The side lengths of the triangle are 12 cm, 64 cm, and 65 cm.
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let's denote the length of the shorter leg as "x". Then, according to the problem statement, the length of the longer leg is "16 cm more than four times the length of the shorter leg", which can be expressed as 4x + 16.
Also, the length of the hypotenuse is "17 cm more than four times the length of the shorter leg", which can be expressed as 4x + 17.
Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse.
So, we can write an equation as follows:
x² + (4x + 16)² = (4x + 17)²
Simplifying this equation, we get:
x² + 16x² + 128x + 256 = 16x² + 136x + 289
Bringing all the terms to one side, we get:
x² - 8x - 33 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = -8, and c = -33.
Plugging in these values, we get:
x = (8 ± √(8^2 - 4(1)(-33))) / 2(1)
x = (8 ± √(256)) / 2
x = 4 ± 8
Therefore, we have two possible values for x: x = -4 or x = 12. Since the length of a side of a triangle cannot be negative, we reject x = -4 and conclude that x = 12.
Substituting this value of x into the expressions we derived earlier, we get:
Length of shorter leg: x = 12 cm
Length of longer leg: 4x + 16 = 4(12) + 16 = 64 cm
Length of hypotenuse: 4x + 17 = 4(12) + 17 = 65 cm
Hence , the triangle is solved
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What is the greatest common factor of 18 and 12?
Answer:
6
Step-by-step explanation:
y=.2x proportional or non-propertional
Answer:
If the ratios are equivalent then the relationship is proportional. With the graph, the origin is 0,0 (the starting point). A straight line through the origin = proportional. equation is of the form y=kx (y=2x).
]
2 What is measurement between two points called? Distance, Time, Velocity or Speed
Answer:
Distance is the measurement between two points
how do you find the distance between two negative fractions
Answer:
Use the number line and split the whole numbers into fractions
Step-by-step explanation:
Example: If a number line goes from -10 all the way to +10, and you are trying to find the distance between -2 1/4 and -7 3/4. You would split the number line into fourths and then locate -7 3/4. You would then count up to -2 1/4 to get 4 3/4.
Hopefully this makes sense!
W-4y+z=0 for z (please show work)
Answer: z=-w+4y
Step-by-step explanation:
W-4y+z=0
Calculate product
w-4y+z+0
Move variables to the right
Write in normal form 2.8 x 10⁶ ?
Answer
The answer is2600000
A number decreased by 22 is 44. Which equation can be used to solve this problem
Answer:
44+22=x or x-22=44
Step-by-step explanation:
X is the unknown, and so x decreased (minus) 22 is(equals) 44, so x-22=44.
Hope this helps please mark brainliest :D
A cube has a volume of 125 square inches. What is the length of each edge?
Answer:
5 inches
Step-by-step explanation:
formula for cube volume is l^3
so 5^3 is equal to
5 x 5 x 5
which is
25 x 5
equals
125
Hope this helps!
Answer:
5 inches
Step-by-step explanation:
V=a^3
5^3 is 125 so the answer is 5
can you please help me with this question
bbbbbbbbbbb
bbbbbbbbbbbbb
bbbbbbbbbbb
ohh yea did i mention the answer is b?
Answer:
the answer would be b
good luck!
Kayla hikes 25 meters in 13.7 seconds. Which of the following closest to how far she will hike in 6 minutes, if she maintains the same pace
Answer:
197.28 meters in 6 minutes
Step-by-step explanation:
13.7 seconds ÷ 25 meters = 0.548 meters in 1 second
6 minutes = 360 seconds (6 minutes x 60 seconds in every minute = 360 seconds)
0.548 meters in 1 second x 360 seconds = 197.28 meters in 6 minutes
Hopefully this helped! Sorry if wrong. You are loved and you are beautiful/handsome!
-Bee
In ΔXYZ, the measure of ∠Z=90°, ZY = 4, XZ = 3, and YX = 5. What ratio represents the tangent of ∠X?
Answer:
[tex]tan\ X= \frac{4}{3}[/tex]
Step-by-step explanation:
Given
[tex]Z=90\°[/tex]
[tex]ZY = 4[/tex]
[tex]XZ = 3[/tex]
[tex]YX = 5[/tex]
Required
Determine tan x
This question can be illustrated using the attached image
Tan of an angle is calculated as:
[tex]tan \theta = \frac{Opposite}{Adjacent}[/tex]
In this case, it is:
[tex]tan\ X= \frac{ZY}{XZ}[/tex]
Substitute values for ZY and XZ
[tex]tan\ X= \frac{4}{3}[/tex]
Hence, the required ratio is 4/3
Answer:
4/3
Step-by-step explanation:
Using one of the two interest formulas previously discussed, how long will it take $50,000 to
grow to $900,000 at 20% annual interest compounded quarterly? Round to the nearest
tenth.
Answer:
It will take 10 weeks
Step-by-step explanation:
im biggest brain
A camera is capable of snapping (3/4) of a picture per. how long will take the camera to snap 6 picture
Please help....... thanks
Answer:
7 weeks
Step-by-step explanation:
49 divided by 7 is 7
In an equation, y varies directly as x
varies. If y = 42 when x = 56, what is
the value of x when y = 18?
A )24
B )28
C )32
D )36
Answer:
It's going to be B.
Step-by-step explanation:
Select the correct answer. Kylie has finished creating her résumé. What should be her final step to complete the résumé? A. include a photograph B. include her contact details C. proofread the document D. mention her age
Answer:
C. Proofread the document
Step-by-step explanation:
All of the other steps should have already been done when she was creating her résumé. Hope this helps!
how many sides does this polygon have?
Answer:
[tex]it \: has \: \boxed{ nine} \: sides[/tex]
Answer: it acctually has 10 sides
Step-by-step explanation:
How do you write 1 2/3 as a decimal.
Answer:
1.7
Step-by-step explanation:
Guys Whats 20 ÷ 6 Bc idk
Answer:
3.3333333333reapeating decimal i already told you that
Step-by-step explanation:
Answer:
10/3
Step-by-step explanation:
Your dog eats 7/8Ib of food in 4 meals . How much food does your dog eat per meal?
Answer:
0.21875
Step-by-step explanation:
7/8 divided by 4 = 0.21875lb
A track team contains sprinters numbered 1,2,3,4,5 and distance runners numbered 1,2. Let S be the event of selecting a sprinter, D the event of selecting a distance runner, E the event of selecting an even numbered runner, and the event of selecting an odd runner. Selecting the sprinter numbered 1 is one outcome of which of the following events? Select all correct answers. Select all that apply: O DANDO ODORE DORO 00 OE' OS AND E
Answer:
D or O
E'
Step-by-step explanation:
Because the runner is a sprinter and the number is odd, the runner is an example of S and O. Therefore, it is also an example of E′ (not even) and D OR O.
For sprinter numbered 1 is outcome of S, D and O events.
Events to be determine that contain sprinter number 1. We have number of events that is for sprinter, distance runner, odd numbered, even numbered as S,D,O and E respectively.
Sample space = (1, 2, 3, 4, 5).
Probability can be defined as the possibility of the desired event to be happened.
Here, Numbered 1 is odd number, a sprinter and also a distance runner.
So, Numbered 1 is contain in S, D and O.
Thus, for sprinter numbered 1 is outcome of S, D and O events.
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Write the equation for a line with a slope of 2 that passes through the point (1,4)
Answer:
y=2x+2 in slope-intercept form
y-4=2(x-1) in point-slope form
Step-by-step explanation:
I used the slope to find other points and the the y-intercept to put it into slope-intercept form.
I plugged the numbers into the formula and got the point-slope equation.
HELP ME FIND SLOPE RATE CHANGE WILL GIVE BRAINLIEST
Answer:
1. RS= slope of 5/2
2. Pt= slope of -6/1 or -6
3.PQ= slope of 1/5
4. TS=slope of 0
5. QR= slope of -1/2
Step-by-step explanation:
Rise / run then simplify
Adam is climbing up the stairs in a building. At a certain point, Adam starts counting the steps and when he reaches the last step, he has counted 56 steps. If he knows that there are a total of 100 steps in the building, how many steps did he climb before he started counting the steps?
Answer:
He climed 3 steps before he started counting the steps.
Step-by-step explanation:
pls mark me as a branliest
Answer:
The answer is he climbed 44 steps. Hope this helped :D
Step-by-step explanation:
This exercise uses the radioactive decay model The burial cloth of an Egyptian mummy is estimated to contain 60% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon- 14 is 5730 years. Round your answer to the nearest ten years.)
Answer:
4257 years
Step-by-step explanation:
Given that:
Half-life of carbon 14 (t1/2) = 5730
Estimated carbon 14 content = 60% of amount of carbon 14 = 0.6
Using the model :
m(t) = mo*e^-rt
Decay rate (r) = In2/t1/2 = 0.00012
mo = initial mass
Hence,
Mass of carbon 14 in mummy m(t) = 0.6mo
0.6mo = mo*e^-(0.00012 * t)
0.6 = e^-(0.00012 * t)
Take the ln of both sides
In(0.6) = - 0.00012t
−0.510825 = - 0.00012t
t = 0.510825 / 0.00012
t = 4256.875
t = 4257 (nearest whole number)
Graph this line using the slope and y-intercept:
Y= 1/8X + 4
Click to select points on the graph.
10
9
8
o
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Submit
Answer:
98765432123459 that is te answer
Step-by-step explanation:
Karen spent 39 minutes knitting 3 hats. In all, how many hats could Karen knit in 117 minutes
What is the slope and y-intercept of the equation 3(y-2) + 6(x+1)-2 = 02
Answer:
i think its b
Step-by-step explanation:
just quessing though
Let x = 2 + 8i and xy = –2 + 26i. What is y?
Answer: 3+i
Answer:
3 + i
Step-by-step explanation:
The solution for the complex function is equal to y = 3 + i.
What is a complex function?The function which is made up of the real numbers, as well as imaginary numbers, are called complex numbers these numbers are represented by a +ib form where the first part is the real part and the second part is the imaginary form.
The given complex functions are x = 2 + 8i and xy is -2+ 26i. The value of y will be calculated as below:-
xy = -2+ 26i.
y = ( -2+ 26i ) / x
y = ( -2+ 26i ) / ( 2 + 8i )
The value of the function will be calculated by rationalizing the function. When p and q are integers and q is not equal to zero, a result is a rational number, which has the form p/q. This ratio is between two integers.
The fundamental distinction between a fraction and a rational number is that fractions are always positive while rational numbers can be either positive or negative.
[tex]y =\dfrac{-2+26i}{2+8i} = \dfrac{-1+3i}{1+4i}[/tex]
[tex]y =\dfrac{-1+3i}{1+4i}\times \dfrac{1-4i}{1-4i}[/tex]
[tex]y = \dfrac{-1+4i+13i+52}{1+16}[/tex]
[tex]y = \dfrac{17i+51}{17}[/tex]
y = 3+i
Therefore, the solution for the complex function is equal to y = 3 + i.
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Which inequality is shown?
Answer:
affirmative action
Step-by-step explanation:
