Assume that triangle ABC is ≅ triangle PQR. Which of the following congruence statements are correct? Check all that apply.
Answers
The correct congruent statement are as follows:
∠R ≅ ∠CAB ≅ PQHow to find the congruent side and angles of congruent triangle?The triangle ABC and PQR are congruent triangle.
Therefore,
ΔABC ≅ ΔPQR
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Therefore,
∠A ≅ ∠P
∠B ≅ ∠Q
∠C ≅ ∠R
Hence,
AB ≅ PQ
AC ≅ PR
BC ≅ QR
Therefore, the correct congruent statement are as follows:
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Related Questions
Where's the bus? Jayden takes the same bus to
work every morning. The amount of time (in min-
utes) that he has to wait for the bus to arrive can be
modeled by a uniform distribution on the interval
from 0 minutes to 10 minutes.
a) draw a density curve to model the amount of time that Jayden has to wait for the bus. Be sure to include scales on both axes.
b) on what percent of days does Jayden wait more than 7 minutes for the bus?
c) find the 38th percentile of this distribution.
Answers
Using the uniform distribution, we have that:
a) The graph is given at the end of the answer.
b) Jayden waits more than 7 minutes 30% of the days.
c) The 38th percentile is of 3.8 minutes.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
For this problem, the bounds are given as follows:
a = 0, b = 10.
As shown in the graph at the end of the answer.
The probability of waiting more than 7 minutes is:
[tex]P(X > 7) = \frac{10 - 7}{10 - 0} = 0.7[/tex]
Jayden waits more than 7 minutes 30% of the days.
The 38th percentile is x for which P(X < x) = 0.38, hence:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
0.38 = x/10
x = 3.8.
The 38th percentile is of 3.8 minutes.
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Angle 2 is an____angle and is_____to angle 1.
Angle 5 is an____angle and is_____to angle 8.
Answers
Answer:
Angle 2: Acute, supplementary
Angle 5: Obtuse, congruent
Step-by-step explanation:
An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees. A supplementary angle is an angle equal to 180 degrees when added to another angle. (Angle 1 + angle 2 = 180 degrees.) Congruent angles are equal to each other in degrees. (Angle 5 = angle 8.)
In the image above angle 3 is 79 degrees, what is angle 11?
Answers
Since in the image above angle 3 is 79 degrees, angle 11 is also equal to 79 degrees based on the vertical angles theorem.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the vertical angles theorem?The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
In Geometry, when two (2) parallel lines are cut by a transversal, the interior angles that are formed on the same side of the transversal are supplementary angles, which makes:
Angle 3 = Angle 14
Angle 14 = Angle 9
Angle 3 ≅ Angle 9 (Congruent angles or supplements of the same angle)
By applying the vertical angles theorem, we have:
Angle 9 ≅ Angle 11 = 79 degrees.
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SOMEONE HELP PLEASE ME
Answers
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
How to Interpret Conditional Statements?
Suppose we have a conditional statement, If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then; If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.
The conditional statement is given as;
If p, then not q.
1) The converse of the function is; If not q, then p
2) The Inverse of the function is; If not p, then q.
3) The contrapositive of the function is; If q, then not p
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The denominator of a rational number is greater than its numerator by 2. If 5
is subtracted from the numerator and 5 is added to its denominator, the new
number becomes 1
4
. Find the number.
Answers
Based on the word problem, the number is 9
What is a Rational Number?This refers to the type of number that is expressed as the ratio of two integers that has a non-zero denominator.
Calculations and ParametersLet the numerator be x
Let the denominator be x+2
If 5 is subtracted from the numerator
x - 5
If 5 is added to the denominator
x +2 + 5
x-5/x+7= 1/4
Cross multiply the values
It becomes
4x- 20 = x+ 7
3x= 27
x= 9
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In Exercises 4 and 5, find the area of the polygon with the given vertices.
4. P(1,1) Q(-2,1), R(-1,-4)
5. A(3,7), B(5,7), C(3,-7), D(5,-7)
Answers
Answer:
#4: 7.5
#5: 28
Step-by-step explanation:
Polygon in #4
is a triangle
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height h = (1/2)b.h
So area of this triangle = (1/2) (3) (5) = 15/2 = 7.5
Polygon in #5
is a rectangle with length = 7 - (-7) = 7 +7 = 14
and width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28
Hope that helps
The area of the polygon for exercise 4 is 7.5 square units and for exercise 5 the area is 28 square units.
What is an area?The space occupied by the object in two-dimensional space is called as the area.
For a triangle, the area will be calculated as,
base = 1 - (-2) = 1+2 = 3
height = 1-(-4) = 1 + 4 = 5
Area of a triangle with base b and height,
h = (1/2)b.h
Area of this triangle,
A = (1/2) (3) (5) = 15/2 = 7.5
Rectangle with length = 7 - (-7) = 7 +7 = 14
Rectangle width = 5-3 = 2
Area of a rectangle with length l and width w = lw
Area of this rectangle = 14 x 2 = 28 square units
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Find any points of discontinuity for each rational function. y= x²-x-2 / 3 x²-7 x+2
Answers
The point of discontinuity for y= x²-x-2 / 3 x²-7 x+2 is x= 1/3 and x= 2.
What is discontinuous function?
Mathematics, functions, and applications all place a premium on continuous functions. But not every function is continuous. A function is said to have a discontinuity there if it is not continuous at that point in its domain.
Given,
y = x²-x-2 / 3 x²-7 x+2
It can be expressed in the form of -
⇒ y = (x-2) (x+1) / (3x-1) (x-2)
The function will be undefined if the denominator will be 0
⇒ 3x-1 = 0
⇒ x = 1/3
⇒ x-2 = 0
⇒x = 2
So, we can conclude that the given function will be having points of discontinuity as x = 2, 1/3
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cuantos enteros hay en 384/135
Answers
Please helppppp no wowo
Answers
Answer:
d-(8,15)
Step-by-step explanation:
69497694646946464646463434644
A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
a. Which equation describes the relationship between a and c ?
Answers
Equation that describes the relationship between a and c is c = 750 / a
The domain of the function is - 5 ≤ a ≤ 50
The range of the function is - 50 ≤ c ≤ 150
Given,
Total money spent is = $750
Thus, our equation become,
ca = 750
solving for c,
c = 750 / a
The domain and range of function is -
a ≤ 5
Now, each award should be less than 50.
= 50 ≤ c
using equation, ac = 750
maximum value for a = 75.
we can say that domain is
5 ≤ a ≤ 50
Finally, by substituting a = 5 we can see that the maximum for c is 150.
This gives range for c as -
50 ≤ c ≤ 150
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HELP ME PLS
Use f(x) = |x|
f(x) is shifted left 5 and shifted up 2 to create
te g(x). Write the equation g(x)
Answers
Answer:
g(x) = | x + 5 | + 2
Step-by-step explanation:
given f(x) then f(x ± h ) represents a horizontal translation of f(x)
• if x > 0 then a shift to the left of h units
• if x < 0 then a shift to the right of h units
here f(x) is shifted left by 5 units , then
g(x) = | x + 5 |
given f(x) then f(x) + k represents a vertical translation of f(x)
• if k > 0 then a shift up of k units
• if k < 0 then a shift down of k units
here f(x) is shifted up 2 units , then
g(x) = | x + 5 | + 2
Subtract. 10,000 - 6,128
Answers
Answer:
3872
Step-by-step explanation:
10,000 - 6,128 = 3872
use calculator man
1. Identify as algebraic expression, numerical expression or equation:
a) 3x+1
b) 3+x=5
c) 2²-6(347),
Answers
Answer:
a) algebraic expression
b) equation
c) numerical expression
Step-by-step explanation:
Hope this helps......if not then sorry for wasting your time and may God bless you<3
3 - 1/2d = 3/2d + 4 - d.
I don't get the fractions, they confuse me and I don't know what to do with them to be able to finish the problem.
Answers
The solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7
How to evaluate the expression?The expression is given as
3 - 1/2d = 3/2d + 4 - d.
Multiply through the expression by 2
So, we have
6 - d = 3d + 8 - 2d
Evaluate the like terms
6 - d = d + 8
Evaluate the like terms
2d = -14
Divide by 2
d = -7
Hence, the solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7
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A number which was tripled and added to 4, totals 40. What is the number?
Answers
Answer:
x=12
Step-by-step explanation:
Our equation: 3x + 4= 40
40-4=36. 36/3 = 12
let h(x) = 3x+2 if h(x) = 11 find x
Answers
Answer:
3
Step-by-step explanation:
11 = 3x+2
9 = 3x
x = 3
The diagram below shows a section of the steel support structure of a roller coaster. Use the diagram for the problem below. Given segment JK is parallel to segment PL, m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)°, what is the measure, in degrees, of ∠JKL and ∠PLK? (HINT: m∠JKL and m∠PLK is not 90 degrees)
Answers
The measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
What are parallel segments?Parallel segments are defined as lines on a plane that never meets.
The properties of parallel segments include:
The vertically opposite angles are equalThe corresponding angles are equalThe alternate exterior angles are equalThe alternate interior angles are equalGiven the angles;
m∠JKL = (10x + 5)° m∠PLK = (12x - 1)°We can see that the two angles are vertically opposite angles and thus equal.
Then,
m∠JKL = m∠PLK
substitute the values
10x + 5 = 12x - 1
collect like terms
10x - 12x = -1 - 5
-2x = - 6
Make 'x' the subject of formula
x = 3
But:
m∠JKL = (10x + 5)° = 10(2) + 5 = 25°
m∠PLK = (12x - 1)° = 12(2) - 1 = 23°
Thus, the measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
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ethans cooking recipe uses 3 cups of sugar to make 21 cookies mias recipe uses 4 cups to make 28 cookies which has a greater sugar/cookie ratio
Answers
Evaluate the expression if x = 6, y = 4, and z = 2: xy + z
Answers
The value of the expression xy + z is 26 when x = 6, y = 4, and z = 2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?The expression is given as
xy + z
The values are given as
x = 6, y = 4, and z = 2
The expression can then be represented as
xy + z = 6 * 4 + 2
Evaluate the product
So, we have
xy + z = 24 + 2
Evaluate the sum
So, we have
xy + z = 26
Hence, the value of the expression xy + z is 26 when x = 6, y = 4, and z = 2
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You have $28, and you want to get half-dollar from the bank to give to children who come into
your store. How many half-dollar coins are in $28?
Answers
The total number of half-dollar coins are in $28 given to children who come into your store is 56.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
You have $28, and you want to get half-dollar from the bank to give to children who come into your store.
According to given question we have
Half-dollar from the bank= $28
1/2 =28
1=28*2
1=56
So, the total number of half-dollar coins given to children who come into
your store is 56.
Therefore, the total number of half-dollar coins are in $28 given to children who come into your store is 56.
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Write an absolute value equation representing all numbers x whose distance from 5 is 3 units.
Answers
The absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).
How to illustrate the information?It should be noted that from the information, we are to write an absolute value equation representing all numbers x whose distance from 5 is 3 units.
Therefore, the absolute value equation representing all numbers x will be illustrated as:
x - 3 = 5.
It should be noted that we will solve for x
Therefore, x - 3 = 5
Collect like terms
x = 5 + 3.
x = 8
Therefore, the absolute value equation representing all numbers x whose distance from 5 is 3 units.eiol be x = (-3, 8).
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Find the sum of (6-t-t²) and (10t + t²).
and write the sum from the question too
Answers
Fest expression.
(6-t-t²)
Second expression is
(10+t²)
We have to find the sure of these expressions
(6-t-t²)+10+t².
6-t-t²+10+t²
Now, we take the same to coefficient at the same side
-t²+t²-t+10+6. [ -t²+t² = 0]
-t+16
-t+16 is the sum of first and 2nd expression .
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Space Use the formula for maximum velocity v=-0.0098 t+c ln R . Find the mass ratio of a rocket with an exhaust velocity of 3.1km/s, a firing time of 50s, and a maximum shuttle velocity of 6.9km/s .
Answers
The mass ratio of the rocket is 10.8468 kg/C.
