We will investigate the sequence of transformations associated with pre-image and image of a polygon.
Two polygons named ( A and B ) are given on a cartesian coordinate grid. Polygon A is congruent to polygon B. The concept of congruency relays that all the inetrior angles and sides of a polygon remains the same.
There is a list of transformations that are allowed:
\(\text{Rotation, reflection, translation, dilation}\)However, when we impose the condition that the congruency of polygons we will remove the " dilation " transformation because the stretch or shrink off any figure will violate the condition of transformation. Therefore, the polygons to be remain congruent to one another there are only three possibilities:
\(\text{Rotation, reflection, translation}\)We will see what sequence of transformation will impose the polygon A directly onto polygon B. We will investigate each transformation as follows:
\(\text{reflection}\)Allows the exact mirror image across any straight line specified. A polygon in the third quadrant can be reflected into the second quadrant by reflection across the line:
\(\text{reflection across y = 0 }\)The above gives us an image in the second quadrant.
We see that the new reflection is displaced 3 units to the left of polygon B. So we need to translate the entire reflected image 3 units to the right for it lie on top of polygon B. Therefore,
\(\text{Translation to right off 3 units}\)So the sequence of transformations becomes:
\(\begin{gathered} \text{reflection across y = 0} \\ \text{Translation to right by 3 units} \end{gathered}\)Translating english expressions to mathematical expressions
Identify the following as either expression or sentence
1. 8x + 18
2. 2 < 5
3. The set {}
4. 36 degrees
5. x = 3x - 5
The following area tagged expression or sentence as;
1. Expression
2. Expression
3. Sentence
4. Sentence
5. Expression
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variables, terms, coefficients, factors and constants.
These expressions are also identified with various mathematical or arithmetic operations, such as;
ParenthesesBracketAdditionSubtractionMultiplicationDivisionLearn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
if n/100 is greater than 7 but less than 8, then give two values that N could be.
For n/100 greater than 7, we have:
\(\begin{gathered} \frac{n}{100}>7 \\ \frac{n}{100}\cdot100>7\cdot100 \\ n>700 \end{gathered}\)For n/100 less than 8:
\(\begin{gathered} \frac{n}{100}<8 \\ \frac{n}{100}\cdot100<8\cdot100 \\ n<800 \end{gathered}\)Therefore, The values could be greater than 700 to less than 800.
We can choose the values of 734 and 762 for n.
Answer:
n = 734
n = 762
Try to find this answer! Thank you!
The growth factor for one generation of a bacteria culture is given by the function g(t)=ln(2)t, in which t is the time it takes for the generation to mature to its full size based on the energy resources and environmental conditions available in the culture. What happens to t if g(t) is cut in half?
t=
Points possible: 1
Allowed attempts: 3
Question 2
What happens to t?
If g(t) is cut in half, then t is
If g(t) is cut in half, then t is doubled. Halving the growth factor halves the rate of growth, reducing the time required for a generation to develop to full size.
What do you mean by growth factor?Growth factor refers to a mathematical expression or a metric that measures the rate of increase or growth of a quantity over time. It is used in many fields such as biology, economics, finance, and others to quantify the increase in size, population, revenue, or any other variable of interest. The growth factor can be represented as a ratio, percentage, or an exponential function and is used to predict future growth based on past trends.
3 potential points
Three tries are permitted.
If g(t) is divided in half, t is also divided in half. This is because the growth factor is a measure of the rate of growth, and halving it equals halves the rate of growth. As a result, the time required for a generation to develop to full size is cut in half.
To know more about rate visit:
brainly.com/question/29765585
#SPJ1
Helppp:)))!!!!!!!!!!!!!!!!!!!!!
Answer:
hw do you expect anyone to do that
Step-by-step explanation:
Answer:
uh
Step-by-step explanation:
The function y = 14 +2.31x + 4.50 can be used to determine the cost in dollars for an Uber ride of x miles which takes no longer than 10 minutes. What is
the rate of change of the cost in dollars with respect to the number of miles?
Answer:
2.32dollar/mileStep-by-step explanation:
step one:
Given the function
y = 14 +2.31x + 4.50
we can solve for the rate of change by applying differentiation.
step two:
differentiating y which is cost with respect to x which is the miles
dy/dx= 0+2.32+0
dy/dx=2.32
Hence the rate of change of cost in the dollar to a mile is
2.32dollar/mile
NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii
Answer:
7) Domain: (-∞, ∞)
Range: [-1, ∞)
8) Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 5From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
From inspection of the graph, the minimum y-value is y = -1.
The end behavior of the relation is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the range of the relation is restricted: [-1, ∞)
Question 6From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
The end behavior of the function is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
A, B & C form a triangle where
∠
BAC = 90°.
AB = 4.6 mm and CA = 12.6 mm.
Find the length of BC, giving your answer rounded to 1 DP.
Step-by-step explanation:
answer is correct plz mark me as vrilliant
Please see screenshot.
Answer:
See below
Step-by-step explanation:
which is the best estimate for the number of times the coin will land up 10 20 50 80 100
A rectangle is divided into same size squares one row covers 1/8 of the whole rectangle there are 3 squares in each row how many squares are in a whole triangle
Answer:
it is one square
Step-by-step explanation:
in the middle is room for one but anywhere else isn't
The net of a rectangular prism and its dimensions are shown in the diagram.
7.5 in.
7.5 in.
3 in.
3 in.
11.5 in.
11.5 in.
What is the total surface area of the rectangular prism in square inches?
A 143.25 in.2
B 241.5 in.?
C 258.75 in
D 286.5 in.?
Answer:
D.
Step-by-step explanation:
Given: Dimensions of a rectangular prism are \(7.5\,\,inches,3\,\,inches\,,\,11.5\,\,inches\)
To find: total surface area of the rectangular prism in square inches
Solution:
Length of the rectangular prism (l) = 7.5 inches
Breadth of the rectangular prism (b) = 3 inches
Height of the rectangular prism (h) = 11.5 inches
Total surface area of the rectangular prism = 2(lb+bh+hl)
= \(2(7.5\times3+3\times11.5+11.5\times7.5 )\)
\(2(7.5\times3+3\times11.5+11.5\times7.5 )=2(22.5+34.5+86.25)\\=2(143.25)\\=286.5\,\,square \,\,inches\)
So, option D is correct
Answer:
D! I got it correcttt
Step-by-step explanation:
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly.
The desired monthly yield at the retirement time will be equal to $565,714.28.
Compound Interest may be defined as the interest earned by the bank on the basis of principle and also accumulated interest which increases exponentially and not linearly with respect to time. In calculating compound interest, the amount earned at the end of first year becomes principle for the next year and so on. Compound interest can be calculated, annually, half-yearly or quarterly etc.
Time for which work is planned = 40 years, Principle = $4500 and APR = 8.4% = 0.084/12 = 0.007.
The value of n = 12 × 25 = 300
The amount can be calculated by the formula A = P/r [1 - (1 + r) ⁻ⁿ]
A = (4500/0.007) [1 - (1 + 0.007) ⁻³⁰⁰]
A = 642,857.14 [1 - 0.12]
A = 642,857.14 × 0.88
A = $565,714.28 which is required amount.
Learn more about Compound Interest at:
brainly.com/question/13463611
#SPJ9
Complete Question:
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly. What monthly deposits are required to achieve the desired monthly yield at retirement?
what is 2 3/4 as a improper fraction
Answer:
11/4
Step-by-step explanation:
2x4=8
3+8=11
11/4
Find the value of x
Show work
The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.
How can you tell if a perspective is supplemental or complementary?Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.
What is the name for a 270 degree angle?Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.
Since it is a right angle triangle,
hence
\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)
To know more about complimentary visit:-
brainly.com/question/20693383
#SPJ1
Please help me solve!
1. The probability of selecting a 3 of Diamonds is 1/52.
2. The probability of selecting a Club or Diamond is 1/2.
3. The probability of selecting a number smaller than 9 is 9/13.
1. The probability of selecting a 3 of Diamonds:
There is only one 3 of Diamonds in the deck, and the total number of cards in the deck is 52. Therefore, the probability of selecting a 3 of Diamonds is 1/52.
2. The probability of selecting a Club or Diamond:
There are 13 Clubs and 13 Diamonds in the deck, making a total of 26 cards. The probability of selecting a Club or Diamond is the ratio of the number of favorable outcomes (Club or Diamond) to the total number of possible outcomes (52 cards). Therefore, the probability is 26/52, which simplifies to 1/2.
3. The probability of selecting a number smaller than 9:
There are four suits in the deck (Clubs, Diamonds, Hearts, and Spades), and each suit has cards numbered 2 to 10. So, there are 4 suits * 9 cards per suit = 36 cards that are numbered smaller than 9.
The probability of selecting a number smaller than 9 is the ratio of the number of favorable outcomes (36 cards) to the total number of possible outcomes (52 cards). Therefore, the probability is 36/52, which simplifies to 9/13.
For more such questions on probability visit:
https://brainly.com/question/23286309
#SPJ8
Get me right twinnnn
Answer:
\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)
hope it helps:)
Answer:3x-21
Step-by-step explanation:
\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21
Find the value of x, 6,4, 3x, 4x+1
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
604 Daria and her brother want to make 100 bracelets to sell at a craft fair.They have made some already, Daria made this graph to show how they canreach their goal. The equation of Daria's line is y = 14x + 30 where y is thenumber of bracelets and x is the time in hours.a. What is the slope of the line?b. What is the y-intercept?Number of BraceletsAquation under the graph of its line.
