3. Consider the following diagram.
Find the values of m and n that prove the two triangles are congruent by the
HL Theorem.
Answers
Answer:
m = 3, n = 6
Step-by-step explanation:
The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.
From the diagram, comparing the hypotenuse of the triangles;
4m + 1 = 13
4m = 13 - 1
= 12
m = [tex]\frac{12}{4}[/tex]
= 3
m = 3
Also, comparing the sides;
2m + n = 8m - 2n
substitute the value of m to have,
6 + n = 24 - 2n
collect like terms,
n + 2n = 24 - 6
3n = 18
n = [tex]\frac{18}{3}[/tex]
= 6
n = 6
m = 3, n = 6
To solve the problem we must know about HL theorem.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
The value of m and n are 3 and 6, respectively.
Given to us
The hypotenuse of the first triangle = 13One leg of the first triangle = 2m+nThe hypotenuse of the second triangle = 4m+1One leg of the second triangle = 8m - 2nAccording to the HL theoremIf the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore,
the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
Hypotenuse Congruent[tex]4m + 1 =13\\\\4m=13-1\\\\m=\dfrac{12}{4}\\\\m=3[/tex]
Corresponding Congruent sides[tex]2m+n = 8m-2n\\[/tex]
Substitute the value of m,
[tex]2(3)+n = 8(3)-2n\\\\6+n = 24-2n\\\\6-24 = -2n-n\\\\-18 = -3n\\\\n=\dfrac{-18}{-3}\\\\n = 6[/tex]
Hence, the value of m and n are 3 and 6, respectively.
Learn more about HL theorem:
https://brainly.com/question/11804042
Related Questions
8
9
16
18
24
27
36
32
45
Which number completes the table of equivalent ratios?
A)
38
B)
40
o
42
D)
44
Answers
Answer:
40
Step-by-step explanation:
...... ...... ...... ..... .
NEED GENIUS HELP!!!
Select the function that's represented in the graph.
Question options:
A)
ƒ(x) = –(x + 2)² – 3
B)
ƒ(x) = (x + 2)² – 3
C)
ƒ(x) = –(x – 2)² – 3
D)
ƒ(x) = (x – 2)² – 3
Answers
Answer: A
Step-by-step explanation:
If you look at option A and ignore the -(x+2)^2, it would say f(x) = -3.
So the vertex has y-coordinate -3.
Because the coefficient of -(x+2)^2 is negative, the graph opens downward.
Because it says -(x+2)^2 instead of -(x-2)^2, it will be on the left side of the graph.
The graph meets all of these conditions.
The graph described in option B opens upwards.
The graph described in option C opens upwards and the vertex is in the fourth quadrant.
The graph described in option D opens downwards, but the vertex is in the fourth quadrant.
What is the value of x?
A right angle is shown divided into two parts. The measure of one part of the right angle is 30 degrees. The measure of the other part is 4x.
15
30
45
60
Answers
Answer:
x = 15
Step-by-step explanation:
We are told that a right angle is divided into two parts
A right angle = 90°
Part A = 30°
Part B = 4x
Hence:
30° + 4x = 90°
Collect like terms
4x = 90° - 30°
4x = 60°
4x = 60/4
x = 15
Therefore, the value of x = 15
Answer:
ITS 15!!!!!! :))))
How many minutes are there in 4 1/4
hours?
mins
Pls help
Answers
Answer:
255 minutes
Step-by-step explanation:
A right-angled triangle has sides of lengths (x+5)cm, (x-3)cm and 9cm. Calculate the value of x. Give your answer to 3 significant figures. (Quadratic Formula)
Answers
Answer:
x = (3.95 and -5.95)
Step-by-step explanation:
Given:
Hypotenuse = 9 cm
Perpendicular = (x+5) cm
Base = (x-3) cm
Find:
Value of x
Computation:
Using Pythagoras theorem
Hypotenuse² = Perpendicular² + Base²
9² = (x+5)² + (x-3)²
81 = x² + 25 + 10x + x² + 9 - 6x
2x² + 4x - 47 = 0
Quadratic Formula
x = [-b±√b²-4ac] / 2a
x = [-4±√16+376] / 2(2)
x = (3.95 and -5.95)
help please i will mark brainliest if correct
Answers
PLEASE HELP ME I’M REALLY FAR BEHIND IN MATH! I’LL MARK BRAINLIEST! (Looks at picture)
Answers
Answer:
x=1
Step-by-step explanation:
4x+5=9
-5 -5
4x=4
4/4
=1
x=1
Answer:
x=1.......
Step-by-step explanation:
Your welcome
Which values represent solutions to cos
$(# - x) =
sin x, where x € (0,21)?
(0.7)
0 (0.3
Answers
Answer:
C option
Step-by-step explanation:
C is the correct solution of to above equation
OK PLEASE HELP ME. IVE BEEN TRYING TO REMEMBER HOW TO SOLVE THIS BUT IM FIND IT IT REALLY DIFFICULT
Quadrilateral JKLM has vertices J(–7, –2), K(–2, –2), L(–3, –4), and M(–6, –4). Find the midpoints of each of the sides JM and KL.
Answers
Step-by-step explanation:
X-value of Midpoint of J(-7, -2) and M(-6, -4)
= [(-7) + (-6)] / 2 = -6.5.
Y-value of Midpoint of J(-7, -2) and M(-6, -4)
= [(-2) + (-4)] / 2 = -3.
X-value of Midpoint of K(-2, -2) and L(-3, -4)
= [(-2) + -3)] / 2 = -2.5.
Y-value of Midpoint of K(-2, -2) and L(-3, -4)
= [(-2) + (-4)] / 2 = -3.
We have (-6.5, -3) and (-2.5, 3).
The correct answer is Option D.
A town manager reports that revenue for a given year is $563,878. The budget director predicts the revenue will increase by 7% per year. How much revenue will the town have available in 6 years? (round to the nearest cent)
Answers
Answer:
below
Step-by-step explanation:
the yearly multiplier
= 1.07
After 6 years revenue wii, b 563878 * 1.07^6
= $846,228.83.
PLEASE HELP AM BEING TIMED
The value of W is:
The value of X is:
Answers
X=60
Brainliest?
Please show the work
Answers
Answer:
C
Step-by-step explanation:
Here's a trick:
Find the last number of the equation and look at your factors to see which numbers you can multiply to get that answer
in this case the last number of x^3-8x^2+17x-10 is -10
*IF IT HAS A NEGATIVE, ALWAYS REMEMBER TO INCLUDE IT*
Then look at the options and see what numbers can get you -10 but include the factor that they give you.
in this case C has the numbers as -1×-5×-2 gives you -10
now to check by using the box method, which is much easier to do, and put pick 2 of those factors and check if it's right
Solve for b. ab+c=d. 1.b=a+c/d 2.b=a/(c-d) 3.b=(d-c)/a
Answers
Answer:3
Step-by-step explanation:
OMG HELPPPPPP!!!!!!!!
Answers
PLEASE HELP ASAP!! will mark brainliest!!
What is the equation of the line shown in this graph?
Answers
This is because it’s a horizontal line at 1.
Step-by-step explanation:
The line is a horizontal line of the form y = a, where a is a real constant.
Since the line passes through the points (-4, 1) and (2, 1) with y-values of 1,
Equation of the line: y = 1.
On the second day of a hiking trip the tourist covered a 17% bigger distance than on the first day . By how many percent of their average speed change from the first to the second day if on the second day they were hiking for a 20% longer time
Answers
Answer:
2.5%
Step-by-step explanation:
x=distance y=time
x has been increased by 17%
100%+17% = 117%
y has been increased by 20%
100%+20%=120%
Now let's make the percentages into decimals. 117%=1.17 120%=1.2
To find the average speed you do the distance traveled divided by the time taken.
Average speed = 2.5%
What is the percent change from 6,000 to 9,000
Answers
Answer: 50% would be the correct answer.
-4x+50<58−8x+44≥60 AND−4x+50<58
Solve for x
Answers
Answeridek
Step-by-step explanation:
Can you help me please
Answers
Answer:
a)x=5 b)x=4
Step-by-step explanation:
a)9.5×2=19
3x+4=19
19-4=15
15÷3=5
x=5
b)5×3=15
7+2x=15
15-7=8
8÷2=4
x=4
hope this helps
Henry received $500 for his birthday which he intends to invest in an account that pays simple interest at the rate of 12% per year. How much will be in the account
Answers
Answer:
$560
Step-by-step explanation:
Given that :
Principal, P= $500
Interest rate, r = 12% per year
Amount in account after 1 year
Time = 1 year
Using the relation :
A = P(1 + rt)
A = final amount in account
A = $500(1 + 0.12(1))
A = $500(1 + 0.12)
A = $500(1.12)
A = $560
can somebody solve 2 and 3 for me?
Answers
Answer:
2. D) 275
3. C
Step-by-step explanation:
2. 20 divided by 10 = 2
550 divided by 2= 275
3. 35 times 8= 550$
1 month is 35$
2 months is 70$ (35+35)
4 months is 140$ (70+70)
6 months is 210$ (140+70)
HOPE THIS HELPS!!!
Answer:
2. D) 275
3. C
Step-by-step explanation:
2. 20 divided by 10 = 2
550 divided by 2= 275
3. 35 times 8= 550$
1 month is 35$
2 months is 70$ 35+35
4 months is 140$ 70+70
6 months is 210$ 140+70)
A paintball court charges an initial entrance fee plus a fixed price per ball. PPP represents the total price (in dollars) as a function of the number of balls used nn. P=0.80n+5.50P=0.80n+5.50P, equals, 0, point, 80, n, plus, 5, point, 50 What is the price for 101010 balls, not including the entrance fee?
Answers
Question:
A paintball court charges an initial entrance fee plus a fixed price per ball. P represents the total price (in dollars) as a function of the number of balls used n.
P=0.80n+5.50
What is the price for 10 balls, not including the entrance fee?
Answer:
$8
Step-by-step explanation:
We are given the function:
P=0.80n+5.50
Where n represents the number of balls. From this function, the entrance fee = 5.50
We are asked to calculate the price for 10 balls without the entrance fee. This is given as:
0.80n = 0.80 × 10 balls
= $8
The price for 10 balls, not including the entrance fee is $8
Answer:
The answer is 8
Step-by-step explanation:
In an experiment , the temperature of a solution is -5/8 degrees. The temperature drops 1 1/2 degrees. What is the temperature after the drop?
Answers
Answer:
- 2 1/8 degrees
Step-by-step explanation:
Given
Initial temperature of a solution = -5/8 degrees
Amount drop = 1 1/2 degrees
Temperature after the drop = -5/8 - 1 1/2
Temperature after the drop = -5/8 - 3/2
Temperature after the drop = -5-12/8
Temperature after the drop = -17/8
Hence the temperature after the drop is - 2 1/8 degrees
simplify the expression
Answers
Answer:
24/64..........................
Step-by-step explanation:
hope this helped
College essay for UC Santa Barbara has to be 500 words long but the actual essay can vary by as much as 20 words. Write an absolute value inequality that could find the range of possible number of words for the essay.
|x - 20| ≤ 500
|x + 20| ≥ 500
|x + 500| ≥ 20
|x - 500| ≤ 20
Answers
Answer:
|x - 500| ≤ 20
Step-by-step explanation:
R1 - Writing and using formulae
Miss Joplin is planning the resources for a maths lesson.
She needs...
1 ruler per pupil plus 4 spare
5 pieces of dondy paper per pupil
. 5 pieces of card per pupil plus 7 spare.
V=
Write down formulae for the number of rulers (r)
and the amount of dotty paper (d) and card (c).
Jse p for the number of pupils.
d =
c =
[6]
Answers
Answer:
im trying to do a challenge because this kid deleted all my answers
Step-by-step explanation:
[tex]y = |x + 2| [/tex]
What is thw Domain and the Range
Answers
The domain is the x value and the range is the y value.
Because x is a variable it can be any real number so the domain would be negative infinity to infinity.
Because the domain is negative infinity to infinity, then the range is also negative infinity to infinity.
In Hawaii a volcano is about to explodel At 6:00 am a device placed inside the volcano
measures the temperature at 69.5 degrees Celsius. Every 3 minutes the temperature
rises 1/5 a degree. If the Volcano explodes at 1455 degrees Celsius how many hours do
they have to evacuate a nearby city?
Will Mark BRAINLIEST to the correct answer
Answers
Complete question :
In Hawaii a volcano is about to explodel At 6:00 am a device placed inside the volcano
measures the temperature at 69.5 degrees Celsius. Every 3 minutes the temperature
rises 1/5 a degree. If the Volcano explodes at 145.5 degrees Celsius how many hours do
they have to evacuate a nearby city?
Will Mark BRAINLIEST to the correct answer
Answer:
19 hours
Step-by-step explanation:
Given that:
Temperature of volcano at 6:00 am = 69.5°C
Average rise in temperature per 3 minute = 1/5
Hence, rise in temperature per minute = 0.0666666°C
Temperature at which volcano will explode = 145.5°C
Hence, change in temperature :
(145.5°C - 69.5°C) = 76°C
Hence, temperature will have to rise by 76°C
Rise in temperature / rate of temperature increase
= 76°C / 0.0666666°C
= 1140.0011 minutes
= 1140.0011 / 60
= 19.0000019 hours
= 19 hours
Of the students at Milton middle school 171 are girls if 45% of the students are girls how many total students are there at milton middle school
Answers
Answer:
380
Step-by-step explanation:
171:45=3,8
3,8*100=380
I need an answer really quick.
Answers
Answer:
Switch to the other streaming service
Step-by-step explanation:
So, 96$ with a 12% increase is $107.52.
But if you do 8.75×12 you get $105.
So Clare should switch to the other music stream.