Larry is reroofing his house. Each side of the roof measures 14 feet from the eave to the ridge. The horizontal distance between the eaves is
20 feet.
x
14 feet
14 feet
20 feet
The measure of the angle between the two sides of the roof is approximately
Reset
Next
Answers
Answer:
91.2°
Step-by-step explanation:
There are several ways to find the a.pex angle of an isosceles triangle with all side lengths given. One of them is using the Law of Cosines:
c² = a² +b² -2ab·cos(C)
Solving for the angle C, we find ...
C = arccos((a² +b² -c²)/(2ab))
__
Here, we have a=b=14 and c=20. The angle is ...
C = arccos((14² +14² -20²)/(2·14·14)) = arccos(-8/392)
C ≈ 91.16938°
The interior angle at the peak of the roof is about 91.2°.
Related Questions
Find the x- and y-intercepts of the quadratic function below. Give non-integer
coordinates in fractional form.
f(x) = 2x2 - 5x + 3
-
Answers
Answer:
Step-by-step explanation:
Order the numbers from least to greatest. −34, 0.5, 23,−73, 1.2 The order of the numbers from least to greatest
Answers
Answer:
-73, -34, 0.5, 1.2, 23
Step-by-step explanation:
Hope this helps:)....if not sorry for wasting your time and may God bless you:)
true or false? criminal cases cannot be brought before a jury trial
Answers
Answer:
Step-by-step explanation:
True
linear exponential function
y=5.3×
Answers
Answer:
y=5x
which means 3 will be dedicated to 5
so 5=3y
13, 19, 25, ...
Find the 48th term.
Answers
Answer:
so you should add 6 to 13 in case to find 19, then add 6 to 19 to get to 25.
so the first is 13 and we keep adding 6 to get to the answer. we do it 47 times. so we have 13+ (6) (47) = 295 which is the 48th term.
The 12th term of the arithmetic sequence13, 19, 25,... is 79.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, an arithmetic sequence 13, 19, 25,...
The first term a₁ = 13 and the common difference is = (25 - 19) = (19 - 13) = 6.
We know nth term of an arithmetic sequence is aₙ = a₁ + (n - 1).d.
∴ The 12th term of this arithmetic sequence is a₁₂ = a₁ + (12 - 1).d
a₁₂ = 13 + (12 - 1).6.
a₁₂ = 13 + 11.6
a₁₂ = 13 + 66.
a₁₂ = 79.
learn more about arithmetic sequence here :
https://brainly.com/question/10396151
#SPJ2
-3(10)
Simplify
[Multiplication with integers]
Answers
Answer:
[tex]\boxed{\sf{-30}}[/tex]
Step-by-step explanation:
To solve this problem, all you have to do is solve by order of operations.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract-3(10)First, remove parenthesis.
Multiply.
-3*10
Solve.
[tex]\sf{-3*10=\boxed{\sf{-30}}[/tex]
-30
Therefore, the correct answer is -30.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
-30
Step-by-step explanation:
it is adding 10 three times, but then you add the negative after
so it is 10+10+10 because you are multiplying it by 3
you could also add 3 ten times because the communitive property
so 3+3+3+3+3+3+3+3+3+3
you would do the same whether the -3 was in parentheses or not
The dotted lines show how piano wire
is used to slice this cube. What will be
the shape of the cross section?
Answers
Answer:
C. rectangle (not a square)
Step-by-step explanation:
So image that the wire just sliced that piece of the cube right off:
It would give you a triangular prism,
HOWEVER, this is asking for the cross section:
The part of this triangular prism that was actually connected to the cube
and in this case, it would show that the bottom of the cut off part is rectangle.
You can also think of this as: What shape would be left over on the cube?
Cutting this piece off would give you a shape left over that is a rectangle.
What is the average rate of change of the function y = 3 cos x on the interval [π/2, π]?
Answers
Answer:
¹
Step-by-step explanation:
Average Rate of Change is
ts
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
Here b is pi, a is pi/2,
[tex] \cos(\pi) = - 1[/tex]
[tex] \cos( \frac{\pi}{2} ) = 0[/tex]
So we have
[tex] \frac{ - 1 - 0}{ \frac{\pi}{2} } = \frac{ - 1}{ \frac{\pi}{2} } [/tex]
Answer:
-2/pi
Step-by-step explanation:
What is the mean (average) of
a, a, b, b, b,c
Answers
Answer:
Ans might be a+b+c
Step-by-step explanation:
Hope the picture will help
Use the Virtual Dice Roller and roll two dice three times (or grab a pair of dice at home!).
Record the sum of the two dice for each virtual roll.
The first virtual roll is how many work shirts you have in your closet.
The second roll is how many pairs of work pants you have in your closet.
The third roll is how many pairs of work shoes you have in your closet.
Calculate and explain how many different ways can you dress every morning. Show all calculations.
