Let ​f(x)=x^2−4 and ​g(x)=16−x. Perform the composition or operation indicated. ​(fg)(1​)

Distance using absolute value for each example are given below:

As given in the question,

Distance Using Absolute Value

Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.

1) –15 and 35

Distance Using Number Line     –15 – (–35) = –15 + 35 = 20

Absolute Value Statement    |–15 – (–35)| = 20

2) 47 and –12

Distance Using Number Line    47 – (–12) = 47 + 12 = 59

Absolute Value Statement     |47 – (–12)| = 59

3) –43 and 27

Distance Using Number Line     –43 – (–27) = –43+27 = – 16

Absolute Value Statement      |–43 – (–27)| = 16

4) –10 and 4

Distance Using Number Line     –10 – 4 = –14

Absolute Value Statement     |–10 – 4| = 14

5) 50 and –25

Distance Using Number Line     50 – (–25) = 50 + 25 = 75

Absolute Value Statement     |50 – (–25)| = 75

6) 36 and –19

Distance Using Number Line     36 – (–19) = 36+19 = 55

Absolute Value Statement    |36 – (–19)| = 55

7) –30 and –40

Distance Using Number Line    –30 – (–40) = –30 + 40 = 10

Absolute Value Statement    |–30 – (–40)| = 10

8) –2 and –45

Distance Using Number Line     –2 – (–45) = –2 + 45 = 43

Absolute Value Statement    |–2 – (–45)| = 43

9) 18 and 46

Distance Using Number Line     18 – 46 = –28

Absolute Value Statement    |18 – 46| = 28

10) –10 and –44

Distance Using Number Line      –10 – (–44) = –10 + 44 = 34

Absolute Value Statement    |–10 – (–44)| = 34

11) –28 and 41

Distance Using Number Line       –28 – 41 = –69

Absolute Value Statement     |–28 – 41| = 69

12) 7 and –9

Distance Using Number Line       7 – (–9) = 7+9 = 16

Absolute Value Statement      |7 – (–9)| = 16

13) –52 and 28

Distance Using Number Line       –52 – 28 = –80

Absolute Value Statement      |–52 – 28| = 80

14) 22 and –50

Distance Using Number Line       22 – (–50) = 22 + 50 = 72

Absolute Value Statement       |22 – (–50)| = 72

15) –4 and –31

Distance Using Number Line       –4 – (–31) = –4 + 31 = 27

Absolute Value Statement       |–4 – (–31)| = 27

16) 19 and 51

Distance Using Number Line       19 – 51 = –32

Absolute Value Statement     |19 – 51| = 32

17) 0 and –38

Distance Using Number Line       0 – (–38) = 0+ 38 = 38

Absolute Value Statement      |0 – (–38)| = 38

18) 2 and –14

Distance Using Number Line       2 – (–14) = 2+14 = 16

Absolute Value Statement       |2 – (–14)| = 16

Therefore, distance using absolute value for each example are given below:

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Based on the number of shares outstanding and the market value, the price the stock is currently selling for is  $31.40

To find the selling price of the stock the formula is:

= Equity value of stock / Number of stock outstanding

The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.

The selling price of the stock today then is:

= Equity value of stock / Number of stock outstanding

= 569,600 / 19,000

= $31.40

Full question is:
What is the stock selling for today?

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( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12

( 2 ) If p and q is 16 then the direct variation is 1

Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.

There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.

If p varies directly as q

for p = 4.5

when q = 12

Then p = kq

4.5 = 12k

k = 12/4.5

k = 8/3

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Answer:

0.04122137404 is the answer

Answer: 0.041221374

Step-by-step explanation: According to Bing, 0.041221374 is your answer.

To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.

In the question ,

it is given that

to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .

so , the ratio of yellow paint to blue paint  [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]

writing in the simplified form , we get

= 4/5 × 2/1

= 8/5

So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,

let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .

[tex]\frac{8}{5} =\frac{x}{3}[/tex]

On simplifying

x = 24/5

x = 4.8

so yellow paint required is 4.8 gallons

Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.

