=\dfrac{12}{2}=6\to(1,\ 6)[/tex]
for x = -5
[tex]y=\dfrac{1}{2}(-5)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to(-5,\ 3)[/tex]
Helpppppppppppp me please
Answer:
8*6 + 12*h ≥144
Step-by-step explanation:
8 dollars at the movie theater
12 dollars at the restaurant
scheduled 6 hours at the movie theater
need to make at least 144 dollars
The money he makes is the hours times the rate
rate * hours at movie theater + rate *hours at restaurant
This must be greater than or equal to 144
Let h be the hours at the movie theater
8*6 + 12*h ≥144
Rahul simplified an expression. His work is shown below.
7(8.5-1.5)+8divided by2
Step 1. 7(7)+8 divided by 2
Step 2. 49+8 divided 2
Step 3. 57 divided by 2
Step 4. 28.5
Where did Rahul make his first mistake?
Answer: Step 3
Step-by-step explanation:
He should have divided 8 by 2 and then added it to 49.
In the third step, Rahul made his first mistake. Simplification is to be done using the BODMAS rule.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
Rahul simplified an expression. His work is shown below.
The expression is given below.
7 (8.5 - 1.5) + 8 / 2
Step 1. 7 (7) + 8 / 2
Step 2. 49 + 8 / 2
Step 3. 49 + 4
Step 4. 53
In the third step, Rahul made his first mistake.
More about the simplification link is given below.
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A parabola with vertex (1,5) and y-intercept
(0,2) crosses the x-axis in two places. One x-
intercept is at (-0.29,0). Find the other x-
intercept. Separate the values with a comma.
Answer:
So the other x-intercept we are looking for is (2.29 , 0).
Step-by-step explanation:
The equation for a parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex] where (h,k) is the vertex.
So we are given (h,k)=(1,5) so let's plug that in. This gives us the following equation for our parabola:
[tex]y=a(x-1)^2+5[/tex].
Now we need to find [tex]a[/tex]. Let's find [tex]a[/tex] by using another point (x,y) given. We are given that (0,2) is on our parabola. So when x is 0, y is 2.
This gives us the equation:
[tex]2=a(0-1)^2+5[/tex]
[tex]2=a(-1)^2+5[/tex]
[tex]2=a(1)+5[/tex]
[tex]2=a+5[/tex]
[tex]2-5=a[/tex]
[tex]-3=a[/tex]
So our parabola in vertex form looks like this:
[tex]y=-3(x-1)^2+5[/tex]
Now we are asked to find the x-intercepts.
You can find the x-intercepts by setting y equal to 0 and solving for x.
So let's do that:
[tex]0=-3(x-1)^2+5[/tex]
Subtract 5 on both sides:
[tex]-5=-3(x-1)^2[/tex]
Divide both sides by -3:
[tex]\frac{5}{3}=(x-1)^2[/tex]
Take the square root of both sides:
[tex]\pm \sqrt{\frac{5}{3}}=x-1[/tex]
Add 1 on both sides:
[tex]\pm \sqrt{\frac{5}{3}}+1=x[/tex]
So the two solutions in exact form are
[tex]x=\sqrt{\frac{5}{3}}+1 \text{ or } -\sqrt{\frac{5}{3}}+1[/tex]
Putting both into calculator (separately) gives:
[tex]x \approx 2.29 \text{ or } -0.29[/tex]
So the other x-intercept we are looking for is (2.29 , 0).
Write the equation of the line shown in the graph. Please help.
Answer:
y = 3
Step-by-step explanation:
The y-coordinate of all points on the graph is 3.
The equation is y = 3
Answer:
y = 3
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.
In this case the line passes through points with a y- coordinate of 3, hence
Equation of horizontal line is y = 3
Circle A has been dissected into 16 congruent sectors. The base of one sector is 1.95 units, and its height is 4.9 units. What is the approximate area of circle A?
circle A is dissected into 16 congruent sectors, one sector is highlighted
27.52 units2
48.92 units2
75.39 units2
76.44 units2
Answer:
[tex]A=76.44\ units^{2}[/tex]
Step-by-step explanation:
To find the approximate area of the circle, calculate the area of one sector and then multiply by 16
Remember that
The area of a triangle (one sector) is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
therefore
The approximate area of the circle is equal to
[tex]A=(16)\frac{1}{2}(1.95)(4.9)[/tex]
[tex]A=76.44\ units^{2}[/tex]
Answer:
D.76.44 square units
Step-by-step explanation:
We are given that
Base of one sector=b=1.95 units
Height of sector=h=4.9 units
Total number of sectors=16
Area of one sector is equal to area of triangle (approximately)
Area of sector=[tex]\frac{1}{2}bh[/tex]
Using the formula
Area of one sector=[tex]\frac{1}{2}(1.95)(4.9)=4.7775[/tex] square units
Area of circle A=[tex]16\times [/tex]area of sector
Area of circle A=[tex]16\times 4.7775=76.44[/tex] square units
Hence,option D is true.
