Answers
The two triangles are similar, ABC is an enlargement of RST by scale factor 2.5. So all lengths are 2.5 times larger than the lengths for RST
This gives us lengths of 30, 32.5 and 12.5
Adding these together gives us 75 for the perimeter
B) 30
We can work out the missing side of RST using Pythagoras’ theorem, it is 12
(12x5)/2 = 30
C) 187.5
We can use the same method as in B and use the formula for the area of a triangle to work out that the area for ABC is 187.5
Related Questions
The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent
Answers
Answer:
p(t) = 100×1.0153^(12t)1.53% per monthStep-by-step explanation:
In general, the function will be written ...
p(t) = (initial value)×(growth factor)^t
where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...
growth factor = 1 + growth rate
Here, the growth rate is given as 20% per year, so the growth factor per year is ...
1 +20% = 1.20
The initial value is given as 100, so we can write the exponential function as ...
p(t) = 100×1.20^t
__
The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.
p(t) = 100×(1.20^(1/12))^( 12t)
p(t) = 100×1.0153^(12t) . . . . population exponential function
This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...
1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change
Answers:
Function is [tex]P(t) = 100(1.0153)^{12t}\\\\[/tex]Monthly growth rate is roughly 1.53%=====================================================
Explanation:
The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).
Dividing the "before" and "after" population amounts gets us 120/100 = 1.20
If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be
[tex]P(t) = 100(1.20)^t[/tex]
where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.
If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.
---------------------
Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.
Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973
Divide this amount over the initial population to find m.
m = 101.530947049973/100 = 1.01530947049973
So we get m = 1.0153 after rounding to four decimal places.
The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%
The pigeon population is increasing by roughly 1.53% each month.
This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.
---------------------
An alternative way to compute this value is to use this formula
m = (1+r)^(1/12)
We'll plug in the annual rate r = 0.20 to get:
m = (1+r)^(1/12)
m = (1+0.20)^(1/12)
m = 1.01530947049973
m = 1.0153
We get the same approximate value as earlier.
---------------------
Whichever method you use, you should get roughly m = 1.0153
We're given that A = 100 is the initial population
So we'll then be able to form this function
[tex]P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\[/tex]
This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.
Once again, for comparison we have...
[tex]P(t) = 100(1.20)^{t}\\\\[/tex] for annual growth[tex]P(t) = 100(1.0153)^{12t}\\\\[/tex] for monthly growthEach function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.
---------------------
You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is [tex]P(t) = 100(1.0153)^{t}\\\\[/tex] and show that an error happens.
If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.
[tex]P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\[/tex]
That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.
Angelique Calculated the slope of a line that passed through points (-5,4) and (2,-3) her work is shown below. identify her error and correct her mistakes.
Answers
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 4 ) and (x₂, y₂ ) = (2, - 3 )
m = [tex]\frac{-3-4}{2-(-5)}[/tex]
Her error was subtracting 5 from 2 instead of - 5 from 2
m = [tex]\frac{-7}{2+5}[/tex] = [tex]\frac{-7}{7}[/tex] = - 1 ← corrected solution
A group of students are working on a project. They complete 30%percent of the project in 12 hours. If they continue to work at the same speed, how many hours will it take the group to finish the project
Answers
Answer: 40 HOURS
Step-by-step explanation:
If the students complete 30% of the project in 12 hours,
that means:
12 h................................30%
? h...................................100%
(12*100)/30= 40H
THE STUDENTS NEED 40H TO COMPLETE THE PROJECT
It will take 40 hours for the group to finish the project.
How many hours will it take the group to finish the project?
If the students complete 30% of the project in 12 hours,
that means:
⇒ 12 h = 30%
⇒ ? h = 100%
By using percentage theory:
Percentage formula = (Value/Total value) × 100.
⇒ (12*100)/30= 40H
The answer is 40 hours.
What are a percentage and its formula?
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100.
Learn more about percentage here: brainly.com/question/843074
#SPJ2
Giving brainliestttyttttt
Answers
Answer:
C
Step-by-step explanation:
Because its right
What’s the figure name
Answers
Answer:
Line GH or Line HG
Step-by-step explanation:
Hope it help !!