Answers
The simulation of the virtual dice roller illustrates combination and sample space
There are 36 different ways you can dress every morning
How to determine the number of ways of dressing?The sample space of the two dice are:
Die 1 = {1,2,3,4,5,6}
Die 2 = {1,2,3,4,5,6}
From the above sample space, we have the sample size to be:
n(Die 1) = 6
n(Die 2) = 6
The sample size of the experiment would be:
n = n(Die 1) * n(Die 1)
Substitute known values
n = 6 * 6
Evaluate the product
n = 36
The above represents the different ways you can dress every morning.
Hence, there are 36 different ways you can dress every morning
Read more about sample space at:
https://brainly.com/question/10837034
Help picture below problem 11
Answers
Answer:
48
Step-by-step explanation:
vertical angles are equal
Answer:
48
Step-by-step explanation:
This is because vertical angles (which is opposite of each other when the two lines cross) are congruent, meaning they have the same angles.
I need help with this question please
Answers
[tex]v(y) = 0[/tex]
[tex] - 32t + 105 = 0[/tex]
[tex]t = \frac{ - 105}{ - 32} = 3.28[/tex]
[tex]h = - 16(3.28) {}^{2} + 105(3.28) + 17[/tex]
[tex]h = 189.26[/tex]
please Show the algebraic work steps thank you
Answers
Answer:
-0.125
Step-by-step explanation:
Shown in the image above
A tree is 18 feet tall and casts a shadow
that is 22 feet long. How far is it from the
end of the shadow to the top of the tree?
Show your work.
Answers
Answer:
28.42 feet
Step-by-step explanation:
Given
Height of tree = 18 feetLength of shadow = 22 feetTo Find
Distance b/w top of tree and end of shadowSolving
This resembles a right triangle⇒ We can use Pythagorean Theorem!⇒ 18² + 22² = L²⇒ L² = 324 + 484⇒ L² = 808⇒ L = 2√202 ⇒ L = 2 x 14.21⇒ L = 28.42 feetAnswer:
28.4 feet
Step-by-step explanation:
The question can be solved by using Pythagoras Theorem.
Given:-
Height of tree :- 18 feet (Perpendicular)
length of shadow :- 22 feet (Base)
To find:-
Distance of shadow from the end to the top of the tree
Solution:-
We know the Pythagoras theorem,
Which is , H² = P² + B²
So putting the given value , we get
H² = 18²+22²
H² = 324 + 484
H = √ 808 feet
H = 28.4 feet
The 92 children who were asked when they took their first lesson
Answers
Answer:
I need more to solve!!
Have an amazing day!!
Write the first three terms of the sequence whose general term is an=(3n)!.
Answers
Answer:
3, 6, 9
Step-by-step explanation:
an=3n
a(1)=3(1)= 3
a(2)=3(2)= 6
a(3)=3(3)= 9
A square pyramid has a base with a side length of 7.5 feet and lateral faces with heights of 16 feet. Write an expression that can be used to find the surface area, in square feet, of the square pyramid.
Please provide an expression, not just the surface area please :)
Answers
Check the picture below.
so the surface area of the pyramid will be the sum of the areas of the base and the four triangular faces.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(7.5)(16) \right]}~~ + ~~\stackrel{\textit{rectangular base}}{(7.5)(7.5)}}\implies 240~~ + ~~56.25\implies 296.25~ft^2[/tex]
-2x+ 3y=-15 3x+2y = -23 solve by elimination
Answers
Answer:
x=237/7 and y=-199/7
Explanation:
Multiply the second equation by 2, then add the equations together.
(−2x+3y=−153)
2(x+2y=−23)
Becomes:
−2x+3y=−153
2x+4y=−46
Add these equations to eliminate x:
7y=−199
Then solve 7y=−199 for y:
7y=−199
(Divide both sides by 7)
y=−199/7
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
−2x+3y=−153
Substitute −199/7 for y in−2x+3y=−153:
Add 597/7 to both sides
Divide both sides by -2
Julie's grades for this term test are 85' 88' and 97. In addition for the three tests that Julie already had, there will b just one more test. Julie needs to earn at least ________ point for the last test to get no less than A for the term. "A" means the average of 93 or more.
Answers
The score Julia has to have on her last test to have an A for the term is 102.
What is the least score?The first step is to determine the sum of her scores on the first three tests: 85 + 88 + 97 = 270
Now determine the score on the last test that would give an average of 93
(270 + x)/ 4 = 93
270 + x = 93 x 4
372 - 270 = x
x = 102
To learn more about average, please check: https://brainly.com/question/25842202
Find the distance between FD
F=(4,6) D=(0,-1)
Answers
Answer:
Final answer -
[tex]d(FD) = \sqrt{65 } \: units[/tex]
hope helpful :D
Make x the subject of the formula
y = x^2
Answers
Answer:
[tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle \large{y=x^2}[/tex]
Make ‘x’ the subject of the formula by square root both sides:
[tex]\displaystyle \large{\sqrt{y}=\sqrt{x^2}}[/tex]
Cancel the square root and square in RHS and write plus-minus in LHS:
[tex]\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}[/tex]
Therefore, the solution is [tex]\displaystyle \large{x=\pm \sqrt{y}}[/tex]
__________________________________________________________
Summary
To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.
You may also be curious why do you have to add plus-minus on another side when cancelling [tex]\displaystyle \large{\sqrt{x^2}}[/tex] because [tex]\displaystyle \large{\sqrt{x^2}=|x|}[/tex] and [tex]\displaystyle \large{|x|}[/tex] for their positive and their counterparts (opposite/negative) will always give same y-value.
From an example:
[tex]\displaystyle \large{\sqrt{x^2}=4}[/tex] can be rewritten as [tex]\displaystyle \large{|x|=4}[/tex], cancel absolute sign/square root then write plus-minus which the solution is [tex]\displaystyle \large{x=\pm 4}[/tex] and if you substitute x = 4 or -4, the equation will be true for both values.
__________________________________________________________
Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
Ryan buys some jumpers to sell on a stall.
He spends £130 buying 40 jumpers.
He sells 80% of the jumpers for £12 each.
He then puts the rest of the jumpers on a Buy one get one half price offer.
He manages to sell half the remaining jumpers using this offer.
How much profit does Ryan make?
Answers
32*£12 = £384
40-32=8
4*12=£48
4*6=£24
384+48+24=£456
456-130= £326 profit
Find the product of 4+3i and its conjugate.the answer is a +bi where
Answers
The value of a and b in the product of 4+3i and its conjugate in the format a + bi are 25 and 0.
What is conjugate?The conjugate is where we change the sign in the middle of two terms. For example:
3y + 1
conjugate of 3y + 1 is 3y - 1.
Therefore, the conjugate of 4 + 3i is 4 - 3i.
The product of 4 + 3i and its conjugate is as follows:
(4 + 3i)(4 - 3i) = 16 - 12i + 12i - 9(i)²
Therefore,
16 - 9i²
i² = -1
Hence,
16 - 9(-1) = 25
It can be written in the form a complex form → (25 + 0.i)
Therefore, a = 25 and b = 0.
learn more on conjugate here: https://brainly.com/question/20757260
Applying probability concepts
Answers
Answer:
See below ↓
Step-by-step explanation:
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is trueProbability can range in from 0 to 1The probability Choosing a card from the deck of cardApplications
Flipping a coinThrowing a dice in the airPulling a red ball out of a bucket of red and white ballsWinning a lucky drawOf all the events in a sample space adds up to 1The area of the figure below
Answers
Answer:
32 square milimeters
Step-by-step explanation:
3/4 of 24= 18 (rectangle 8X3)
4x2=8 (rectangle 4x2)
half of 12 =6 (rectangle 4x3)
18+8+6 =32
Drag each expression to its equivalent.
Answers
Answer:
5x+4=2x+3-x+1+4x
7x=3+2x+4+5x-7
2x+3=8+10x-8x-5
2x+3-x+1+4x = 5x+4 and 7x-5-2x+9 = 5x +4
3+2x+4+5x-7 = 7x and x-1+2x+2+4x-1 = 7x
3+2x+4+5x-7 = 7x and x+6-2x-3=2x+3
These are the equivalent expressions.
What is an expression?
It is a sentence with a minimum of two numbers or variables and at least one math operation.
Given expression can be solved like:
1. 2x+3-x+1+4x = 5x+4
Which is same as the first option.
2. 7x-5-2x+9 = 5x +4
Which is same as the first option.
3. 8+10x-8x-5 = 2x+3
Which is same as the third option.
4. 3+2x+4+5x-7 = 7x
Which is same as the second option.
5. x-1+2x+2+4x-1 = 7x
Which is same as the second option.
6. 4x+6-2x-3=2x+3
Which is same as the third option.
Hence, the equivalent options are :
2x+3-x+1+4x = 5x+4 and 7x-5-2x+9 = 5x +4
3+2x+4+5x-7 = 7x and x-1+2x+2+4x-1 = 7x
3+2x+4+5x-7 = 7x and x+6-2x-3=2x+3
To learn more about expression, use the link given below:
https://brainly.com/question/14083225
#SPJ2
how many integers from 100 to 999, inclusive, don't include the numbers 2,4,6,8? PLS HELP I WILL MARK BRAINLIEST
Answers
Answer:
243
Step-by-step explanation:
999-100= 899 integers
200s 400s 600s 800s excluded so 400 numbers excluded
899 - 400 = 499
20s 40s 60s 80s which are 40 integers x 4 = 160
499 - 160 = 339
2s 4s 6s 8s which are 4 integers x 6 x 4 ( 4 from each 100 ) = 96
339 - 96 = 243 integers
Which field is required when importing vendors
Answers
Import field: Tax Identification Number, Tax Number for Customers or Vendors. Tax Identification Number (customers) or Tax ID Number (vendors).
Shawn is typing paper for a class. He can type 1 6/11 pages in 1/3 of an hour. How many pages can shawn type in in one hour
Answers
Answer:
4 7/11
Step-by-step explanation:
1 6/11 * 3 = 3 18/11 = 4 7/11
What is the answer for this 4² × 4²
Answers
Answer:
4squared is 16 so 16×16=256
hope it help
Answer:
4^2=16 multiplyin 16 by 16 gets you 256
Step-by-step explanation: