Answer:
5.23 units
Step-by-step explanation:
Let the length of arc be l
[tex]central \: \angle \: ( \theta) = 60 \degree \\ radius \: (r) = 5 \: units \\ \\ \because \: l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ \\ \therefore \: l = \frac{60 \degree}{360 \degree} \times 2 \times 3.14 \times 5 \\ \\ \therefore \: l = \frac{1 }{6} \times 31.4 \\ \\ \therefore \: l = 5.23 \: units[/tex]
Prove that the following is a right – isosceles triangle.
Show work
Answer:
Proved down
Step-by-step explanation:
To prove that a triangle is isosceles use the distance formula to find the length of its side and check if there are two sides equal.
To prove that a triangle is right find the square of the longest side and then find the sum of the squares of the other two sides, if the two answers are equal, then the triangle is right (converse of Pythagoras Theorem).
The formula of the distance between two points is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∵ x = (-1 , 5) and y = (4 , 4)
∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 4
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4
- Substitute them in the formula of the distance to find xy
∵ [tex]xy=\sqrt{(4--1)^{2}+(4-5)^{2}}=\sqrt{25+1}[/tex]
∴ [tex]xy=\sqrt{26}[/tex]
∵ x = (-1 , 5) and z = (-2 , 0)
∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = -2
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 0
- Substitute them in the formula of the distance to find xz
∵ [tex]xz=\sqrt{(-2--1)^{2}+(0-5)^{2}}=\sqrt{1+25}[/tex]
∴ [tex]xz=\sqrt{26}[/tex]
∵ xy = xz
- The isosceles triangle has two equal sides
∴ Δ xyz is an isosceles triangle
∵ y = (4 , 4) and z = (-2 , 0)
∴ [tex]x_{1}[/tex] = 4 and [tex]x_{2}[/tex] = -2
∴ [tex]y_{1}[/tex] = 4 and [tex]y_{2}[/tex] = 0
- Substitute them in the formula of the distance to find yz
∵ [tex]yz=\sqrt{(-2-4)^{2}+(0-4)^{2}}=\sqrt{36+16}[/tex]
∴ [tex]yz=\sqrt{52}[/tex]
yz is the longest side lets find its square
∵ (yz)² = ([tex]\sqrt{52}[/tex] )²
∴ (yz)² = 52
- Lets find the sum of the squares of the other two sides
∵ (xy)² + (xz)² = ([tex]\sqrt{26}[/tex] )² + ([tex]\sqrt{26}[/tex] )²
∴ (xy)² + (xz)² = 26 + 26 = 52
∴ (yz)² = (xy)² + (xz)²
- That means the angle opposite to yz is a right angle
∴ Δ xyz is a right isosceles triangle
10n = 40 ( solve for n )
Answer:
4
Step-by-step explanation:
10 times 4 equals 40
4 will be the value of n for the given expression.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, an expression 10n = 40
Simplifying the equation for n
=> 10n = 40
divide by 10 into both sides
=> 10n/10 = 40/10
=> n = 4
Therefore, the value of n for the given expression will be 4.
Learn more about algebraic Expression here:
https://brainly.com/question/953809
#SPJ5
An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars.
The factored expression is 15(p - 2) . The discount per pair of shoe is $2
Using the expression given:
15p - 30Factorize :
The greatest common factor of 15 and 30 is 15
15(p - 2)Hence, the factored expression Using GCF is 15(p - 2)
b.)
The discount on the purchase is the constant value:
Total discount = 30Number of shoes = 15
Discount per pair = Total discount/ Number of shoe pairs
Discount per pair of shoes = 30/15 = $2
Therefore, the discount on each pair of shoes is $2
Complete Question:
An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars. a. Factor the expression using the GCF.
15p−30=
b. The discount per pair of shoes is $
575,000,000
write the number in scientific notation
Answer:
in scientific notation the answer is 5.75x10^8
Answer: [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex]
Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.
So here, we have 5.75000000 and notice that there
is only one digit to the left of the decimal point.
Next, we count the number of places the decimal point would
need to move to get back to the original number, 575,000,000.
Since we would need to move the decimal point 8 places to the right,
we have an exponent of positive 8.
Now, scientific notation is always expressed as a number between 1 and 10 including 1 but not 10 and it is multiplied by 10 to a certain power that must be an integer.
So we have [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex].
Notice that the exponent is positive.
This is because we would need to move the decimal point to the right in order to get back to the original number.
So 575,000,000 can be written in scientific notation
as [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex] or just [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].
Remember that we can drop zeroes at the end of a decimal.
So we have [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].
If we flip an unfair coin, suppose the probability to get a 'Head' is 0.6 each time. In a random sample of 75 tosses, let p denote the proportion of getting a 'Head' in the 75 tosses. What is the standard error of the sample proportion p .
Answer:
Step-by-step explanation:
The following scenarious represent relations that can be graphed. for which of the graphs should the data values be continous ? explain why or why not.
a) The mass of a stack of coins as a function of the number of coins.
b) The temperature in Vancouver as a function of the time of day.
c) the mass of an animal as a function of its range.
d) the price of a carton of milk as a function of the size of the carton.
Answer:
I would say c
Step-by-step explanation:
determine the perimeter of AGN .
Given:
Given that AGN is a triangle with circle inscribed in it.
The circle touch the triangle at the point R, T and E.
The length of AR is 35 units.
The length of RG is 21 units.
The length of NE is 19 units.
We need to determine the perimeter of the triangle AGN.
Length of GE:
Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".
Since, RG and EG from an exterior point G are tangents to the circle, then RG and EG are congruent.
Thus, we have;
[tex]RG=EG[/tex]
[tex]21=EG[/tex]
Thus, the length of GE is 21 units.
Length of TN:
Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".
Since, TN and NE from an exterior point N are tangents to the circle, then TN and NE are congruent.
Thus, we have;
[tex]TN=NE[/tex]
[tex]TN=19[/tex]
Thus, the length of TN is 19 units.
Length of AT:
Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".
Since, AT and AR from an exterior point A are tangents to the circle, then AT and AR are congruent.
Thus, we have;
[tex]AT=AR[/tex]
[tex]AT=35[/tex]
Thus, the length of AT is 35 units.
Perimeter of AGN:
The perimeter of AGN is given by
[tex]\triangle AGN=AR+RG+GE+EN+TN+AT[/tex]
Substituting the values, we get;
[tex]\triangle AGN=35+21+21+19+19+35[/tex]
[tex]\triangle AGN=150[/tex]
Thus, the perimeter of the triangle AGN is 150 units.
Answer:
150
Step-by-step explanation:
Segment AE divides the triangle into two congruent right angle triangles
AG = AN = 35 + 21 = 56
NG = 2(19) = 38
Perimeter = 56 + 56 + 38
150
Number 15 can anyone help me figure this out I have 15 points to give out if you give answer pls !!last question
Answer:
1438.52544
Step-by-step explanation:
2 What is the minimum amount of information you need in order to calculate the slope of a line?
Answer:
y=mx+b
Step-by-step explanation:
The formula to find the slope is y=mx+b
hope this helps
Answer:
you need to know what the pairs of numbers match to get a possible answer
Step-by-step explanation:
once u know that you can do the rest of the math and it depends how to multiply
Question 3 of 5
2 Points
Which factor is most important for classifying two species into the same
group?
O
A. The species have the same set of traits.
O
B. The species have different common ancestors.
O
C. The species have the same common name.
O
D. The species live in the same place.
SUBMIT
The most vital factor for classifying two species into the same group is if they evolved from a shared ancestor, reflecting their place in the same clade and genetic similarities.
The most important factor for classifying two species into the same group is their evolutionary history, specifically whether they evolved from a shared ancestor. When scientists classify species, they adhere to the fundamental principle that all members of a group, or "clade," must have a recent common ancestor that is not shared with species from other groups. This is based on the idea that species within the same group will share more genetic similarities and phylogenetic traits than with those from different groups due to their more recent common ancestry.
Option A might seem plausible, as species in a group often share similar traits, but shared traits alone are not enough for classification without evolutionary context. Option C is incorrect because common names do not reflect scientific classification. Option D is also incorrect as geographic location is not a determinant for taxonomic classification. Thus, the correct answer to the original question is B, "The species have different common ancestors," as having a recent common ancestor is the most critical criterion for grouping species together.
Round your answer to the nearest tenth of a degree
Answer:
x = 51.1 degrees
Step-by-step explanation:
We notice that we can use the sine formula.
Why?
Well because Sin x = (opposite side) / hypotenuse
sin x = 7/9
x = arcsin 7/9 = 51.05755 degrees
rounded to the nearest tenth.
x = 51.1 degrees
Jerry is using the floor plans
for his new home to help him
purchase base molding for
the place where the walls
meet the floor. The plans are
drawn using a scale of 14
inch represents 1 foot. He
measures the walls on the
floor plan with a ruler and
finds that they total 2372
inches. If molding costs
$2.10 per foot, how much
will Jerry spend on molding?
Jerry will spend $355.7988 on molding.
What is Scale Factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
we have,
Scale: 1 foot = 14 inches
As, the measurement of walls is 2372 inches.
The, using Scale the wall measured
= 2372/14
= 169.428 foot
Now, the molding costs $2.10 per foot then the cost of 169.428 foot is
= 169.428 x 2.10
= $355.7988
Learn more about Scale here:
https://brainly.com/question/30215119
#SPJ7
The amount of money nick spent on 12 cans of soda was $3. Write an equation relating the amount spent to the the number of cans purchased. Then find out how many cans you can buy for $28.50.
Answer:
12y=$3
114 cans
Step-by-step explanation:
Let the cost of every can be represented by y. Therefore, for 12 cans, the cost will be the product of y cans and 12 hence cost is 12y
Since the cost incurred is $3 then we can represent these as
12y=$3
To solve for y, we divide both sides by 12 hence
Y=$3/12=$0.25
To find the number of cans that one will get with a buget of $28.5, we divide the budget by the cost of a can. This will be $28.5/$0.25=114 cans
What is the mode of the following numbers? 6 , 4 , 1 , 9 , 3 , 8 , 3 , 5 , 10
List the numbers from least to greatest:
1, 3, 3, 4, 5, 6, 8, 9, 10
Mode: ( most number repeated in the list)
Mode: 3
The mode of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 3, as it is the number that appears most frequently in the set.
The question asks to find the mode of the following numbers: 6, 4, 1, 9, 3, 8, 3, 5, 10. The mode is a measure of central tendency that represents the most frequently occurring number in a set of values. To find the mode, we need to count how many times each number occurs in our set.
1 occurs 1 time3 occurs 2 times4 occurs 1 time5 occurs 1 time6 occurs 1 time8 occurs 1 time9 occurs 1 time10 occurs 1 timeSince the number 3 appears more frequently than any other number in the set, occurring twice, the mode of this set of numbers is 3.
Helppp !!
Choose the point-slope form of the equation of this line.
A.) y – 8 = –5(x – 3)
B.) y – 8 = –5(x + 3)
C.) y + 8 = –5(x – 3)
D.) y + 8 = –5(x + 3)
Answer:
the answer is c
Step-by-step explanation:
Answer:
C. y + 8 = –5(x – 3)
second part is also C. y = –5x + 7
Step-by-step explanation:
For every 140 feet that Kelly rides on her bicycle, the wheels turn 20 times. About how many times do the wheels turn in 5 miles? (1 mile = 5,280 feet) Round your answer to the nearest whole number.
Answer: The wheels turn about 3771 times in 5 miles.
Step-by-step explanation:
Given, Kelly rides on her bicycle such that the number of times wheels turn for every 140 feet = 20
Turns for every feet = [tex]\dfrac{20}{140}=\dfrac{1}{7}[/tex] ...(i)
To find : Number of times wheels turn in 5 miles.
Since , 1 mile = 5,280 feet
Then, 5 miles = 5 x (5,280 feet) = 26,400 feet
Now , Number of times the wheels turn in 26,400 feet = 26400 x (Turns for every feet)
[tex]26400\times\dfrac{1}{7}=3771.42857143\approx3771[/tex] [From (i)
Hence, the wheels turn about 3771 times in 5 miles.
You invest $500 in an account that has an annual interest rate of 8%, compounded weekly for 12 years. What is the equivalent interest rate and how many times will the money be compounded? How much will you have?
Answer:
[tex]i_m=8.322\%\\\\624 \ compoundings\\\\A_{12}=\$1,304.88[/tex]
Step-by-step explanation:
#The equivalent interest rate per annum is equal to the effective interest rate.
