f(x) = −3|x −1| + 4

If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be  984N.

As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.

We are required to calculate the force required to compress this spring by 1.2 cms

To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as

[F = (k * x)]

Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and

(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.

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Answer:7 6/10 is the answer if you turn a fraction into a decimal like so

7.5=7.5, 7 6/10=7.6, 7 2/5=7.4, 7.02=7.02 i hope i helped

Step-by-step explanation:

Answer:  [tex]7\frac{6}{10}[/tex] is closest to 8.

Step-by-step explanation:

[tex]7\frac{6}{10} =\frac{70}{10} +\frac{6}{10} = \frac{76}{10} = 7.6[/tex]

[tex]7\frac{2}{5} = \frac{35}{5} +\frac{2}{5} =\frac{37}{5} =7.4[/tex]

7.02 < 7.4 < 7.5 < 7.6

7.02 < [tex]7\frac{2}{5}[/tex] < 7.5 < [tex]7\frac{6}{10}[/tex]

Answer:

it algebra

Step-by-step explanation:

10x-6x=4x

Then the equation becomes

4x+9=-19

Then you subtract the 9 from -19

4x=-28

Now you have to separate the 4 from x

4x/4 and -28/4

So now you get

X=-7

Answer:

Step-by-step explanation:

30.25g=296.6511625 m/s^2

The measure of the exterior angle is a = 54

Where is the exterior angle?

the exterior angle 2a = a + 10 + 44

                               2a  = a + 54

                                 2a - a = 54

                                      a = 54

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Answer:

Pues hablemos primero de lo que sucede antes de apagar la luz y usemos como ejemplo el viaje de un solo fotón.

Un fotón proveniente de un bombillo de luz blanca se dispara en línea recta hacia la pared. El material que cubre la pared, en este caso la pintura, tiene ciertas propiedades físicas y la energía del fotón es absorbida por un electrón de algún átomo de esa superficie. Ocurre una excitación del electrón, el cual ahora tiene más energía de la que normalmente tiene en su estado fundamental, y para regresar a su estado fundamental emite parte de esa energía como un nuevo fotón, este último de menor energía (frecuencia) que el anterior. La frecuencia dependerá del material y esa nueva frecuencia es la que da color a la pared. La luz blanca está compuesta por fotones de distintas frecuencias. Los de baja frecuencia son absorbidos y lo que se emite es en forma de calor, lo cual no puedes ver con tus ojos. Los de alta frecuencia tienen suficiente energía para que la energía que se re-emite sea visible y posiblemente sea re-emitida, cada vez con menos energía. Uno habla de que la luz “rebota” en el objeto. (Aunque “rebotar” no es necesariamente la acción correcta, voy a usar el término para simplificar).

Ahora digamos que ese fotón que “rebotó” en la pared rebota en otra pared y otra pared. Ese fotón es solo visible si en ese rebotar llega a tu ojo antes de que su energía sea demasiado baja. No podemos ver el calor ni las microondas que son fotones de baja energía. Al final la energía se va a convertir en calor, el cual es invisible al ojo humano.

Ese es el trayecto de un solo fotón. El bombillo produce un flujo de fotones en todas direcciones. Hay que recordar que esos fotones viajan a la velocidad de la luz. Cuando el bombillo se apaga, se interrumpe el flujo de fotones. Si se movieran a la velocidad del agua en una manguera, verías el flujo rebotando por varios segundos hasta que los fotones que más han rebotado desaparecen de tu vista por aquello de la baja frecuencia energética. Pero al viajar a la velocidad de la luz, el tamaño de la habitación se hace irrelevante y nuestra experiencia es prácticamente instantánea.

¿A donde va la luz? La luz no sale de la habitación sino que la calienta.

27.80% is percentage of items .

What percentage means?

Mean = 7

standard deviation = 3 ounces

Required % = p (5.6<x < 7.1 ) × 100 = ?

z = x - μ/σ = 5.6 - 7/2

 z = 7.1 - 7/2 = 0.05

∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )

   p( z < 0.05 ) - p (  z < - 0.7)

= 0.51994 - 0.24196 ≅ 0.2780

So, required % =  0.2780 × 100

                         = 27.80%

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8.32 Km is the distance of how much it would be covered

A unit rate means a quantity at a rate of one of something.

