These triangles are scaled copies of each other. Four right triangles labeled F, B, G, and H. Triangle F has the vertical side labeled 8, the horizontal side labeled 6, and the longest side labeled 10. Triangle B has the vertical side labeled 2, the horizontal side labeled 3 halves, and the longest side labeled 5 halves. Triangle G has the vertical side labeled 4, the horizontal side labeled 3, and the longest side labeled 5. Triangle H has the vertical side labeled 8 thirds, the horizontal side labeled 2, and the longest side labeled 10 thirds. For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first? Remember that area is scale factor x scale factor. Use Triangle G and Triangle F
Answers
Answer:
The question is not complete, below is the completed question:
These triangles are scaled copies of each other. Four right triangles labeled F, B, G, and H. Triangle F has the vertical side labeled 8, the horizontal side labeled 6, and the longest side labeled 10. Triangle B has the vertical side labeled 2, the horizontal side labeled 3 halves, and the longest side labeled 5 halves. Triangle G has the vertical side labeled 4, the horizontal side labeled 3, and the longest side labeled 5. Triangle H has the vertical side labeled 8 thirds, the horizontal side labeled 2, and the longest side labeled 10 thirds. For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first? Remember that area is scale factor x scale factor.
1. Triangle G and Triangle F
2. Triangle G and Triangle B
3. Triangle B and Triangle F
4. Triangle F and Triangle H
5. Triangle G and Triangle H
6. Triangle H and Triangle B
Answer:
1. Triangle G and Triangle F = 4 times
2. Triangle G and Triangle B = 0.2 times
3. Triangle B and Triangle F = 16 times
4. Triangle F and Triangle H = 0.11 times
5. Triangle G and Triangle H = 0.44 times
6. Triangle H and Triangle B = 0.56 times
Step-by-step explanation:
using the image of the triangles attached to this solution, let us calculate the area of each pair of triangles
1. Area of Triangle = [tex]\frac{base\ \times\ height}{2}[/tex]
[tex]F = \frac{6 \times 8}{2} = \frac{48}{2} = 24\\B = \frac{\frac{3}{2} \times 2 }{2} = \frac{3}{2} = \frac{3}{2}\\ G = \frac{3 \times4}{2}= \frac{12}{2} = 6\\ H = \frac{2 \times \frac{8}{3} }{2} = \frac{16}{6} = \frac{8}{3}[/tex]
To find by how many times the second triangle is larger than the first, we will calculate the ratio of the areas of the second triangle to the first
1. Triangle G and Triangle F = 24:6 = 4
∴ The area of triangle F is 4 times larger than triangle G
2. Triangle G and Triangle B = 3/2 : 6 = [tex]\frac{1}{4}[/tex] = 0.2
∴ The area of triangle B is 0.2 times larger than triangle G
3. Triangle B and Triangle F = [tex]24 : \frac{3}{2} = 16[/tex]
∴ The area of triangle F is 16 times larger than triangle B
4. Triangle F and Triangle H = [tex]\frac{8}{3} : 24 = \frac{1}{9} = 0.11[/tex]
∴ The area of triangle H is 0.11 times larger than triangle F
5. Triangle G and Triangle H = [tex]\frac{8}{3} : 6 = \frac{4}{9} = 0.44[/tex]
∴ The area of triangle H is 0.44 times larger than triangle G
6. Triangle H and Triangle B = [tex]\frac{3}{2} : \frac{8}{3} = \frac{9}{16} = 0.56[/tex]
∴ The area of triangle B is 0.56 times larger than triangle H
Related Questions
how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)
Answers
-3-3= -6 2-3=-1
-6/-1=6
Y=6x+b
3=6 x 3
3=18
Subtract both sides by 18
B=-15
Answer= y=6x-15
I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
Answers
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
Consider each expression. if x = -2, is the value of the expression
a positive number? Select Yes or No.
A. -2(x - 2)
Yes
No
B. –3x(5 – 4x)
Yes
No
C. x + 6x
O Yes O No
Answers
Answer:
Yes
Yes
No
Step-by-step explanation:
Given value x = -2;
Problem, is the expression a positive number ?
A. -2(x - 2)
if x = -2
-2(-2 - 2)
= -2 (-4)
= 8
Yes
B. -3x(5 - 4x)
if x = -2
-3 x -2(5 - 4(-2))
= 6 (5 + 8)
= 6 x 13
= 78
Yes
C. x + 6x
if x = -2
-2 + 6(-2)
= -2 - 12
= - 14
No
On average, Carson saves about 53% of his allowance each month. When creating a circle graph of what Carson does
with his money, which of the following fractions would be the best to represent how much he saves?
