(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe?
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Answers
Find Q
tanQ=Perpendicular/BasetanQ=4/15tanQ=0.26Q=tan^-¹(0.26)Q=14.6°Not safe
Apply Pythagorean theorem
PR²=4²+15²=16+225=241
PR=√241Answer:
a) not safe
b) 15.5 ft (nearest tenth)
Step-by-step explanation:
Part (a)Tan trig ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = xO = PV = 4 ftA = RV = VQ = 15 ftSubstituting the given values into the formula and solving for x:
[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]
[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]
[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]
As 14.9° is not between 18° and 27°, the roof is not safe.
-------------------------------------------------------------------------------------------------
Part (b)Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = RV = VQ = 15 ftb = PV = 4 ftc = PRSubstituting the given values into the formula and solving for PR:
[tex]\implies \sf 15^2+4^2=PR^2[/tex]
[tex]\implies \sf 225+16=PR^2[/tex]
[tex]\implies \sf PR^2=241[/tex]
[tex]\implies \sf PR=\sqrt{241}[/tex]
[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]
Related Questions
18 people are trying out for a soccer team. How
1
I goalie,
many different ways could you choose
5-defenders, 6 midfielders, and 3 forwards?
Answers
Answer:
Using arrangements with repetitions, it is found that they can be grouped in 46,200 ways.
What is the arrangements formula?
Step-by-step explanation:
Look at the picture below
The median number of shoes for the girls is greater than the median number of shoes for the boys.
The median number of shoes for the boys is greater than the median number of shoes for the girls
The mean number of shoes for the boys is greater than the mean number of shoes for the girls.
The value of Q3 for the boys is greater than the value of Q3 for the girls
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Answer:
The median number of shoes for the girls is greater than the median number of shoes for the boys.
GIVING BRAINLIEST!!!!!
Answers
Answer:
option 1, 2
Step-by-step explanation:
since R is between Q and S
____________________
Q (3x+6) R (5x-2) S
--------------(12x - 4)-------------
Q S
so
QR + RS = QS
[tex](3x+6) + (5x - 2) = 12x - 4\\(3x + 5x) + (6 - 2) = 12x - 4\\(8x) + (4) = 12x - 4\\8x + 4 - 4 = 12x - 4 -4\\8x = 12x - 8\\8x - 12x = 12x - 12x - 8\\-4x = -8\\\frac{-4x}{-4} = \frac{-8}{-4}[/tex]
Answer:
2
Step-by-step explanation:
It mentions R is between points Q and S.
Hence, QR + RS = QS.
3x + 6 + 5x - 2 = 12x - 48x + 4 = 12x - 412x - 8x = 4 + 44x = 8x = 2how know ????????????
Answers
Answer:
0.16
Step-by-step explanation:
AND = Probability(of 1)*Probability(of 2)
OR = Probability(of 1)+Probability(of 2)
probability of spinning red = 0.2 or 20%
probability of NOT spinning red = 0.8 or 80%
The question says "AND" so 0.2 * 0.8 = 0.16 or 16%
Hope this helps!!!
Please mark as brainliest!!!
PLEASE HELP ILL MAKE YOU THE BRAINIEST!! For what value of X must ABCD be a parallelogram?
Answers
Answer:
because angle DCA is equal to angle CAB so side DC is parallel to side AB=> DCAB is a parallelogram=> 20x-7=15x+3=>x=2
I don't understand this equation, I need a little help...
x + 14 = 14, x
Answers
explanation: 0+14=14
There are 20 angelfish in a pet store. The fish are placed
into 5 tanks with the same number of fish in each tank.
How many fish are in each tank?
Answers
Answer:
4 fish in each tank.
Step-by-step explanation:
20/5 = 4
Simplify.
√63 somebody please help
Answers
Answer:
7.93
Step-by-step explanation:
Find the nth term of this number sequence 2, 4, 6, 8, ...
