The possible transformations that establish congruence between shapes are dilation, translation, and reflection.
Explanation:The possible rules that represent a transformation mapping one shape onto another to establish congruence are:
A) A dilation by a scale factor of 3 about the origin.B) A translation to the right 2 and down 6.C) A reflection across the line y=2.A dilation by a scale factor of 3 about the origin stretches or shrinks the shape uniformly in all directions. A translation moves the shape without changing its size or shape. A reflection across a line is a flip of the shape over that line. These transformations can establish congruence between shapes.
Transformations that establish congruence between shapes by preserving size, shape, and orientation ensure that the transformed shape aligns with the original shape. The correct answer is option
B) A translation to the right 2 and down 6.
C) A reflection across the line y=2.
D) A counter-closckwise rotation of 90 degrees about the origin.
The rules that represent transformations mapping one shape onto another to establish congruence are:
B) A translation to the right 2 and down 6, which preserves both size and shape, simply moving the shape to a different location without changing its orientation or proportions.
C) A reflection across the line y=2, which reflects the shape across a line, maintaining its size and shape but reversing its orientation.
D) A counter-clockwise rotation of 90 degrees about the origin, which rotates the shape by a right angle, preserving its size and shape while changing its orientation.
These transformations preserve congruence by maintaining the size, shape, and orientation of the original shape.
Options B, C, and D represent transformations that map one shape onto another to establish their congruence, preserving size, shape, and orientation.
Between 1:30 P.M. and 1:50 P.M.,40 gallons of water leaked into a boat.At what rate in gallon per hour was the water leaking in to boat?
Answer:
120 gallons per hour.
Step-by-step explanation:
Between 1:30 P.M. and 1:50 P.M., 40 gallons of water leaked into a boat.
We know, the (1: 50 P.M. - 1: 30 P.M.) = 20 minutes.
So, the time span is of 20 minutes and the amount of water leaked into is 40 gallons.
Therefore, the amount of water that will leak into the boat in 60 minutes is [tex]\frac{40 \times 60}{20} = 120[/tex] gallons.
So, the rate in gallons per hour of the leaking water is 120 gallons per hour. (Answer)
What is the slope of the line passing through (0, 5) and (-12, 2) ? Enter your answer in the box.
Final answer:
The slope of the line passing through (0, 5) and (-12, 2) is calculated using the slope formula and is found to be 1/4.
Explanation:
The slope of the line passing through the points (0, 5) and (-12, 2) can be calculated using the formula slope (m) = (rise)/(run), where 'rise' is the change in the y-values and 'run' is the change in the x-values. To find the slope, we subtract the y-value of the second point from the y-value of the first point and divide by the subtraction of the x-value of the second point from the x-value of the first point: m = (5 - 2) / (0 - (-12)) = 3 / 12 = 1/4. Therefore, the slope of the line is 1/4.
Find two consecutive positive integers whose product is 552.
Answer:
The numbers are 23 and 24
Step-by-step explanation:
Let
x ----> the first positive consecutive integer
x+1 ----> the second positive consecutive integer
we know that
The product of the two consecutive positive integers is 552
so
The algebraic expression that represent this situation is
[tex]x(x+1)=552[/tex]
Convert to expanded form
[tex]x^2+x-552=0[/tex]
Solve the quadratic equation by graphing
The roots of the equation are
[tex]x_1=-24[/tex] ----> the number cannot be negative
[tex]x_2=23[/tex]
see the attached figure
therefore
[tex]x=23\\x+1=24[/tex]
The numbers are 23 and 24
To find two consecutive positive integers whose product is 552, set up the equation x(x + 1) = 552, expand and solve the quadratic equation.
Explanation:To find two consecutive positive integers whose product is 552, we can set up the equation x(x + 1) = 552, where x represents the smaller integer.
Expanding the equation, we get x^2 + x - 552 = 0. This is a quadratic equation, and we can solve it by factoring or using the quadratic formula.
Factoring the quadratic equation, we find that (x - 23)(x + 24) = 0. So the two consecutive positive integers are 23 and 24.
10. A toy store received a shipment of 17 cases of
teddy bears. Use compatible numbers to estimate
the total number of teddy bears in the shipment.
estimate
12 bears per case
Answer:
17 × 12 = 204 teddy bears
Step-by-step explanation:
17 cases, 12 bears in each case
If f(x) = x - 5, then match each of the following.
Click the item in the left column. Use the plus sign to move it up or the minus sign to move it down until it matches the correct entry in the right column. Lock your answer in place by clicking the square beside the item. (A checkmark means it is locked.)
0 f(-1)
-4 f(0)
-5 f(1)
3 f(2)
-6 f(5)
-3 f(8)
Answer:
f(-1) = -6
f(0) = -5
f(1) = -4
f(2) = -3
f(5) = 0
f(8) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[Function] f(x) = x - 5
f(-1) is x = -1 for function f(x)
f(0) is x = 0 for function f(x)
f(1) is x = 1 for function f(x)
f(2) is x = 2 for function f(x)
f(5) is x = 5 for function f(x)
f(8) is x = 8 for function f(x)
Step 2: Evaluate
f(-1)
Substitute in x [Function f(x)]: f(-1) = -1 - 5Subtract: f(-1) = -6f(0)
Substitute in x [Function f(x)]: f(0) = 0 - 5Subtract: f(0) = -5f(1)
Substitute in x [Function f(x)]: f(1) = 1 - 5Subtract: f(1) = -4f(2)
Substitute in x [Function f(x)]: f(2) = 2 - 5Subtract: f(2) = -3f(5)
Substitute in x [Function f(x)]: f(5) = 5 - 5Subtract: f(5) = 0f(8)
Substitute in x [Function f(x)]: f(8) = 8 - 5Subtract: f(8) = 3How many ways can 5 people-A, B, C, D, and E-sit in a row at a movie theater if (a) A
and B must sit together; (b) C must sit to the right of, but not necessarily next to, B; (C) D
and E will not sit next to each other?
The population of Woodstock, GA is about 23,896 people, and the city encompasses
11.3 square miles. What is the population density of Woodstock?
211.47 people per square mile
Answer:
2114.7 people per square mile
Step-by-step explanation:
Population density can be calculated by dividing the total number of people by the area.
23,896 people ÷ 11.3 square miles
≈ 2114.7 people per square mile (rounded number)
Your answer is one decimal place off.
Molly and George earned 352 points together. Molly has half the number of points as George. Which equation could represent this situation? Let g represent the number of points George earned.
A. g+2g =352
B. g+1/2g =352
C. g+g/2 =352
D. 1/2g = 352
Answer: A. g+2g =352
Step-by-step explanation:
Let points : g
If molly has half of George then let
Let molly : 1
Let George: 2
Therefore g*1 =g
And g*2 = 2g
So, g+2g = 352
trigonometry problem
Answer:
The values are x = 0° or x = 60°
Step-by-step explanation:
Given:
[tex]\cos x + \frac{1}{\sqrt{3} }\times \sin x = 1[/tex]
Let it be in the form of
[tex]a\cos x + b\sin x = 1[/tex] such that
a = 1
[tex]b=\frac{1}{\sqrt{3} }[/tex]
We have
[tex]\sqrt{(a^{2}+b^{2} )}=\sqrt{(1^{2}+(\frac{1}{\sqrt{3} }) ^{2} )}\\=\sqrt{\frac{4}{3}}\\=\frac{2}{\sqrt{3} }[/tex]
Now, Dividing both the side by [tex]\frac{2}{\sqrt{3} }[/tex] we get
[tex]\frac{\sqrt{3} }{2}\cos x + \frac{1}{2}\sin x =\frac{\sqrt{3} }{2}\\[/tex]
We Know
[tex]\sin 60 =\frac{\sqrt{3} }{2}\\and\\\cos 60 = \frac{1}{2}[/tex]
Now by replacing with above values we get
[tex]\sin 60\times \cos x + \cos 60\times \sin x = \frac{\sqrt{3} }{2}\\[/tex]
Also we have formula
[tex]\sin A\times \cos B + \cos A\times \sin B = \sin (A+B)[/tex]
By applying the above Formula we get
[tex]\sin (60+x)=\frac{\sqrt{3} }{2}\\[/tex]
Also ,
[tex]\sin (60)=\frac{\sqrt{3} }{2}\\and\\\sin (120)=\frac{\sqrt{3} }{2}[/tex]
Comparing we get
60 + x = 60 or 60 + x = 120
∴ x = 0° ∴ x = 120 - 60 = 60°
Therefore, the values are x = 0° or x = 60° i.e between 0° to 360°
The cost of a babysitting on a cruise is 10 for the first hour, and 12 for each additional hour. If the total cost of baby Aaron was 58, how many hours was Aaron at the sitter?
Answer:
5 hours was Aaron at the sitter
Explanation:
Cost of baby sitting for the first hour: 10
Cost of baby sitting for additional hour= 12
Total cost of babysitting= 58
Since the cost of first hour is 10
Hence the remaining cost after first hour
= 54-10
=48
Which means 1 hour is consumed in the first hour
Now to calculate the remaining hours for every additional hour
= [tex]\frac{48}{12}[/tex]
=4 hours
Hence the total hour Aaron was with the sitter
= 1 hour + 4 hours
= 5 hours
(3+5^2) dividend by 4+19
Answer:
26
Step-by-step explanation:
Answer: 26
Step-by-step explanation:
Find (f/g)(x).
Please help !!
Answer:D
Step-by-step explanation:
factorise 2x²-16x+32
x²-8x+16
(x-4)²
factorise 4x²-2x-20
2x²-x-10
2x²+4x-5x-10
2x(x+2)-5(x+2)
(2x-5)(x+2)
solving for (f/g)(x)
(x-4)²/(x+2)÷(2x-5)(x+2)/(x-4)²
(x-4)²/(x+2)*(x-4)²/(2x-5)(x+2)
(x-4)⁴/(2x-5)(x+2)²
GETS BRAINILIST!!!!9.85 ÷ 1.25 = ______ Numerical Answers Expected! Answer for Blank 1:
Answer:
7.88
Step-by-step explanation:
Answer: 7,88
Explanation
394 students play a wind instrument. If 2/5 of the students play a wind instrument, how many students in the district participate in the school music program
Answer:
About 158 students in the district participate in the school music program.
Step-by-step explanation:
394(2/5)=788/5=157.6
The table below shows the numbers of tickets sold at a movie theater on Friday.
NUMBER OF TICKETS SOLD
Day
Adult Tickets
Children's
Tickets
1,678
976
Friday
Saturday
The number of each type of ticket sold on Saturday is described below.
• Adult tickets-2 times as many as the number of adult tickets sold
on Friday
• Children's tickets-3 times as many as the number of children's
tickets sold on Friday
Complete the table above to show the numbers of tickets sold on Saturday.
What is the total number of tickets sold over these two days?
Answer:
Find the question in the attachment below.
Number of tickets sold on Saturday [tex]=6986[/tex]
Number of tickets sold over the days [tex]=9640[/tex]
Step-by-step explanation:
a.
Number of tickets sold on Saturday
Twice as many as the number of adult tickets [tex]=2\times 976= 1952[/tex]
Three times as many as the number of children's tickets [tex]3\times 1678=5034[/tex]
Total number of tickets sold on Saturday =[tex](1952+5034)=6986[/tex]
b.
Total number of tickets sold on Friday and Saturday
Summation of adult and children's ticket on both the days.
[tex]=(6986+976+1678)=9640[/tex]
So total tickets sold on Saturday is [tex]6986[/tex] and tickets sold on both days [tex]=9640[/tex]
Is mean absolute deviation a measure of center
measure of variation ?
or a
A. measure of center
B. measure of variation
The mean absolute deviation is a measure of variation in a dataset, not its center. It helps indicates how spread out the data is from the mean value.
Explanation:The mean absolute deviation is not a measure of center,instead, it is a measure of variation. The center of a data set is typically represented by measures like the mean, median, or mode. These describe the common, central value in the dataset.
Conversely, the mean absolute deviation is a statistical tool used for understanding the dispersion or variation in a set of values. It gives an average of the absolute differences between each data point and the mean of the data set. This helps identify how spread out the data is from the mean.
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Divide nine by three then subtract two double the results
Answer:
2
Step-by-step explanation:
When n basketball uniforms are purchased, the cost, C, of each uniform is given by the equation.
C = 40n + 260
If the total cost of the teams uniforms is $860, how many uniforms were purchased? What property of equality is the first step to use when solving this equation?
A.
Addition property of equality; n = 8
B.
Division property of equality; n = 6
C.
Multiplication property of equality; n = 13
D.
Subtraction property of equality; n = 15
Answer:
D. Subtraction property of equality; n = 15
Step-by-step explanation:
Given equation that shows the cost of n basketballs uniforms,
C = 40n + 260
According to the question,
Total cost = $ 860,
⇒ 40n + 260 = 860
Using subtraction property of equality, subtract 260 on both sides,
⇒ 40n = 860 - 260
⇒ 40n = 600
Using division property of equality, divide both sides by 40.
⇒ n = [tex]\frac{600}{40}[/tex] = 15.
Hence, 15 uniforms were purchased.
i.e. Option D is correct.
Solve for c. a(c + b)=d
c=d − ab/b
c=d + ab/a
c=ab − d/a
c=d − ab/a
Answer:
c = (d - ab) / aStep-by-step explanation:
a(c + b) = d // We multiply a by c and b (addition is distributive)
ac + ab = d // We let the c addend in the left
ac = d - ab // We divide by a
c = (d - ab) / a
Answer: Hi Hi I know this is like a year late but I would like to be able to help future people with this question.
The correct answer is: c=d+ab/a (B)
Isolate the variable by dividing each side by factors that don't contain the variable.
I really hope this helps people, have a happy halloween :D
Andrew’s math teacher entered the seventh-grade students in a math competition. There was an enrollment fee of $30 and also an $11 charge for each packet of 10 tests. The total cost was $151. How many tests were purchased?
use a tape diagram to solve and if-then statement
Answer:
p=11 packets were purchased
Step-by-step explanation:
30+11p=151
11p=121
then
121/11
so
p=11
Hope I understood the question :/
Answer:
Step-by-step explanation:
I believe the correct answer is that Andrew's Math Teacher purchased 11 packets of 10 tests each, meaning that the total number of test would be 110. I got this by subtracting the $30 entrance fee from the $151. After doing this we are left with $121. I then divided the $121 by the cost per packet and I was left with 11 packets. Since every packet contains 10 tests I multiplied that by the number of packets to get the final answer... 110 tests purchased.
how do I do this PLEASE HELP ME!!!!
Answer:
23 quarters and 12 dimes
Step-by-step explanation:
Jennifer’s bill for lunch was $15.00 If Jennifer left a 20% tip, which proportion would BEST represent how to find how much tip she should leave? A x15=100/20 B x15=20/100 C 15x=20/100 D 20x=15/100
Answer:
B
Step-by-step explanation:
20% is 20 out of 100
and that's how you find out how much of a tip you should leave.
The proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100
Let the amount of tip h left be expressed as x
Given the following parameters
Bill for lunch = $15.00Tip = 20%To find the amount of tip Jennifer dropped;
Price of tip = 20% of 15
x = 20/100 * 15
x/15 = 20/100
Hence the proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100
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write inverse of the given function [(5,3) (-2,4) (7,-2)
The inverse is: {(3,5), (4,-2), (-2,7)}
Step-by-step explanation:
In the inverse of a function, the output becomes input and the input becomes output i.e. the functions is reversed.
Given function is:
[(5,3) (-2,4) (7,-2)]
The order of elements in ordered pairs will be reversed. The second elements will be on first place and first element will be on second place.
So,
The inverse is: {(3,5), (4,-2), (-2,7)}
Keywords: Functions, inverse
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The inverse of the given function (5,3), (-2,4), (7,-2) is (3,5), (4,-2), (-2,7).
The inverse of a function is created by swapping each input-output pair.
For the given function with ordered pairs (5,3), (-2,4), and (7,-2), we can find the inverse by switching each pair's coordinates. This yields the inverse ordered pairs (3,5), (4,-2), (-2,7). Remember that the inverse function only exists if the original function is bijective, meaning each output is paired with exactly one input.
Find an exponential function with a horizontal asymptote y = - 7 whose graph contains the points (0.- 6) and (1,6).
The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:
y = [tex]e^{(ln(13)x)} - 7[/tex].
To find an exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6), we can use the general form of an exponential function:
[tex]y = A * e^{(kx)} + C[/tex]
where A is the initial value, k is the growth/decay rate, e is the base of the natural logarithm (approximately 2.71828), x is the independent variable, and C is the y-coordinate of the horizontal asymptote.
Step 1: Determine the value of C (the y-coordinate of the horizontal asymptote):
Since the asymptote is y = -7, we set C = -7.
Step 2: Use the given points to find A and k:
For point (0, -6):
-6 = A * e⁰ - 7
-6 + 7 = A
A = 1
For point (1, 6):
6 = 1 * [tex]e^{(k*1)[/tex] - 7
13 = [tex]e^{k[/tex]
Step 3: Solve for k:
Take the natural logarithm of both sides: ln(13) = k
Step 4: Write the exponential function:
The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:
y = [tex]e^{(ln(13)x)} - 7[/tex].
This function will have a horizontal asymptote at y = -7 and pass through the given points (0, -6) and (1, 6).
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Evaluate the expression below (5.2+6.3) - 12 ÷ 2.5
Answer:6.7
Step-by-step explanation:5.2+6.3=11.5 then you do -12 divided by 2.5 and get -4.8 then you add the answers together but that won’t work because different signs subtract and you get positive 6.7
To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, you first perform the division. Then, substitute the result and add the numbers inside the parentheses. Finally, subtract the result from the addition.
Explanation:To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, we start by performing the division. 12 ÷ 2.5 equals 4.8. Now, we substitute this result into the expression, so the expression becomes (5.2+6.3) - 4.8. Next, we add the numbers inside the parentheses together, giving us 11.5. Finally, we subtract 4.8 from 11.5, resulting in 6.7.
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Wich is longer? A cabinet that is 3/4s foot or a shingle that is 2/3s foot? How much longer?
Answer:
The cabinet is longer by 1/12 foot.
Step-by-step explanation:
3/4 x 3/3 = 9/12
2/3 x 4/4 = 8/12
Find the circumference and area of a circle with diameter 6 inches. Use 3.14 for pi.
(need answer asap please)
was flying her model airplane. It took the airplane 5 seconds to go 90 feet. What was the average rate of speed of the model airplane, in feet per second
Answer:
The average rate of speed of the model airplane, per second is 18 feet.
Step-by-step explanation:
Given:
It took the model airplane 5 seconds to go 90 feet.
Now, to find the average rate of speed in feet per second.
So, in 5 seconds the airplane go to = 90 feet.
In 1 second the airplane go to = 90 ÷ 5 feet.
Therefore, by dividing 90 feet by 5 seconds we get = 18 feet.
Thus, the average rate of speed of the model airplane, per second is 18 feet.
Lora, a campaign manager, distributes flyers to 35% of the homes in her community. Lora distributes flyers to 630 homes. How many homes are in her community?
To calculate the total number of homes in Lora's community, the number of flyers distributed (630) is divided by the percentage of homes that received flyers (35%), resulting in a total of 1800 homes.
To find the total number of homes in Lora's community, we need to set up a proportion where the number of flyers delivered represents 35% of all homes. Since Lora distributed flyers to 630, that is 35% of the total homes. Using the percentage formula:
Total Homes = Distributed Flyers / Percentage of Homes
So, in this case, it would be:
Total Homes = 630 / 0.35
Dividing 630 homes by 0.35 (35% as a decimal) gives us:
Total Homes = 1800
Therefore, there are 1800 homes in Lora's community.
Which situation best describes the transformation between f(x) = 10x and g(x) = –2 · 10x?
The graph of g(x) = –2 · 10x is transcribed 2 units to the right.
The graph of g(x) = –2 · 10x is transcribed 2 units to the left.
The graph of g(x) = –2 · 10x is compressed vertically and reflected across the x-axis.
The graph of g(x) = –2 · 10x is stretched vertically and reflected across the x-axis.
Answer:
The graph of g(x) = –2 · 10x is stretched vertically and reflected across the x-axis.
Step-by-step explanation:
Answer:
D. The graph of g(x) = –2 · 10x is stretched vertically and reflected across the x-axis.
Step-by-step explanation: