Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,
The triangles ABC and XYZ are similar by SAS similarity, as,
AC = XZ = 5,
AB = YZ = 13
∠ ACB = ∠ XZY
When you translate and then rotate triangle ABC, you will get triangle XYZ.
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What is the formula for horizontal and vertical?
Horizontal asymptotes is a horizontal line and its equation is y=k
vertical asymptotes is a vertical line and its eqaution is x=k
In these given lines we can find horizontal and vertical asymptotes.
What is the formula for horizontal asymtotes?To find the horizontal asymptotes ,we compare the degree of the numerator with the degree of denomenator.
f(x)=ax^n/bx^m
if degree of numerator is greater than degree of denominator then does not exist horizontal asymptotes.
what is the formula for vertical asymptotes?To find the vertical asymptotes , we use
f(x)= p(x)/q(x)
To set the denominator q(x) to zero ,and solve the value for x.
where p(x) and q(X) are polynomial functions and q(x) [tex]\neq[/tex] 0
vertical asymptotes is x=k where k represents real zero of q(x).
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suppose the length of time (in minutes) going through customs at u.s. airports with global entry (goes) is normally distributed with a population mean of 40 minutes and a population standard deviation of 12 minutes. what is the approximate wait time for the fastest 4% of passengers?
The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.
What is Standard Deviation?
It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.
The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.
The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.
To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.
Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.
So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.
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There are 6 seniors on student council. Two of them will be chosen to go to
an all-district meeting. How
many ways are there to choose the students who
will go to the meeting?
Decide if this is a permutation or a combination, and then find the number of
ways to choose the students who go.
By using the property of combination, it can be calculated that -
This is a problem of combination.
There are 15 ways to choose the students who will go to the meeting
What is combination?
Combination is the process of selection some objects from a group of items where the order of the selection do not matter
This is a problem of combination
Number of seniors = 6
Number of students will go to the all district meeting = 2
Number of ways to choose the students who will go to the meeting =
[tex]{6 \choose 2}[/tex]
= [tex]\frac{6!}{(6 - 2)! \times 2!}[/tex]
= 15
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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot The Cruisers scored are 24 and 19 points respectively.
How to find the number of two and three points made?The Cruisers scored a total of 105 points in a basketball game. They also had a total of 43 baskets, of which some were two-point shots and some of were three-point shots.
Therefore, the number of two-points and three-points the cruiser scored is as follows:
x = number of two-points
y = number of three-points
So;
x + y = 43 -------1
Also;
2x + 3y = 105 -----2
Multiplying equation(1) by 2
2x + 2y = 86
2x + 3y = 105
Subtract equation(i) from equation(ii)
y = 19
To find x:
x = 43 - 19
x = 24
Therefore,
number of two-points = 24
number of three-points = 19
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Which equation is the inverse of 2 x 2 )= 8 7 y?
[tex]y=2[/tex] ± [tex]\sqrt{28+4x}[/tex] is the equation that equals 2(x - 2)2 = 8(7 + y).
Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other. In most cases, a number's inverse refers to its reciprocal, or x - 1 = 1 / x. When a number is combined with its reciprocal, or inverse, the result is 1, or 1.
Considering the equation:
[tex]2(x-2)^2=8(7+y)[/tex]
Change the x and y variables.
[tex]2(y-2)^2=8(7+x)[/tex]
In terms of x, solve for y.
We have two sides, therefore divide them by two.
[tex](y-2)^2=4(7+x)[/tex]
Using the distribution property, [tex]a.(b+c)=a.b+a.c[/tex]
[tex](y-2)^2=28+4x[/tex]
Square-rooting both sides yields:
[tex]y-2=[/tex]±[tex]\sqrt{28+4x}[/tex]
our two sides plus two;
[tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex]
As a result, equation [tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex] is the opposite of [tex]2(x-2)^2=8(7+y)[/tex]
The complete question is:-
Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?