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The product (a - b)(a + b) is called the special binomial product, when simplified it is called algebraic identity of two squares and, when simplified it is equivalent to a² - b²

An equivalent, simpler (typically shorter) mathematical expression is substituted for the original one through the process of simplification.

In propositional logic, simplification is a valid immediate inference, argument form, and inference rule that draws the conclusion that if the conjunction A + B is true, then A + B is true as well. By deriving one of the conjuncts of a conjunction on a line by itself, the rule enables the brevity of longer proofs.

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The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.

The points which form a triangle are:

H(3,-1) ; I(-6,-1) and J(3,-9)

Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:

To find the length we have to find the distance between the points.

Using distance formula i.e.

[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]

Let the length of the sides be A1, A2 , A3

On applying the distance formula to H(3,-1) and I(-6,-1) ;

We get,

A1 =  [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]

    = [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]

    = [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]

    = [tex]\sqrt{81}[/tex]

    = 9

On applying the distance formula to  I(-6,-1) and J(3,-9);

We get,

A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]

     = [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]

     = [tex]\sqrt{[ 81 + 64 ][/tex]

     = [tex]\sqrt{145}[/tex]

    = 12.04

On applying the distance formula to J(3,-9) and H(3,-1);

We get,

A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]

     =  [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]

     = [tex]\sqrt{ [ 0 + 64 ][/tex]

     =[tex]\sqrt{64}[/tex]

     = 8

Hence,

The perimeter is 9 + 12.04 + 8 = 29.04

The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.

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Answer:

The solution to the question will be explained better using the image below

Concept:

The formula to calculate momentum is given below as

The first momentum will be

The second momentum will be

Since they are moving in different directions,

We will substract both momentums

Hence,

The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis

Answer:

141 each

Step-by-step explanation:

Answer:

(x+1)(x-5)

Step-by-step explanation:

From the graph it can be observed that line fits curve and line has positive slope as increase in hours cause increase in miles.

The line with postive slope represent the positive relation between the variables. So there is postive association between miles and time spent for running.

Answer: positive association

Answer:

First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0

Step-by-step explanation:

The new coordinates of the point N after the given dilation transformation is; (-2, 6)

From the attached image, we see the given triangle MNP. We see that it's coordinates are;

M(-1, -2)

N(0, 2)

O(2, -2)

Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.

Thus, triangle MNP will be dilated according to the rule  (x,y), where point P is the center of dilation.

Given the coordinate N = (0, 2)

The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:

(x, y) = (2x - 2), (2x + 2)

Thus;

N = (0, 2) → N'(2(0) - 2), (2(2) + 2)

= N'(-2, 6)

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Given a function f(x), we can write the function g(x), where g(x) is the reflection over teh y-axis of f(x) by:

In this case, the function given is:

Thus the reflection over the y-axis is:

Now simplify:

hus the answer is:

g (x) = -5x+8 (second option)

The value of n is 0.06.

Given:

The mass of Earth is 5.97 × 10²⁴ kg.

The mass of Mercury is 3.29 × 10²³ kg.

The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.

The ratio of the mass of Earth to the mass of Mercury can be calculated as,

= mass of Earth/mass of Mercury

⇒  [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]

⇒ n = 0.0551

⇒ n ≅ 0.06 ( 2 significant figures)

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The cell phone will takes about 4.7 seconds to reach the ground.

There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.

They are listed below as:

[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]

where u = initial velocity of the considered object

v = final velocity of the object

a = acceleration of the object

s = distance traveled by the object in 't' time.

Given that hang glider dropped his cell phone from a height of 450 feet:

Acceleration is rate of change of velocity.

[tex]s = ut + \dfrac{1}{2} at^2[/tex]

Height = h = 450 feet

Gravitational Acceleration = g = 9.8 feet/s²

Initial Velocity = u = 0 m/s

h = 1/2at²

h = √2h/g

h = √2 x 450/ 9.8

h = 9.58 s.

Therefore, the cell phone will take 9.58 seconds to reach the ground.