The distance traveled with 2 liters of petrol is 47.9 km.

A unit rate means a quantity at a rate of one of something.

It is written with a denominator of one. 

Example:

Man can walk 6km in 2 hours.

In one hour a man can walk 3 km.

We have,

A vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol.

This can be written as:

524/25 km = 7/8 liters

Multiply both sides by 8/7

8/7 x 524/25 km = 1 liter

23.95 km = 1 liter _____(1)

Now,

Multiply 2 on both sides of (1)

2 x 1 liter = 2 x 23.95 km

2 liter = 47.9 km

Thus,

The distance traveled with 2 liters of petrol is 47.9 km.

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It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.

A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.

Here is how the transformation of a function can occur

Any change can occur during the transformation of a function.

Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

A function sets the value of one set's elements to the value of another set's specified element.

Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.

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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

The function is a type of relation, or rule, that maps one input to a specific single output.

A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:

Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)

Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d

Stretching would be as Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given that the parent function is; f(x)=x³,

And the transformed function is; g(x)=(x+2)³ - 6.

Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

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The Solution:

Given the equation that modeled the population of fish after time (t) in years as below:

part 1:

We are to find the initial population of fish. This means we are to find the value of p when t = 0.

Part 2:

We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.

Note: double of 250 fish is 2x250 = 500 fish.

Dividing both sides by 3, we get

Taking the natural log of both sides, we get

Answer:

Step-by-step explanation:

So, you have to isolate the variable. Think of it as finding how many plants she gave fertilizer to. 0.4n+8=25, when moving the 8 to the other side, it becomes negative. 0.4n=25-8. 0.4n=17. You then find the variable n. think of it as dividing 17 by 0.4 or multiplying n a certain number of times to find the number of plants.17/0.4 is 42.5. therefore, she gave 42 plants fertilizer, depending on what your teacher wanted to count. If she says round down, 42. If she wants to round up, 43. If she wants to be specific, 42.5. I would personally put the decimal.

I WILL USE CROSS MULTIPLICATION

[tex] \frac{4}{7x} = 28 \\ 4 = 28(7x) \\ 196x = 4 \\ \frac{196x}{196} = \frac{4}{196} \\ x = \frac{1}{49} [/tex]

ATTACHED IS THE SOLUTION

Answer:

16

Step-by-step explanation:

7x=28x4

7x=112

x=112/7

x=16

Answer: 5.13

Step-by-step explanation:

1) Set up the equation

3.8(1.35)

2) Solve

5.13

Answer:

If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?

The most appropriate form for equation of circle will be given by-

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

What is equation of circle?

A round figure whose all points on the boundary maintains a fixed distance from a point known as the centre of the circle and the fixed distance is called the radius of the circle.

If radius of a circle is doubled, we will obtain the diameter of the circle.

Equation of circle

[tex](x-a)^2 + (y-b)^2 = r ^2[/tex]

where (a, b) is the centre of the circle and r is the radius of the circle.

Here,

[tex]x^2 + y^2 + 10x-6y + 15 = 0[/tex]

[tex]x^2 + 2\times x\times 5 + 5^2 -5^2 +y^2 -2\times y\times 3 + 3^2 - 3^2 + 15 = 0\\(x+5)^2 + (y-3)^2-25-9+15=0\\(x+5)^2 + (y-3)^2-19=0\\(x+5)^2 + (y-3)^2=19\\ (x+5)^2 + (y-3)^2=\sqrt{19}^2\\[/tex]

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

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The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

So, the flat rate is $7 and we're charged $0.65 per mile:

Then the suitable expression will be:

Cost if we traveled 15 miles:

So, 0.65x = y where x = 15.

It would cost $9.75 for 15 miles.

Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

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Answer:

Step-by-step explanation:

So, what you need to do is find out the formula for this question. And your answer will come out to be x=32

The total number of students that are on the team is e. 210 if the ratio of  freshmen to sophomores to juniors to seniors is 1:3:4:6

As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;

Freshmen = 1x

Sophomores = 3x

Juniors = 4x

Seniors = 6x

As the number of juniors on the team is 60, therefore;

4x = 60

To determine the value of x we divide both sides by 4;

4x/4 = 60/4

x = 15

Now the total number of students can be found by substituting the value of x;

1x + 3x + 4x + 6x

1(15) + 3(15) + 4(15) + 6(15) = 210

Hence, the total number of students on the team is 210.

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Let

y -----> candle heigh in centimeters

x ----> burning time in hours

In this problem we have the ordered pairs

(5,22.5) and (17,16.5)

step 1

Find out the slope

m=(16.5-22.5)/(17-5)

m=-6/12

m=-1/2 -----> is negative because is a decreasing function

step 2

Find out the equation in slope-intercept form

y=mx+b

we have

m=-1/2

point (5,22.5)

substitute

22.5=-(1/2)(5)+b

solve for b

b=22.5+2.5

b=25

therefore

y=-(1/2)x+25

step 3

For x=7 hours

substitute in the equation

y=-(1/2)(7)+25

y=-3.5+25

Answer:

translates up 8 and 5 left

Step-by-step explanation:

To find the distance (x) it translate up, -3 + x = 5 where x = 8

To find the distance (x) it translate left, 2 + x = 7 where x = 5

Answer:

(x, y) → (x-5, y+8)

Step-by-step explanation:

A translation is a type of transformation that moves a figure up, down, left or right.

Calculate the change in the coordinates by subtracting the coordinates of point D from the coordinates of point D':

[tex]\implies (x_{D'}-x_D, y_{D'}-y_D)[/tex]

[tex]\implies (2-7, 5-(-3))[/tex]

[tex]\implies (-5, 8)[/tex]

Therefore, to map point D onto point D', move 5 units left and 8 units up.

Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:

The expression given: 7/6 x 3  can be calculated to get 7/2

This is a basic math operation that helps to determine the product of two or more numbers.

The numbers given here include a whole number and a fraction

A fraction refers  to classification of numbers to be represented as having a stroke dividing the two groups of numbers.

The numbers on top is referred to as numerators while the numbers below is referred to as the denominator

in the question the fraction is 7/6: The numerator is 7 while the denominator is 6

= 7/6 * 3

= 7/2

= 3.5

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The expression which is equivalent to; 2x² - 2x + 7 as required in the task content is; 2 (x - 0.5)² + 6.5.

It follows from the task content that the expression which is equivalent to; 2x² - 2x + 7 is to be determined.

Therefore, since the expression whose equivalent is to be determined is; 2x² - 2x + 7; we have;

2x² - 2x + 7

By completing the square method; we have;

2(x² - x) + 7

2 {(x - 0.5)² - 0.25} + 7.

2 (x - 0.5)² - 0.5 + 7

2 (x - 0.5)² + 6.5

Therefore, the required expression which is equivalent to the given expression is; 2 (x - 0.5)² + 6.5.

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The annual percentage yield is 1.55% for any account if the interest is compounded daily.

Given that Island bank is advertising a special 1.55% APR for long-term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily.

Principal (P) = $40000

Interest rate(r) = 1.55% = 0.0155

Number of periods (n) = 365

The formula for Annual Percentage Yield (APY) for an account that is compounded continuously is given as

APY = [1 + (r/n)ⁿ - 1]

Substitute the values in the formula to get

= [1 + (0.0155/365)³⁶⁵ - 1]

= [1 + 0.000042)³⁶⁵ - 1]

= [1.000042]³⁶⁵- 1

= 1.015448 - 1

= 1.55%

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The amount of money that Kamauri has at first will be 32.22.

From the information, it was stated that after paying 5.12 for salad, Kamauri has 27.10.

Based on the information given, the total amount of money that he had at first will be the addition of the cost of salad and the change left.

This will be illustrated as:

= 5.12 + 27.10

= 32.22

The amount is 32.22.

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After paying 5.12 for salad, Kamauri has 27.10. What was the total amount of money that he had at first?

The various values using mathematical operations are;

1) B: 70

2) C:  1300

3) A: 0.0063

4) B: 0.0037

5) B:  80

1) We want to multiply 0.7 times 100.

