Find missing formula for both questions


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Answer:

Axis of Symmetry: x = 1

Vertex: (1,7)

Step-by-step explanation:

The standard form of an equation for a parabola is

ax² + bx + c

So converted to standard form, the equation is

y = -x² + 2x + 6,

where

a = -1,  b = 2, and c = 6

The axis of symmetry of a parabola follows the formula

x = -b/(2a)

--> x = -2/(2*(-1))

--> x = 1

This is also the x-coordinate of the vertex.

To get the y-coordinates of the vertex, substitute 1 into x:

y=6+2x-x²

y=6+2(1)-(1)²

y = 7

So the coordinates of the vertex is (1,7)

Answer: 26 pays

Step-by-step explanation:

y = 2.115 + 0.842

= 2.957

no explanation

The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.

What is  inflection points ?

An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.

First find the extrema (zeros of the derivative).

f (x) = 12x^5 - 5x^4

f '(x) = 60x^4 -20x^3

= 20x^3(3x - 1)

x = 0      x =1/3

So the extrema occur at x = 0 and x =1/3.

Now find the inflection points (zeros of the 2ndderivative).

f '(x) = 60x^4 -20x3^

f ''(x) = 240x^3 -60x^2

= 60x^2(4x - 1)

x = 0      x =1/4

The inflection points occur at x = 0 and x =1/4.

Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.

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The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.

What is  inflection points ?

An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.

First find the extrema (zeros of the derivative).

f (x) = 12x^5 - 5x^4

f '(x) = 60x^4 -20x^3

= 20x^3(3x - 1)

x = 0      x =1/3

So the extrema occur at x = 0 and x =1/3.

Now find the inflection points (zeros of the 2ndderivative).

f '(x) = 60x^4 -20x3^

f ''(x) = 240x^3 -60x^2

= 60x^2(4x - 1)

x = 0      x =1/4

The inflection points occur at x = 0 and x =1/4.

Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.

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The simplest form of  [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be  8.66025403784 .

A fraction is  in  its  simplest form   when   the    numerator   and   the denominator have  no common factors besides one.

Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.

Given the equation is;

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

Now solving it ,

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

By adding this we get,

[tex]5\sqrt{3}[/tex]  (∵ [tex]\sqrt{3}[/tex] is common in both )

= 8.66025403784

The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is  8.66025403784.

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The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5

From the question, we have the following parameters that can be used in our computation:

x^4 – 3x^3 – 7x + 1 ÷ x + 2

Rewrite as

x⁴ – 3x³ – 7x + 1 ÷ x + 2

This means that

Divisor = x + 2

Dividend = x⁴ – 3x³ – 7x + 1

Using the synthetic division, we have the following setup

-2 |    1     -3    -7     1

Bring down the first factor

-2 |    1     -3    -7     1

        1

Multiply by -2

-2 |    1     -3    -7     1

              -2

        1

Repeat the above steps as follows

So, we have

-2 |    1     -3    -7     1

              -2    10    -6

        1      -5    3    5

The last number represents the remainder of the division

This means that

Remainder = 5

Quotient = x³ - 5x² + 3x

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Answer:

225 minutes

Step-by-step explanation:

rate x time x people = 1 job

The rate:

[tex]\frac{1 job}{3poplex5 hours}[/tex]

[tex]\frac{1}{15}[/tex] x t x 4 = 1

[tex]\frac{4}{15}[/tex] t = 1  Multiply both sides by [tex]\frac{15}{4}[/tex]

[tex](\frac{15}{4})[/tex][tex]\frac{4}{15}[/tex] t = 1 [tex](\frac{15}{4})[/tex]

t = [tex]\frac{15}{4}[/tex] hours

[tex]\frac{15}{4}[/tex] x [tex]\frac{60}{1}[/tex]  To find out how many minutes.  4 and 60 share a factor of 4.  I will use that to work with smaller numbers

[tex]\frac{15}{1}[/tex] x [tex]\frac{15}{1}[/tex] = [tex]\frac{225}{1}[/tex] = 225 minutes

The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.

Let M = speed of the motorcycle.

Hence, speed of the car = 2M - 30.

Distance covered = Time taken x Speed.

Hence in 2 hours,

Distance covered by motorcycle = 2M

Distance covered by car = 2(2M-30).

Given, the car is 20 miles ahead of the motorcycle.

Hence,

2(2M-30) = 2M + 20

4M-60 = 2M + 20

2M = 80

M = 40

2M-30 = 2(40)-30 = 80-30 = 50

Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.

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Answer:

It's not true = as you can see, the value of y is not the same, so the whole thing is false.

