Answer:
t = 30°y = 60°z = 90°Step-by-step explanation:
The given relations can be used to write three equations for the angle values.
Setupt + y + z = 180 . . . . . sum of all angle measures
y + z = 5t . . . . . . . . second and third total 5 times the first
y + 30 = z . . . . . . third angle is 30 more than the second.
__
SolutionUsing the third equation to substitute for z in the first two equations gives ...
t + y + (y +30) = 180 ⇒ t +2y +30 = 180
y + (y +30) = 5t ⇒ 2y +30 = 5t
Using the second of these equations to substitute for (2y+30) in the first, we have ...
t +5t = 180
t = 180/6 = 30 . . . . . . divide by the coefficient of t
Using this value in our equation for 5t gives ...
2y +30 = 5(30)
2y = 120
y = 60
Then the value of angle z is ...
y +30 = z = 60 +30
z = 90
The first, second, and third angles are 30°, 60°, and 90°, respectively.
I will mark brainly, please help me solve this question.
If the rate of inflation per annum is 15% per annum, how long will iti take for the price of an item to double?
Answer:
it will take approximately 6.67 annum(years) to double the price of an item that is inflated by 15% each annum(year)
If Mike walks to school and rides his bicycle back at home it takes him 90 minutes. If he rides his bicycle both ways it takes him 30 minutes. How long would it take the trip to school and back walking? Assume he walks at a constant speed and also rides the bicycle at a constant speed.
Answer:
2 hours 30 minutes
Step-by-step explanation:
Mike rides to School and back for 30 minutes. It means that he rides to school 15 minutes.
90min-15min = 75min (one way, walking)
2*75min = 150min = 2h 30min
Mike's will walk to school and back home 2h 30min
What is the sum of the solutions to the equation below?
8x^2 + 2x - 3 = 0
A) 3/8 B) 1/4 C) -1/4 D - 3/8
Answer:
(x−1)43x3−8x2+10 can be resolved into partial fraction as x−1A+(x−1)2B+(x−1)3C+(x−1)4D
So , 3x3−8x2+10=A(x−1)3+B(x−1)2+C(x−1)+D
Put x=1 , we get 3−8+10=D
D=5
Comparing the coefficient of x3 on both sides we get , A=3 .
So equation reduces to 3x3−8x2+10=3(x−1)3+B(x−1)2+C(x−1)+5
Now compare the constant on both sides , 10=−3+B−C+5
=>8=B−C - (1)
Comparing the coefficent of x2 we get −8=−9+B
=>B=1
So , put B=1 in (1) , we get C=−7
Therefore , (x−1)43x3−8x2+10=x−13+(x−1)21−(x−1)37+(x−1)45
Step-by-step explanation:
hope it helps
A regular octagon with side length = 5.3 meters. What is the total area of the shape? Round to two
decimal places at the end of your calculation.
Answer:
97.31 [tex]m^2[/tex]
Step-by-step explanation:
The area of the octagon is:
[tex]\frac{8 * 5.3 * 2.65\sqrt{3} }{2}[/tex] ~97.31 m^2
.
Ben deposits $1,750 into each of two savings accounts.
Account I earns 2.75% annual simple interest
Account II earns 2.75% interest compounded annually
Ben does not make any additional deposits or withdrawals. Which amount is closest to the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years?
The difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years is $1.32.
What is the differnce in the interest?Simple interest is when only the amount deposited increases in value.
Simple interest = deposit x interest rate x time
1750 x 0.0275 x 2 = $96.25
Interest earned with compounding = future value - amount deposited.
The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate N = number of years1750 x (1/0275)^2 = $1847.57
$1847.57 - $1750 = $97.57
Difference in interest; $97.57 - $96.25 = $1.32
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Question 5
Thank you
A calendar use seven boxes of nails to build 10 bird houses he used blank of a box on each birdhouse
Will give brainliest pls answer!!
Find the volume of the rectangular
prism.
A)29 cm³
B) 87 cm³
C)288 cm³
D)576 cm³
Answer:
D) 576 cubic cm
Step-by-step explanation:
[tex]16 \times 9 \times 4 = 576[/tex]
Answer:
the answer is D
Step-by-step explanation:
volume =height × length × width
so 9×4×16= 576
Can someone help me with this problem?
[tex]~~~~~\dfrac 13 \ln\left(x^6 \right) +\dfrac 12 \ln\left(x^2\right) = \ln x^a\\\\\implies \ln \left(x^6 \right)^{\tfrac 13} + \ln \left(x^2 \right)^{\tfrac 12} = \ln x^a\\ \\\implies \ln x^2 + \ln x = \ln x^a\\\\\implies \ln(x^2 \cdot x) = \ln x^a \\\\\implies \ln x^3 = \ln x^a\\ \\\implies 3 \ln x = a \ln x\\\\\implies a =3[/tex]
Which graph shows the line that best fits the data points given?
I need it ASAP
Please and Thank You! :)
Answer:
c
Step-by-step explanation:
the line goes thru most of the points and it's in the same direction also bc i had that same question a couple days ago
PLEASE HELP ME!!!
Question 1 Part D (2 points): Which of the following is NOT an example of the closure property as it relates to polynomials?
A.
(x + 2)(2x - 1) = 2x² + 3x - 2
B.
(x³ - x² + 4) - (2x² + 5) = x³ - 3x² - 1
C.
(2x)(0) = 0
D.
(2x³ - x² - 5x + 4) + (x³ - 2x² + 1) = 3x³ - 3x² - 5x + 5
E.
None of the above because all are examples of the closure property as it relates to polynomials
None of the above because all are examples of the closure property as it relates to polynomials.
Closure property of the functionA function is known to be closed if its input value is equal to its output.
Accordng to the question, we need to select the function that obeys the law of closure.
To select the correct polynmials, we need to determine the function that has its left hand side equal to the right.
From the given options,we can see that all their right hand sides are equal to the left, hence we can conclude that "none of the above because all are examples of the closure property as it relates to polynomials"
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How can we use the distributive property to find an expression equivalent to
15(x + 2)? Place the steps in order.
CLEAR
Answer:
15x+30
Step-by-step explanation:
multiply 15 and x + multiply 15 and 2
15x+30
What is the measure of each angle of a regular 17-gon? If necessary, round to the nearest tenth.
For a regular 17-gon, the measure of the internal angles is:
a = 158.8°
How to measure the internal angles?
The measure of the sum of the internal angles of a regular figure of N sides is:
(N - 2)*180°
For the case where N = 17, we have:
(17 - 2)*180° = 2,700°
That is the measure of the sum of the internal angles, and we have 17 of them, so the measure of each angle is:
2,700°/17 = 158.8°
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please answer it
I need it now
What's the area of the composite figure?
Answer:
[tex]\huge\boxed{\bf\: 83 \: yd^{2}}[/tex]
Step-by-step explanation:
Consider rectangle ABCD.
Here,
AB = DC = 9 yd (length = l)
AD = BC = 7 yd (width = w)
Area of this rectangle:
= l * b
= 9 * 7
= 63 yd²
[tex]\rule{150pt}{2pt}[/tex]
Now, take rectangle DEGF.
Here,
DE = FG = 5 yd (length = l)
DF = EG = 4 yd (width = w)
Area of this rectangle:
= l * b
= 5 * 4
= 20 yd²
[tex]\rule{150pt}{2pt}[/tex]
Total area of the compisite figure:
= Area of rectangle ABCD + Area of rectangle DEGF
= 63 yd² + 20 yd²
= 83 yd²
[tex]\rule{150pt}{2pt}[/tex]
Refer to the attachment for the labelling of the figure.
How many ways can you place the letters in the word "PASTURE" into groups of four letters without repetition?
Using the permutation formula, it is found that there are 840 ways to place the letters.
The order in which the letters are placed is important, as PAST is a different arrangement that PTAS, for example, hence the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 letters are taken from a set of 7, hence:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
There are 840 ways to place the letters.
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Answer:35
Step-by-step explanation:
Tickets for a carnival cost $8 for children and $12 for adults. The carnival sold a total of 233 tickets and collected $2,156. How many children’s tickets were sold?
A.
180
B.
160
C.
73
D.
108
The management of a restaurant has been studying whether or not new customers return within a month. The collected data reveal that 60% of the new customers have returned. If 90 new customers dine at the restaurant this month, what is the probability that at least 60 will return next month? Use Normal approximation to Binomial distribution.
Using the normal approximation to the binomial, it is found that there is a 0.119 = 11.9% probability that at least 60 will return next month.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem, we have that:
60% of the new customers have returned, hence p = 0.6.90 new customers dine at the restaurant this month, hence n = 90.Thus, the mean and the standard error for the approximation are given as follows:
[tex]\mu = np = 90(0.6) = 54[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{90(0.6)(0.4)} = 4.6476[/tex]Using continuity correction, the probability that at least 60 will return next month is P(X > 60 - 0.5) = P(X > 59.5), which is 1 subtracted by the p-value of Z when X = 59.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{59.5 - 54}{4.6476}[/tex]
Z = 1.18
Z = 1.18 has a p-value of 0.881.
1 - 0.881 = 0.119.
0.119 = 11.9% probability that at least 60 will return next month.
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Landry is going to wrap a birthday present for his mom. He needs to know how much wrapping paper he needs to wrap the present with no overlap.
volume
or
surface area
Answer:
surface area
Step-by-step explanation:
Wrapping paper covers the surface of an object.
To know how much paper he needs, Landry will need to determine the surface area of the present.
help please and ty lol
Answer:
A=35.5 degrees
Step-by-step explanation:
Check out the photo. Leave a comment if anything's not clear.
answer this. pleaaaaseeee
Answer:
look at analysis
Step-by-step explanation:
11. 23.81
12.
part A
y is 12 and x is 4
part B
4
part C
5×12×4
240
49
Jerrelle spent $0.60 on five stickers. Each sticker costs the same amount. How much
did each sticker cost?
A
$0.06
B
$0.12
с
$1.20
D $5
Answer:
A. $0.60
Step-by-step explanation:
there are 5 strikers that cost $0.60 each, so the answer is letter A.
