Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building. If he places the ladder at a 60° angle with the ground, about how long is the ladder?
The height of the ladder will be;
⇒ 20√3 feet
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building.
And, He places the ladder at a 60° angle with the ground.
Now,
Let the height of the ladder = h
So, We can formulate;
⇒ sin 60° = 30/h
⇒ √3/2 = 30/h
⇒ h = 30 × 2/√3
⇒ h = 20√3
Thus, The height of the ladder = 20√3 feet
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how to solve 46.2 x 10 with a negative 2 exponent
The lengths of three sides of a quadrilateral are shown below: Side 1: 1y2 + 3y − 6 Side 2: 4y − 7 + 2y2 Side 3: 3y2 − 8 + 5y The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26. Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points) Part B: What is the length of the fourth side of the quadrilateral? (4 points) Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.
Answer:
Part A: 12y^2+9y-21
Part B: 4y^2+6y^2+7y-5
Part C: A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number. Polynomials are closed under the same operations as integers.
Step-by-step explanation:
Hope this helps!!
The question is "Find the number of elements in the following sets"
I sort of get it but it docks me points every time I get it wrong so I don't want to risk it
P(A)=25,P(B|A)=920,P(A∩B)=?
We use the product rule in probability to find P(A∩B) = P(B|A) * P(A). Substituting given values, P(A∩B) = (9/20) * 25, which equals 11.25.
Explanation:The subject area of this question is probability, a topic within mathematics. Here, we are asked to find the intersection of Events A and B given the probabilities of A and the conditional probability of B given A. The rule of product in probability states that P(A∩B) = P(B|A) * P(A).
Let's calculate: P(B|A) is given as 9/20 while P(A) is 25. Thus,
P(A∩B) = P(B|A) * P(A) = (9/20) * 25 = 11.25
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for which of the following numbers does 5 appear in the tens place ?
*check all that applies*
a. 125.634
b. 56.89
c. 1250
d. 3.5
e. 92.57
Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time?
there are 60 minutes marks on a clock
360/60 = 6
6 degree between every minute
From 1:25 to 1:50 there are 25 minutes
25 x 6 = for a total of 150 degrees
150*pi/180 = 5pi/6 radians. ( 2.61799 radians)
Total distance the tip of minute hand has traveled in this time = 2pi*(4 in) * (5pi/6)/(2pi) = 10pi/3 inches (10.47 inches)
Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
PLZ HEEEEEEEELPPPPPPPP!!!!!!!!!
I don't know the answer can someone pls help me
line QP =
11.5*(11.5 +24) = 11.5 * 35.5 = 408.25
SqRT(408.25) = 20.205
round answer to 20 units
20 POINTS PLUS BRAINLIEST!!!
Which function is represented in the table of values?
x 0 -1 -2 -3
y 2 4 8 16
A.
y=2^x
B.
y=2(1/2)
C.
y=-2^x
D.
y=(1/2)^x
If 3a2 – 5ab – 2b2 is factored, one of the factors might be:
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.
h=1+13t-5t^2
Find all values of t for which the ball's height is 8 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].
What is equation?An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.
How to solve equation?We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.
So,
1+13t-[tex]5t^{2}[/tex]=8
[tex]-5t^{2}[/tex]+13t+1-8=0
[tex]-5t^{2}[/tex]+13t-7=0
Removing negative signs.
[tex]5t^{2}[/tex]-13t+7=0
We cannot solve through factorization so e use the following formula:
x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]
t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5
t=(13+-[tex]\sqrt{169-140}[/tex])/10
t=(13+5.38)/10, (13-5.38)/10
t=1.838, 0.762
By rounding off to nearest hundred t=1.84, 0.76.
Hence value of t for which h=8 meters are 1.84 and 0.76.
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Please help !
(cos Θ − cos Θ)^2 + (cos Θ + cos Θ)^2
Answer: The required simplified form is [tex]4\cos^2\theta.[/tex]
Step-by-step explanation: We are given to simplify the following trigonometric expression :
[tex]T=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2.[/tex]
To simplify, first we need to evaluate the terms within the brackets.
The simplification is as follows :
[tex]T\\\\=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2\\\\=0^2+(2\cos\theta)^2\\\\=0+4\cos^2\theta\\\\=4\cos^2\theta.[/tex]
Thus, the required simplified form is [tex]4\cos^2\theta.[/tex]
Factor the following.
If the perimeter of the adult pinball machine is 172 inches, what is the length, in inches of ? Type the numeric answer only in the box below.
PLEASE HELP ME!!!!
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answer:
Step-by-step explanation:
Part A: The two points that represent this situation are (3,43) and (8,113). To put this in standard form, I will first find the slope-intercept form. I did this in the image below.
Now, to find the standard form I will rearrange, 14x -y +1 = 0.
Part B: To put this in function notation I simply take my slope-intercept equation of y=14x+1, and replace y with f(x) so, f(x)=14x+1
Part C: To graph this, put the y, intercept at 1, and give the line a slope of 14/1. Label the x-axis with hours, from 0 - 8, and the y-axis with dollars, from 0-150.
what is the least common multiple of X and Y? X=2*2*2*2 Y=2*2*2*3
The scale of a map is 1 1/4 inches = 100 miles. On that map, 2 cities are 4 1/8 inches short. What is the actual distance between the cities?
need to divide 4 1/8 by 1 1/4
4 1/8 = 33/8
1 1/4 = 5/4
33/8 / 5/4 = 33/8 * 4/5 = 132/40 reduces to 33/10 = 3 3/10
100* 3 3/10 = 330 miles
Final answer:
Using the map scale of 1 1/4 inches equals 100 miles, and the measured map distance of 4 1/8 inches, the actual distance between the two cities is calculated to be 330 miles.
Explanation:
To find the actual distance between two cities on a map, we can set up a proportion based on the scale of the map. In this case, the scale is 1 1/4 inches = 100 miles. The measured distance on the map between the two cities is 4 1/8 inches.
We'll convert these measurements to an easier-to-calculate form by changing the mixed numbers to improper fractions.
First, we convert 1 1/4 inches to an improper fraction: 1 1/4 = 5/4 inches. Likewise, we convert 4 1/8 inches to an improper fraction: 4 1/8 = 33/8 inches. Now we set up the proportion using the scale.
(5/4 inches) / (100 miles) = (33/8 inches) / (x miles)
To solve for x, cross-multiply and divide:
(5/4) * x = (33/8) * 100
x = (33/8 * 100) / (5/4)
x = (33 * 100 * 4) / (8 * 5)
x = (33 * 4) / (2)
x = 66 miles
Therefore, the actual distance between the two cities is 330 miles.
D: y> -1/3 x+1 helpppp
Rewrite the rational exponent as a radical.
5 to the 3 over 4 power, to the 2 over 3 power
A.the cube root of 5 squared
B. the twelfth root of 5
C. the square root of 5
D.the cube root of 5 the fourth power
Help!!!!! Identify KPN
Answer:
it is 70
Step-by-step explanation:
I guessed and got it right, lol
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.
Answer: D
Step-by-step explanation: took the test
Someone please help me out!
try it with a couple different numbers
try 4: 1^2 +2^2 +3^2 +4^2 = 1 +4 +9 +16 =30
formula: 4(4+1)(2*4+1)/6 = 4*5*9 = 180/6=30
this one works
now try 5
1^2 + 2^2+3^2+4^2+5^2 = 55
formula: 5(5+1)(2*5+1)/6 = 5*6*11 = 330/6=55
I tried a larger number ( 14) as well and it worked
so you can say that this is true
How to subtract a negative fraction from a positive fraction?
determine the value of x in the diagram where lines a and b are parallel
25°
15°
75°
55°
Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°. Approximately how tall is the tree?
Find two consecutive positive integers such that thw sqaure of the first decreased by 25 equa;s three times the second
A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after the Express train starts will the it overtake the Local?
Answer:
2.5 hrs.
Hope this helps <3
if <6 = <10 and <5 = <7, which describes all the lines that must be parallel?