Answer:
line segmentStep-by-step explanation:
a point to a point which makes a straight line is called a line segment
As a car owner/lessee, it is not a requirement to have minimum coverage auto insurance.
T or F
Answers
Answer: False
Step-by-step explanation:
deposited $7,500 into a savings account 5 years ago. The simple interest rate is 2%. How much money did earn in interest?
Answers
Answer:
$750
Step-by-step explanation:
simple interest equation is:
I (interest) = P (principal) x R (interest rate, as a decimal) x T (time, in years)
I = 7500 x .02 x 5
I = 750
The following shapes are congruent. Write the correct congruence statement for shape MJZP.
A. BLXY
B. LXYB
C. XYBL
D. YBLX
Answers
Answer:
B. LXYB.
Step-by-step explanation:
What is the value of the expression shown below, when p= 1 and q= 4
Answers
Answer:
The correct answer is 5.
Step-by-step explanation:
I got 100% on the assignment
This graph represents the design of a child’s slide what is the slope of the slide
Answers
Answer:
I think it is 1/2 because it goes up 1 over 2
Use the linear combination method to solve the system of equations PLZ HELP I WILL GIVE BRAINLIEST AND ITS WORTH A LOT OF POINTS, PLZZZZZZZZZZZZZZZZ
2x-3y=13
2x+4y=-8
Answers
2x+4y=-8...(2)
Multiply equation 2 by -1 to eliminate x
2x-3y=13
+ -2x-4y=8
—————
-7y=21
y=-3
Substitute y=-3 into equation 2
2x+4(-3)=-8
x=2
Therefore, the solution to the system is (2, -3)
Calculate the distance between the points M=(-1,-2) and C=(-9, 2) in the coordinate plane.
Round your answer to the nearest hundredth.
Answers
Answer:
8.9443
Step-by-step explanation:
d = √((x2-x1)2 + (y2-y1)2)
Step by step procedure:
Find the difference between coordinates:
(x2-x1) = (-9 - -1) = -8
(y2-y1) = (2 - -2) = 4
Square the results and sum them up:
(-8)2 + (4)2 = 64 + 16 = 80
Now Find the square root and that's your result:
Exact solution: √80 = 4√5
Approximate solution: 8.9443
Write a function rule for "The output is three times the input increased by two
A) y=5x
B) y=3x+2
C) y=3x - 2
D) y=2x+3
Answers
X is the input.
Three times the input would be 3x
Increased by two would be adding two at the end.
Answer: B. y = 3x + 2
1. Which value is the closest to 0.9.997?
a.
1,000
b.
81
C.
10,000
d.
10
Answers
I think the answer would be D. 10 is closest to 0.9997
11. A bank teller has a total of 124 bills in five-dollar bills and ten-dollar bills. The total value of the
money is $840. How many ten-dollar bills does she have?
Answers
The total money of the value is $840 then you would subtract. $840-$620=$220.
Divide that by ten so, $220/10= 22.
She has 22 ten dollar bills.
10. Mrs. Taylor wants to lay new carpet in the entrance and hallway of her home as shown below. The carpet she selected sells for $2.50 a square foot. How much will it cost to lay the carpet in the entrance and hallway?
Answers
.this is all the question
Answers
Answer:
Answer: 2
Step-by-step explanation:
Someone please help me
Answers
Can someone also help me with this one? Thank you very much!
Answers
Answer:
10950 feet
Step-by-step explanation:
1 mile is 5280 feet
5280*2=10560
10560+390=10950
:)
Answer:
Your answer would be 10950!
Step-by-step explanation:
There are 5280 Feet in a mile. It says that there are 2 MILES and 390 FEET. We Multiply 2 by 5280 to get 10560 feet.Lastly, we add 10560 and 390 to get 10950Apple + Orange = $20
Apple is twice the price of the orange
How much does the apple cost?