Now, 0.7 can be expressed as 0.7 = 7/10. Thus;

0.7 * 100 = 7/10 * 100 = 70

2) We want to multiply 0.13 by 10000.

0.13 can be expressed as;

0.13 = 13/100. Thus;

0.13 * 10000 = 13/100 * 10000 = 1300

3) We want to multiply 0.63 times 0.01.

They can be expressed as;

63/100 * 1/100 = 63/10000 = 0.0063

4) Divide 0.37 by 100.

0.37 can be expressed as 37/100. Thus;

0.37/100 = 37/100 ÷ 100

= 37/100 * 1/100 = 37/10000 = 0.0037

5) Divide 0.8 divided by 0.01.

They can be expressed as;

8/10  ÷ 1/100

= 8/10 * 100/1

= 80

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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation, i.e, a new weight function, as follows: We want the elements with maximum weight to have minimum weight and. In other words, two weight functions need to be mutually opposite in this sense. Therefore, if we denote the maximum weight of all the elements with w ∗ : w ∗ = max w(x) x ∈ S we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly. Since we want the weight function to be strictly positive, we finish our construction with: w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation,

or a new weight function, as follows:

We want the elements with maximum weight to have minimum weight a In other words, two weight functions need to be mutually opposite in this sense.

Therefore, if we denote the maximum weight of all the elements with

w ∗ : w ∗ = max w(x) x ∈ S

we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly.

Since we want the weight function to be strictly positive, we finish our construction with:

w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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Answer:

-1

Step-by-step explanation:

when you change g[×] to g[-2] , 3x+5 change to 3[-2] +5

y = f(2x)  ⇒ Shrink the graph of function f(X) by half horizontally .

What is function and example?

y = f((1/2)x)) ⇒ Stretch the graph of f(x) horizontally by factor 2 .

y=2f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

                     Shrink the graph twice ( vertically) .

y = f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

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In the polynomial expression f(x) = x³ + px² +  qx +r, the values of p is 1/5, q is -66/5 and r is 12.

Polynomial:

Polynomial means an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Given,

Here we have the polynomial f(x) = x³ + px² +  qx +r

And it is divisible by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2.

Here we need to find the value of p, q and r.

Let us consider that the equations,

x + 2 = 0 then x = -2

x - 1 = 0 then x = 1

x - 3 = 0 then x = 3.

Now, apply these values on the polynomial expression then we get,

f(-2) = (-2)³ + p(-2)² +  q(-2) +r = -48

f(-2) = -8 + 4p - 2q +r = -48

f(-2) = 4p - 2q +r = -48 + 8

f(-2) = 4p - 2q + r = -40 ----------------------(1)

Apply the value of x as 1, then we get

f(1) = (1)³ + p(1)² +  q(1) +r = 0

f(1) = 1 + p + q + r = 0

f(1) = p + q + r = -1 ----------------------(2)

Apply the value of x as 3, then we get

f(3) = (3)³ + p(3)² +  q(3) + r = 2

f(3) = 27 + 9p + 3q + r = 2

f(3) = 9p + 3q + r = -25 ----------------------(3)

Now we have to solve the equation (2) and (1), then we get,

=> (4p -p) + (-2q - q) + (r - r) = -40 - (-1)

=> 3p -3p = -39

Divide it by 3, then we get

=> p - q = -13 ----------------------(4)

Similarly, solve equations (2) and (3), then we get,

=> (9p - p) + (3q - q) + (r - r) = -25 - (-1)

=> 8p + 2q = -24

Divide it by 2, then we get,

=> 4p + q = -12 ---------------------------(5)

Solve the equations (4) and (5), then we get,

=> (4p + p) + (q - q) = -12 - (-13)

=> 5p = 1

=> p = 1/5

Apply the value of p on equation (4), then we get the value of q as,

=> (1/5) - q = -13

=> -q = -13 -1/5

=> -q = -66/5

Apply the value of p and q on equation (2), then we get,

=> 1/5 + (-66/5) + r = -1

=> -65/5 + r = -1

=> -13 + r = -1

=> r = 12

Therefore, the value of p is 1/5, q is -66/5 and r is 12.

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