F(x)=x^2 what is g(x)?

The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

3 years ago

A boat has a speed of 15 mph in still water. It travels downstream from Greentown to Glenavon in g hours. It then goes back upst

valentina_108 [34]

Answer:

The distance from Greentown to Glenavon is D1 = g*(15+x) miles downstream.

The distance from Glenavon to Cambria is D2 = g*(15-x) miles upstream.

The difference D1 - D2 is 2 miles, according to the condition.

It gives you an equation g*(15+x) - g*(15-x) = 2, which you can easily solve and find "x", the rate of the current. x = 1/g miles per hour.

7 0

3 years ago

Doug purchased land for $8,000 in 1995. The value of the land depreciated by 4% each year after 1995. Write an exponential funct

Mashutka [201]

Answer:

$6.012

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

ΔMNP is an isosceles triangle with MN ≈NP. If ∠ M = 3x + 1 and ∠ N = x - 11. What is the measure of ∠P?

s2008m [1.1K]

Start with an equation summing all the angles in this triangle:

180 = <M + <N + <P

we are given <M and <N but not <P. But, since MN=NP, the angle <P is the same as the angle <M (isosceles, make a drawing to see). So

180 = 2<M + <N

180 = 2(3x+1) + x-11

180 = 7x - 9

x = 27

<P = 3*27+1 = 82 degrees

4 0

3 years ago

For Judy's birthday, her friend gave her a gift card. She went to the clothing store and bought a total of $178.25 worth of clot

vladimir1956 [14]

Answer:

<h3>The percentage is <u>60%</u> of the total amount paid with the gift card. </h3>

Step-by-step explanation:

Given:

Total worth of clothing is $178.25 and the amount paid with cash is $71.30.

Let us find the part of amount paid with the gift card:

Amount of gift card(G) = Total worth(T) - Amount paid in cash(C).

$G\ =\ 178.25-71.30$

$G\ =\ 106.95$ .

So, the amount paid with the gift card is $106.95.

Now, according to question:

$\frac{106.95}{178.25}\times100$

$=0.6\times100$

$=60$ %.

Therefore, the percentage is <u>60%</u> of the total amount paid with the gift card.

6 0

3 years ago