A triangular fence has sides that measure 11 yards, 30 yards, and 35 yards. What is the measure of the greatest angle that is formed? Round to the nearest whole degree.
Answer:
108°
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]35^{2}[/tex] = [tex]11^{2}[/tex] + [tex]30^{2}[/tex]
[tex]\frac{204}{-660}[/tex] = [tex]\frac{-660 cos}{-660}[/tex]
cos = -0.309
The measure of the greatest angle in the triangular fence is approximately 108.5 degrees. To find the measure of the greatest angle in the triangular fence, you can use the Law of Cosines.
The Law of Cosines states:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where c is the side opposite the angle C, and a and b are the other two sides of the triangle.
In this case, the sides of the triangle are:
a = 11 yards
b = 30 yards
c = 35 yards
Now, let's find the measure of angle C (the angle opposite the side with length 35 yards):
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)\\35^2 = 11^2 + 30^2 - 2 * 11 * 30 * cos(C)\\1225 = 121 + 900 - 660 * cos(C)\\1225 = 1021 - 660 * cos(C)\\[/tex]
Now, isolate cos(C) by moving the terms around:
[tex]660 * cos(C) = 1021 - 1225\\660 * cos(C) = -204[/tex]
Now, divide by 660 to find cos(C):
[tex]\cos(C) \approx -0.3091[/tex]
Now, find the measure of angle C by taking the inverse cosine (cos^-1) of -0.3091:
[tex]C \approx cos^-1(-0.3091)\\C \approx 108.5 degrees[/tex] (rounded to one decimal place)
Since this is the angle opposite the side with length 35 yards, it is the greatest angle in the triangle.
So, the measure of the greatest angle in the triangular fence is approximately 108.5 degrees.
To know more about angle:
https://brainly.com/question/30147425
#SPJ2
Find the zeros of the following function
Answer:
15 and -20
Step-by-step explanation:
The zeros/ roots are the x intercepts of the graph
Sandy programmed a website's checkout process with an equation to calculate the amount customers will be charged when they download so. The website offers a discount. If one song is brought at the full price of $1.29, then each additional song is 99 cent State an equation that represents the cost, f(×) and when X songs are downloaded
Answer:
f(x) = 0.99x + 0.3
Step-by-step explanation:
f(x) = 1.29 + 0.99(x - 1)
Distribute
f(x) = 1.29 + 0.99x - 0.99
Combine like terms
f(x) = 0.99x + 0.3
Lesson 17
Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?
The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).
What is Pythagoras theorem?The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -
(hypotenuse)² = (base)² + (perpendicular)²
Given is a right angle triangle with hypotenuse as 14.5 meters and
opposite side as 6.3 meters.
We can write sine of the angle (θ) as -
sin(θ) = P/H
sin(θ) = Opposite side/Hypotenuse
sin(θ) = 6.3/14.5
(θ) = sin⁻¹(6.3/14.5)
Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).
To solve more questions on Pythagoras theorem, visit the link below -
brainly.com/question/343682
#SPJ1
helppppppppppppppppppp
Answer:
Angle × =180 - 126
Angle × = 54
What is the pattern in this sequence? −3,1,5,9,13, ...
Answer:
Pattern is: +4
Step-by-step explanation:
an arithmetic series/ pattern since the next number is got by adding 4 to tge previous number
The diameter of a circle has endpoints P(-6,-11 ) and Q(4, 7). Write an equation for the circle. Be sure to show and explain all work. Thank you!
Answer:
(x + 1)^2 + (y + 2)^2 = 106
Step-by-step explanation:
The formula for a circle is
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the raadius
--------------------------------------
The center is the midpoint of the diameter end points
(h, k) = ( (-6 + 4)/2 , (-11 + 7)/2 )
(h, k) = (-1, -2)
The radius is the distance from the center to an endpoint
Using (h, k) and Q
r^2 = (4 - -1)^2 + (7 - -2)^2
r^2 = 5^2 + 9^2
r^2 = 106
-------------------------------
Plug into the circle formula
(x + 1)^2 + (y + 2)^2 = 106
In the diagram below, QR is parallel to NO. If NQ = 12, QR 20, and NO = 35, find the length of QP. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.