1/2 1/4 3/10. 3/4
Answers
Answer:
1/2
Step-by-step explanation:
1/2 would be the best fraction to represent how much he saves.
Justin bought 40 packs of baseball cards for $64, if he sells 10 packs how much should he charge?
Answers
Answer:
14 dollars
Step-by-step explanation:
If he sells 10 packs, then it will be 4 times less than 40, which means that the pricwe will be 4 times less, or 64 dollars divided by 4 = 14 dollars
Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. The members are identified by numbering them 00 through 34.
Answers
Answer:
Metro Toledo Automobile Dealers Association
a) The mean revenue
= Total Revenue from the dealer service departments/35
b) The sample of five include 27, 23, 32, 11, and 13
c) Using systematic random sampling, the dealers included in the sample are: 7, 13, 19, 25, and 31.
Step-by-step explanation:
a) The mean value is the total value divided by the number of elements. The mean revenue is, therefore, the total revenue from the dealer service departments divided by the number of dealers. This gives an average revenue from each dealer, which is a statistic to describe the population.
b) The sample of five cannot include any number that is outside the population. For example, 85 is not a number allocated to any dealer in the indicated population, therefore, it cannot form part of the population sample.
c) The systematic random sampling starts from 7 and chooses the sixth number after 7. Therefore, the next four numbers are multiples of 6. This is why we choose 13, 19, 25, and 31.
"The intersection of two planes is a line" is a statement that is generally accepted as true, but
cannot be proven to be true. What type of statement is this?
1. defined
2. undefined
3. postulate
4. proof
Answers
A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.
PLEASE HELPPPPPP
the side length of the base of a rectangular prism with a height of 18 inches can be found with the equation b=(v/18)^1/2 v is the volume of the prism find the side length of the base of the volume of the prism is 4050 cubic meters
Answers
Answer:
15 if b is supposed to the side length, √15 if b is the base which is a square.
Step-by-step explanation:
if a number contains decimal places then it is an irrational number
Answers
Answer:
sometimes true
Step-by-step explanation:
Please help if you know how to do this, thanks
Answers
9514 1404 393
Answer:
4) y = -3(x+2)^2 +4; y = -3x^2-12x-8; ABC=(-3, -12, -8)
5) y = 0.5(x-1)^2-2; y = 0.5x^2-x-1.5; (h,k) = (1, -2)
6) y = -0.3(x+2)^2-6; y = -0.3x^2-1.2x-7.2; (h,k) = (-2, -6)
Step-by-step explanation:
Writing a quadratic equation through a set of points is most easily done using the regression function of a graphing calculator or spreadsheet.
4) see the first attachment
y = -3(x+2)^2 +4 . . . vertex form
y = -3x^2 -12x -8 . . . standard form (A, B, C) = (-3, -12, -8)
__
5) see the second attachment
y = 0.5(x -1)^2 -2 . . . vertex form; vertex = (1, -2)
y = 0.5x^2 -x -1.5 . . . standard form
__
6) see the third attachment
y = -0.3(x +2)^2 -6 . . . vertex form; vertex = (-2, -6)
y = -0.3x^2 -1.2x -7.2 . . . standard form
_____
Doing this without machine help requires you pick a form of the equation you want, fill in the x- and y-values for three of the given points, then solve the resulting equations for the unknown parameters. Usually, we use the form ...
y = ax^2 +bx +c
which will result in three linear equations for a, b, c. Those can be solved by any of the usual methods.
the first 5 multiples of 18 after 0 are?
Answers
Answer:
18,36,54,72,90 are first five multiples of 18
Step-by-step explanation:
Answer:
18,36,54,72,90
Step-by-step explanation:
Which travels faster: a car that travels 6 miles in 10 minutes at a constant speed, or a train that travels 6 miles in 8 minutes at a constant speed? Explain how
you
Answers
Answer: 29 :)
Step-by-step explanation:
Toni is shopping for clothes at the store she buys 8 shirts for $8.00 what is the unit rate for the shirts?
Answers
Answer:
$1.00
Step-by-step explanation:
The unit rate in this scenario would be $1.00 , meaning that Toni is paying $1.00 for every shirt. This can be calculated by dividing the total price that she is paying for the shirts by the total number of shirts that Toni is purchasing like so...
$8.00 / 8 = $1.00 per shirt
The unit rate is basically the value over the denominator of 1 which would be the case as seen above since $1 buys 1 shirt ([tex]\frac{1 dollar}{1 shirt}[/tex]) as opposed to $8 dollars 8 shirts ([tex]\frac{8 dollars}{8 shirts}[/tex]) as mentioned in the question.
