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FinnZ [79.3K]
3 years ago
15

14) Are these TRUE or FALSE?3/1= 1/33/1 = 13/3 = 1​

Mathematics
1 answer:
vaieri [72.5K]3 years ago
8 0

Answer:

False, false, true

Step-by-step explanation:

3/1 = 1/3 False

3/1 = 1 False

3/3 = 1 True

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Write a equation of a hyperbola given the foci and the asymptotes
professor190 [17]

Solution:

The standard equation of a hyperbola is expressed as

\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ ----equation 1}

The asymptote of n hyperbola is expressed as

y=\pm\frac{a}{b}(x-h)+k

Given that the asymptotes are

y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x

This implies that

a=3,\text{ and b=4}

To evaluate the value of h and k,

undefined

3 0
1 year ago
Given ΔMNO, find the measure of ∠LMN.
Novay_Z [31]

Answer:

  104°

Step-by-step explanation:

If segments NO and NM are congruent, then angles NMO and NOM are congruent. So, their supplements, angles NML and NOP are congruent. That is ...

  ∠NML ≅ ∠NOP = 104°

  ∠NML = 104°

3 0
3 years ago
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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred
Paha777 [63]

Answer:

Step-by-step explanation:

Treat this like compound interest:  Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P.  Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

                   ln 3

ln (1 + r) = ---------------

                    100

              = 1.0986 / 100 = 0.01986

We must solve this for r.  Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today.  Use the same equation:  A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

or

A = 20(3)^4, or

A = 81

The population after 400 years is 81.

8 0
3 years ago
Felix has $100 in the bank and writes a check for $150. He now has
MAXImum [283]

Answer:

Felix has 250 dollars

No change

Lucas has 5 dollars

Step-by-step explanation:

5 0
2 years ago
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Which statements are true about a triangular pyramid? Check all that apply.
miss Akunina [59]

Answer:

It has exactly four faces that are triangles.

It has 4 vertices.

It has 6 edges.

Step-by-step explanation:

A triangular pyramid is also termed as a tetrahedron.

The properties of a triangular pyramid include:

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Among the four faces, any one of them can be considered to be the base of the pyramid.

The faces are of equal shape and size.

The edges have the same length.

The triangles are equilateral.

4 0
3 years ago
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