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3 years ago

Which fraction is halfway between 3/7 and 10/21

Mathematics

1 answer:

Aleks [24]3 years ago

6 0

Answer:

B) 19/42

Step-by-step explanation:

To find the fraction halfway between 3/7 and 10/21 we first find the difference between the fractions, half it, and then add it back on to the smaller one.

Because 10/21 > 3/7 we subtract in that order

$\frac{10}{21} - \frac{3}{7} = \frac{10}{21} - \frac{9}{21} = \frac{1}{21}$

Half of 1/21 is 1/42 and so the fraction halfway between 3/7 and 10/21 is

$\frac{3}{7} + \frac{1}{42} = \frac{18}{42} + \frac{1}{42} = \frac{19}{42}$

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3 years ago

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The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =

andrey2020 [161]

we have

$f(x)=x^{2}-2x-3$

Find the roots

Equate the function to zero

$x^{2}-2x-3=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}-2x=3$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}-2x+1=3+1$

$x^{2}-2x+1=4$

Rewrite as perfect squares

$(x-1)^{2}=4$

Square root both sides

$(x-1)=(+/-)2$

$x=1(+/-)2$

$x=1+2=3$

$x=1-2=-1$

therefore

<u>the answer is</u>

$x=3$

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3 years ago

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A ladder reaches the top of a 20 foot building. the ladder is 4.5 feet away from the building. how long is the ladder?

KATRIN_1 [288]

Answer:

Step-by-step explanation:

do that with pithagoras:

20² + 4,5² = x²

400 + 20,25 = x²

420,25 = x²

x = $\sqrt{420,25}$

x ~ 20,5

Letter C: 20,5 feet

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3 years ago

Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan 1/2 θ

mrs_skeptik [129]

Answer:

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...

Anyways, the half angle identity for tangent is

$tan(\frac{\theta}{2})=\frac{sin\theta}{1+cos\theta}$

There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.

If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) }$ which simplifies a bit to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{5}{5} -\frac{4}{5} }$ and a bit more to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{1}{5} }$

Bring up the lower fraction and flip it to divide to get

$tan(\frac{\theta}{2})=-\frac{3}{5}*\frac{5}{1}$ which of course simplifies to

-3. Choice A.

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3 years ago

10) Thirty-seven percent of the American population has blood type O+. What is the probability that at least four of the next fi

lisabon 2012 [21]

Answer:

0.06597

Step-by-step explanation:

Given that thirty-seven percent of the American population has blood type O+

Five Americans are tested for blood group.

Assuming these five Americans are not related, we can say that each person is independent of the other to have O+ blood group.

Also probability of any one having this blood group = p = 0.37

So X no of Americans out of five who were having this blood group is binomial with p =0.37 and n =5

Required probability

=The probability that at least four of the next five Americans tested will have blood type O+

= $P(X\geq 4)\\= P(X=4)+P(x=5)\\= 5C4 (0.37)^4 (1-0.37) + 5C5 (0.37)^5\\= 0.06597$

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3 years ago

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