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2 years ago

Submit your answers in simplest radical form. help :(

Mathematics

2 answers:

rusak2 [61]2 years ago

8 0

Answer:

x = 6√2, y = 6

Step-by-step explanation:

This is an isosceles triangle as one angle measures 45° and the other is a right angle, so it measures 90°.

Therefore, you know that y will equal 6.

You have to multiply a by √2 to find x.

6 x √2 = 6√2

Hope this helps!

Leokris [45]2 years ago

4 0

Answer:

x = 6 $\sqrt{2}$

y = 6

Step-by-step explanation:

in a 45-45-90 triangle the two legs are equal, so XY = YZ

also, the leg to hypotenuse ratio is 1 : $\sqrt{2}$

so x = 6 · $\sqrt{2}$

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A group of employees is stranded on top of a 120 feet building because a fire occurred. Your goal is to throw a rope from a 60 f

Paul [167]

Step-by-step explanation:

-16t² + 64t + 60 = 120

this is a quadratic equation, and its points of f(t) = 0 can be calculated. there are usual 2 such solutions for a quadratic equation.

so, we need to bring it to a form that ends in "= 0".

-16t² + 64t - 60 = 0

that is also the same as

-4t² + 16t - 15 = 0

the formula for the solutions of such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = -4

b = 16

c = -15

so,

t = (-16 ± sqrt(256 - 4×-4×-15))/(2×-4) =

= (-16 ± sqrt(256 - 240))/-8 =

= (-16 ± sqrt(16))/-8 = (-16 ± 4)/-8

t1 = (-16 + 4)/-8 = -12/-8 = 3/2

t2 = (-16 - 4)/-8 = -20/-8 = 5/2

so, it depends on what the unit of time t is. let's assume seconds.

therefore, the rope will reach the top of the building while going up after 3/2 = 1 1/2 = 1.5 seconds.

and then, as the shot rope makes a curve and comes back down again (that is why we have 2 solutions : the rope will reach the height of 120ft during its flight path twice : once while still going up, and once when coming back down again) it will be at the height of the top of the building after 5/2 = 2 1/2 = 2.5 seconds.

so, it depends if the people there can grab it at the first chance, and if the path of the rope would allow them to grab it also again on its way back down. this we don't know.

I therefore guess, that your teacher is aiming for the first solution.

4 0

2 years ago

Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. What rate of return h

Kay [80]

The rate of interest is 25%

<u>Explanation:</u>

Given:

Principal, P = $2,000

Amount, A = $2500

Time, t = 1 year

Rate of Interest, r = ?

We know:

$Amount = P(1+\frac{r}{100})^t$

On substituting the value we get:

$2500 = 2000 (1 + \frac{r}{100})^1\\ \\\frac{25}{20}= (1+\frac{r}{100})\\$

$\frac{5}{20} = \frac{r}{100}\\ \\r = \frac{100 X 5}{20} \\\\r = 25$

Therefore, the rate of interest is 25%

5 0

3 years ago

Read 2 more answers

Simplify if possible

Anarel [89]

The answer is the last choice 2 1/2

8 0

3 years ago

Read 2 more answers

This is kinda confusing can someone help explain!!

AURORKA [14]

Answer: all i can say is this for an edu guess

2 6 and 4 would be 40 or 30

3 5 and 7 would be 110 or 120

8 would be 20 or 10

also this was the first answer

7 0

2 years ago

Read 2 more answers

The point nearest to the origin on a line is at (4, -4). Find the standard form of the equation of the line.

Scrat [10]

Just did a specific one of these; let's do the general case.

The point nearest the origin is (a,b).

The line from the origin through the point is

$bx - ay = 0$

The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):

$ax + by = a^2 + b^2$

$ax + by -( a^2 + b^2) = 0$

That's standard form; let's plug in the numbers:

$4 x - 4 y - 32 = 0$

$x - y - 8 = 0$

5 0

3 years ago