Given that y = 14x + 30
Then when compared to the equation of a straight line y = mx + c
m = 14, where m is the slope
c = 30, where c is the intercept
⦁ Mr. A likes playing a game and the probability that he wins this game is p. He enters the casino and he promises himself that he plays the game until he wins one time and then he stops. Let X be the number of plays in order to win one time. ⦁ What are the values of X? ⦁ What is the probability that X=n?. Prove that it satisfies the PMF conditions. ⦁ Calculate E(X) ⦁ Calculate V(X) ⦁ Study the memoryless property of X.
The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
How to determine the values of X?From the complete question, we understand that Mr. A wants to plays the game until he wins
This means that
He might win at the first game and he might win after n attempts
So, the values of X are
X = 0, 1, 2, 3, 4.......n
Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
The probability that X = nThe probability of x is represented as:
P(x) = nCx * p^x * (1 - p)^(n-x)
So, the probability that X = n is:
P(n) = nCn * p^n * (1 - p)^(n - n)
Evaluate the exponent
P(n) = nCn * p^n * 1
Evaluate the combination expression
P(n) = 1 * p^n * 1
This gives
P(n) = p^n
Hence, the probability that X = n is p^n
Prove that it satisfies the PMF conditions.The distribution satisfies PMF conditions because
The sum of the probabilities is 1 No probability is negativeEach probability value is between 0 and 1 (inclusive)Calculate E(X)The expected value E(x) is calculated using
E(x) = n * p
So, we have:
E(x) = np
Hence, the value of E(x) is np
Calculate V(X)The variance V(x) is calculated using
V(x) = √n * p * (1 - p)
So, we have:
V(x) = √np(1 - p)
Hence, the value of V(x) is √np(1 - p)
Study the memoryless property of X.The memoryless property of X is that each probability of X is independent
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
a small gecko is 3/4 inch long. a larger gecko is 11 1/3 times as long. how long is the larger gecko?
Answer:
127/12
Step-by-step explanation:
11 1/3- 3/4
A scuba diver descends in the water at a rate of 15 feet per minute for 2.6 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 28 feet per minute for 2 minutes. What is the scuba diver's position relative to sea level after the 4.6 minutes? Show your answer as a decimal.
Answer:
\({ \longrightarrow{ \sf{2.6 minutes \longleftarrow}}}\)
Step-by-step explanation:
Scuba diver is going downward with cetain speed for 2.6 minutes
(
�
−
4
)
2
(x−4)
2
as a trinomial in standard form.
The trinomial in standard form for the expression (x - 4)² is x² - 8x + 16.
Expressing the trinomial in standard formTo expand (x - 4)², we can use the formula for the square of a binomial:
(a - b)² = a² - 2ab + b²
In this case, a = x and b = 4.
Substituting into the formula, we get:
(x - 4)² = x² - 2(x)(4) + 4²
Simplifying the expression, we get:
(x - 4)² = x² - 8x + 16
Therefore, the trinomial in standard form for (x - 4)² is x² - 8x + 16.
Read more about trinomial at
https://brainly.com/question/10799926
#SPJ1
Two cars are traveling towards a hotel on the same road. From the edge of the hotel, 600 feet high, Spiderman sits on the rooftop thinking about the depression angle needed to reach each car. If the depression angle to the nearest car is 52 degrees, and the depression angle to the farther car is 46 degrees, how far apart must the two cars be from each other?
Make a sketch, solve the problem, and round your answer to the nearest hundredth of a foot.
The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.
To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.
In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:
tan(52) = 600 / d1
Rearranging the equation to solve for d1:
d1 = 600 / tan(52)
Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:
tan(46) = 600 / d2
Rearranging the equation to solve for d2:
d2 = 600 / tan(46)
Using a calculator, we can compute:
d1 ≈ 504.61 feet
d2 ≈ 681.95 feet
The distance between the two cars is the difference between d2 and d1:
Distance = d2 - d1
Plugging in the values, we have:
Distance ≈ 681.95 - 504.61
Distance ≈ 177.34 feet
For more such question on angles. visit :
https://brainly.com/question/25770607
#SPJ8
Sketch the lines through the point with the indicated slopes. Make the sketches on the same set of coordinate axes
Point
Slopes
(1, 1)
(a) 3 (b) -3 (c) -5/2 (d) Undefined
The sketch for slope is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Point Slopes
(1, 1) (a) 3
_ (b) -3
_ (c) -5/2
_ (d) Undefined
a) Now, using slope intercept form
y - 1= 3 (x-1)
y- 1= 3x- 3
y= 3x - 2
(b) Equation of a line has a slope -3 is given by
y - 1= (-3) (x-1)
y-1 = 3- 3x
y = -3x + 4
(c) Equation of a line has a slope -5/2 is given by
y - 1= (-5/2) (x-1)
y-1 = -5/2x + 5/2
y= -5/2x + 7/2
(d) The line parallel to y axis and passes through given point : x=1
"undefined" means the line is vertical.
