Let assume "M" is the midpoint of the segment AB. Find AM. AM= x+7 MB=2x A. 7 B. 14 C. 12 D. 9

Answer:

C)  Domain:  all real numbers x except x = ±2

E)  f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{3x^2}{x^2-4}\)

The domain of a function is the set of all possible input values (x-values).

A rational function is undefined when the denominator is equal to zero.

The denominator of the given function is zero when:

\(\implies x^2-4=0\)

\(\implies x^2=4\)

\(\implies \sqrt{x^2}=\sqrt{4}\)

\(\implies x= \pm 2\)

Therefore the domain of the function is:

The excluded x-values are x = -2 and x = 2.

To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:

\(x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...\)

\(x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...\)

\(x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...\)

\(x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...\)

Therefore, the behaviour of the function near the excluded x-values:

The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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\(x7 - 2 \: or \: x \leqslant - 3\)

The answer in length

The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.

Its the sum of length of the sides used to made the given figure.

Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.

Area is what is on the inside.

The perimeter is the outside of the hole thing.

Hence, the length is used to measure the distance between to end points or edges.

so 17 meters measurement represent the length.

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Answer:

-8

Step-by-step explanation:

I've taken a picture of the way I solved the equation.

first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)

In order to find the value of f(-1), you can start by finding the value of f(1) and then proceed for the next step.

As you have already noted, writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) will not give you a specific branch. Instead, you can write z13+z14 as follows:

(z-1)(z12+z11+z10+...+1)

Then, you can use the fact that f(1)=0 to solve for the value of z12+z11+z10+...+1. This will give you a specific value for f(1).

To find the value of f(-1), you can use the following relationship:

f(-1) = f(1) * (-1)13 * (-1)14

Substituting the value you found for f(1) and evaluating the expression will give you the value of f(-1).

As for the condition "not defined on the negative imaginary axis", this means that the branch of f(z) is not defined for any complex number with a negative imaginary part. This is because the 13th and 14th roots of a complex number are not unique when the imaginary part is negative, so the function is not defined for these values.

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Answer:

8  5/648

Step-by-step explanation:

y = 5x ^ -3 + 4x^2

dy /dx = 5 * -3 x^ -4 + 4 * 2x ^ 1

           = -15 x ^ -4 + 8x

Now take the second derivative

dy^2/ dx^2 = -15  * -4 x^-5 +8

                   = 60 x^ -5 +8

                   = 60 /x^5   +8

Evaluate at x = 6

                   = 60 / 6^5  +8

                    60/7776 +8

                   5/648 + 8

                  8  5/648

Answer:

i do not care

Step-by-step explanation:

Answer: x = 2,340 homes without children

There are 2,340 homes without children.

Step-by-step explanation:

'x' represent the number of homes without children

'y' represent the number of homes with children

x : y = 9 : 7

Since the total number of homes is 4160 means x + y = 4160.

From x + y = 4160 follows y = 4160 - x.

Plug y = 4160 - x into x : y = 9 : 7

x : (4160 - x) = 9 : 7

Answer:

26

Step-by-step explanation:

if she is 8 years older, then is just 34-8 which is 26

Answer:

0.0005123

Step-by-step explanation:

The scientific notation 5.123e-4 is same as 5.123×10^-4 or 5.123×10-4. Thus, to get the answer to 5.123e-4 as a decimal, we multiply 5.123 by 10 to the power of -4.

= 5.123e-4

= 5.123 × 10-4

= 0.0005123

Answer:

f(x) = 5x – 1

to find the inverse equate f(x) to y

That will be

f(x) = y

>>>>

Interchange the terms >>>

x = 5y - 1

then make y the subject

then we have

5y = x + 1

then if you divide both sides by 5

y = x+1/5

therefore f^-1(x)= x + 1/5

hope this helps you

(Brainliest?)

Step-by-step explanation:

Answer:

It 2 that is the mean it is that because the median is the middle score in a set of given numbers. The mode is the most frequently occurring score in a set of given numbers.

Step-by-step explanation:

Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

Answer:

huh?

Step-by-step explanation:

Let's simplify step-by-step.

−3x+3x3−2x2+2−(8−4x+3x2)

Distribute the Negative Sign:

=−3x+3x3−2x2+2+−1(8−4x+3x2)

=−3x+3x3+−2x2+2+(−1)(8)+−1(−4x)+−1(3x2)

=−3x+3x3+−2x2+2+−8+4x+−3x2

Combine Like Terms:

=−3x+3x3+−2x2+2+−8+4x+−3x2

=(3x3)+(−2x2+−3x2)+(−3x+4x)+(2+−8)

=3x3+−5x2+x+−6

Answer:

=3x3−5x2+x−6

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Answer:

tis a translation. nothing has changed but the position

Answer:

translation

Step-by-step explanation:

The total volume of 3:12 is 90 gallons  

In math, the term Ratio is used to compare two or more numbers or quantities. It indicates how small or big a quantity is when compared to each other. In a ratio, the comparison between two values is done by using division.  

Here we have    

54 gallons is the volume of 2:7

=> As we know 2+7 = 9

Therefore, for 9 parts = 54 gallons of volume

=> 1 part = 54/9 = 6 gallons of volume

Here we need to find 3: 12

For 3 parts = 3 × 6 gallons of volume = 18 gallons

For 12 parts = 12 × 6 gallons of volume = 72 gallons

=> total volume = 18 gallons + 72 gallons = 90 gallons

Therefore,

The total volume of 3:12 is 90 gallons  

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The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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Answer:c, the answer is c

Step-by-step explanation:

1) The best way to tackle this question is to sketch this out:

Note that, we need to know the height of that trapezoid. So, let's trace a parallel line from the vertex to the larger base of that trapezoid.

2) As we can see, we can now realize the existence of a right triangle, so let's make use of the Pythagorean Theorem to find a congruent side parallel to the height "x":

Thus, that's the approximate measurement of x, to the nearest tenth.

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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Work Shown:

3(x+2) - 4(x-1)

3(-3+2) - 4(-3-1)

3(-1) - 4(-4)

-3 + 16

13

Therefore, 3(x+2) - 4(x-1) = 13 when x = -3

In other words, the solution to 3(x+2) - 4(x-1) = 13 is x = -3.

Answer:

The equation \(4\cdot x^{2} + 20\cdot x + 25 = 0\) is equal to \(\left(x + \frac{5}{2} \right)^{2} = 0\).

Step-by-step explanation:

Let be the equation \(4\cdot x^{2} + 20\cdot x + 25 = 0\), we proceed to rewrite the equation solely by algebraic means:

1) \(4\cdot x^{2} + 20\cdot x + 25 = 0\) Given

2) \((2\cdot x)^{2} + 10\cdot (2\cdot x) + 25 = 0\) Definition of power/Associative property

3) \((2\cdot x + 5)^{2} = 0\)   Perfect square trinomial

4) \(2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0\) Distributive property/\((a\cdot b)^{c} = a^{c}\cdot b^{c}\)

5) \(4\cdot (x + \frac{5}{2} )^{2} = 0\) Definition of power

6) \(\left(x + \frac{5}{2} \right)^{2} = 0\) Compatibility with multiplication/Commutative and modulative properties/\(a\cdot 0 = 0\)

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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