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Elodia [21]
3 years ago
13

Check What is the slope of the line on the graph?

Mathematics
1 answer:
katen-ka-za [31]3 years ago
7 0
Slope: the tilt. it equals rise over run. so 1/2
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The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased
White raven [17]

<em><u>Statement:</u></em>

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

<em><u>To find out:</u></em>

The length of the larger side of the right angled triangle.

<em><u>Solution:</u></em>

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = \frac {(52 - 6y)}{4} ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, \frac {(2704-624y +36y²)}{16} + y² = 52

or, \frac {(2704-624y +36y² + 16y²)}{16}= 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

<em><u>Answer:</u></em>

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0
2 years ago
When working with a function, every x has exactly _____ unique y-value(s).
Rashid [163]

Answer:

The answer is B.

Step-by-step explanation:

A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it. While a function may NOT have two y-values assigned to the same x-value, it may have two x-values assigned to the same y-value. Function: each x-value has only ONE y-value!

Hope this helps :)

4 0
3 years ago
Read 2 more answers
What does this mean? please help
slavikrds [6]
If you're looking for the slope, the answer is 103.
4 0
3 years ago
there are 5 walnut trees currently in the park park workers will plant 8 more walnut trees today how many walnut trees will the
Salsk061 [2.6K]

Answer:13

Step-by-step explanation:

8 0
2 years ago
You deposit $1200 in an account. The account earns $120 simple
iVinArrow [24]

We have to find the unit rate, so we have to divide what you earned in interest by the amount of months.

120/8=15

So you earn $15 per month

---

sorry if this doesn't help

7 0
3 years ago
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