Answer:
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
The rule we have is (x, y)→(2x, 2y). This means that each x-coordinate and each y-coordinate are multiplied by 2. This is a dilation by a factor of 2.
This will stretch the image by a factor of 2; this means the sides will be twice as long. This means they will not be congruent.
Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .
Step-by-step explanation:
Rigid motions form congruent figures, the common rigid motions are:
1) translation (moves figure about some distance)
2) reflection (creates mirror image)
3) rotation (rotate figure about some degrees)
Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
Here the coordinates of the image are increased by using a scale factor 2.
So △D′E′F′ must be an enlargement of △DEF.
⇒△D′E′F′ is a dilation of △DEF
It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The students at Campbell High School have been planting trees as part of an ongoing service project. This month, they averaged 15 trees per participant. That is 150% more trees than their average the last time they did it. What was their average last time?
___ trees
Final answer:
The average number of trees planted by participants last time was 10 trees, calculated by understanding the percentage increase and using basic arithmetic.
Explanation:
The average number of trees planted by participants last time was 10 trees.
To solve this, we know that the current average is 15 trees per participant, which is 150% more than the last average. This means the current average is 250% of the last average. To find the last average, you divide the current average by 2.5 (250%), giving you 6. Then, you calculate 150% of 6, which equals 9. Adding 6 and 9 together gets you 15 trees, the current average, confirming the last average was 10 trees.
What is the next number in the sequence? 3, 6, 12, , ... place an x by the pattern of the sequence. add 2 subtract 2 times 2?
Dana was picking strawberries to sell and placing them in baskets on a table. the number of strawberries in the basket is 4 more than the number of baskets on a table. if b represents the number of baskets on each table, which expression can be used to represent the number of strawberries on 5 tables? 5b4 5(b + 4) 5b(b + 4) 5b + 4
What is the percent increase modeled in the function f(x)=30(1.25)*
A. 30%
B. 1.25%
C. 25%
D. 75%
the increase would be 1.25-1 = 0.25 = 25%
Answer is C
If you shift the quadratic parent function, f(x) = x2, left 12 units, what is the equation of the new function?
A. g(x) = (x – 12)2
B. g(x) = (x + 12)2
C. g(x) = x2 – 12
D. g(x) = x2 + 12
karen says that 6 is a common factor of 2 and 3 ken says that 6 is a common multiple of 2 and 3 who is correct
Scientists estimate that sea level has risen about _____ over the past 100 years.
A. 10 to 25 meters
B. 0 to 1 centimeters
C. 10 to 25 centimeters
D. 100 to 250 centimeters
Answer: The answer is (C) 10 to 25 centimetres.
Step-by-step explanation: We are to select the correct range by which the sea level has risen about over the last 100 years.
Scientists estimates that because of warming of the ocean and increased melting of land-based ice such as glaciers and ice sheets, the level of sea has risen from 10 to 25 centimetres over the last 100 years.
Thus, (C) is the correct option.
A jar contains n nickels and d dimes. There are 20 coins in the jar, and the total value of the coins is $1.40. How many nickels and how many dimes are in the jar?
For f(x)=4x squared -3 and g(x)=x +1 find (f - g)(x) PLEASE HELPP
The volume of a can (right circular cylinder) is 10 cubic feet. the curved surface area is the area of the side. write the curved surface area s as a function of the radius r. s =
The volume formula of a cylinder is given as:
V = π r^2 h
So plugging in the value of the volume:
10 ft^3 = π r^2 h
h = 10 / (π r^2) ---> eqtn 1
The formula for the surface area of cylinder is:
s = 2 π r h + 2 π r^2
plugging in eqtn 1:
s = 2 π r [10 / (π r^2)] + 2 π r^2
s = (20 / r) + 2 π r^2 (ANSWER)
Yesterday raina had c baseball cards .today she got 24 more . Using c , write an expression for the total number of baseball cards she has now .
How many integers less than 1000 have no factors (other than 1) in common with 1000?
You flip a coin and then roll a fair six sided die. Then the coin lands heads up and the die shows a one
A wildlife biologist catches and releases 20 fish from two different lakes at random locations. he catches 10 fish at lake palmer and 10 fish at lake dalton. he measures the length of each fish to the nearest quarter of an inch. palmer dalton first quartile 6.75 5.5 second quartile (median) 10.25 6.75 third quartile 13 7.5 based on the samples, what generalization can be made? at least 25 percent of the fish in both lakes are no longer than 6 inches. the interquartile range for lake dalton is 2 inches greater than the interquartile range for lake palmer. the first quartile value at lake palmer is 1.25 inches longer than the first quartile value at lake dalton. not enough information is provided to draw any of these conclusions.
Answer:
The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton.
Step-by-step explanation:
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes?
74.3%
55.2%
44.8%
37.2%
Actually variation is simply equivalent to the square of the correlation coefficient r. So we can say that:
variation = r^2
So given an r value of 0.743, so the variation is:
variation = 0.743^2
variation = 0.552
Answer:
55.2%
Round 28,573 to the nearest thousand
One hundred percent of the fish in a pond are goldfish. i take 10$\%$ of the goldfish out of the pond. what percentage of goldfish does the pond now contain?
1) AB¯≅AD¯ Given
2)∠ACD is a right angle.- Given
3) m∠ACD=90° -Definition of right angle
4) m∠ACB=90° -Given
5) m∠ACB=m∠ACD -Transitive Property of Equality
6) ∠ACB≅∠ACD Definition of congruent angles
7) C is the midpoint of BD¯ Given
8)C bisects BD¯ ?
9) BC¯≅CD¯ Definition of bisect
10) AC¯≅AC¯ Reflexive Property of Congruence
11) △ABC≅△ADC -SAS Congruence Postulate
What is the correct reason for Statement 8?
Given
Definition of bisect
Definition of congruent segments
Definition of midpoint
Answer:
By definition of midpoint.
Step-by-step explanation:
proof:
1.Statement: [tex]\overline{AB}\cong \overline{AD}[/tex].
Reason: Given.
2.Statement: [tex]\angleACD[/tex] is a right angle.
Reason:Given.
3.Statement:[tex]m\angle ACD=90^{\circ}[/tex].
Reason: By definition of right angle.
4.Statement: [tex]m\angle ACB=90^{\circ}[/tex].
Reason: Given.
5.Statement: [tex]m\angle ACB=m\angle ACD[/tex]
Reason: Transitive property of equality.
6. Statement:[tex] m\angle ACB\cong m\angle ACD[/tex].
Reason: By definition of congruent triangles.
7.C is the midpoint of [tex]\overline {BD}[/tex].
Reason: Given.
8.Statement: C bisect [tex]\overline{BD}[/tex]
Reason: By definition of midpoint.
9.Statement:[tex]\overline{BC}\cong \overline{CD}[/tex]
Reason: By definition of bisect.
10.Statement:[tex]\overline{AC}\cong\overline{AC}[/tex]
Reason: By reflexive property of congruence.
11.Statement:[tex]\triangle ABC\cong \triangle ADC[/tex].
Reason: SAS congruence postulate.
what is the value of x (I will give 20 points to best answer)
Answer options
61
37
85
122
The value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
The angles are shown in the picture.
As we know, from the definition of vertically opposite angles, the angles when two lines intersect each other and at the intersecting point.
The first angle = 2x + 24
The second angle = 146
Equating both the angles:
2x + 24 = 146
2x = 146 - 24
2x = 122
x = 122/2
x = 61
Thus, the value of x is 61 after using the concept of vertically opposite angles option (A) 61 is correct.
Learn more about the vertically opposite angles here:
brainly.com/question/24287162
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What is the area of the figure?
Assume that all angles are right angles.
A. 980 square inches
B. 1000 square inches
C. 1200 square inches
D. 1100 square inches
A equation whose solutions form a straight line on a coordinate plane is a what
Evaluate the given expression if k=-84
5 |k+10| - |4k|
3/8(z+11)=y solve for z in the literal equation
25% of what number is 9
can you explain how you got your answer and show your answer too.
Thank You
If 75 cans cost 56.25 dollars how much would it be for 3 cans
56.25 / 75 = 0.75 for each can
0.75 *3 = $2.25 for 3 cans
A function is given. Determine the average rate of change of the function between the given values of the variable: f(x)= 4x^2; x=3, x=3+h
The lengths of the sides of a triangle are represented by 3 consecutive even integers. if the perimeter of the triangle is 72 feet, find the lengths of its sides
Under which condition does a country with a small GDP have a large per capita income?
If the boolean expression a is true and b is false, the value of the logical expression a and b is ________.
Two sisters, Allie and Bonnie are saving money for a trip to Europe. Allie has $1500 and adds $500 each month to this amount. Bonnie has $2300 and adds $400 each month to this amount. How many months must Allie save to exceed the amount of money that Bonnie has saved