Final answer:
If two angles of one triangle are congruent to two angles in another triangle, the third angles must also be congruent since the sum of angles in any triangle must equal 180 degrees. This principle is supported by geometric theorems about the properties of triangles and the requirements for their congruence and similarity.
Explanation:
If two angles of one triangle are congruent to two angles in another triangle, then the third angles in both triangles must also be congruent. This is because the sum of the angles in any triangle must equal 180 degrees or two right angles. Since two angles are congruent in both triangles, whatever is left from the 180 degrees after subtracting these two angles must be what is left for the third angle, making them congruent by necessity.
There are several related theorems in geometry that confirm this. Theorem 11, also known as the Side-Angle-Side (SAS) Postulate, states that if one side and the two adjacent angles of two triangles are congruent, then the triangles are congruent. While this theorem refers mainly to the congruency of triangles, it supports our understanding that if two angles are congruent, the third must be as well to satisfy the congruence of all three angles.
Furthermore, in the context of similar triangles, when two triangles have congruent angles, they are similar, meaning all their angles are congruent, and their sides are in proportion. However, if we only consider the angles, as in the original question, knowing that two angles are congruent across two triangles is enough to deduct that the third angles will be congruent, regardless of side lengths or overall similarity.
Jovan bought a bond with a face value of 15,000 and a coupon rate of 8.5%. The bond will mature in 15 years. How much interest will he receive semiannually
Sophie did an anyonymous survey and collected her friends' credit scores. the scores she found are listed in the table below. what is the mean credit score in this group? (round to the nearest whole point, if applicable.) 682 601 744 674 701 790 676 638 773
a. 698
b. 695
c. 676
d. 701
To find the mean of the data, you will combine all values together and then spread them all out evenly to create one value that represents the data.
In math this involves adding the data together and then dividing the sum by how many pieces of data there are.
682 + 601 + 744 + 674 + 701 + 790 + 676 + 638 + 773 = 6279
6279/9 = 697.66...
The rounded credit score is 698 (Choice A).
Using the mean concept, it is found that the mean credit score in this group is given by:
a. 698
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, there are 9 observations, which are:
682 601 744 674 701 790 676 638 773
Hence, the mean is given by:
[tex]M = \frac{682 + 601 + 744 + 674 + 701 + 790 + 676 + 638 + 773}{9} = 698[/tex]
Hence option a is correct.
More can be learned about the mean concept at https://brainly.com/question/25639778
someone help a sister out
Six times a number decreased by 10 is eight
if point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1 then p must have coordinates of?
If the ratio is 1:1 then the point must be a mid-point. Then the coordinate of the mid-point P is (–2, 8).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
If point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1.
We know that if the ratio is 1:1 then the point must be a mid-point.
Let the coordinate of point P be (x, y)
Then we have
[tex]\rm (x,y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})\\\\(x,y) = (\dfrac{-5+1}{2}, \dfrac{11+5}{2})\\\\(x,y) = (\dfrac{-4}{2} , \dfrac{16}{2})\\\\(x,y) =(-2, 8)[/tex]
The coordinate of the mid-point P is (–2, 8).
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
What’s is the value of the digit 5 in the number 57,634?
5,000
1,000
50,000
10,000
The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0
4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
Explanation:To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.Therefore, f(-3) = -8 and f(2) = 4.
Learn more about Determining values of a function here:https://brainly.com/question/32738253
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Alisha has a $15,000 car loan with a 6 percent interest rate that is compounded annually. How much will she have paid at the end of the five-year loan term?
total amount = P (1 + i)t
$19,500.25
$15,900.50
$20,073.50
Answer:
20,073.50
Step-by-step explanation:
i used the formula
The highest point in Africa is Mount Kilimanjaro in Tanzania, with an altitude of 5895 meters above sea level. The lowest point on the continent is Lake Assal in Djibouti. It is 155 meters below sea level. FInd the difference between the altitudes.
Answer:
6050 meters
Step-by-step explanation:
The difference between the altitudes will be the distance from the highest point of kilimanjaroto the lowest point on lake assai.
This distance will be the distance from the highest point of kilimanjaro to the sea level (5895m) plus the distance from the sea level to the lowest point on lake assai (155m, this distances wont be negative because it is taken as a distance from a point of reference not as a value below 0). Like this:
[tex]5895m+155m=6050m[/tex]
PLEASE HELP!!!!!! MEDAL TO RIGHT ANSWER! Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.
A.) Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0
B.) Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
1.)0= -16t^2 + 135t + 76; 0.5 s
2.)0= -16t^2 + 135t + 76; 9 s,
Determine whether the statement is always, sometimes, or never true. Complete the explanation. In parallelogram MNPQ, the diagonals MP and NQ meet at R with MR = 7 cm and RP = 5 cm. ; diagonals of a parallelogram each other.
In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, the statement is always true.
Explanation:The statement is always true. In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, if MR = 7 cm and RP = 5 cm, then NR = 7 cm and RQ = 5 cm. The diagonals MP and NQ meet at point R, so we have MR = NR and RP = RQ, confirming that the statement is always true.
Learn more about Parallelogram diagonals here:https://brainly.com/question/23888635
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the equation Y= -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, in seconds, after she threw the apple. How long did it take the apple to hit the ground? Round your answer to the neares hundreth.
Is (a-3) a factor of (a^3-6a^2+29)?
At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Out of all those people, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on on Saturday?
Elliot got some new trading cards.He has 4 packs with 20 cards each. Another pack has only 8 cards which equation show a way to find how much cards Elliot has in all?
A.c=(4×8)+20
B.c=4+20+8
C.c=(4×20)+8
2.
How can you tell when a quadratic equation has two identical, rational solutions? (1 point)
when the radicand is negative
when b in the quadratic formula is greater than the radicand
when the radicand equals zero
when the radicand is not a perfect square,
A segment can have more than one bisector.
True
False
Which of the following sets of whole numbers represents all the even three-digit numbers with a 6 in the hundreds place and 3 in the tens place? 361; 363; 365; 367; 369 630; 632; 634; 636; 638 360; 633; 635; 637; 639
You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research on the model you are looking at and obtain the following information:
Suggested retail price - $18,790
Depreciation per year - $1385 (It is assumed that this value is constant.)
The following table represents the value of the car after n years of ownership.
Answer: D on edge
Step-by-step explanation:
Can someone please explain how to find this answer? thanks
∠ RQS and ∠ TQS are a linear pair where m∠ RQS = 2x + 4 and m∠ TQS = 6x + 20
1. Solve for x.
2. Find m∠ RQS and m∠ TQS
3. Show how you can check your answer
I want help to understand how to solve the problem because I have others to solve also.,
Answer:
∠RQSangle r q s and ∠TQSangle t q s are supplementary angles, so the sum of the angles should equal 180.
Step-by-step explanation:
Find the GCF of the monomials 118a^2 and 121b^2.
f(5)= 3.14r^{2}
pls help
Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month? A) 3 B) 4 C) 5
Answer:
the answer is actually 4
Step-by-step explanation:
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@ganeshie8
Which of the following would appear in the Credits column of a bank statement for a checking account?
A. An online bill payment
B. Interest earned
C. Bank fees
D. An ATM withdrawal
Answer:
Interest earned
Step-by-step explanation:
(APEX)
Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
I believe i understand it but have to ask it would be the common difference is -10 bevause you would take -1-9 and get -10?,
Which of the following polynomials corresponds to the product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3?
The product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3 is 4x^2 + 5x + 5xy - 16y^2 + 19y - 27.
Explanation:The product of two multivariate polynomials can be found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. In this case, we have:
(4x - 3y + 5)(x + 2y - -3) = 4x(x + 2y - -3) - 3y(x + 2y - -3) + 5(x + 2y - -3)
Using the distributive property, we can simplify this to:
4x^2 + 8xy - 12x - 3xy - 6y^2 + 9y + 5x + 10y - -15
Combining like terms:
4x^2 + 5x + 5xy - 16y^2 + 19y - 27
Patrick compared the slope of the function g(x) = -2x - 8 to the slope of the linear function shown in the table below. Let m = the slope of g(x) and n = the slope of h(x).
Which statement is true? Choose all that apply.
A. m < n
B. m > n
C. m = n
D. both slopes have the same sign.
E. both slopes have different signs.
Estimate 92.49 - 63.854 by first rounding each number to the nearest whole number.