Options:
–2(x – 2)^2 = –8(7 + y)
y= 1/4 x^2 -x -6
y= -2 +/- sqrt of 28+4x
y= 2 +/- sqrt of 28+4x
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4. Volume of a cone is (1/3)3.14r²h. Solve for h.
The required solution would be h = 3Vr²/3.14 for h, where V is the volume of a cone.
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
The volume of the cone (V ) = 1/3πhr²
We have been given that the volume of a cone is (1/3)3.14r²h
We have to determine the solution for h
As per the given question, we have
⇒ V = (1/3)3.14r²h
Multiply by 3 into the above equation,
⇒ 3V = 3.14r²h
Divided by 3.14 into both sides
⇒ 3V/3.14 = r²h
⇒ h = 3Vr²/3.14
Therefore, the required solution would be h = 3Vr²/3.14.
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Is equidistant from all points on the circle?
The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.
Every point in a circle is equally distance from the center. Similar to a sphere, every point on a sphere is equally distance from the center.
Two equal chords on a circle indicate that they are equally spaced from the circle's center.
The incenter of a triangle is the point that is equally far from each of its sides. A median is a line segment that has one of its endpoints in the vertex of a triangle and the other endpoint in the midpoint of the side opposite the vertex. The three medians of a triangle meet in the centroid.
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How do you find the missing side of a triangle without a calculator?
We can find out the missing values of the sides of a triangle by using trigonometry functions like sin, cos, and tan.
If one angle and perpendicular are given then the other side means hypotenuse can be found out by sin function.
Sin Ф = perpendicular/hypotenuse
If one angle and hypotenuse are given then the other side means base can be found out by the Cos function.
CosФ = base/ hypotenuse
If one angle and base are given then the other side means perpendicular can be found out by the tan function.
Tan Ф= perpendicular/ base
Therefore the missing sides can be found by trigonometric function while one angle is given.
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Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
The tree is 10.77 meters tall.
Step-by-step explanation:
The given diagram is an example of similar triangles. Look at the image I attached to my response to see this problem in terms of triangles.
The triangle that is formed by Alyssa and her shadow and the triangle that is formed by the tree and its shadow is an example of similar triangles because they both share an internal angle.
As per the similar triangles theorem, the ratios of the corresponding sides of both sides are proportional.
Thus, we have to make a proportion of the corresponding sides of both triangles to solve for the height of the tree. Let x = the height of the tree.
Proportion: [tex]\frac{BE}{BC} = \frac{DE}{AC}\\[/tex]
BE = 4.25 meters
BC = 27.75 meters
DE = 1.65 meters
AC = x meters
[tex]\frac{4.25}{27.75} = \frac{1.65}{x}[/tex]
Now, cross multiply to solve for x.
[tex]4.25x = 1.65(27.75)\\4.25x = 45.7875\\x = 10.77[/tex]
∴ The tree is 10.77 meters tall!
The height of the tree to the nearest hundredth of a meter is,
⇒ 10.77 meters
We have to given that;
Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree.
Now, we can make a proportion of the corresponding sides of both triangles to solve for the height of the tree.
And, Let us assume that,
x = the height of the tree
Hence, We get;
⇒ (27.75 - 23.5) / 27.75 = 1.65 / x
Solve for x;
⇒ 4.25 / 27.75 = 1.65 / x
Cross multiply we get;
⇒ 4.25x = 1.65 x 27.75
⇒ 4.25x = 45.78
⇒ x = 10.77 meters
Thus, The height of the tree to the nearest hundredth of a meter is,
⇒ 10.77 meters
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What is the relationship between numerator and denominator?
The denominator of a fraction represents the number of equal parts in a whole, while the numerator represents the number of parts considered.
What is a fraction?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator.In a simple fraction, they are both integers. A complex fraction has a fraction in either the denominator or the numerator. The denominator of a proper fraction is less than the numerator. A numerator is the total number of parts.A denominator is the lowest number in a fraction that represents the number of equal parts into which an item is divided. It is the fraction divisor.A fraction as p/q can be thought of as p parts, which is the numerator of a whole object, divided into q equal parts which is denominator.To learn more about fraction refer to :
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Can anyone help me answer this question?
