Yes the statement of my cousin that rotations, translations, and reflections will result in the congruence of corresponding lines, line segments, and angles is true
How is this statement true?Yes, this is true. Congruence refers to the idea that two geometric figures are identical in size and shape. Translations, rotations, and reflections are rigid motions that preserve distances and angles, meaning that corresponding lines, line segments, and angles in the figures will remain congruent after the transformation.
This is because these transformations only involve shifting, rotating, or flipping the figure, but not changing its shape or size.
Read more on congruence here:https://brainly.com/question/2938476
#SPJ1
HELP FAST WILL GIVE 60 POINTS For THE RIGHT ANSWER
A repeating decimal like 0.2222222.... is a rational number and can be written as the fraction 2/9.
A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100.
A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number that can be written as the fraction 1514013912/5000000
The square root of a perfect square is a rational number and also a whole number.
The square root of a prime number is an irrational number.
What are rational and irrational numbers?
The definition of a rational number is one that may be stated as a fraction or as a portion of a whole number. For example -7, 2/3, 3.75 Numbers that cannot be stated as a fraction or ratio of two integers are referred to be irrational numbers. There is no limit to how one might convey them. For example √2, √3, e
Learn more about rational and irrational numbers at: https://brainly.com/question/20400557
#SPJ1
HELP ASAP QUESTION 2!
The area of the circular section is equal to 3π square meters. (Correct choice: C)
How to find the area of a circular section
Herein we find the case of a circular section whose area must be found by the following formula:
A = (θ / 360) · π · R²
Where:
θ - Central angle, in degrees.R - Radius, in meters.A - Area, in square meters.If we know that θ = 270° and R = 2 m, then the area of the circular section is:
A = (270 / 360) · π · (2 m)²
A = (3π / 4) · (2 m)²
A = 3π m²
To learn more on circular sections: https://brainly.com/question/13672518
#SPJ1
Mark and his three friends ate dinner out last night. Their bill totaled $52.35, the tax was 8.5% and they left their server an 18% tip. If they split the bill evenly, how much did each person pay? Round to the nearest cent.
Answer:
$56.84
Step-by-step explanation:
52.35 + 8.5% + 18% ÷ 4 = $56.84475
Simplify (3x2+9x-1)+(-5x2+6x-10)
brian is splitting 4 quarts of ice cream with members of the team. If the ice cream is split evenly, how many cups will each person get
Each person will get 1 [tex]\frac{7}{9}[/tex] cups of ice cream.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that, Brian is splitting 4 quarts of ice cream with members of the team.
Assume the number of members of the team = 9
We have to find how many cups each member gets.
First we have to convert the measurement quarts to cups.
1 quart = 2 pints
1 pint = 2 cups
1 quart = 2 × 2 cups = 4 cups
We have 4 quarts of ice cream.
4 quarts = 4 × 4 = 16 cups
Number of cups each member gets = 16/9 cups = 1 [tex]\frac{7}{9}[/tex] cups
Hence there will be 1 [tex]\frac{7}{9}[/tex] cups for each member.
Learn more about Division here :
https://brainly.com/question/14775006
#SPJ1
please help me with this problem
The images of the functions are listed below:
Case 1: f(x) = √(- x) (Correct choice: A)
Case 2: f(x) = √(x - 4) (Correct choice: D)
Case 3: f(x) = √x - 3 (Correct choice: A)
Case 4: f(x) = √(x - 4) - 4 (Correct choice: A)
How to use rigid transformations on functions
In this problem we find four cases of functions that must be transformed by rigid transformations. Rigid transformations are transformations applied on functions such that its features are not altered. We should apply, if possible, the following rigid transformations:
Reflection across the y-axis
f(x) → f(- x)
Translation to the right
f(x) → f(x - k), where k > 0
Translation downward
f(x) → f(x) - k, where k > 0
Now we proceed to determine the image of each function:
Case 1
f(x) = √x
Reflection across the y-axis
f(x) = √(- x)
Case 2
Translation 4 units right
f(x) = √(x - 4)
Case 3
Translation 3 units down
f(x) = √x - 3
Case 4
Translation 4 units right and 4 units down
f(x) = √(x - 4) - 4
To learn more on rigid transformations: https://brainly.com/question/28004150
#SPJ1
Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 14 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 1 part(s) from among the 14 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.
Round your answers to four decimal places.
(a) What is the probability that the inspector finds exactly one nonconforming part?
(b) What is the probability that the inspector finds at least one nonconforming part?
The probability values
(a) P(X=1) = 0.2696(b) P(at least one nonconforming part) = 0.8845The probability that the inspector finds exactly one nonconforming partFrom the question, we have the following parameters that can be used in our computation:
n = 14
p = 2/14
The probability P(x =1) can be calculated as
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
In this case, we have
P(x = 1) = C(14, 1) * (2/14)^1 * (1 - (2/14))^(13
Evaluate
P(x = 1) = 0.2696
The probability that the inspector finds at least one nonconforming partThe probability P(x >= 1) can be calculated as
P(x) = 1 - P(0)
In this case, we have
P(x >= 1) = 1 - [C(14, 0) * (2/14)^0 * (1 - (2/14))^(14)]
Evaluate
P(x >= 1) = 0.8845
Read more about probability at
https://brainly.com/question/251701
#SPJ1
how to get the volume of a rectangular pyramid
Answer:
length x width x height divided by 3
Kelly can run 1/2 mile in 3 minutes. How far does
Kelly run in 1 minute if he runs at the same pace the
entire time?
Kelly can run 1/2 mile in 3 minutes. 1/6 mile Kelly run in 1 minute if he runs at the same pace the entire time.
What makes anything a mile?The word "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards.
Kelly can run 1/2 mile in 3 minutes so the ratio is 1/2 mile per 3 minutes
= [tex]\frac{\frac{1}{2} }{3}[/tex]
For transforming 3 to 1 we need to divide by 3 because we have to keep the ratio value, we have to divide also the numerator by 3 :
= [tex]\frac{\frac{1}{2} }{3} \times \frac{\frac{1}{3} }{\frac{1}{3}}[/tex]
[tex]= \frac{\frac{1}{2} \times \frac{1}{3} }{3 \times \frac{1}{3} }[/tex]
= 1/6 / 1
= 1/6
Learn more about the Miles here: https://brainly.com/question/29806974
#SPJ1
Determine when the function is positive, negative, increasing, or decreasing: y = -9ˣ
suppose 5x^{2} +5x+xy=4 and y(4)=-24. Find y^'(4) by implicit differentiation.
Your answer:
if 5x² +5x+xy=4 then the value of y'(4) is -21/4
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given expression is 5x² +5x+xy=4
Five times of x square plus five times of x plus x times of y equal to four.
Differentiate with respect to x.
10x+5+y(x)+xy'(x)
if x=4
10(4)+5+y(4)+4y'(4)=0
40+5-24+4y'(4)=0
21+4y'(4)=0
4y'(4)=-21
Divide both sides by 4
y'(4)=-21/4
Hence, if 5x² +5x+xy=4 then the value of y'(4) is -21/4
To learn more on Differentiation click:
https://brainly.com/question/24898810
#SPJ1
What is the total length of 3km, 464m, 8km, 550m and
The total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km. Thus Option d is correct
The total length of 3km, 464m, 8km, 550m and 900m in kilometre
As we know that 1000m = 1 km, now
= 3000 + 464 + 8000 + 550 + 900
= 12914 m
= 12.914 km
Thus, the total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km
Learn more about length
https://brainly.com/question/2497593
Let f(x) = √x-5 for x ≥ 5
Find f^-1(2)
Answer: To find the inverse of the function f(x), we need to switch the roles of x and y, so that x becomes the dependent variable and y becomes the independent variable. Then, we need to solve for x in terms of y.
Let y = √x - 5, then x = y^2 + 5.
To find f^-1(2), we need to substitute 2 for y in the equation x = y^2 + 5:
x = 2^2 + 5 = 9
So f^-1(2) = 9.
This means that the inverse of f(x) at 2 is 9. In other words, if f(x) = 2, then x = 9.
Step-by-step explanation:
What is the weighted average length of the nails in the drawer?
A. 350 cm
B. 333 cm
C. 5.00 cm
D. 3.50 cm
Caleb has 12 grams of tea. He bought 5/4 of that amount for his mom. How many grams did Cameron get his mom?
Answer: Caleb bought 15 grams for his mom
Step-by-step explanation:
5/4 is equal to 1.25, so Caleb bought 1.25 x 12 grams.
1.25 x 12 = 15 grams.
Let a and b be a pair of vectors, and let θ be the angle between them. Show that ||a ×b||= ||a||||b||sin θ|.
You are not allowed to use the cross product formula directly!
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
The range of the quadratic function is {y |0 ≤ y < 9}
What is the range of a function?The range of a function is the set of output values of the graph. In other words mean the range of a function is the set of y values of the graph.
Given,
Parabola opens from
Closed circle point = (-2, 4) , then decreases
y ≤ 4
vertex = (0,0)
at vertex y = 0
then increases to
Open circle point = (3, 9)
y < 9.
It can be concluded,
value of y is such that 0 ≤ y < 9.
Range = {y | 0 ≤ y < 9}
Hence, the range of the function is {y | 0 ≤ y < 9}
Learn more about parabola here:
brainly.com/question/2264373
#SPJ1
Can someone answer this?
Answer:
Step-by-step explanation:
1+1=2 your welcome
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
To know more about Intersection points visit,
https://brainly.com/question/29248863
#SPJ4
Lourdes can buy 3-packs of paper for $10.50, or she can buy 4-packs of paper for $13.50. She wants to buy 12 packs of paper. How much more will she spend if she buys only 3-packs of paper
Lourdes will spend an amount of $1.50 more if she buys only 3-packs of paper.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
If Lourdes buys only 3-packs of paper, she will need to buy 12 / 3 = 4 sets of paper.
At $10.50 per set, this will cost her 4 x $10.50 = $42.
If Lourdes buys only 4-packs of paper, she will need to buy 12 / 4 = 3 sets of paper.
At $13.50 per set, this will cost her 3 x $13.50 = $40.50.
So, Lourdes will spend $42 - $40.50 = $1.50 more if she buys only 3-packs of paper.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ1
Question 8
Imagine you are planning to use circles to visually compare the populations of North
Carolina (10,300,000), California (39,800,000), and Ohio (11,600,000). The size of each
population will be represented by the area of each circle, not the radius. The circle for
Ohio will have a radius of 8. Round each answer to the nearest tenth.
What should the area of the circle representing the population of California? Round
your answer to one decimal place.
Area =
cm²
Hint
Create a proportion to find the area of Ohio first. Then use the area formula to find the
radius.
The area of the circle representing the population of California is 689.5 units
What is area of the circle?
Area of the circle is is them measure of size of circle. The area of circle is given by pi* r^2. where r is the radius of the circle which is equal to half the diameter. and pi is a mathematical constant. its value is 3.14.
We are given that the radius representing a circle for ohio is 8
Area of circle = 3.14 * (8^2)
Area of circle = 200.96
Now the area of the circle representing the population of California
given by,
= (39800000*200.96)/11600000
= 689.5
Hence the area of the circle representing population of California is 689.5
Given below is the a problem to find the area of the circle. Please refer the link below
https://brainly.com/question/27696929
#SPJ1
What is the inverse of a function?
A function for which the domain remains the same, and reciprocal values of the range are used
A function for which the values or the domain and the range are interchanged
A function for which the range remains the same, and reciprocal values of the domain are used
The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.
What is an inverse function?The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.
Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.
For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:
x = 2y + 3
2y = x - 3
y = (x - 3)/2
Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.
Learn more about inverse functions here:
https://brainly.com/question/30350743
#SPJ1
100-40+10-100-20+20-+10
Answer:
-40
Step-by-step explanation:
100-40+10-100-20+20-(+10)
=60+10-100-20+20-10
=70-100-20+20-10
=-30-20+20-10
=-50+20-10
=-30-10
=-40
Richard and Teo have a combined age of 36. Richard is 15 years older than twice Teo's age. How old are Richard and Teo?
Teo is 10.5 years old and Richard is 25.5 years old.
How old are Richard and Teo?Represent Teo's age with x.
Using the above as a guide, we have the following:
Richard = x + 15
Their combined age is 36
So, we have the following representation
x + (x + 15) = 36
Evaluate the like terms
2x + 15 = 36
2x = 21
x = 10.5
Recall that
Richard = x + 15
So, we have
Richard = 10.5 + 15
Richard = 25.5
So Teo is 10.5 years old
Read more about numbers at
https://brainly.com/question/10853762
#SPJ1
Determine the domain for the interval of decrease.
d
Distance (km)
60
50
40
30
20
10
8 9 10 11 12 1 2 3 4
am
noon
p.m.
Time of the day
A2≤x≤5
B8≤x≤ 10
3≤x≤5
Answer:
The domain for the interval of decrease is 3 ≤ x ≤ 5
Find the GCF of 35x^5y and 42x^5y^3.
Answer:
x^5y
Step-by-step explanation:
To find the greatest common factor (GCF) of 35x^5y and 42x^5y^3, we need to find the largest expression that divides into both of these polynomials.
The common factor in both of these polynomials is x^5y, which is the GCF. So, the GCF of 35x^5y and 42x^5y^3 is x^5y.
write an exponential function that has a y-intercept of -4 and passes through the points (1, -1.6) and (2, -0.64)
The function can be used to model the exponential growth or decay that occurs in real-life situations that fit this particular pattern is y = 4(-0.4)ˣ + -4
An exponential function is a mathematical function that has the form
=> y = abˣ,
where a is a constant and b is the base of the exponential.
To start, we will use the first point, (1, -1.6), to write an equation that relates x and y. Let's call the constant a in our exponential function "k". Using the point (1, -1.6), we can write the equation:
=> -1.6 = k * b¹
Next, we will use the second point, (2, -0.64), to write another equation that relates x and y. Using the point (2, -0.64), we can write the equation:
=> -0.64 = k * b²
Now that we have two equations, we can solve for the two unknowns, k and b, by dividing the two equations:
=> (-0.64) / (-1.6) = k * b² / k * b¹
b = (0.64 / -1.6)¹
b = -0.4
With b determined, we can substitute it back into one of the equations and solve for k:
=> -1.6 = k * (-0.4)¹
=> k = -1.6 / (-0.4)
=> k = 4
So our exponential function that passes through the points (1, -1.6) and (2, -0.64) and has a y-intercept of -4 is:
y = 4 * (-0.4)ˣ + -4
To know more about exponential function here.
https://brainly.com/question/2456547
#SPJ4
Simplify 25a/7 times 2a/5
Give your answer as a single fraction in its simplest form.
Answer:
10a²/7
Step-by-step explanation:
25a/7×2a/5
50a²/35
10a²/7
Answer:
lamohehsphbejrokrbbrjirorvv!hskosbbbwjoajwwjorvvrjfoisbbsiosbwbddpsba hzidb djfofvdjododvowjwwjfpgrdhvrjforvveif fbbrhfjvrjdoddvririvrhrHieojeh
find the dilated coordinates with the scale factor of 1/5
The dilated coordinates:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
Coordinates: D(-7, 0), E(-7, -5), F(-2, -5).
The shape is dilated by the scale factor of 1/5.
The dilation rule:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
Hence, the dilated coordinates are given above.
To learn more about the dilation in geometry;
https://brainly.com/question/10713409
#SPJ1
The complete question:
Find the dilated coordinates with the scale factor of 1/5,
D(-7, 0), E(-7, -5), F(-2, -5).
Andrew wins 4 fencing bouts for every 3 that he loses. If he had 35 bouts during the last year, how many bouts did he win?
The number of bouts that Andrew won during the last would be = 20 bouts.
How to calculate the number of bouts won?The number of fencing bouts that Andrew won = 4
The number of bouts he losses every 4 wins = 3 bouts
The total number of bouts he is having this year = 35 bouts.
The number of bouts he won amongst the number that he lost would be calculated as;
= 4+3 = 7
= 4/7 × 35/1
= 4× 5 = 20 bouts.
Learn more about division here:
https://brainly.com/question/25289437
#SPJ1