What is mass ratio of a rocket?An indicator of a rocket's effectiveness is its mass ratio. It describes the ratio of the rocket's wet mass to its dry mass, or how much more massive the vehicle is with propellant than without.Given:
v = - 0.0098(t) + c (ln (R) ), where:v = maximum shuttle velocityt = firing timec = velocity of exhaustR = mass ratioHere, c = 3.1 km/s, t = 50s, v = 6.9km/sTo find: Mass ratio (R) = ?
Finding:
On substituting the values of 'c', 't', 'v', we get:
6.9 = - 0.0098 (50) + 3.1 (ln (R) )
=> 6.9 + 0.49 = 3.1 (ln (R) )
=> 7.39 = 3.1 (ln (R) )
=> ln (R) = [tex]\frac{7.39}{3.1}[/tex]
=> R = [tex]e^{\frac{739}{310}}[/tex] ≈ 10.8468
Hence, the mass ratio of the rocket is 10.8468 kg/C.
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five balls are randomly chosen, without replacement, from an urn that contains 5 red, 6 white, and 7 blue balls. find the probability that at least one ball of each color is chosen.
Answers
The probability that at least one ball of each color is chosen is 105/8568.
Given that:-
Number of red balls in the urn = 5
Number of white balls in the urn = 6
Number of blue balls in the urn = 7
We have to find the probability that at least one ball of each color is chosen.
Let us consider the that 1 ball of each color has been chosen.
Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.
Now we have to choose 2 balls from them.
Hence,
Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = [tex]^{15}C_2=105[/tex]
Total number of ways in which we can choose 5 balls from 18 balls =
[tex]^{18}C_5=8568[/tex]
Hence,
Probability that at least one ball of each color is chosen = 105/8568
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What is the x -intercept of f(x)=x³-x²+1 ? Round the answer to the nearest hundredth.
Answers
The x -intercept of f(x)=x³-x²-1 is x=1.46557.
What are Cubic polynomials?Cubic polynomials are polynomials with the highest degree of three. A cubic polynomial can only have three roots or solutions. We must find the X intercept for the given cubic polynomial in the given example.So, to find the x-intercept of f(x)=x³-x²-1:
To find the x-intercept, substitute y = 0.
Using the long division method, we obtain:
x³-x²-1/x-1.46557 = x²+0.46557x+0.68232x = 1.46577 and x²+0.46557x+0.68232 = 0x = -0.2328 ± 0.7925i ∉ RTherefore, the x -intercept of f(x)=x³-x²-1 is x=1.46557.
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The correct question is given below:
What is the x-intercept of f(x)=x³-x²-1? Round the answer to the nearest hundredth.
solve -8n+4(1+5n)=-6n-14
Answers
Evaluate
5.7 x 0.049 / 0.681
Give your answer rounded to 2 DP.
Answers
Answer:
0.41
Step-by-step explanation:
How do we solve the formula for the indicated variable
Answers
Answer:
z = Fn +s.
Step-by-step explanation:
F = (z - s)/n
z - s = Fn
z = Fn +s.
ZA and ZB are vertical angles. If mA = (6x – 16)° and mZB = (4x + 22)°,
then find the measure of ZB.
Answers
As A and B are vertical angles, the measures of angle A and B is 98° each.
What in geometry are Vertical Angles?When two lines collide, vertical angles are created. The angles that are directly opposite one another, out of the four that are generated, are vertical angles. Additionally, they are known as "vertically opposed angles." All of these angles are equal.
Vertical angles are created when two straight lines cross. Angles vertically are consistently congruent and equal. As the two sets of non-adjacent angles created by crossing two lines superimpose on one another, vertical angles are congruent.
As A and B are vertical angles,
6x - 16 = 4x + 22
⇒ 2x = 38
⇒ x = 19
Measure of Angle A is 98°
Measure of Angle B is 98°
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Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:
Length: 13x - 9 units
Width: 4.5x + 8 units
If the length is greater than the width, which inequality represents this situation?
Answers
The inequality that represents the given situation is 13x - 9 > 4.5x + 8
Writing an InequalityFrom the question, we are to determine the inequality that represents the given situation
From the given information, we have that
The length of the laptop is given by 13x - 9 units
and
The width of the laptop is given by 4.5x + 8 units
If the length is greater than the width, then we can write that
13x -9 > 4.5x + 8
Hence, the inequality is 13x - 9 > 4.5x + 8
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