Let A, B, C e sets. Which of the following properties is the cumulative law?
a. A ∪ B = B ∪ A
b. A ∩ B = B ∩ A
c. A ∩ B = B ∪ A
d. (A ∪ B) ∪ C = A ∪ (B ∪ C)
The property that represents the commutative law of sets is given as follows:
d. (A ∪ B) ∪ C = A ∪ (B ∪ C)
What is the commutative law of sets?The cumulative law of sets states that the order in which the union operation is made does not change the resulting set of these multiple union operations.
The symbol that represents the union operation is given as follows:
∪.
Hence statement d is the correct statement of the commutative law of sets, as:
In (A ∪ B) ∪ C, the union of A and B is first obtained, and then united with set C.In A ∪ (B ∪ C), the union of B and C is first obtained, and then united with set A.For both cases, the resulting set is the same.
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solve this equation using zero product property and show the work
(x-5)(x+7)=0
According to question,
Given data,
We know that;
Zero product property,
ab =0
either a or b or both must be zero.
(x-5) (x+7) = 0
Where a=(x-5)
b= (x+7)
then,
x-5=0(both side equation adding +5)
+5=+5
So,
x = 5
therefore,
x+7=0(both side equation substrate -7)
-7=-7
So,
x=7
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find the x number i will gave 10 points
Answer:
x is 5 cm
Step-by-step explanation:
x is half of the diagonal and we can see that the diagonal is 10 cm
and half of 10 is
Six lines are drawn, no two of which are parallel. If no more than two of the lines pass through any one point, what is the number of triangles formed?
Answer: I believe 20.
Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.
EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
combinations
C(n,r)= n! / (r! * (n−r)!)
n = 6 : total number of lines
r = 3 : because its 3 lines to make a triangle
6 lines
6C3 = 20 triangles
quora glenn clemens
mathplanet
How do I calculate how much paint I need?
According to good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats.
It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home.
Every paint has a spread rate that controls how many square feet may be covered each gallon. A good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats. Choosing the proper quantity of paint for steel is a tough matter because high-quality paint is expensive and you don't want to overbuy. To avoid overbuying paint, we advise simply purchasing 80% of the projected amount at first and the remaining 20% after you are nearly completed.
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WILL MAKE BRAINLIEST!!! Cheese is sold in packages of 8 and buns are sold in packages of 12. Harvey makes each burger with 1 patty and 1 bun. Harvey wants to buy enough cheese and buns to make burgers with no cheese or buns left over. At least how many burgers will Harvey make?
what’s the equation when the points are (3,-6) and (5,-5)
Answer:0.5x - y -7.5 = 0
Step-by-step explanation:
The square root of a negative number is supposed to not exist/be an imaginary number.
Am I right? Is this operation right?
Answer: You are correct, because negative number don't have real square roots
Step-by-step explanation:
Matt shot an 86 on the golf course on Monday then on Friday he shot a 95 what is the percentage of change rounded to the nearest 10th of a percent?
Answer:
increase 10.5 percent
Step-by-step explanation:
..
If your starting balance is $250, what is your new balance after a withdrawal of $56.50 and a deposit of $25.00?
Answer:
$218.5
Step-by-step explanation:
its $218.5 because 250 - 56.50 = 193.5 and 193.5 + 25.00 + 218.5
How do you make 5 with 4 2s?
The equation to form 5 with 4 2s is 2 + 2+ (2/2).
Explain the method of BODMAS?Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.
B-Brackets, O-Orders (powers/exponents as well as roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, is also known as BODMAS in some areas.Brackets, then order (or "of" in some curricula), next multiplication and division, finally addition and subtraction is an acronym for the order of operations in mathematics, with B coming first and AS coming last.The formation of 5 with 4 2s is -
= 2 + 2+ (2/2)
= 2 + 2 + 1
= 5
Thus, the expression to form 5 with 4 2s is 2 + 2+ (2/2).
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What is the volume of a pyramid with a base area of a square and a height of a cube?
The volume of the pyramid with the given base area of square and height of the cube is given by: V = ( 1/3) × ( y)² × (h).
As given in the question,
Base of the given pyramid is square in shape.
Base area of the pyramid is given by:
Let 'y' be the side length of the square base.
Area of the square base = ( side length )²
= y²
let 'h' be the height of the cube
Volume (V) of the pyramid = ( 1/3 ) × Base area × height
⇒Volume of the pyramid = ( 1/3 ) × y² × h
Therefore, the volume of the pyramid with square base and height of the cube is equal to Volume of the pyramid = ( 1/3 ) × y² × h.
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What degree is a 3 to 1 slope?
Answer:
Slope
Angle (degrees) Gradient Grade (%)
2 to 1 = 3.493 to 1 = 5.244 to 1 = 6.99Therefore, the correct answer is 5.24
. a pole is carried down a hallway 9 ft wide. at the end of the hall, there is a right-angled turn into a narrower hallway 6 ft wide. what is the length of the longest pole that can be carried horizontally around the corner?
Using the geometry of the right angle triangle. Since, The narrower hallway is 6ft. The answer is 6ft.
What do you mean by geometry?A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.
What is a right angle triangle?A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
Larger hallway= 9 ft
narrower hallway=6 ft
Since, After turning in the corner, The pole should be carried through the 6ft wide hall. The maximum length of the pole is 6ft.
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how many ways are there that no two students will have the same birth date in a class of size 60?
The number of ways in a class of size 60 where no two students will have the same birth date is 365 x 364 x 363 x 362 x ........... x 306.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of students = 60
We will assume 365 days in a year.
Now,
The first student will have 365 possible days for his birthday.
The second student will have 364 possible days for his birthday.
In this way,
The last student will have (365 - 59) possible days for his birthday.
Now,
The number of possible ways for 60 students.
= 365 x 364 x 363 x 362 x ........... x 306
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Can a 2 year old count?
Therefore , the 2 year old children can able to count to 1 to 100 counting by making them learn.
By counting, what do you mean?The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number,
variable then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."
Here,
Every child is different in how they grow and learn, yet many
Children as young as two years old may count past ten and learn their numbers from 1 to 100.
They could be ready to try numbering in fives or using other skip counting strategies (5, 10, 15, 20, and so on).
As soon as you can, begin teaching your child how to recognise
numbers.
As a result, by making the toddlers study, two-year-olds can count to one hundred.
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What is the median of 8 5 7 9 11 6?
For the given observation 5,6,7,8,9,11 the Median is 7.5
The median is one of the metrics of central tendency. The middle value in a group of numbers is known as the median. It divides a given data sample into the higher half and the lower half. At least half of the observations fall below the median and at least half of the observations fall above the median.
If a data collection contains an even number of observations, the median can be determined as follows:
Sort the information either by ascending or by descending.
Identify the (n/2)nd and [(n/2) + 1] th observations if there are an even number of observations (let's say n).
The median of the provided data is equal to the average of the top two observations (as determined in step 2).
Here n = 6, So [6/2 + (6/2)+1}/2
=> Median = 7.5.
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what is the slope between (7,-4) and (2,-4)
Answer:
0
Step-by-step explanation:
Rise over run.
Difference between y is 0.
Difference between x is 5.
0/5 = 0.
Answer:
m = 0
Step-by-step explanation:
Slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y stay the same, and the x decrease by 5, so the slope is
m = 0/5
At which root does the graph of f x x 5 3 x 2 2 touch the x axis?
The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.
What is root of graph ?
A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph.
What is axis ?
An axis in mathematics is defined as a line that is used to make or mark measurements.
Have given , f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex]
⇒ [tex](x-5)^{3} * (x+2)^{2}[/tex]= 0.
But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.
⇒ [tex](x-5)^{3}[/tex]= 0 and \[tex](x+2)^{2}[/tex] = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x = 5 and x = - 2.
The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.
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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 15 centimeters and a height of 12 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
The Answer Is 1,837 cm