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3 years ago

What geometric constructions can have a perpendicular bisector?

Mathematics

1 answer:

Andrews [41]3 years ago

5 0

Answer:

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

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Please help with this

slava [35]

Answer:

D) x= $\frac{-2+-2\sqrt{7} }{3}$

Step-by-step explanation:

The quadratic formula is : $\frac{-b+-\sqrt{b^2-4ac} }{2a}$

A in terms of this question=9

B in terms of the question is 12

C in terms of the question is -24.

This question is an example of a quadratic equation. To work this out you may first need a calculator. The first step is to substitute the values of a,b and c into the formula. So once substituted the formula of $\frac{-b+-\sqrt{b^2-4ac} }{2a}$ becomes $\frac{(-12)+-\sqrt{(12)^2-4*(9)*(-24)} }{2(9)}$ . Although when written in a calculator there will not be a plus and minus button and so you would have to do this separately.

However when substituting the values it would be best practice to put them in brackets.

1) Substitute the values into the equation for +.

$\frac{(-12)+\sqrt{(12)^2-4*(9)*(-24)} }{2(9)}=\frac{-2+2\sqrt{7} }{3} /1.097167541$

2) Substitute the values into the equation for -.

$\frac{(-12)-\sqrt{(12)^2-4*(9)*(-24)} }{2(9)}=\frac{-2+2\sqrt{7} }{3} /-2.430500874$

8 0

3 years ago

Find the integral using substitution or a formula.

Nadusha1986 [10]

$\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx$

Derivative of the denominator:
$\rm (x^2+2x+5)'=2x+2$

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

$\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx$

and then split the fraction,

$\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx$

Based on our previous test, we know that a simple substitution will work for the first integral: $\rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx$

So the first integral changes,

$\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx$

integrating to a log,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx$

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

$\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2$

So we have this going on,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx$

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx$

Bringing all that stuff together as a single square,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx$

Making the substitution: $\rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx$

giving us,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du$

simplying a lil bit,

$\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du$

and hopefully from this point you recognize your arctangent integral,

$\rm ln|x^2+2x+5|+\frac52arctan(u)$

undo your substitution as a final step,
and include a constant of integration,

$\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c$

Hope that helps!
Lemme know if any steps were too confusing.

8 0

3 years ago

Preparing for a visit to London, a New York resident exchanged 3,500

Aleksandr [31]

It's 28 pounds. 3,500/125 = 28 pounds.

3 0

3 years ago

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A box contains 8 red markers, 5 green markers, and 5 blue markers. Once a marker is pulled from the box, it is replaced, and the

Andru [333]

Well. add all of these up 8+5+5. we know 5+5 is 10. and 10+8 is 18. so 18 is the denominator. There are 8 red markers and 5 blue markers at 8 and 5 up. 8+5 is 13 right? So the numerator will be 13. but the probability of picking a blue then a red is 13 alone or if you are ask for out of the amount of markers there are, its 13/18. so the probability is 13 or 13/18.

3 0

3 years ago

A cube has a volume of 0.216 ft?. What is the length of each side of the cube?

const2013 [10]

Answer:

the answer is 0.054

3 0

3 years ago

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