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enyata [817]
3 years ago
11

Translate the sentence into an equation. Two less than the quotient of a number and 7 equals 8 . Use the variable y for the unkn

own number.
Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0
I believe the answer would be 
(x/7)-2= 8
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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
Find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3). express answer in standard form
Anestetic [448]

Answer:

Final answer is x-6y=23

Step-by-step explanation:

We need to find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3).

So first we need to find the slope of given line.

rewirite x=6y-5 in y=mx+b form

x+5=6y

\frac{1}{6}x+\frac{5}{6}=y

Compare given equation with y=mx+b

we get: m=1/6

We know that parallel equations has equal slope.

Then slope of required line m=1/6

Now plug the given point (5,-3) and slope m=1/6 into point slope formula:

y-y_1=m\left(x-x_1\right)

y-(-3)=\frac{1}{6}\left(x-5\right)

y+3=\frac{1}{6}x-\frac{5}{6}

y=\frac{1}{6}x-\frac{5}{6}-3

y=\frac{1}{6}x-\frac{23}{6}

Now we need to rewrite that equation in standard form. Ax+By=C.

6y=x-23

x-23=6y

x-6y=23

Hence final answer is x-6y=23

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Step-by-step explanation:

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Phantasy [73]

If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative

The quadratic formula is

x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

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3 years ago
Principal: $1000, annual interest rate: 4.8%, time: 2 yr
Anna11 [10]

Answer: $1096

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