1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melisa1 [442]
3 years ago
8

One side of a right triangle is 2 cm shorter than the hypotenuse and 7 cm longer than the third side. find the lengths of the si

des of the triangle.
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0
The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.
If the hypotenuse - H
Then one side is - H - 2
Third side is 7 cm shorter then H-2
Therefore it’s H -2-7 = H -9
According to Pythagoras theorem
Square of hypotenuse = sum of the squares of the other 2 sides
H² = (H-9)² + (H-2)²
H² = H² -18H + 81 + H² -4H + 4
0 =H² -22H +85
This is a quadratic equation
0 = H² - 17H -5H +85
0 = H (H - 17) -5(H-17)
(H-17) (H-5) =0
H -17=0 or H-5=0
H could be 17 cm or 5 cm
If H =5 cm then
Side 1 -H-2 = 3 cm
And side 2 - H-9 = -4 cm
Since lengths cannot be negative values
H isn’t 5 cm
Therefore H =17 cm
1 side is H-2 = 15 cm
2nd side H -9 = 8 cm
Three sides are 17 cm, 15 cm and 8 cm
You might be interested in
Find the Roots of the following polynomial. <br><br> x3−5x2+6x = 0
ICE Princess25 [194]

Answer:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

((x3) - 5x2) - 6x = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

x3 - 5x2 - 6x = x • (x2 - 5x - 6)

4 0
3 years ago
Read 2 more answers
Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
SOVA2 [1]

y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

Over each subinterval, we approximate f(x) with the quadratic polynomial

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that the integral we want to find can be estimated as

\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

5 0
3 years ago
PLEASEEE HELPP MEE WITH MATHHH NUMBERS 8 AND 12!!!!!!
Usimov [2.4K]

Answer: edit* here you go! both answers here :) sorry for the wait!!!

Step-by-step explanation:

8 0
3 years ago
Lines l and m intersect at point p and are perpendicular. if a point q is reflected across l and then across m, what transformat
artcher [175]
Rotating 180 degrees about the point p. 

If they are perpendicular reflecting across each one will have the same effect as if the point was rotated 180 degrees about the certain point.
7 0
3 years ago
Help me please I'm stuck! With the first column
frosja888 [35]
1. \frac{n}{4}

2. -2+5n or 5n-2

3. (12s)+150 where s=number of students

4. 3(32)+1(53)=96+53=159 per hour, so 159h

9. √105 is irrational, -4 is an integer, 4/3 is a rational number, order is -4,3/4, √105

10. 3²=9, 4²=16, so between 3 and 4, but closer to 4, so √14≈4

11. that is the associative property, it deals with moving parentahees around

12. 2(6.25)+1(5.50)+2(2.75)=2(6.25+2.75)+1(5.50)=2(9)+5.5=18+5.5=23.5

13. yes, because they are both 2 less than 3 times of a number

14. maybe 18 times 3, so (4²+2) times 3=54
5 0
4 years ago
Other questions:
  • What is the slope of y= -3/5x-2
    13·2 answers
  • A computer programmer worked for 10 hours and earned $70,which is a rate of dollars per hour.
    8·1 answer
  • Which expression is equivalent to 9(w+8)?<br> 72W<br> 9W+72<br> 9W+8<br> 17W
    7·2 answers
  • How many arrangements of three digits can be formed from the digits zero through nine
    6·1 answer
  • I need help plz .........................
    5·2 answers
  • Can someone explain this to me? what I need to do?
    6·1 answer
  • Which is the equation for the statement: The result of subtracting a number from 3/4 is 7?
    7·1 answer
  • Which value of p is a solution to p x 1/3=6
    12·1 answer
  • El peso en gramos de las cajas de cereales de cierta marca siguen una distribución Normal con media de 500g y desviación de 5g [
    14·1 answer
  • Soo uhh ye I need help-
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!