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2 years ago

One vertex of an equilateral triangle is at the origin and the other vertex is at (3,4)

Mathematics

2 answers:

Keith_Richards [23]2 years ago

4 0

Answer:

(5 , 0)

Step-by-step explanation:

Illusion [34]2 years ago

3 0

Answer:

5 units

Step-by-step explanation:

Points:

(0, 0) and (3, 4)

The distance:

d= √(4-0)²+(3-0)² = √16+9= √25 = 5

Sides of the triangle are 5

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The following data was collected from a simple random sample of a population.

aivan3 [116]

Answer:

Step-by-step explanation:

This problem is analogous to the extraction of 6 elements from a total of 10 elements. It's the same if they are marbles, chips, or in this case, people, as here we don't care about the order of the selection as we only are drawing a sample.

Thus, the problem implies solving the amount of possible combinations of 10 people if we take by 6. There is a formula for this and is:

10 C 6 = 10!(6!4!)

If we operate, knowing that for any number x, x!=x*(x-1)*(x-2)*...*1

10 C 6 = 10!(6!4!) = 10*9*8*7*6*...*1 / [(6*5*...*1) * (4*3*2*1)]

10 C 6 = 10*9*8*7*6! / [(6*5*...*1) * (4*3*2*1)]

We have a 6! multiplying and another dividing, so they get eliminated, and as 4*2=8 and 9=3*3

10 C 6 = 10*9*8*7*/ [(4*3*2*1)] = 10*3*3*8*7*/ [(8*3*1)]

We can eliminate the 8s and one of the 3s on the numerator with the one on the denominator:

10 C 6 = 10*3*7*/1 = 210/1= 210

So, option C

5 0

3 years ago

Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

borishaifa [10]

Implicit defferentation

remember that dy/dx y= dy/dx

so
take derivitive of both sides
$2x+2y \space\ \frac{dy}{dx}=0$
solve for $\frac{dy}{dx}$
minus 2x both sides
$2y \space\ \frac{dy}{dx}=-2x$
divide both sides by 2y
$\frac{dy}{dx}=\frac{-2x}{2y}$
$\frac{dy}{dx}=\frac{-x}{y}$

when is the slope equal to $\frac{5}{12}$
solve for $\frac{dy}{dx}=\frac{5}{12}$
$\frac{dy}{dx}=\frac{5}{12}$
$\frac{5}{12}=\frac{-x}{y}$
$5y=-12x$
$y=\frac{-12}{5}x$
find where the circle and this line intersects

substitute $\frac{-12}{5}x$ for y
$x^2+(\frac{-12}{5}x)^2=676$
$x^2+\frac{144}{25}x^2=676$
$\frac{25}{25}x^2+\frac{144}{25}x^2=676$
$\frac{169}{25}x^2=676$
times both sides by $\frac{25}{169}$
$x^2=100$
sqrt both sides, take positive and negative roots
x=+/-10

sub back

$y=\frac{-12}{5}x$
$y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)$
$y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}$
$y=-24 \space\ or \space\ 24$

the points are (10,-24) and (-10,24)

8 0

3 years ago

Write the inequality that represents the sentence, "Four less than a number is greater than 58."

puteri [66]

Answer:

n-4>58

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find X<br> Please help asap!!

Law Incorporation [45]

I assume X= 100, since it look like 100 degree angle is equal to X angle

3 0

2 years ago

Read 2 more answers

Graph the absolute value function.<br> f(x)=|x+3|+2<br> vertex:?<br> table of values:?

adelina 88 [10]

$1^o:Graph\ line\ x+3\ (red\ color)\\
2^o:reflect\ negatives\ over\ x-axis\Rightarrow|x+3|(blue\ color)\\
3^o:Raise\ the\ graph\ two\ units\ up.(green\ color)\\
The\ rest\ is\ visible\ on\ the\ graph.$

8 0

3 years ago