What is the rationale for the above result?[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore
QR/NO = PQ/PN
⇒ 20/35 = PQ/PQ +12
This is because:
PN = PQ + NQ; which is also
PN = PQ +12
(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms
240= 35 PQ - 20 PQ
240 = 15PQ; Divide both sides by 15
⇒ 240/15 = 15PQ/15
⇒ 16 = PQ
Therefore, QP = PQ which is equal to 16.
Learn more about Geometric Forms:
https://brainly.com/question/29273438
#SPJ1
please help me thank you
Answer:
52 cm²
Step-by-step explanation:
There are 3 distinct faces:
one with sides 2 and 3
one with sides 2 and 4
one with sides 3 and 4
There are two of each distinct face (they are accros each other)
so we find their areas (we times by two as there are two of each face)
2×3×2=12
2×4×2=16
3×4×2=24
Finally we add the values:
12+16+24=52 cm²
WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
Answer: 2.403 × 10^3 atoms
Step-by-step explanation:
10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.
Solve for a : 2.8=14a
Answer:
a=0.2
Step-by-step explanation:
Let's solve your equation step-by-step.
2.8=14a
Step 1: Flip the equation.
14a=2.8
Step 2: Divide both sides by 14.
14a/ 14 = 2.8/ 14
a=0.2
Answer:
a=0.2
Find X. Please show steps, thank you.
Answer:
C=10
Step-by-step explanation:
Super-Mart sells a pack of 20 Pokemon cards for $1.30. Another store, Price-Town, sells a pack of 15 Pokemon cards for $1.05. Which store is offering the better deal
Answer:
Price-Town
Step-by-step explanation:
:D
anyone know this click to see links will get reported
Answer:
exponents, exponents, parenthesis, parenthesis/exponents, parenthesis.
Step-by-step explanation:
PLEASE HELP!!
The equation of a circle is (x+10)2+(y−4)2=100.
What is the center and radius of the circle?
Responses
center: (10, −4); radius: 10,000
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10,000
center: (−10, 4); radius: 10,000
center: , begin ordered pair negative 10 comma 4 end ordered pair, ; radius: 10,000
center: (10, −4); radius: 10
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10
center: (−10, 4); radius: 10
The center of the circle is (-10,4) and the radius is 10.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x+10)² + (y−4)² = 100
(x+10)² + (y−4)² = 10²
Compare the equations and find the center and radius,
Center = ( h,k) = ( -10,4)
Radius = r = 10
To know more about circle follow
https://brainly.com/question/1506955
#SPJ1
Can someone please tell me the answer
Answer:
E, 5, 3
Step-by-step explanation:
We just need to connect the rectangle with dots equally placed.
This morning, Carmen car had 18.61 gallons of fuel. now, 3.9 gallons left. How much fuel did Carmen use
Y’all helppppp questions on the photo
The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?
expression can be defined as with the minimum of two variables or numbers and at least one math operation.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
To learn more about expression from the given link.
brainly.com/question/1859113
#SPJ1
The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?expression can be defined as with the minimum of two variables or numbers and at least one math operation.
What is division?Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
To learn more about expression from the given link.
brainly.com/question/1859113
#SPJ1
Math XL for School Practice X
Savvas Realize
Savvas Realize
X+
O
со
#savvasrealize.com/community/classes/6446abfc58e14d32a84d6d5ef61987af/assignments/707714e9bd28418bbf75c5bdb8bdaa48/content/84494512...
o
8-9; MathXL for School: Practice & Problem Solving
Due 05/11/21
X8.9.PS-14
Question Help
2 cm
A glass bead has the shape of a rectangular prism with a smaller rectangular
prism removed. What is the volume of the glass that forms the bead?
2am
6cm
7 cm
6 cm
(The figure is not to scale)
The volume of the glass that forms the bead is cm3,
Answer:
224 cm³Step-by-step explanation:
Required volume is:
6*6*7 - 2*2*7 = 224 cm³Please help will mark Brainly
What is the type of tax paid when you buy a new pair of blue jeans?
A) sales tax
B) income tax property tax
C) property tax
D) pay roll tax
Answer:
It's sales tax I believe
The first term of a linear sequence is 3 and the 8th term is 31. find the common difference
Answer:
The common difference is 4.
Step-by-step explanation:
[tex]a_n=a_1+(n-1)d[/tex] You get to term number n by starting with term number 1 and adding the common difference d n-1 times.
[tex]a_1=3\text{, and }a_8=31[/tex]
[tex]a_8=a_1+(8-1)d\\\\31=3+7d\\\\28=7d\\\\d=4[/tex]
I meet a boy and asked about his age,he said he don't know his age but his age is half of the age of his mum and who is five years lest than his Father. The total age of the three is one hundred,now how old will each be the son,mother and the father if there overall age is hundred years?
Answer:
i had a stroke while reading this
Step-by-step explanation:
Answer:
son: 19
mother: 38
father: 43
Step-by-step explanation:
x + 2x + 2x+5 = 100
5x = 95
x = 19
write the equation in it's simplest form or as
[tex] \sqrt[n]{b} [/tex]
[tex] \sqrt[3]{56} [/tex]
9514 1404 393
Answer:
2∛7
Step-by-step explanation:
Putting the expression in simplest form will factor cubes from under the radical.
[tex]\displaystyle\sqrt[3]{56}=\sqrt[3]{2^3\cdot7}=\boxed{2\sqrt[3]{7}}[/tex]
Question below in photo!! Please answer! Will mark BRAINLIEST! ⬇⬇⬇⬇⬇⬇⬇
Please answer ALL questions in order for BRAINLIEST! NO links or else you will be reported and maybe even get banned.
Answer:
1) draw a line from (2,4) to (6,4)
2) 27.5
3) 16
4) 43.5
5) $97.88
Step-by-step explanation:
1) draw a line from (2,4) to (6,4)
2) (7+4)/2=5.5x5=27.5
3) 4x4=16
4) 27.5+16=43.5
5) 43.5x2.25= 97.875 = $97.88
5. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.
Answer:
The actual SAT score is 2024.
The equivalent ACT score is 29.49.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
SAT score that is in the 95th percentile
Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that [tex]\mu = 1511, \sigma = 312[/tex]
95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 1511}{312}[/tex]
[tex]X - 1511 = 1.645*312[/tex]
[tex]X = 2024[/tex]
The actual SAT score is 2024.
Equivalent ACT score:
The equivalent ACT score is the 95th percentile of ACT scores.
Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that [tex]\mu = 21.1, \sigma = 5.1[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 21.1}{5.1}[/tex]
[tex]X - 21.1 = 1.645*5.1[/tex]
[tex]X = 29.49[/tex]
The equivalent ACT score is 29.49.
Sally can paint a room in 3 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together?
Answer:
2h
Step-by-step explanation:
You can solve this one by adding their rates, but you have to invert the numbers they give you to find the rate. Rate is measured in something per unit of time, and "per" indicates division. So the rates are: 1/3 of an hour (Sally) and 1/6 of an hour (Steve). So add the rates: 1/3 + 1/6 = 1/2. (1/3 is 2/6, and 2/6 + 1/6 = 3/6). Since their combined rate is 1/2 of a room in one hour, it takes them two hours to paint the room.
The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
What is the age range of drivers who own an 8-year-old car?
The required range of drivers who own 8 years car is 23years.
Given that,
The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
We have to determine,
The age range of drivers who own an 8-year-old car.
According to the question,
The Range is the difference between the lowest and highest values.
Therefore,
The age range of drivers who own 8 years old car is 17,25 and 40 years.
Then,
Range of drivers who own 8 years car = highest value of range - lowest value of age.
Range of age of drivers who own 8 years car = 40 - 17 = 23years
Hence, The required range of drivers who own 8 years car is 23years.
To know more about Range click the link given below.
https://brainly.com/question/19387334
The difference of two numbers is 3. Their sum is 13.
Answer:
8 and 5
Step-by-step explanation:
Find the inverse of the function.
y = -4x
Write your answer in the form ax + b. Simplify any fractions.
y =
Help please
Answer:
The inverse function is [tex]y = -\frac{x}{4}[/tex]
Step-by-step explanation:
Inverse of a function:
To find the inverse of a function, we exchange x by y, then we isolate y.
y = -4x
Finding the inverse:
[tex]x = -4y[/tex]
[tex]4y = -x[/tex]
[tex]y = -\frac{x}{4}[/tex]
So
The inverse function is [tex]y = -\frac{x}{4}[/tex]