Step-by-step explanation:

First, Solve for y:

(5 y + 3)^2 - 20 = 0

Add 20 to both sides:

(5 y + 3)^2 = 20

Take the square root of both sides:

5 y + 3 = 2 sqrt(5) or 5 y + 3 = -2 sqrt(5)

Subtract 3 from both sides:

5 y = 2 sqrt(5) - 3 or 5 y + 3 = -2 sqrt(5)

Divide both sides by 5:

y = 2/sqrt(5) - 3/5 or 5 y + 3 = -2 sqrt(5)

Subtract 3 from both sides:

y = 2/sqrt(5) - 3/5 or 5 y = -3 - 2 sqrt(5)

Divide both sides by 5:

Answer: y = 2/sqrt(5) - 3/5 or y = -3/5 - 2/sqrt(5)

___________________________

Solve for y:

(5 y - 3)^2 = 0

Take the square root of both sides:

5 y - 3 = 0

Add 3 to both sides:

5 y = 3

Divide both sides by 5:

Answer: y = 3/5

Answer:

c = 5

Step-by-step explanation:

The slope is the change in y over the change in x. Or as I memorized RISE OVER RUN. Also in physics, you can write ∆y/∆x. Delta (∆) just means change.

Using this equation we have

The slope = m = 3 = ∆y/∆x

m = (-1 - c)/(-8 - -6) = (-1 - c)/(-8+6) = (-1 - c)/(-2) = 3

Now multiply both sides of the equation by -2 and you get

(-1 - c) = 3•(-2) = -6

Almost there!

Now we have the equation

-1 - c = -6

Add one to both sides and you get

-1+1-c = -6 +1

Simplified that equals

-c = -5

Then to get our answer we have to go from negative to positive.

Multiplying both sides by -1 we get

-1 • -c = -1 • -5

c = 5

Now CHECK!

Plug c into the equation ∆y/∆x and you get a slope of 3 which proves the answer is right.

The value of x is 12 .

Given ,

angle DEH as exterior angle and angle  E, C, D as interior angles .

What is the relation between interior & exterior angles of a triangle ?

Interior angle refer to all those angles that are inside a shape. On the other hand, the exterior angle is an angle that is made by the side of the shape and a line drawn out from an adjacent side.

Furthermore, the exterior angle is equal to the sum of the non-adjacent interior angles .

Calculations

angle  DEH = angle C + angle D

9x + 22 = 5x + 10 + 60

9x - 5x = 70 - 22

   4x     = 48

     x      = 12

The value of x is 12 .

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Answer:

0.0086

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.

Answer:

The total cost for the three buildings was $6,034,250.

Step-by-step explanation:

Given,

The first sold for $1,259,300,

the second sold for $2,839,750,

the third sold for $1,935,200.

We add these three sold cost of apartment buildings

$1,259,300 + $2,839,750 +  $1,935,200 = $6,034,250.

To calculate the total cost of three things, you will need to add the individual costs of each item together.

1. Determine the cost of each item. Add together the cost of all three items. This total is the cost of the three items.

2. If the items are sold as a package, determine the cost of the package. This is the cost of the three items.

3. If the items are sold at a discounted rate, calculate the total cost of each item after the discount has been applied. Add together the costs of the three items after the discount has been applied. This total is the cost of the three items.

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Answer:

To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:

Time (minutes) Water Level (centimeters)

0 0

1 6

2 12

3 18

4 24

5 30

6 36

7 42

8 48

9 54

10 60

11 66

12 72

13 78

14 84

15 90

16 96

17 102

18 108

19 114

20 120

We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).

The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.

Step-by-step explanation:

The equation of the line is (b) y = 2.25x - 6.25

From the question, we have the following parameters that can be used in our computation:

Points = (3, 1/2) and (5, 5)

A linear equation can be represented as

y = mx + c

Substitute the known values in the above equation, so, we have the following representation

1/2 = 3m + c

5 = 5m + c

Subtract the equations

2m = 4.5

Divide by 2

m = 2.25

Substitute m = 2.25 in 5 = 5m + c

5 = 5 * 2.25 + c

So, we have

c = 5 - 5 * 2.25

Evaluate

c = -6.25

Recall that

y = mx + c

So, we have

y = 2.25x - 6.25

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Complete question

Select the equation for the line crossing the points (3,1/2) and (5,5).​

(a) y = 5x + 2

(b) y = 2.25x - 6.25

(c) y = 2.25x + 6.25

(d) y = -5x - 2

Answer:

Step-by-step explanation:

Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.

On solving the provided question, we can say that - by equation, total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.

R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr

total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

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The angle of the elevation comes to be 41.94 degrees.

The angle of elevation is the angle that is to be formed between the horizontal line and the given line of sight. If the line of sight is upward from the given horizontal line, then the angle formed is an angle of the elevation.

The most crucial area of mathematics is trigonometry. Combining the Greek "Trigonon" and "Metron," which respectively mean "triangle" and "measure," creates the word "trigonometry." It is the examination of the relationship between a right-angled triangle's sides and angles. By employing formulas and identities based on this relationship, it is thus possible to determine the measure of a right-angled triangle's unknown dimensions.

As in the case of right angled Triangle

From Trigonometry,

tan (α) =  [tex]\frac{124}{138}[/tex]

α = arctan(  [tex]\frac{124}{138}[/tex] )

α = 41.94 degrees

and in radians = 0.732

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Answer:

15/8

Step-by-step explanation:

Doing the inverse would be to simply flip the fraction which gives us 15/8

hope this helped and have a good day/night

The solutions to the equation word problems are as follows;

1) Amount jane will have is 50 + 2d

2) Amount Elis will have = 24 + 6d

3) The equation is; 50 + 2d = 24 + 6d

4) Amount each has saved = $63

We are given that;

Amount Jane has = $50

Amount Elis has = $24

Amount saved by Jane each day = $2

Amount saved by Elis each day = $6

1) After d days of saving, amount jane will have is;

A = 50 + 2d

2) After d days of saving, amount Elis will have is;

A = 24 + 6d

3) The equation that will be used to show when Joan and Elis would have saved same amount is;

50 + 2d = 24 + 6d

4) 50 + 2d = 24 + 6d

26 = 4d

d = 26/4

d = 6.5 days

Amount each has saved = 50 + 2(6.5) = $63

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Answer:

The surface area of a sphere is 2461.76 units.

Step-by-step explanation:

where,

π = 3.14 or 22/7

r = radius of sphere

Here, we know that

radius = diameter ÷ 2 = 28/2 = 14 units

So,

A = 4 π r²

A = 4 × 3.14 × (14)² units

A = 12.56 × 196 units

A = 2461.76 units

Thus, The surface area of a sphere is 2461.76 units.

Answer:  the surface area of the sphere of diameter 28cm is 2464 cm²

Step-by-step explanation:

     Given, diameter = 28 cm

      hence, radius of the sphere = d/2 = 28/2 =14 cm

 Therefore, the surface area of a sphere of radius (r) = 4пr²

                 where п= 22/7= 3.14

                                            = 4×3.14×14×14

                                            = 2464 cm²

Answer:

  24 years

Step-by-step explanation:

You want to know the number of years it will take an account's value to exceed $300, given it was opened with $100 and earns 4.8% interest compounded annually.

The value of the account earning compound interest is ...

  A = P(1 +r)^t

where principal P is earning interest at rate r for t years.

Solving for t, we get ...

  A/P = (1 +r)^t

  log(A/P) = t·log(1+r)

  t = log(A/P)/log(1 +r) = log(300/100)/log(1 +0.048)

  t = log(3)/log(1.048) ≈ 23.433

For the value to exceed $300, it will take 24 years.

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Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Solving a system of equations we can see that the length is 22 feet and the width is 16 feet.

For a rectangle of length L and width W, the area is given by the formula:

A = L*W

Here we know that the rectangular room has an area of 352 square feet, and we also know that the length of the room is 6 feet mroe than the width of the room, then we can write a system of equations:

352 = L*W

L = W + 6

To solve that system, we can substitute the second equation in the first one, we will get:

352 = (W + 6)* W

352 = W^2 + 6W

W^2 + 6W - 352 = 0

So we have a quadratic equation, the solutions give:

[tex]W = \frac{-6 \pm \sqrt{6^2 - 4*1*(-352)} }{2} \\\\W = \frac{-6 \pm 38 }{2}[/tex]

We take the positive value as the with, so:

W = (-6 + 38)/2

W = 16

And the length is 6 feet longer than that, so:

L = 16 + 6 = 22

Then the length is 22 feet, and the width is 16 feet.

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Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:

P' = P ← 6 ↓ 2

Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.

Answer: -27

Step-by-step explanation:

To solve for x, we have to make f alone.

f+24=-3       [subtract both sides by 24]

f=-27

The answer is -27.

Answer: -27

Step-by-step explanation: f+24+-3 to find f subtract 24 from -3. which equals -27 it might not be the proper way but it works. :)

The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

Hence, The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

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The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]

What are Exponents?

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.

Solution:

To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved

Since we are required to find the number of times the value os greater so we will divide the numbers

3^21 / 3^19

By rule of exponents if a^b/a^c then we can write it as a^(b-c)

Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9

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