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The given sequence is in Arithmetic progression, and we have to find its nth term ~
So, let's get it solved ~
First term of the sequence is :
a = 2Common difference is :
d = 6 - 4 = 4 - 2 = 2Now, if we have to write the 2nd Term with respect to first one, we can write :
2nd Term = a + (2 - 1)d = a + d = 2 + 2 = 4similarly ~
3rd Term = a + (3 - 1)d = a + 2d = 2 + 4 = 64th Term = a + (4 - 1)d = a + 3d = 2 + 6 = 8Therefore, I similar pattern ~
[tex] \qquad \sf \dashrightarrow \: nth \: term = a + (n - 1)d[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 + (n - 1)2[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + (n - 1))[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2(1 + n - 1)[/tex]
[tex] \qquad \sf \dashrightarrow \: nth \: term = 2 n [/tex]
Feel free to ask your doubts, if you have any ~
Answer:
2nStep-by-step explanation:
from the number sequence above, each term except the first is generated by adding 2 to the term immediately preceding it.
the nth term of the sequence is usually designated Tn, and it's usually a function of n
from the number sequence
T1= 2
T2 = 2+2= 4
T3= 4+2= 6
T4= 6+2= 8
therefore, Tn= 2+2×(n-1)
= 2+2n-2
=2-2+2n= 2n
therefore, the nth term of the number sequence= 2n3 x 5/6 = ? x 1/6
those are fractions btw and what number makes the equation true?
PLEASE NO LINKS
Answers
Answer:
15
Step-by-step explanation:
[tex]3 \times \frac{5}{6} = \frac{15}{6} = 15 \times \frac{1}{6} [/tex]
The weather forecast warns of morning fog today.
You may only be able to see 0.6 miles in front of you.
How many feet is this?
Answers
Answer:
ANSWER ✏️3168[tex] \: \: \pink{\bold{\underline{\underline{ ☛explanation}}}}[/tex]
.
lmile=5280 feet 50 0.6mile =3168 feet
#WOULD have helped
#CARRY ON LEARNING
#BRAIN-LIEST
correct my answer in case it is wrong
1 A jewelry salesperson eams 55% commission on all sales. Today he sold $7,770 in jewelry. What is his total commission earned? The total commission the salesperson earned is $ (Round to the nearest cent as needed.)
Answers
Answer:
$4,273.50
Step-by-step explanation:
Multiplying the total sale amount by 55% commission :
7,770 x 55%7,770 x 0.557,770 x 11/20388.50 x 11$4,273.50Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house. how long does it take jasmin to rake leaves at the second house.
Answers
The Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Jasmin rakes leaves at two different houses. it takes her 2 1/3 hours to rake leaves at the first house. it takes her 1/2 of that time to rake leaves at the second house.
From the problem:
[tex]= \rm 2\dfrac{1}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{3}\times \dfrac{1}{2}[/tex]
[tex]= \rm \dfrac{7}{6}[/tex]
[tex]= \rm 1\dfrac{1}{6}[/tex]
Thus, the Jasmine take 1 whole 1/6 seconds to rake leaves at the second house.
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A sociologist wishes to test . the sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. to calculate a p-value for the test in excel, the sociologist should use:
Answers
Answer:
One-sample Z-test
Step-by-step explanation:
As the sample size is greater than 30, assuming the data is a simple random sample, and that the data has a normal distribution, the sociologist should conduct a one-sample z-test to calculate the p-value.
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 28 2-by-4s laid side by side. Simplify your answer
Answers
Work Shown:
3 1/2 inches = 3.5 inches
total width = 28*3.5 = 98 inches
The required total width of 28 2 - by -4s laid side by side is 98 inches.
Given,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. to determine the total width of 28 2-by-4s laid side by side.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The width of a 2-by-4 piece of wood is actually 3 1/2 inches.
Now, the width of 28 2-by-4 woods laid side by side,
= 28 * 3 1 / 2
= 28 * 7 / 2
= 98
Thus, the required total width of 28 2 - by -4s laid side by side is 98 inches.
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help me iiwh this quesrion
Answers
Answer:
3 is $8 and 14 is about 18%
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
since the annual rate is 2% and you wait 6 months which is half a year
you'd get 1% of 800 so it'd be 8.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
in the exponent of 3.
So, the given function is actually f(x) = 3^x +9
Now, we need to find the range of given
function.
We can see that first term is and exponential
term 3^x and second term is 9
We know that 3^x will always be greater than
O.
Therefore, 3^x +9 would always be greater
than 9.
Therefore, range would be y>9.
So, the correct option is B) (y | y > 9}.
Sam is d years old. Rupert's age is of Sam's age. lan is 15 years older than Rupert. If lan is 26 years old, a) write an equation in terms of d. b) what is Sam's age?
Answers
Answer: d = 11 bc 26 - 15 would equal 11
What is limit of startfraction x squared x minus 12 over x squared minus 3 x endfraction as x approaches 3? 0 startfraction 7 over 3 endfraction 4 dne
Answers
The limit of the expression [tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]a s x approaches 3 is -1/2
How to determine the limit?The expression is given as:
[tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]
As the variable x approaches 3, the limit is represented as:
[tex]\lim_{x \to 3} f(x)[/tex]
So, we have:
[tex]\lim_{x \to 3} = \frac{3^2 - 12}{3^2 - 3}[/tex]
Evaluate the exponents
[tex]\lim_{x \to 3} = \frac{-3}{6}[/tex]
Evaluate the quotient
[tex]\lim_{x \to 3} = -\frac{1}{2}[/tex]
Hence, the limit of the expression as x approaches 3 is -1/2
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Answer:
B. 7/3
Step-by-step explanation:
Took the final test and this was the correct answer
how to do this please help me
Answers
Answer: ∠BAC = 70°
Step-by-step explanation:
We will use the "Exterior Angle Property" which states that an exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
This means that (6a) + (7a) = 130° which we can solve.
(6a) + (7a) = 130°
13a = 130
a = 10°
Now that we have the value of a, we can solve for the angle BAC.
7a
7(10)
70°
Urgent Please Help!!!!
What percentage of scores lie in the shaded region? Use the empirical rule to find your answer.
Answers
Answer:
81.5%
Step-by-step explanation:
DO NOT ANSWER IF YOU DON'T KNOW. AND NO GUESSES!
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2, –9
–1, –1
0, 9
1, 21
2, 35
Answer choices:
1
9
11
22
Answers
Answer:
11
Step-by-step explanation:
I used a bunch of formulas that would clog this page, so I can't put them down. Sorry if it's wrong
_X 11 = 99 what is the missing number ?
Answers
Answer:
missing number its 9
Step-by-step explanation:
Ti find the answer you divide 99 by 11 and you find your answer
Need answers for this
Answers
Answer:
Step-by-step explanation:
Mean, Median,mode[tex]\boxed{Mean = \dfrac{Sum \ of \ all \ data}{number \ of data}}[/tex]
[tex]\sf = \dfrac{234 + 247 + 236+212+248+243+176+195}{8}\\\\= \dfrac{1791}{8}\\\\= 223.875[/tex]
Median:Arrange the numbers in ascending order.
176 , 195 , 212 , 234 , 236 , 243 , 247, 248
Number of data is even. So, median will be the average of 234 and 236
Median = average of the middle two terms.
[tex]\sf = \dfrac{234+236}{2}\\\\ =\dfrac{470}{2}\\\\= 235[/tex]
Mode is the data which is occurring more number of times.
Range = maximum - minimum
= 248 - 176
= 72
(r^-7)^6 im looking for anwser
Answers
Answer:
( r^-7 )^6 = r^-42 ( in exponential form )
( or )
1 / r^42 ( in fractional form )
Step-by-step explanation:
( r^-7 )^6
Formula : -
( a^m )^n = a^( mn )
Here,
a = r
m = - 7
r = 6
mn
= - 7 * 6
= - 42
Hence,
( r^-7 )^6 = r^-42 ( in exponential form )
( or )
( r^-7 )^6 = 1 / r^42 ( in fractional form )
use the method of elimination to find the equation of the line in y=mx+b form, that passes through each set of points (3,10) and (5,18)
Answers
Answer:
The answer is y=4x-2
Step-by-step explanation:
If someone could help that’d be great!
Answers
Answer:
6.6 ft
Step-by-step explanation:
The area of a triangle is given by the formula: [tex]A=\frac{1}{2}bh[/tex].
In this case, the base b equals the height h.
[tex]\therefore A=\frac{1}{2}h^2 \rightarrow h=\sqrt{2A}[/tex]
Given: A = 22 ft²
[tex]\therefore h=\sqrt{2A} = \sqrt{2(22 \text{ ft}^2)} = \sqrt{44}\text{ ft} \approx 6.6 \text{ ft}[/tex]
Please help with this. I don’t understand what I’m doing. It’s due tonight
Answers
Answer:
.0006
Step-by-step explanation:
I'm not sure if this is correct.. sorry if this is wrong.. :(
Please help me with my math please.?
Answers
Answer:
x = 6, y = 0, m = -1
y = mx + b
0 = -1(6) + b
0 = -6 + b
6 = b
y = -1x + (6)
Step-by-step explanation:
^^^
See answer, pretty simple.
So
equation
y=mx+b0=-1(6)+bb-6=0b=6So equation
y=-x+618.5 yd
11.7 yd
6.3 yd
14.3 yd
the surface area
