MATHEMATICS MIDDLE SCHOOL

Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find the value of x.

Answers

Answer 1

Answer:

Answer:

x=4

Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

$AC^2 = AB^2 + BC^2$

step 2:-

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

$(a + b)^2 = a^2 +2ab+b^2$

289 = 4x^2 +9(x^2+2x+1)

$13x^2 +18x-280 = 0$

finding factors 70 X 52 = 3640

$13x^2 +70x-52x-280 = 0$

$13x^2 -52x+ 70x-280 = 0$

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and $13x =-70$

x=4 and $x=(-70)/(13)$

we can not choose negative value so x value is 4

Final answer:- x = 4

verification:-

$AC^2 = AB^2 + BC^2$

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

Answer 2

Answer:

Answer:

x = 4

Step-by-step explanation:

The length of two legs of a right angle triangle are 2x and 3(x+1).

The length of longest side is 17 units. It means measure of hypotenuse is 17 units.

According to the pythagoras theorem,

$leg_1^2+leg_2^2=hypotenuse^2$

$(2x)^2+(3(x+1))^2=(17)^2$

$4x^2+9(x^2+2x+1)=289$

$4x^2+9x^2+18x+9=289$

$13x^2+18x-280=0$

On splitting the middle terms we get

$13x^2+70x-52x-280=0$

$x(13x+70)-4(13x+70)=0$

$(13x+70)(x-4)=0$

Using zero product property we get

$13x+70=0\Rightarrow x=-(70)/(13)$

$x-4=0\Rightarrow x=4$

The value of x can not be a negaive number, because for negative value of x the value of 2x is negative and side can not be negative.

Therefore, the value of x is 4.

Related Questions

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Y + 7 = -1/7 (x + 4)
Find the mean, median, lower Q, upper Q, Interquartile range (IQR), mode, and range for the following data:3, 3, 7, 21, 2, 5, 16, 58, 2, 9, 2, 2 what is the MODE: what is the UPPER Q:
1. a dictionary measures 24 centimeters by 20 centimeters.the ration of its length to its width is about ______to 1explain4. a ruler is 30 centimeters long and 2.5 centimeters wide. the ratio its length to its width is about _______ to 15.if a ruler is 33.6 centimeters long, how wide would would it have to be too have the same length to width ratio as the ruler in problem 4
1/6% of 295 help ASAP

Round 649,418 to the nearest ten,_____,nearest hundred_____,nearest thousand_____,nearest ten thousand_____,nearest hundred thousand______

Answers

The approximations of 649,418 are as follows;

Nearest ten = 649,420

Nearest hundred = 649,400

Nearest thousand = 649000

Nearest ten thousand = 650000

Nearest hundred thousand = 600000

This is about approximation of whole numbers.

When given whole numbers, the last number from the right is called units and the next is called tens followed by hundreds then thousands, then ten thousands, then hundred thousands e.t.c.

We are given the number 649,418; It means;

Units digit is 8

Tens digit is 1

Hundreds digit is 4

Thousands digit is 9

Ten thousands digit 4

Hundred thousands digit is 6

1) Approximating the nearest tenmeans if the units digit is 5 or more than 5, we add 1 to the tens digit. In this case, we will have; 649,420.

2) Approximating thenearest hundred means if the tens digit is 5 or more than 5, we add 1 to the hundreds digit otherwise we leave it and make every other term to its' right 0 to get; 649,400.

3) Approximating thenearest thousand means if the hundreds digit is 5 or more than 5, we add 1 to the thousands digit otherwise we leave it and make every other term to its's right 0 to get; 649,000.

4) Approximating thenearest ten thousand means if the thousands digit is 5 or more than 5, we add 1 to the ten thousand digit to get 650,000.

5) Approximating the nearest hundred thousandmeans if the ten thousand digit is 5 or more than 5, we add 1 to the hundred thousand digit otherwise we leave it and make every other term 0 to get 600,000.

Read more at; brainly.com/question/13343279

I think the answers are for nearest ten:649,420,nearest hundred:649,400,nearest thousand:649,000,nearest ten thousand:650,000,nearest hundred thousand: 600,000.hope this helps☺

It is possible to divid 15 by a mixed number and get a quotient greater than 15

Answers

yes if its a negative 15

For the past 5 months Pablo's bicycle repair business had these profits or losses: –$85, $70, –$120, –$90, and $35. What was his average profit or loss for these five months?

A.
His average loss was $38 per month.

B.
His average profit was $38 per month.

C.
His average loss was $80 per month.

D.
His average profit was $80 per month

Answers

The average profit (or loss) is found by adding up the profits (or losses) of the past 5 months and divinding the resulting amount by 5 (the number of months). The account is [85 + 70 + 120 + 90 + 35] / 5 = 80. Then the answer is the option C or D. HIs average loss was $80 per month or His average profit was $80 per month.

In a survey, 9 out of 15 students named math as their favorite class.express this rate as a decimal

Answers

Answer: In decimal , it will be expressed as 0.6 .

Step-by-step explanation:

Since we have given that

Total number of students = 15

Number of students names as their favourite class = 9

First we write as a fraction, which is given by

$(9)/(15)\n\n=(3)/(5)$

Now , we will change it into decimal form using division, so it will be given by

$0.6$

Hence, our answer is 0.6.

9/15 reduced to 3/5 which is 0.6

Stacie paid $13.25 for new earphones. The price she paid included a sales tax of 6%.What was the price of the earphones before the tax was added?

A.
$12.46

B.
$12.50

C.
$13.19

D.
$14.05

Answers

Let us assume the original cost of the earphones = x dollars
Then
x * (106/100) = 13.25
x = 13.25 * (100/106)
= 1325/106
= 12.50 dollars
So the actual cost of the earphones was $12.50. The correct option among all the options that are given in the question is the second option or option "B".

Look Down Below For question:

Answers

the cattle train
speed - 36.5 km/h
time - x h

the passenger train
speed - 29.2 km/h
time - (2.4+x) h

The cattle train caught up to the passenger train so the distance they travelled is the same.
Distance is speed times time.

$36.5 * x=29.2 * (2.4+x) \n36.5x=70.08+29.2x \n36.5x-29.2x=70.08 \n7.3x=70.08 \nx=(70.08)/(7.3) \nx=9.6 \n \n 2.4+x=2.4+9.6=12$

The passenger train travelled for 12 hours before the cattle train caught up.

Used brute force to figure this one out and got lucky at t=12.

What you need to know:

$d=\left| x-y \right|$

t = time travelled (in hours)

x = distance passenger train has travelled

y = distance cattle train has travelled

d = distance between both trains in km

------------------------------------

RESULTS AND TIME SNAPSHOTS:

When:

t=0, x=0, y=0, d=0

t=2.4, x=70.08, y=0, d=70.08

t=4.8, x=140.16, y=87.6, d=52.56

t=7.2, x=210.24, y=175.2, d=35.04

t=9.6, x=280.32, y=262.8, d=17.52

t=12, x=350.4, y=350.4, d=0 <-------

So your answer is 12 hours.

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