Rylee read 36 pages of a book before putting
it down for a month. She wants to resume
reading the book that is more than 480 pages
long. She plans on finishing the book in
12 days, reading the same amount each day.
5. Which inequality can be used to determine,
p, the number of pages that Rylee must read
P
each day to attain her goal?
A. 12p - 36 < 480
B. 12p + 36 < 480
C. 12p - 36 > 480
D. 12p + 36 > 480
-
Answer:
D. 12p + 36 > 480
Step-by-step explanation:
The number of pages read is the sum of the number already read (36) and the product of the number read each day (p) and the number of days (12). Rylee wants this number of pages read to be more than 480.
__
The inequality expressing a sum greater than 480 is ...
12p +36 > 480 . . . . choice D
Find the missing side. Round
to the nearest tenth.
Х
y
390
57
X=[?]
Answer:It's 46.2
Step-by-step explanation:
Two great structures are
described below. What is the
difference, in square feet, between the visible
surface area of
the Great Pyramid and the first tower of the World Trade
Center? (Hint: The bottom side is not visible for either
structure.)
On September 11, 2001,
terrorists crashed planes
The Great Pyramid of
Giza, built around 2550
B.C., has a square base
with a length of 756 feet,
and the distance from
the middle of any base
side to the top is 612 feet.
into the World Trade
Center Twin Towers. The
first tower was a
rectangular prism with a
square base whose sides
were 208 feet long. The
tower was 1,368 feet tall.
The difference, in square feet, between the visible surface area of
The Great Pyramid and the first tower of the World Trade Center are 358704.
What is the lateral surface area of this rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The lateral surface area of this rectangular prism = Perimeter x height
The Great Pyramid of Giza, has a square base with a length of 756 feet, and the distance from the middle of any base side to the top is 612 feet.
The first tower was a rectangular prism with a square base whose sides
were 208 feet long. The tower was 1,368 feet tall.
Total surface area = base area + (1/2 × perimeter × slant height)
Perimeter of base = 4 × 756 = 3024 feet
Slant height = 612 feet
Base area = 756² = 571536 feet²
The total surface area
[tex]= 571536 + (1/2 \times 3024 \times 612)\\ 1496880 feet^2[/tex]
The surface area of this rectangular prism = Perimeter x height
Perimeter of base = 4 × 208 = 832 feet
Area = [tex]832 \times 1368\\\\1138176[/tex]
The difference, in square feet, between the visible surface area of
the Great Pyramid and the first tower of the World Trade Center are 358704.
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You randomly choose a marble from a jar. The jar contains 3 red marbles, 10 blue marbles, 8 green marbles, and 4 yellow marbles. Find the probability of choosing a blue marble.
Answer:
total marbles=3+10+8+4=25 marbles total
10 blue marbles/25 total marbles
10/25=2/5 probability
Step-by-step explanation:
Ben and Carson went to the movies with friends. Ben purchased 3 popcorn and 2 boxes of candy for $41. Carson purchased 1 popcorn and 2 boxes of candy for $29. How much did the popcorn cost?
Answer:
$6
Step-by-step explanation:
B- 3P+2C=$41
C-1P+2C=$29
since they both bought at least 1 popcorn and 2 candy you can just subtract 29 from 41. you get 12 which equals the other 2 popcorns that ben bought
12/2=6
since you need to find the price of 1 popcorn you have to divide 12 by 2
What is the surface area of the cylinder with height 8 ft and radius 3 ft? Round your
answer to the nearest thousandth.
A: 186.885
B: 195.004
C: 205.132
D: 207.345
We know that,
The surface of a cylinder is given by,
2πr(r + h)h= heightr= radiusso,
the surface area of the given cylinder would be,
⇢2π*3(3+8)⇢6π*11⇢66π⇢207.345Write the equation of the parabola that has the vertex at point (2,-11) and passes through the point (0,5).
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{vertex}{(\stackrel{h}{2}~~,~~\stackrel{k}{-11})}\qquad y=a(x-2)^2-11\qquad \qquad \textit{we also know that} \begin{cases} x=0\\ y=5 \end{cases} \\\\\\ 5=a(0-2)^2-11\implies 16=4a\implies \cfrac{16}{4}=a\implies 4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=4(x-2)^2-11~\hfill[/tex]
The equation of the parabola that has the vertex at point (2,-11) and passes through the point (0,5) is y = 4 (x - 2)² - 11.
What is Parabola?A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.
The general form of a parabola is,
y = a (x - h)² + k
where (h, k) is the vertex.
Given vertex is (2, -11).
Equation is,
y = a(x - 2)² - 11
Also, given that the parabola passes through the point (0, 5).
Substituting,
5 = a (0 - 2)² - 11
⇒ 5 = 4a - 11
⇒ a = 4
So the required equation is, y = 4 (x - 2)² - 11.
Hence the equation of the given parabola is y = 4 (x - 2)² - 11.
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Which of these figures has a line of symmetry drawn correctly?
Shape A and Shape B
Shape B and Shape D
Shape A
Shape C