The equation $f\left(x\right)=2x-9$ translated 6 units up is $g\left(x\right)=$ .

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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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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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 parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

The given equation is 3x+3y²+6y+3=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Left

Vertex: (0, -1)

Focus: (-1/4, -1)

Axis of symmetry: y=-1

Directrix: x = 1/4

The coordinate points to plot (2, 0.41), (-2, -2.41), (-1, 0), (-1, -2) and (0, -1).

The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

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Answer:

-1

Step-by-step explanation:

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

The elevation is 848 feet.

The word elevation is often used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying aeroplanes or orbiting satellites, and depth is used to describe locations below the surface.

A geographical feature's elevation is determined by how high it is above the mean sea level (MSL). Accordingly, elevation is the distance between the height that corresponds to the ocean's surface and the top of the feature.

Given:

Hilda hiked up 530 feet,

down 602 feet,

up 1003 feet,

and down 89 feet to get to the lake.

Taking all similar cases together

Hiked up

= 530 + 1003

= 1533 feet

and, hiked down

=602+83

= 685

Thus, the elevation is

= 1533 - 685

= 848

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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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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:

Answer down below!

Step-by-step explanation:

(Part a):

So we have the information that after 20 minutes, the submarine descended 480 feet.

To find how many feet it descended per minute, all we need to do is divide 480 and 20 which will give us 24

Every 1 minute, the submarine descended 24 feet.

(Part b):

Now that we have how many feet it descended per minute, we have to make an expression that goes along with it.

Our unknown variable in this case will have to have to be the feet.

We can use the letter f to express that. We can also use the letter m to express our minutes in the end

So after 24(f) = m

(Part c):

After 5 Minutes: 120 ft

After 10 Minutes: 240 ft

After 15 Minutes: 360 ft

After 18 Minutes: 432 ft

Answer:

-3

Step-by-step explanation:

It was quite easy

Answer:

Step-by-step explanation: factor out x2

from the expression x2 (x+11) -3x-33

Factor out-3 from the expression x2 (x-+11) -3(x+11)

Factor out x+11 your solution is x2 (x+11) (x-3).

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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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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Answer:

400

Step-by-step explanation:

=

1

We know that:

3 R=4% 1 = 48

T =3 R = 4% into formula 48 2 Substitute

1=Prt

48= Prt

Solve the equation:

3 × 0.04x= 48

3

X = 400

so Pablo invested 400$

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:

6.3 * 10^3

Step-by-step explanation:

6.3 * 10^3

:]

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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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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If she wants to meet her target distance 3/20 steps need to be taken.

Emily made the decision to walk 4/5 kilometers every day in order to keep healthy. She walked a distance of 2/5 miles to work and a distance of 1 mile for lunch.

The desired range is 4/5 miles.

walked for 2/5 miles and for 1/4 miles.

Total miles walked is [tex]\frac{2}{5} + \frac{1}{4}[/tex]

= [tex]\frac{13}{20}[/tex]

Mileage walked overall is +

LCD is 20

add the fractions after matching the denominators

The desired range is 4 to 5 miles.

Now deduct the distance you walked from the goal distance.

[tex]\frac{4}{5} - \frac{13}{20} \\\\\frac{16}{20} - \frac{13}{20} \\\\\frac{3}{20}[/tex]

the required walking distance is 3/20

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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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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?

Answer:

a)

f(1/2) = 2

g(-1) = -3/2

Step-by-step explanation:

for f(x) = 2x + 1 substitute the x with 1/2

2(1/2) +  1 then solve

1+1

2

for g(x) = 3x - 1/2x + 1 substitute with -1

3(-1) - 1/2(-1) +1 then solve

-3 + 1/2 + 1

-3/2

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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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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Answer:

Step-by-step explanation:

30.25g=296.6511625 m/s^2

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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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.

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?