32 = [4(2 + 5) - 2 • 6]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\bold{{32 = [4(2 + 5) - 2\times6]}}[/tex]
[tex]\text{[4(2 + 5) - 2} \ \times \ 6][/tex]
[tex]\text{Do PEMDAS}\downarrow[/tex]
[tex]\huge\text{Parentheses}\\\huge\text{Exponents}\\\huge\text{Multiplication}[/tex] [tex]\huge\text{Division}\\\huge\text{Addition}\\\huge\text{Substraction}[/tex]
[tex]\huge\text{First, we do PARENTHESES}[/tex]
[tex]\huge\text{2 + 5 which equals 7}[/tex]
[tex]\huge\text{4(7) - 2(6)}[/tex]
[tex]\huge\text{Next step is multiplication since we don't have}[/tex] [tex]\huge\text{exponents}[/tex]
[tex]\huge\text{4(7) = 28}\\\\\huge{\text{2(6) = 12 }[/tex]
[tex]\huge\text{Thirdly, we have to do subtraction since}[/tex] [tex]\huge\text{we don't have have any division or addition}[/tex]
[tex]\huge\text{28 - 12 = 16}[/tex]
[tex]\boxed{\boxed{\huge\bf{Answer: 32\neq16\ so,\ it \ is \ FALSE}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Consider the equation and its solution.
-15(x-[])=25
-15x+30=25
-15x=-5
x=1/3
What number should be in the empty box?
A. -30
B. -2
C. 2
D. 30
Answer:
The correct answer is C. 2.
Step-by-step explanation:
To solve this problem, we should begin with the second step and work backwards in order to find the unknown value. If given the equation -15x + 30 = 25, we should factor out a -15 to simplify. This method is shown below.
-15x + 30 = 25
-15(x-2) = 25
We know this is correct because if we redistribute the -15 through the parentheses using the distributive property, we would get our original equation again. In other words, this answer is confirmed by the fact that -15 * -2 equals positive 30.
However, we need to look closely at the question that is asked. The box that we must fill in is already preceded by a negative sign, thus the correct answer is C. 2.
We can check our work by replacing the box with the number 2, getting -15(x-2) + 30 = 25, which was the equation we got earlier.
Hope this helps!
Answer:
Thank Me later lol
The weight of an object is the force generated by Earth's gravity accelerating the object's ______.
Answer:
mass
Step-by-step explanation:
From the universal law of gravity
[tex]F=G\frac{Mm}{r^2}[/tex]
Where
G = Gravitational constant = 6.674×10⁻¹¹ m³/kg⋅s²
M = Mass of Earth = 5.972×10²⁴ kg
r = Radius of Earth = 6.371×10⁶ m
[tex]\\\Rightarrow ma=G\frac{Mm}{r^2}\\\Rightarrow a=G\frac{M}{r^2}\\\Rightarrow a=6.674\times 10^{-11}\frac{5.972\times 10^{24}}{(6.371\times 10^6)^2}\\\Rightarrow a=9.81\ m/s^2[/tex]
So the force of gravity acting on the mass of an object is
W = m×9.81
∴ Weight of an object is the product of mass and acceleration due to gravity
Using the quadratic formula to solve 5x=6x^2-3, what are the values of x?
Answer:
[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex]
Step-by-step explanation:
First step is to arrange so it is in the form [tex]ax^2+bx+c=0[/tex].
We have [tex]5x=6x^2-3[/tex].
Add we really need to do is subtract 5x on both sides:
[tex]0=6x^2-5x-3[/tex].
Now let's compare [tex]6x^2-5x-3[/tex] to [tex]ax^2+bx+c[/tex].
We have [tex]a=6,b=-5,c=-3[/tex].
The quadratic formula is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
I like to break this into parts:
Part 1: Find [tex]-b[/tex].
Part 2: Find [tex]b^2-4ac[/tex].
Part 3: Find [tex]2a[/tex].
Answering the parts:
Part 1: [tex]-b=5[/tex] since [tex]b=-5[/tex].
Part 2: [tex]b^2-4ac=(-5)^2-4(6)(-3)=25-24(-3)=25+72=97[/tex].
Part 3: [tex]2a=2(6)=12[/tex].
Now our formula in terms of my parts looks like this:
[tex]x=\frac{\text{Part 1} \pm \sqrt{Part 2}}{Part 3}[/tex]
Our formula with my parts evaluated looks like this:
[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex].
Solve for x.
A. 11
B. 17
C. 15
D. 19
The full length of one line times the length of the line outside the circle is equal the the other line.
(7+x)*7 = (13 +8) * 8
Simplify:
7x +49 = 21 * 8
7x +49 = 168
Subtract 49 from each side:
7x = 119
Divide both sides by 7:
x = 17
The answer is B. 17
The value of x for the given circle will be 17 so option (B) will be correct.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circle objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
By theorem in circle
( 13 + 8) × 8 = ( x + 7) × 7
21 × 8 = ( x + 7) × 7
x + 7 = 3 × 8
x = 24 - 7
x = 17
Hence, The value of x for the given circle will be 17.
To learn more about the circle,
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HELP ME!! Please shoe me steps too please
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 5 = - 3(x + 2) ← is in point- slope form
with slope m = - 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
and (a, b) = (6, - 1), hence
y - (- 1) = [tex]\frac{1}{3}[/tex](x - 6), that is
y + 1 = [tex]\frac{1}{3}[/tex](x - 6) → C
Why phaythagores had called a mad person and what was the impact of this statement
Answer: By phaythagores I think you mean pythagorean.
The Pythagorean theorem states that a^2+b^2=c^2. In a right angled triangle the square of the long side is equal to the sum of the squares of the other two sides.
Step-by-step explanation: Pythagoras was a greek philosopher and mathematician. He was often described as one of the purest mathematicians of his time. He had many followers and his teachings are still renowned today.The mystical Pythagoras was so excited by this discovery that he became convinced that the whole universe was based on numbers, and that the planets and stars moved according to mathematical equations!
Answer:
the madnes
Step-by-step explanation:
through: (4,-1), perpendicular to y=x+2
Answer:
y = - x + 3
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 )
y = x + 2 ← is in slope- intercept form
with slope m = 1
Given a line with slope m then the slope of a perpendicular line is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1, hence
y = - x + c ← is the partial equation of the perpendicular line
To find c substitute (4, - 1) into the partial equation
- 1 = - 4 + c ⇒ c = - 1 + 4 = 3
y = - x + 3 ← equation of perpendicular line
Ruben sole t-shirts and hats at a festival his total profit was $168 he made a $6 profit for each t-shirt he sold the also made a profit of $54 from selling hats how many t-shirts did he sell
Answer:
19 t-shirts
Step-by-step explanation:
x= number of t-shirts
6x+54=168; now subtract 54 from both sides of the equation
6x=114; now divide both sides by 6 to isolate the "x"
x=19
Find x (x+4)÷3 = (x+8)÷4
Answer:
x=8
Step-by-step explanation:
(x+4) = (x+8)
------ -------
3 4
Multiply each side by 12 to get rid of the fraction
(x+4) = (x+8)
12 *------ ------- *12
3 4
4*(x+4) = (x+8)*3
Distribute
4x+16 = 3x+24
Subtract 3x from each side
4x-3x+16 = 3x-3x+24
x+16 = 24
Subtract 16 from each side
x+16-16 = 24-16
x = 8
Lynne is hiking. When she stands at the base of the mountain, the horizontal
distance between Lynne and the highest point of the mountain is 588 feet. If
the mountain has an elevation of 2610 feet, what is the angle of elevation
from her starting point to the highest point of the mountain? Round your
answer to the nearest whole number.
Answer:
Angle of elevation of the highest point of the mountain is 77°
Step-by-step explanation:
Lynne is hiking. When she stands at the base of the mountain, the horizontal distance between Lynne and the highest point of the mountain is 588 feet.
Elevation of the mountain is 2610 feet.
We have to calculate the angle of elevation ∠C.
tanC = [tex]\frac{2610}{588}[/tex]
tanC = 4.439
C = [tex]tan^{-1}(4.439)[/tex]
C = 77.30 ≈ 77°
Therefore, angle of elevation of the mountain is 77°