-Given 8% compounded weekly( Take 1 yr=52 weeks) the effective interest rate is calculated as:
[tex]i_m=(1+i/m)^m-1\\\\\#where\\i=stated \ interest\ rate\\m=number \ of \ compoundings \ per \ year\\\\\therefore i_m=(1+0.08/52)^{52}-1\\\\=0.08322\approx 8.322\%[/tex]
Hence, the equivalent interest rate is 8.322%
-Assuming one year has 52 weeks, the number of compoundings will be :
[tex]=compoundings \ per \ year \times \ no \ of \ years\\\\=52\times 12\\\\=624\ compoundings[/tex]
-The investment amount after 12 years is calculated as:
[tex]A=P(1+i_m)^n, n=number \ of \ years\\\\=500(1.08322)^{12}\\\\=1304.88[/tex]
Hence, the amount after 12 years is $1304.88
Answer:
8% annual interest rate when compounded weekly =
(1 + .08/ 52)^52 = 1.00153846153846154^52 = 1.08322047419671 =
8.322047419671% equivalent interest rate
In 12 years this will be compounded 624 times
12 year Total = 500 * (1.08322047419671)^12 =
1,304.8852611583 =
1,304.89 (rounded)
Can you help with this, I don't know how to do it
Answer:
105 sqrt(2) =x
Step-by-step explanation:
Since this is a right triangle we can use trig functions
so sin theta = opposite side/hypotenuse
sin 45 = x/210
Multiply each side by 210
210 sin 45 = x
We know sin 45 = sqrt(2)/2
210 * sqrt(2)/2 = x
105 sqrt(2) =x
Answer:
B
Step-by-step explanation:
Using trig ratios
sin(45) = opposite/hypotenuse
sin(45) = x/210
sqrt(2)/2 = x/210
x = 210sqrt(2)/2
x = 105sqrt(2)
M varies inversely as the square of P. If M is 9 when P is 2, then find M when P is 3.
please h e l p
Answer:
Step-by-step explanation:
If two quantities are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable and vice versa.
Given that M varies inversely as the square of P, if we introduce a constant of proportionality, k, the expression becomes
M = k/P²
If M = 9 when P = 2, then
9 = k/2² = k/4
k = 9 × 4 = 36
Therefore, the inverse variation equation is
M = 36/P²
When P = 3,
M = 36/3² = 36/9
M = 4
Find the missing dimension for the figure below*
How and why??
Please help due today..
Rectangle
Area = w × h
w = width
h = height
25ft × x=1125 ft²
=> x=1125 ft²/25 ft
x=45 ft
Answer:
x=1125÷25=45ft
Area=length × width therefore
length= area÷width
A triangle has one angle that measures 31 degrees, one angle that measures 46 degrees, and one angle that measures 103 degrees. A.
equilateral triangle
B.
scalene triangle
C.
right triangle
D.
isosceles triangle
The combination of Wendell and Maggie’s ages is 33. Wendell’s age is 3 less than 3 times the age of Maggie. How old is Wendell?
Step-by-step explanation:
The combination of Wendell and Maggie’s ages is 33. Let Maggie's age is x. It is mentioned that Wendell’s age is 3 less than 3 times the age of Maggie. It means, Wendell’s age is (3x-3).
ATQ,
[tex]x+(3x-3)=33\\\\4x-3=33\\\\4x=36\\\\x=9[/tex]
The age of Maggie is x. So, Wendell's age is :
[tex]y=(3x-3)\\\\y=(3(9)-3)\\\\y=24[/tex]
So, Wendell age is 24 years.
i need blank 1 and blank 2
Answer:
Blank 1: 40
Blank 2: 10
Step-by-step explanation:
You can start by representing the speed of the water as x and the speed of the dolphin as y, and writing an equation.
y+x=50
y-x=30
Adding these two equations together, you get:
2y=80
y=40 for the speed of the dolphin in still water. Now, you an use one of the previous equations to find the speed of the current.
40-x=30
x=10
Hope this helps!
If each necklace chain is 18 inches long, how many necklaces can be made from 137.16 centimeters of silver chain?
Answer:
3
Step-by-step explanation:
to convert the centimeters to inches, divide 137. 16 by 2.54
you should get 54
then divide by 18
you get three
You can make 3 necklaces from 137.16 centimeters of silver chain, given that each necklace is 18 inches long. We first converted the necklace length to centimeters, and then divided the total length of silver chain by the length of each necklace.
Explanation:To find out how many necklaces can be made from 137.16 centimeters of silver chain, we first need to convert the units because the length of the necklace chain is given in inches, while the total amount of silver chain is given in centimeters.
We know that 1 inch is equal to 2.54 centimeters. Therefore, if each necklace is 18 inches long, the length of each necklace in centimeters is 18 inches * 2.54 cm/inch = 45.72 cm.
Now, to find the number of necklaces that can be made, we divide the total length of silver chain by the length of each necklace. That is 137.16 cm / 45.72 cm/necklace = 3 necklaces (rounded down to the nearest whole necklace, because we cannot make a fraction of a necklace).
Learn more about Unit Conversion here:https://brainly.com/question/19420601
#SPJ2
Two similar cones have volume of 343pi cubic centimeters and 512pi cubic centimeters. The height of each cone is equal to 3 times its radius. Find the radius and height of both cones
Answer:
For the first cone: r = 7 cm, h = 21 cm
For the second cone: r = 8 cm, h = 24 cm
Step-by-step explanation:
The volume of the first cone is [tex]343\pi cm^3[/tex]
The volume of the second cone is [tex]512\pi cm^3[/tex]
We are told that the height of each cone is 3 times its radius, hence:
h = 3r
The volume of a cone is given as:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Substituting h = 3r:
[tex]V = \frac{1}{3} \pi r^2(3r)\\\\\\V = \frac{1}{3} \pi (3r^3)\\\\\\V = \pi r^3[/tex]
For the first cone, V = [tex]343\pi cm^3[/tex], radius, r, will be:
[tex]343\pi = \pi r^3\\\\\\=> r^3 = 343\\\\\\r = \sqrt[3]{343} \\\\\\r = 7 cm[/tex]
∴ Its height will be:
h = 3r = 3 * 7 = 21 cm
For the second cone, V = [tex]512\pi cm^3[/tex], radius, r, will be:
[tex]512\pi = \pi r^3\\\\\\=> r^3 = 512\\\\\\r = \sqrt[3]{512} \\\\\\r = 8 cm[/tex]
∴ Its height will be:
h = 3r = 3 * 8 = 24 cm
The radius and height of the first cone are 7 cm and 21 cm respectively while the radius and height of the second cone are 8 cm and 24 cm respectively.
A circle with radius \pink{9}9start color #ff00af, 9, end color #ff00af has a sector with a central angle of \purple{120^\circ}120 ∘ start color #9d38bd, 120, degrees, end color #9d38bd. What is the area of the sector? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
Area of sector = 84.861
Step-by-step explanation:
Given
The radius of the circle = 9
central angle of sector = [tex]120^{o}[/tex]
value of pi π = 3.143
To find : the area of sector = ?
We know that the formula to calculate area of sector is given as:
area of sector = (π [tex]r^{2}[/tex]Θ)/ [tex]360^{o}[/tex]
where, r is radius and Θ is the central angle of the sector
Substituting the known values in above formula, we get
area of sector = (3.143 x [tex]9^{2}[/tex] x [tex]120^{o}[/tex]) / [tex]360^{o}[/tex]
= 84.861
Hence area of sector is 84.861
Answer:
27 pi
Step-by-step explanation:
just did this one
Fill in the missing number to the equivalent ratio 9:15=45: _
Answer:
75
Step-by-step explanation:
9x5=45
15x5=75
Answer:
75
Step-by-step explanation:
9:15=45: _
very similar to cross multiplying
9/15 = (45/ something)
something = 45 / (9/15) = 45 * (15/9) = 5*15 = 75
The width of a rectangle is the length minus 7 units. The area of the rectangle
is 8 units. What is the length, in units, of the rectangle?
Answer:
l=8
Step-by-step explanation:
w=l-7
Area=l*(l-7)=8 u
l^2-7l-8=0
l^2- 8l+l-8=0
l(l-8)+l-8=0
(l-8)*(l+1)=0
l-8=0 , l=8 or
l+1=0, l=-1 impossible
so l=8
To find the length of a rectangle when its width is the length minus 7 units and its area is 8 units, you can set up an equation and solve it. In this case, the length of the rectangle is 8 units.
Explanation:To solve this problem, you need to set up an equation based on the given information. Let's assume the length of the rectangle is 'L'. According to the problem, the width of the rectangle is the length minus 7 units. So, the width can be represented as 'L-7'.
The area of a rectangle is given by the formula 'length x width'. In this case, the area of the rectangle is 8 units. So, the equation would be: L x (L-7) = 8.
To find the length of the rectangle, you need to solve the equation. Expand the equation: L^2 - 7L = 8. Rearrange it to form a quadratic equation: L^2 - 7L - 8 = 0. Factorize or use the quadratic formula to find the values of 'L'. It turns out that the length of the rectangle is 8 units.
Learn more about Finding the length of a rectangle here:https://brainly.com/question/34224051
#SPJ3
Please help! Will give brainliest!
Answer:
The answer to your question is 365040000 lb or 3.65 x 10⁸ lb
Step-by-step explanation:
Data
Rectangular pyramid
base = 100 yd x 78 yd
height = 100 yd
weight of a stone = 468 lb/yd³
Process
1.- Calculate the volume of the pyramid
Volume = area of the base x height
-Substitution
Volume = 100 x 78 x 100
-Simplification
Volume = 780000 yd³
2.- Calculate the weight of the pyramid
468 lb ------------------------ 1 yd³
x ------------------------780000 yd³
x = (780000 x 468) / 1
x = 365040000 lb or 3.65 x 10⁸ lb
what does 4mnt-16mn-t+4 equal to
Answer:(t-4)(4mn-1)
Step-by-step explanation: