In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm
Answers
Answer:
The length of the legs is 8.64cm and 14.64cm respectively
Step-by-step explanation:
I've added an attachment to aid my explanation.
At different intervals, I'll be making reference to it.
Given
[tex]AB = 17[/tex]
[tex]PAMC = 32[/tex]
[tex]PBMC = 25[/tex]
From the attachment, we have:
[tex]y + z = AB[/tex]
Since, M is the Midpoint
[tex]y = z = \½AB[/tex]
Substitute 17 for AB
[tex]y = z = \½ * 17[/tex]
[tex]y = z = 8.5[/tex]
Also, from the attachment
[tex]v + x + z = PAMC[/tex]
[tex]v + x + y = 32[/tex]
Substitute 8.5 for y
[tex]v + x + 8.5 = 32[/tex]
[tex]v + x = 32 - 8.5[/tex]
[tex]v + x = 23.5[/tex] --------- (1)
Also, from the attachment
[tex]v + w + z = 25[/tex]
Substitute 8.5 for z
[tex]v + w + 8.5 = 25[/tex]
[tex]v + w = 25 - 8.5[/tex]
[tex]v + w = 17.5[/tex] ----------- (2)
Subtract (2) from (1)
[tex]v - v + x - w = 23.5 - 17.5[/tex]
[tex]x - w = 6[/tex]
Make x the subject
[tex]x = 6 + w[/tex]
Apply Pythagoras Theorem:
We have that:
[tex]AB^2 = AC^2 + BC^2[/tex]
The above can be replaced with
[tex]17^2 = x^2 + w^2[/tex] (see attachment)
[tex]289 = x^2 + w^2[/tex]
Substitute 6 + w for x
[tex]289 = (6 + w)^2 + w^2[/tex]
[tex]289 = 36 + 12w + w^2 + w^2[/tex]
[tex]289 - 36 = 12w + 2w^2[/tex]
[tex]253 = 12w + 2w^2[/tex]
Reorder
[tex]2w^2 + 12w - 253 = 0[/tex]
Solve using quadratic equation:
[tex]w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 2[/tex]
[tex]b = 12[/tex]
[tex]c = -253[/tex]
[tex]w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}[/tex]
[tex]w = \frac{-12 \± \sqrt{144 + 2024}}{4}[/tex]
[tex]w = \frac{-12 \± \sqrt{2168}}{4}[/tex]
[tex]w = \frac{-12 \± 46.56}{4}[/tex]
Split:
[tex]w = \frac{-12 + 46.56}{4}[/tex] or [tex]w = \frac{-12 - 46.56}{4}[/tex]
[tex]w = \frac{34.56}{4}[/tex] or [tex]w = \frac{-58.56}{4}[/tex]
[tex]w = 8.64[/tex] or [tex]w = -14.64[/tex]
But length can't be negative
So:
[tex]w = 8.64[/tex]
Recall that: [tex]x = 6 + w[/tex]
[tex]x = 6 + 8.64[/tex]
[tex]x = 14.64[/tex]
Hence, the length of the legs is 8.64cm and 14.64cm respectively
Related Questions
.........................................................
Answers
Answer:
The volume of the figure is 126 cubic cm
Step-by-step explanation:
The figure consists of two rectangular prisms of dimensions 6 x 7 x 1 and 3 x7 x 4 respectively.
Calculate the first volume:
[tex]V_1=6~cm\cdot 7~cm\cdot 1~cm= 42~cm^3[/tex]
[tex]V_1= 42~cm^3[/tex]
Calculate the second volume:
[tex]V_2=3~cm\cdot 7~cm\cdot 4~cm= 84~cm^3[/tex]
[tex]V_2= 84~cm^3[/tex]
The total volume of the figure is the sum of both volumes:
[tex]V_t=V_1+V_2=42~cm^3+84~cm^3=126~cm^3[/tex]
The volume of the figure is 126 cubic cm
Which expression is equivalent to (5^(3))^(2)
Answers
Answer:
Step-by-step explanation:
[tex](a^{m} )^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](5^{3} )^{2}[/tex] = [tex]5^{3*2}[/tex] = [tex]5^{6}[/tex] = 15,625
Shoes: $59.97, Shirt: $10.99, Pants: $19.99
Calculate the subtotal.
Answers
Answer:
90.95
Step-by-step explanation:
Answer:
If you add it all up, your answer is $90.95
I need help pronto please it’s due in 15 minutes
Answers
Answer:
yes
Step-by-step explanation:
Answer:
Yes, she is rightYes, she will have $1.65 leftStep-by-step explanation:
2)
"4 friends had a lunch together [...] $33.40"
"They share the bill equality" = 33.40 ÷ 4
Everyone must pay = $8.35
Money left = $10 - $8.35
Money left = $1.65
please help. it would be appreciated.
Answers
Answer:
a
Step-by-step explanation:
What is the domain of the function shown in the graph?
Answers
Answer:
Step-by-step explanation:
domain holds all the x values and for this graph it looks like
0< x < -∞ or just x >0
yet I do not see this answer as an option
if it was range will be the y-values and the answer will be
A. x≥ -1
Mia and Merle together have $285. Mia wins $25 from Merle and then finds she has 4 times as much as Merle. How much did Mia have at first?
Answers
explained: i used the desmos calculator lol
f(x) = 2x4 – 14x3 + 33x2 – 26x
Given that x = 3 + i is a solution of the equatio
f(x) = 0, solve f(x) = 0 completely.
Answers
Answer:
x = 0, 2, 5/2 ± 1/2i
Step-by-step explanation:
I'm not really sure what the question is asking but I'm going to assume you want to find the zeroes of the function.
0 = 2x^4 - 14x^3 + 33x^2 - 26x
~Factor
0 = x(x - 2)(2x² - 10x + 13)
~Set factors to equal 0 and solve
x - 2 = 0
x = 2
2x² - 10x + 13 = 0
~Use quadratic formula
x = 0, 5/2 ± 1/2i
Best of Luck!
Please help! I don’t get this :(
Answers
Answer:
A
Step-by-step explanation:
if $3.50 per bag of five apple how much is one apple
Answers
Answer:
70¢ per apple
Step-by-step explanation:
Because it's $3.50 per bag of 5 apples, you can divide $3.50 and 5 by 5 to get 70¢ per apple.
Answer:
70⊄
Step-by-step explanation:
$3.5 ÷ 5 = 70⊄
Does the equation y+3=2(x+9) include the point (-6,3)?
Please explain how you got the answer! :3
Answers
Answer:
Step-by-step explanation:
if it includes the point should verify the equation
substitute x= -6 and y=3 in the equation
3+3 = 2 ( -6+9) calculate
6 = 6 is true! so YES the equation includes the point
y = x - 2
-2x + 3y = -1
What is x and y?
Answers
Answer:
(5, 3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
y = x - 2
-2x + 3y = -1
Step 2: Solve for x
Substitute in y: -2x + 3(x - 2) = -1Distribute 3: -2x + 3x - 6 = -1Combine like terms: x - 6 = -1Isolate x: x = 5Step 3: Solve for y
Define equation: y = x - 2Substitute in x: y = 5 - 2Subtract: y = 37. The graph of the linear function is shown on the coordinate grid below.
Answers
Answer: C . The slope is -4/3 and the y-intercept is 4.
Step-by-step explanation:
Using the two given points, we will use them to evaluate the slope and the y intercept.
(-1.5,6)
( 4.5,-2)
To find the slope we will find the difference in the y coordinates of the points and divide it by the difference in the x coordinates of the point.
6-(-2) = 8
-1.5 - 4.5 = -6
Slope : 8/-6= -4/3.
Since the slope is -4/3, we will use the formula y= mx + b to find the y intercept. In the formula y= mx + b, the slope is m and b is the y intercept.
Use one of the given points, and input its x and y values into the formula including the slope to solve for b(the y-intercept).
We will use the point, ( -1.5,6)
6 = -4/3(-1.5) + b
6 = 2 + b
-2 -2
b = 4.
b is indeed equal to 4 because it even indicates on the graph that the y intercept is 4 which is where x is equal to 0.
15 POINT QUESTION; I REALLY NEED HELP
A dietician gathered data about the amounts of flour, baking powder, and butter used for several different muffin recipes. She used a graphing tool to organize the data in different scatter plots and found the following lines of best fit:
The relationship between the baking powder used, x, and the flour used, y, is modeled by the equation y = 0.13x + 0.92, and the correlation coefficient for the data is 0.953.
The relationship between the baking powder used, x, and the butter used, y, is modeled by the equation y = 0.24x + 0.76, and the correlation coefficient for the data is 0.802.
The relationship between the flour used, x, and the butter used, y, is modeled by the equation y = 0.86x + 0.52, and the correlation coefficient for the data is 0.693. Which line of best fit can the dietician expect to produce the most reliable predictions?
A. the line modeling the baking powder and the butter used
B. the line modeling the baking powder and the flour used
C. the line modeling the flour and the butter used
D. All three lines will give equally reliable predictions.
Answers
Answer:
the line modeling the baking powder and the flour used
Step-by-step explanation:
plato master test
On comparing the pairwise R - squared value between the three variables, we find that the line modeling the baking powder and the flour used can be expected to produce the most reliable predictions.
What is R - squared value ?R-Squared value is a quantifiable analysis of how well the line of best fit (linear regression model) fits your data. A value closer to 1 (100%) is usually good.
The coefficient of determination - R - squared value is square of the correlation coefficient.
R - squared value of the relationship between baking powder and flour used = 0.953² = 0.908
R - squared value of the relationship between baking powder and butter used = 0.802² = 0.643
R - squared value of the relationship between flour and butter used = 0.693² = 0.48
Since, on comparing the R - squared values of the three relationships, we find that the R - squared value of the relationship between baking powder and flour used is largest. Thus, line of best fit between baking powder and flour is expected to produce the most reliable predictions.
Learn more about R - squared value here
https://brainly.com/question/813508
#SPJ2
Three more than a number times six is fifteen
Answers
Answer:
3 + 2=5
5 x 6 = 15?
Step-by-step explanation:
2.4 x 102 and 2.4 x 103 expressed in scientific notation?
Answers
Hope this helped!
Also can I please have Brainliest?
a necklace contains 36 gram of gold 72% of the mass of necklace is gold what is the mass of the necklace
Answers
Answer:
50 grams
Step-by-step explanation:
36 grams = 72%
→ Find 1% by dividing both sides by 72
0.5 grams = 1%
→ Times both sides by 100 to find 100%
50 grams = 100%
Step-by-step explanation:
Multiply 32 by 72 to get thw mass.
Find the estimated monthly payment for the following simple interest loan. Round your answer to the nearest dollar.
Answers
Answer:
$184
Step-by-step explanation:
I looked at an APR calculator
What is the constant of proportionality?
Answers
Answer:
B or 5
Step-by-step explanation:
25/5 =5
100/20 = 5
Please help
Thank you
Answers
Answer:
[tex]C)2\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{24}\\=\sqrt{2*2*2*3} \\=\sqrt{4*6}\\=2\sqrt{6}[/tex]
Dan mixed 2 parts of milk and 3 parts of syrup to make a drink. How many parts of milk did Dan mix with each part of syrup? (1 point) Group of answer choices A two over five B two over three C three over five D three over two
Answers
Answer:
B
Step-by-step explanation:
2 parts of milk is mixed with 3 parts of syrup
This implies 2/3 parts of milk is mixed with 1 part of syrup.
its pppppppp pls answer me
both of the questions
BRAINLYEST
Answers
1: D.
2: A.
Random text (I had to make the answer 20 characters or more.
Part 1:
D) 2 2/4
point B is in between the 3 and the half-point of 2. Which is 3/4 of 2.
3/4 + 2 = 2 3/4
Part 2:
C) the 12th day
It will be when Matt has his 2nd quiz and Meg will have her 4th quiz.
6 x 2 = 12
3 x 4 = 12
(it could also be the 6th day [A)] when Matt has his first quiz and Meg has her second quiz)
(its part b to question 9 ) If there are 15 students who don't wear glasses how many students are there in class? PLZ HELP WILL GIVE BRANLIST
Answers
Answer:
there are 25 students in the class and 15 who wear glasses.
Answer:
spaciously 09773616266
Please solve this 8-5x=4x-1
Answers
Answer:
x = 1
Step-by-step explanation:
Answer: x=1
Step-by-step explanation:
8-5x=4x-1--> since there are no like terms, we isolate the x8=9x-1 --> add 5x on both sides9=9x --> add 1 on both sidesx=1 --> divide by 9 on both sidesPLZZz HELP I WILL GIVE BRAINIEST
Answers
Answer:
Step-by-step explanation:
b = bouquet c = centerpieces
13b + 4c = 487
6b + 2c = 232
If u answer all the questions i will give u ez questions with a lot of points
Answers
Answer:
honestly I can not see it
Step-by-step explanation:
Hideki found the solution for the equation below to be r = 66.6(5 + r) = 96 What mistake did Hideki make in solving the equation? What is the correct solution?
A.He did not distribute 6 to r; r = 11.
B.He did not divide both sides by 6; r = 16.
C.He did not multiply both sides by 6; r = 571.
D.He did not subtract 5 from both sides; r = 15.
Answers
Answer:
A
Step-by-step explanation:
Answer:
See for the answer below:
Step-by-step explanation:
The answer is A.
slope is 2 and (−1, 6) is on the line; point-slope form
Answers
Answer:
y-6=2(x-(-1))
Or simplified:
y-6=2(x+1)
Step-by-step explanation:
use the formula: y-y1=m(x-x1)
Which subsets does 65/13 belong? Move the appropriate subsets into this box.
Answers
65/13 could also be an integer.
65/13 = 5, 5 could be everything besides irrational number
So what do you think?
Julie is about to ride a straight water slide. The length of the water slide itself is 20 meters. The splash pool at the end of the slide is 16 meters away from the base of the tower that leads up to the launching platform. How high is the launching platform?
Answers
Answer:
The launching platform height is 12 meters.
Step-by-step explanation: