Answers
The length of the sides of ΔABC are; AB = 2√5, BC = √13, and AC = √17
The length of the sides of ΔDEF are; DE = 2√5, EF = √13, and DF = √17
By the SSS Congruence Theorem, ΔABC ≅ ΔDEF
How to prove triangle congruency postulate?We are given the coordinates of Triangles ABC and DEF as;
A(5, 3), B(7, 7), C(9, 4)
D(-8, 6), E(-12, 8), F(-9, 10)
The formula for distance between two coordinates is;
Distance = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus;
AB = √[(7 - 3)² + (7 - 5)²]
AB = √20
AB = 2√5
Similarly;
BC = √[(4 - 7)² + (9 - 7)²]
BC = √13
AC = √[(4 - 3)² + (9 - 5)²]
AC = √17
Likewise;
DE = √[(8 - 6)² + (-12 + 8)²]
DE = √20
DE = 2√5
Similarly;
EF = √[(10 - 8)² + (-9 + 12)²]
EF = √13
DF = √[(10 - 6)² + (-9 + 8)²]
DF = √17
Since the corresponding sides of the two triangles are equal and as such they can be said to congruent by SSS Congruency.
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Related Questions
HELP PLEASE PLEASE!!!!!!!!
Answers
Answer:
The measure of the third angle is equal to 34°
Step-by-step explanation:
Given that,
The measure of angle 1 is 50°.
The measure of angle 2 is 96°
We need to find the measure of the third angle. We know that the sum of angles of a triangle is equal to 180°. So,
x+50+96=180
x+146=180
x = 180-146
x = 34°
So, the measure of the third angle is equal to 34°.
Can someone please help me with math.
Answers
Answer:
5. B) 55
6. D) 15
Step-by-step explanation:
5.
One of the properties of a triangle is that the sum of angles in a triangle will always equal (180) degrees. One can apply this here, form an equation and solve for (x). Remember, a box around an angle indicates that the measure of the angle is (90) degrees.
90 + x + 35 = 180
Simplify,
125 + x = 180
Inverse operations,
x = 55
6.
This triangle is a right triangle, as mention earlier, a box around an angle indicates that the angle measure is (90) degrees. One of the criteria of a triangle to be considered a right triangle is that it must contain a (90) degree angle. One of the properties of a right triangle is that it follows the Pythagorean theorem, the Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or sides adjacent to the right triangle, and (c) is the hypotenuse or side opposite the right angle.
[tex](9)^2 +(12)^2 = (c)^2[/tex]
Simplify,
[tex]81+144=c^2\\\\225=c^2[/tex]
Inverse operations,
c = 15
Which graph best represents a function with a domain of all real numbers greater than or
equal to 1 and less than or equal to 2?
Answers
The graph best represents a function with a domain of all real numbers greater than or equal to 1 and less than or equal to 2 are area between equation x + y [tex]\geq[/tex] 1 and x + y [tex]\leq[/tex] 2 .
Which function has a domain that includes all real numbers?The collection of all potential inputs for a function is known as its domain. For instance, the domain of f(x)=x2 is all real numbers, and the domain of g(x)=1/x is all real numbers other than x=0.
How do you plot all real values on a graph?The real numbers are all the numbers that make up the real number line, per definition. Thus, all real numbers can be graphed by simply drawing a number line. The number line is a graph of all real numbers since it contains all of the rational numbers.
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Help me
With stepsss pleaseee
Answers
Answer:
Step-by-step explanation:
PLEASE ANSWER ASAP!
The question is on the screenshot
Answers
Answer:
A
Step-by-step explanation:
Cross multiply
2x8 over 3x6
Answer:
B. i beleive
Step-by-step explanation:
Helen told her mom she got 85% on a recent math test. She remembered the test was out of 60. What was her actual mark? *
Answers
Answer: 85% out of how many questions.
Step-by-step explanation:
Please help:( if anyone is good at algebra, assist me in this tragic time
Answers
Step-by-step explanation:
x -2 -1 2 7
y -6 -6 -2 3
All y are in under root
Find the sum of the first 10 terms in this geometric series.
1+3+9+27+...
Answers
Answer:
29524
Step-by-step explanation:
The sum of the first n terms is [tex]S_n=a_1\frac{1-r^n}{1-r}[/tex] where [tex]a_1[/tex] is the first term and r is the common ratio.
For the sequence in this question, [tex]a_1=1,\,r=3[/tex].
[tex]S_10=(1)\frac{1-3^10}{1-3}=\frac{-59048}{-2}=29524[/tex]
Amare is buying museum souvenirs. He buys 3 animal figures
and 6 bookmarks for $33. Later he goes back to buy 3 more
figures and return 3 of the bookmarks, spending another $6.
In the system, fis the price of a figure and b is the price
Al Pisto
of a bookmark.
3f + 6b = 33
3f-3b = 6
How much does each figure cost? How much does each bookmark cost?
Answers
Answer:
Each animal figure cost $2 dollars and each bookmark cost $4.50 dollars
Step-by-step explanation:
I got this answer is because second part of the question it says "Later he goes back to buy 3 more figures and return 3 of the bookmark spending another $6". The information this gives us is that since he bought nothing but animal figures and bought 3 animal figures and spent $6 dollars that tells us that each animal figure cost $2 dollar knowing this we can figure out the first part since in the first part he spent $33 dollars in total and bought 3 animal figures and 6 bookmarks and we know each animal figure cost $2 dollars we know in total he spent $6 dollar on animal figures and he spent $27 dollar on bookmarks doing division 27 divided by the number of bookmarks he bought we figure out the cost of one bookmark so doing this the answer is one animal figure is $2 dollars and one bookmark is $4.50.
I hope this help this is less of a math problem and more of a logic one this took me a while of rereading to figure out!
Give me a thanks.
Can someone help me?
Answers
Answer:
+6 dollars
Step-by-step explanation:
There are two numbers such that one of the numbers is 5 2/7 more than twice the other number. If you multiply the smaller number by 5, the product is twice the larger number. What are the two number? Please no links and answer fast!
Answers
Answer:
Smaller number: 10 4/7
Bigger number: 26 3/7
Step-by-step explanation:
How I did this problem was very simple, so first I made my different numbers, the smaller number being x, and the larger number being
2x+5 2/7. Then, I did the equation 5x=4x+ 74/7. How I got this equation was I multiplied 5 2/7 into 2 and got 74/7. After the equation, I got my answers, then double checked them.
You are welcome!
I need help please, question in photo
Answers
Answer:
A. and F. and B.
:)
A line is parallel to y = 4x + 11 and
intersects the point (-2, 4). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x − x1)
Then write the equation in slope-intercept form.
Enter
Answers
Answer:
y=4x+12
Step-by-step explanation:
if a line is parallel to another they have the same slope ,,
y=mx+c
where m represents the slope
and c represents the intercepted part of y axis
so the slope equals 4 from y=4x+11
to find the intercepted part c ,, substitute by the given point in the equation y=mx+c
(-2,4),, and slope is 4
4= 4×-2+c
4= -8+c
c= 12
so the equation is
y=4x+12
Answer:
y =4x-18
Step-by-step explanation:
y +2 = 4(x - 4)
y +2 =4x-16
y = 4x-18
What is the midpoint of 1 and 2 and 3 and 4?
Answers
The midpoint of 1 and 2 and 3 and 4 is (2,3).
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
Use numbers, fractions, mixed numbers, or decimals to enter two points. The midpoint calculator displays the required research:
Halfway between the two specified pointsOne endpoint and a midpoint are provided.The separation of two endpoints.Additionally, the calculator offers a link to the Slope Calculator, which will solve and display the work necessary to identify the slope, line equations, and x and y intercepts for any given pair of points.To learn more about midpoint:
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answers
Answer:
The values are 13 and 1
I hope this is correct
50 points!!! and BRAINLIEST IF CORRECT
An investment banker is responsible for investing a customer’s money into the greatest interest earning account. The banker has the following options for his customer’s investment:
Account A:
interest rate = 8%
term of investment = 8 years
interest compounded annually Account B:
interest rate = 7%
term of investment = 10 years
interest compounding continuously
Which account, A or B, will earn the customer the greatest amount of interest on his $50,000 investment? In your final answer, include all of your calculations.
Answers
Answer: account b
Step-by-step explanation:
account A will give 92 thousand dollars
account B will give 100 thousand dollars
I put it in a table
Answer:
SEE ANSWER BELOW
Step-by-step explanation:
A. (formula A=P(1+r/n)^nt
P=50,000(1+.08/1)^nt
P=50,000(1+.08)^nt
P=50,000(1.08)^nt
P=50,000 • 1.85
P=92,546.5
B. (formula A=Pe^rt
P=50,000e7 • 10
P=50,000 • 7
P=50,00 •2 .013
P=100689.64
B saves more
Please answer question plz!!!!!
Answers
Answer:
V = 214.32
Step-by-step explanation:
Remark
You have to be a little careful with this question. The temptation is just to take the difference of the heights. That is not correct. The difference has to be multiplied by the base to get the volume.
Formula
V = (h1 - h2)* Base
Givens
h1 = 32.9
h2 = 29.1
Base = 56.4
Solution
V = 56.4 ( 32.9 - 29.2)
V = 56.4 * 3.8
V = 214.32
Using the graph below with the following point find the length of the two diagonals to determine if TUVW is a rectangle or not T(-5,0) U(7,3) V(9,-6) W(-3,-9)
Answers
The lengths of each diagonal are given as follows:
[tex]TV = \sqrt{232}[/tex][tex]WU = \sqrt{244}[/tex]As the lengths are different, the polygon TUVW is not a rectangle.
How to obtain the diagonals?The diagonal length is obtained using the formula for the distance between two points, presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
The first diagonal is TV, and the length is given as follows:
[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]
The second diagonal is WU, and the distance is given as follows:
[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]
A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.
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Decrease #2000 by 20%
Answers
Answer:
400
Step-by-step explanation:
2000 divided by 20% is 400
Simplify
(12 – 3) + 15+5 (-2)
Answers
Answer:
14
Step-by-step explanation:
The multiplication must be done before the addition and subtraction.
(12 – 3) + 15+5 (-2)
becomes (9) + 15 + 5(-2), which in turn becomes
(9) + 15 - 10, or 14
Multiply: -z^3(5 + z - 4z^2)
Answers
Answer:
4z^5 - z^4 - 5z³
Step-by-step explanation:
-5z³ - z^4 + 4z^5
Janelle is on the drill team. At her last
practice, Janelle improved her best time
by 3/8 of a second. Which shows 3/8 written in
decimal form?
Answers
Answer:
3/8=0.375
Step-by-step explanation:
Mary reached chool at 7:30 AM, and left for home at 12:45 PM. How long he tayed in the chool
Anwer with explanation
Answers
Answer:
5 hours and 15 minutes.
Step-by-step explanation:
7:30 - 8:00 is 30 minutes
8:00 - 12:00 is 4 hours
12:00 - 12:45 is 45 minutes
30 minutes plus 45 minutes is 1 hours and 15 minutes
4hours + 1 hour and 15 minutes is
5 hours and 15 minutes
or
5 1/4 hours
or
315 minutes.
I am not sure what form you want.
what’s the perimeter of a rectangle that’s
6m
6m
9m
9m
Answers
Answer:
30
Step-by-step explanation:
perimeter is the outside of a shape so just add them all together honestly
whats the value of x? ill give brainliest
Answers
Answer:
150°
Step-by-step explanation:
180-30=150...............
Answer:
150º
Step-by-step explanation:
the value of q is 180º, so 180 - 30 = 150
What is one way you could use the positive feelings from a situation toward a future motivation?
Develop a positive personal process and focus
Remember the “How could I do better?” mentality
Tell the adults in your life to hold you accountable
Be content with not being successful at everything
Answers
Answer:
One way to use positive feelings from a situation towards future motivation is to focus on the positive aspects of the experience and try to replicate them in the future. For example, if you had a particularly enjoyable and successful project at work, you might try to identify the specific factors that contributed to your success and seek out similar opportunities in the future. This approach can help you to build on your strengths and experiences and maintain a positive and motivated outlook. Additionally, setting specific goals for yourself and tracking your progress can help to keep you motivated and on track towards future success.
Find the
equation of the circle with center at (3, -2) and radius of 3.
Answers
7. You have $2 worth of quarters, dimes, and nickels
and you have 12 total coins. How many of each do you
have?
Answers
Answer:
6 quarters, 4 dimes, and 2 nickels
Your college tuition is $25,000 and it increases by 6% each year.
Answers
Answer:
Your collage tuition will increase by $1,500 each year.
Step-by-step explanation:
To find the answer we will first turn 6% to a decimal by dividing 6 by 100 and we get 0.06. Now multiply $25,000 by 0.06 and we get $1,500. Therefore the answer is $1,500.
The cost to hire a tent consists of two parts. $c + $d per dayThe total cost for 4 days is $27. 10 and for 7 days is $34. 30. Write down two equations in c and d and solve them
Answers
The cost to hire a tent consists of a fixed cost of $17.50 and a variable cost of $2.40 per day.
Let's call the total cost of hiring a tent for 4 days as T4, and the total cost of hiring a tent for 7 days as T7.
The first equation is the cost for 4 days:
T4 = c + 4d
The second equation is the cost for 7 days:
T7 = c + 7d
We know the values of T4 and T7 from the problem statement:
T4 = $27.10 and T7 = $34.30
We can now use these two equations and their corresponding values to solve for c and d:
Substitute the value of T4 into the first equation:
$27.10 = c + 4d
Substitute the value of T7 into the second equation:
$34.30 = c + 7d
Now we have a system of two equations with two variables (c and d).
Subtract 4d from both sides of the first equation:
$27.10 - 4d = c
Subtract c from both sides of the second equation:
$34.30 - c = 7d
Now we can substitute the value from step 4 into step 5:
$34.30 - $27.10 + 4d = 7d
7d = $34.30 - $27.10 + 4d
3d = $7.20
d = $7.20 / 3 = $2.40
Now we have the value of d, we can substitute it back into the first equation to find the value of c:
$27.10 = c + 4d
$27.10 = c + 4($2.40)
$27.10 = c + $9.60
c = $27.10 - $9.60
c = $17.50
Therefore, c= $17.50 and d= $2.40
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