The sum of three times a number and seven is 22
Answers
Answer:
3x+7=22
Step-by-step explanation:
three times a number is
[tex]3\times x=3x[/tex]
so the sum of 3x and 7 is 22
[tex]3x+7=22\\\\3x=15\\\\x=5[/tex]
you can leave it here
[tex]3x+7=22[/tex]
if you need the value of x
then
[tex]x=5[/tex]
Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock
30%. What was the list price of the clock?
holour
Answers
Answer:
942.50
Step-by-step explanation:
725×30% or 0.3 = 217.5
217.5+725=942.5
Y = 3x + 4 Y = 3x + 7
Answers
Answer:
y-7/ 12y+3
Step-by-step explanation:
Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and
UW = 52, determine the numerical length of VW.
Answers
Answer:
VW = 36
Step-by-step explanation:
From the question, we are given:
VW = 5x - 4, UV = 2x,
UW = 52
Hence,
UV + VW= UW
2x + 5x - 4 = 52
7x = 52 + 4
7x = 56
x = 56/7
x = 8
VW = 5x - 4,
VW = 5(8) - 4
VW = 40 - 4
VW = 36
Find the value of x so that the function has given value
M(x)=4x+15; m(x)=7
Answers
7=4x+15
Subtract 15 from both sides
-8=4x
Divide each sides by 4
X=-2
The snack table had 48 cookies displayed. After the first round of students came by, the number decreased by 25%. How many cookies were left on the table?
Answers
Answer:
36 cookies left
Step-by-step explanation:
48×.25=12
48-12=36 cookies
Determine whether the given relations are functions.
Answers
Answer:
Yes, this relation is a function.
Step-by-step explanation:
It is a function because every input (left side) only has one output (right side). It doesn't matter if an output has multiple inputs. As long as an input has only one output, it is a function
Ex: 3 = 8 & 7 NOT an input
4 & 3 = 8 AN input
Evaluate the following expression,
5x [7+ (10-2) + 4)
Answers
Answer: 95x
Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)
Add 7 and 10.
5x(17-2+4)
Add 15 and 4.
5x multiped by 19
Multiply 19 by 5
95x
Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change. What is the probability that the time until the next change is greater than 9.5 days
Answers
Answer:
The probability will be "0.205".
Step-by-step explanation:
The probability that perhaps the time remains greater than 9.5 days before the next shift will indeed be:
⇒ [tex]P(X>9.5)[/tex]
⇒ [tex]1-P(X<9.5)[/tex]
⇒ [tex]1-(1-exp(\frac{-9.5}{6} ))[/tex]
⇒ [tex]0.205[/tex]
Water is an example of a solvent true or false !
Hurry up and answer
Answers
What is a perfect squares
Answers
Answer:
A square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 ×3
HOPE IT WILL HELP U!!!!!!
Kiran says “If I walk 3 miles per hour toward you, and you walk 3.4 miles per hour toward me, it’s the same as if you stay put and I jog 6.4 miles per hour.” What do you think Kiran means by this? Is he correct?
Answers
Answer:
Yes it is the same. Since the total distance left behind per time unit would be the same. Just that He would Do that by himself.
Answer:
yes
Step-by-step explanation:
The price of a technology stock was $9.71 yesterday today the price rose to $9.84 find the percentage increase round your answer to the nearest 10th of a percent
Answers
Answer:
1.34%
Step-by-step explanation:
In order to find the percentage increase between these two prices, we must first find the difference in price. We calculate this by subtracting the final price by the initial price like so...
$9.84 - 9.71 = 0.13
Now we divide the difference by the initial price to find what percentage of the initial price this difference is, since this percentage difference was added to the initial price to get the new and final price point.
0.13 / 9.71 = 0.013388 ... multiply by 100 to get percent value
0.013388 * 100 = 1.3388% or 1.34% rounded.
Please help me with this problem please ;(
Answers
9514 1404 393
Answer:
-2
Step-by-step explanation:
The average rate of change on the interval [3, 9] is ...
(f(9) -f(3))/(9 -3) = (41 -53)/(9 -3) = -12/6 = -2
Find the solution set for this inequality -2 x + 4 > -4x + 8.
Answers
Answer:
x > 2
Step-by-step explanation:
0.005 is 1/10 of 0.05 true or false
Answers
Answer:
i got 1/2000
Step-by-step explanation:
Find the value of x.
Answers
Answer:
12
Step-by-step explanation:
1. the rule: 3:6=6:x;
2. if 3/6=6/x, then x=12.