Learn more about slope here:
https://brainly.com/question/10945523
#SPJ1
Multiple 7/9 to the sum of 8 3/7 and 5 11/14
\( \frac{7}{9} \times (8 \frac{3}{7} + 5 \frac{11}{14}) = \\ \)
\( \frac{7}{9} \times (8 \frac{6}{14} + 5 \frac{11}{14} ) = \\ \)
\( \frac{7}{9} \times (13 \frac{6 + 11}{14}) = \\ \)
\( \frac{7}{9} \times (13 \frac{17}{14}) = \\ \)
\( \frac{7}{9} \times (14 \frac{3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{14 \times 3 + 3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{42 + 3}{14}) = \\ \)
\( \frac{7}{9} \times ( \frac{45}{14}) = \frac{7 \times 45}{9 \times 14} = \frac{5}{2} \\ \)
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Answer:
\(\displaystyle \frac{199}{18}\)
Step-by-step explanation:
Fraction Operations
Before attempting to operate with the given fractions, we need to express all of them in the form a/b, because the last 2 fractions are in mixed form.
\(\displaystyle 8\frac{3}{7}=8+\frac{3}{7}=\frac{8*7+3}{7}=\frac{59}{7}\)
\(\displaystyle 5\frac{11}{14}=5+\frac{11}{14}=\frac{5*14+11}{14}=\frac{81}{14}\)
Now for the sum of the last two fractions:
\(\displaystyle \frac{59}{7}+\frac{81}{14}\)
Make both denominators equal by multiplying by 2 both parts of the first fraction:
\(\displaystyle \frac{59}{7}+\frac{81}{14}=\frac{118}{14}+\frac{81}{14}\)
\(\displaystyle =\frac{118+81}{14}=\frac{199}{14}\)
Now multiply by 7/9:
\(\displaystyle \frac{199}{14}*\frac{7}{9}=\frac{199}{18}\)
i will give mor points ans please
Answer:
Step-by-step explanation:
| − | = | + 9I
THERE ARE TWO POSSIBILITIES
2x-1=4x+9 and 2x-1=-4x-9
2x-4x=9+1 and 2x+4x=-9+1
-2x=10 and 6x=-8
x=-5 and x=-8/6
x=-5 and x=-4/3
SOLUTION SET ={-5,-4/3}
\(\frac{2x-1}{3}-\frac{3x}{4}=\frac{5}{6}\\ taking LCM\\\frac{8x-4-9x}{12}=\frac{5}{6}\\\frac{-1x-24}{12}=\frac{5}{6}\\ by cross multiplication\\6(-1x-4)=12*5\\-6x-24=60\\-6x=60+24\\-6x=84\\\\x=-14\\soltion set {-14}\)
\(10+\sqrt{10m-1}=13\\\sqrt{10m-1}=13-10\\\\\sqrt{10m-1}=3\\ taking square on both sides\\10m-1=3^2\\10m-1=9\\10m=9+1\\10m=10\\m=1\)
the number of solution to a linear equation is 1
2(x - 4) = 6 then x is ----7
Solution of | + | = − is ---------13/3,5/3
What is the answer to this?
The part of a circle that intersects the center of a circle
A private museum charges $40 for a group of 10 or fewer people. A group consisting of more than 10 people must, in
addition to the $40, pay $2 per person for the number of people above 10. For example, a group of 12 pays $44. The
maximum group size is 50.
a) How much does a group of 16 pay?
b) Find a formula for the cost function.
c) What are the domain and range of the cost function? (Hint: Use the graph on the calculator)
Answer:
i hope this helpes
Step-by-step explanation:
a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.
b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.
c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.
Answer:
a) $52
b) C(x) = 40 + 2x, if x > 10 and x ≤ 50
C(x) = 40, if x ≤ 10
c) Domain = {x ≥ 1 and x ≤ 50}
Range = { from 40 to 140}
Graph the function f(x) = cube root x+1
what are the minimum and maximum values on the intervals [-2, 0]?
There is no maximum and minimum values.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=∛(x+1)
Find where the first derivative is equal to 0 to find the local maxima and minima.
By differentiating the given function we get
\(f(x)=(x+1)^{\frac{1}{3} }\)
\(f'(x)=\frac{1}{3(x+1)^{\frac{2}{3} }}\)
For maxima f'(x)=0
0= \(\frac{1}{3(x+1)^{\frac{2}{3} }}\)
No local maxima or minima
Therefore, there is no maximum and minimum values.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1