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3 years ago

How tall is a triangle that is 10ft x 10 ft x 10ft?

2 answers:

Natasha2012 [34]3 years ago

7 0

Are you saying that all 3 sides of the triangle are equal, and are 10-ft each ?

In that case, if you set the triangle down on one of its sides,
the vertex at the top will be 5√3 = about <u>8.66-ft</u> above the table.

Ugo [173]3 years ago

6 0

Square root of 75 or 8.66 rounded. Use Pythagorean Theorem.

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Samuel bought a jacket for $16 in January. The cost of the jacket increased to $24 in September. What percent of the original pr

Assoli18 [71]

Answer:

The answer is option C=150%

Step-by-step explanation:

Original cost of the jacket=$16 in January

Final cost of jacket=$24 in September

What percentage must of the original price is the new?

The new price=the original price×(A percentage)

Where the new price=$24, the original price=$16, and the percentage=(x/100)

24=16×x/100

x=(24×100)/16=150%

The answer is 150%

8 0

3 years ago

Write a fraction that is equivalent to a terminating decimal between .5 and .75?

Dovator [93]

Dhdhdhdjdjhsjsndnjdjdbdndjdjd

8 0

3 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$