Answers
Answer:
Step-by-step explanation:
let price of Orange=x
price of Apple=2x
x+2x=20
3x=20
x=20/3
cost of Apple=2x=2×20/3=40/3=$13 1/3
According to question,
x + 2x = 20
3x = 20
x = 20/3
x = 6.6667
2x = 2 x 6.667 = 13.33
kevin's family left on flight 737 to new york.flight 737 traveled 1346 miles in 3 hours.what is the unit rate?
Answers
Answer:
448 2/3
Step-by-step explanation:
To find miles in 1 hour (the unit rate), divide miles by hours.
(1346 mi)/(3 h) = 448 2/3 mi/h
The unit rate is 448 2/3 miles per hour.
[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]
Here we've been given,
Miles (m) = 1346Time (h) = 3 hours Unit rate = ?The standard formula for unit rate is given by,
[tex]:\implies\sf{Unit \: rate = \frac{miles}{hours} } \\ \\ :\implies\sf{Unit \: rate = \frac{1346 \: miles}{3 \: hours} } \\ \\ :\implies\sf{Unit \: rate = 448 \frac{2}{3} \: \frac{miles}{hour} }[/tex]
The unit rate for the flight 737 is 448 2/3 miles per hour.The value of y varies directly with x.
When y=3, x=1.
What is the value of y when x is 4?
12
3/4
4 1/3
8
Answers
Answer:
12
Step-by-step explanation:
x = 1 y = 3, x = 2 y = 6, x = 3 y = 9, x = 4 y = 12
Answer:
12
Step-by-step explanation:
if x=1 , y =3
if x=4 then y=3×4=12
y=12
is y = 2/3x - 7 proportional or not?
Answers
Answer: No, it is not a direct proportion equation
Explanation:
Direct proportions are always in the form [tex]y = kx[/tex] where k is any nonzero real number. So for example, we could have the equation [tex]y = 9x[/tex]. The y intercept of any direct proportion is always zero. Visually, such equations will go through the origin.
Something like [tex]y = \frac{2}{3}x-7[/tex] has a y intercept of -7 and it doesn't fit the form [tex]y = kx[/tex], so it's not a direct proportion equation.
Unit Rate
Madison can eat 12 eggs in 20 minutes. How many
eggs can she eat in 35 minutes?
Answers
Answer:
37
Step-by-step explanation:
38 + u actually thought lol
Write
48
:
132
:
84
in its simplest form.
Answers
Answer:
4:11:7
Step-by-step explanation:
Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12
Answer:
4:11:7
Step-by-step explanation:
please mark me as brainlest
B. {(15,0),(15,-2)}
Function?
Domain:
Range
Answers
Answers:
Function? No, it's not a functionDomain: {15}Range: {0, -2}===============================================
Explanation:
The domain consists of the set of x coordinates of each point. In this case, we only have one x value listed. The domain is {15}. Use curly braces even if there's only one item. This tells the reader we have a set.
The range is {0,-2} to indicate the y coordinates of the two points.
We don't have a function because x = 15 repeats itself. The input x = 15 leads to multiple outputs at the same time, which isn't allowed if you want a function. You can use the vertical line test as a visual way to see that we don't have a function.
A triangle has interior measures of 45° and 50°. What is the measure of the third angle?
950
850
90°
50
Answers
Answer:
85 degrees
Step-by-step explanation:
the inside of a triangle is always 180 degrees.
180-45-59=85
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeee ty :)
Answers
We know the equation.
=> y = mx + bWe also know the y-intercept is -1.
=> y = mx - 1All we need to do now is to find the slope. We know the slope formula.
=> Rise/Run = Slope=> 4/6 = Slope=> 2/3 = SlopeConclusion:Therefore, our equation is y = 2x/3 - 1
Hoped this helped.
[tex]BrainiacUser1357[/tex]
please help me with this
Answers
LM= 9.9 cm
Please solve this...I can;t do it do it
Answers
Answer:
Area = 867 meters
Step-by-step explanation:
You have a rectangle. This means opposite sides are equal. If you set these expressions equal to each other, you will get two equations with two unknowns, x and y. Next, solve the system of equations to find x and y. Then, use the values to find the length and width of the rectangle. Last, multiply length × width to find the area.