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Value of b is  2Ah - B.

The area that an object's shape designates as being within it. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area. Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.

On a piece of paper, draw a square with a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Numerous 2-D shapes, such as circles, triangles, squares, rectangles, parallelograms, and trapezoids, may be found all around us. On paper, you can trace each of these shapes. Since every shape is distinct and varied, its area is also determined in a different way.

Given Data

A= [tex]\frac{1}{2}[/tex]h ( B + b)

For the value of b

b + B = 2Ah

b = 2Ah - B

Value of b is  2Ah - B.

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Notice that this set of angles is congruent

herefore,

Solving for y ,

nswer: 116

A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.

As given in the question,

Number of identical boxes in a stack=20

Stack of 20 identical boxes are 180 cm tall

Height of 1 box=180/20

                         =9cm

Julia removes 3 boxes from the top

Height of 3 identical boxes=9 × 3

                                             =27 cm

Height of stack after removing 3 boxes from the top

=Original height - height of 3 boxes

=180 -27

=153cm

Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.

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Using proportions, it is found that your walk and jogging rates are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.

One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:

v = d/t.

From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:

v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.

For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:

v = 5/1 = 5 miles per hour.

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The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.

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Answer:

They all have carbon atoms.

Step-by-step explanation:

Answer:I believe it is 15-25

Step-by-step explanation:

I assume the natural logarithm, and not the base-10 log. Parameterize the integral as

[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]

Differentiate twice with respect to [tex]a[/tex].

[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]

[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]

Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].

[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]

[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]

[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]

Let [tex]a=\phi[/tex] to recover the original integral.

[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]

Using various properties of the golden ratio [tex]\phi[/tex], namely

[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]

[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]

[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]

we can simplify the result to

[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]

Answer

Tan (A) = 0.109 radians

Explanation:

The figure given is a right angles triangle

Given that AB = c is the hypotenus

AC = b = adjacent

BC = a = opposite

Tan A can be calculated using SOH CAH TOA

Tan A = opposite / adjacent

Tan A = BC / AC

BC = a = 4.020

We need to find b uisng pythagoras theorem

b = 11.307

Tan A = 4.020 / 11.307

Tan A = 0.3555

A = tan ^-1 (0.3555)

A = 19.570 degrees

Convert degrees to radian

since 1 pi = 180 degrees

x pi = 19.570

Cross multiply

19.570 * 1 = x * 180

x = 19.570 / 180

x = 0.109

Therefore, tan (A) is 0.109 radians

Answer:

c is the answer

Step-by-step explanation:

1.5 x 3 =4.5

4.5 - 0.25

= 4.25

The test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.

To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.

If 2 hours of studying = 44 marks

If 3 hours of studying = 66 marks

If 4 hours of studying = 88 marks

Then total sum of hours of studying = 9 hours

9 hours of studying = Sum of all marks

                                 = 44 + 66 + 88

                                 = 198

1 hour of studying = 198/9

                              = 22 marks

So, the test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

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When the given proportion is solved the value of w is calculated to be 6.

What is proportion?

A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.

When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.

for example 5/10 = 1/2, 5:10 = 1: 2

7:42 = 1 : w

[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]

w = 1 x 6

w = 6

When the given proportion is solved the value of w is calculated to be 6

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Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.

We will need to use the next formulas

Therefore, the surface area is

Lateral Area=116.1 m^2

As for the volume, the volume of a regular pyramid is

In our case,

Therefore,

Volume= 77.9 m^3

For the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to  y = x² - 14x + 48 .

As given in the question,

From the table of ordered pairs, it is observed that the zeros of the quadratic function are at x = 6 and x = 8. The zeros are the points where the y value of the function becomes zero.

An equation of the function in the standard form is given by :

y = (x - 6)(x - 8)

⇒y = x (x - 8) - 6 (x - 8)

⇒ y = x² -8x -6x +48

⇒ y = x² -14x + 48

The quadratic function is represented as the product of the zeros of the graph when plotted on a Cartesian plane.

Therefore, for the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to  y = x² - 14x + 48 .

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