a.The product of two integers is -20.Find the largest possible sum of the two integers?b.The product of two integers is -30.Find the largest possible sum of the two integers.c.Can you generalize the result of a and b?

Answer:

Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.

Step-by-step explanation:

The graph of function f(x) is the parent function.

(Parent functions are the simplest form of a given family of functions).

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Parent function:

[tex]f(x)=x^3[/tex]

Step 1

Multiply the parent function by 6:

[tex]\implies 6f(x)=6x^3[/tex]

Therefore, this is a vertical stretch by a factor of 6.

Step 2

Now make the function negative:

[tex]\implies -6f(x)=-6x^3[/tex]

Therefore, this is a reflection in the x-axis.

Step 3

Finally, add 2 to the function:

[tex]\implies -6f(x)+2=-6x^3+2[/tex]

Therefore, the function has been translated 2 units up.

Conclusion

Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.

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Answer:

1) (4 - 2 + 1)^3

2) 3^2(4 - 1)

3) 3^4/2 + 1

It can be either one of those

Answer:

Step-by-step explanation:

how to make 27 using 1,2,3,4 only once

Remember Pemdas

(2 * 4 + 1) * 3 =

(8 + 1) * 3 =

9 * 3 =

27

Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that

Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.

So, the system of equations to be solved is

[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×(3y+30)+5y=2820

Solving:

3×3y+3×30+5y=2820

9y+90+5y=2820

9y+5y=2820 - 90

14y= 2730

y= 2730÷ 14

y= 195

Remembering that x=3y +30, then:

x= 3×195 + 30

Solving

x=585 +30

x=615

Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

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Answer:

See below

Step-by-step explanation:

Slope = rise / run

           from 0,-1   to  1.5 , 0

               this is    1 / 1.5    =   2/3

y xis intercept = -1

y = 2/3 x   -1            Slope intercept form

2/3 x - y   = 1             another form

2x - 3y = 3                Standard form (I think this is 'standard form' ....yah?)

The decimal expansion of 2 1/6 is 2.167

The expression is given as:

2 1/6

Rewrite the expression as:

2 + 1/6

Express 1/6 as decimal

2 + 0.167

Evaluate the sum

2.167

Hence, the decimal expansion of 2 1/6 is 2.167

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Answer: -4 pounds

Step-by-step explanation:

       The hibernating animal lost 4 pounds. This means we are 4 below wherever the animal's weight was in the beginning. This can be represented with a negative number;

          -4 pounds

The expression for the total revenue from x thousand sales is 155,000x - 100x².

The value of x is 775 cents and the maximum revenue is $60,062,500.

First, come up with an expression for total revenue from x thousand sales:

= (155  - x /10 ) × x × 1,000 units

= 155,000x - 100x²

The value of x would then be:

Derive the function from the total revenue function to give:

0 = 155,000 - 200x

x = 775 cents

The maximum revenue is therefore:

= 155,000(775) - 100(775)²

= $60,062,500

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Answer:

6=6

Step-by-step explanation:

This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1

Hope this helps

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]

[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]

[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

x = -3

Explanation:

[tex]\rightarrow \sf \sqrt[3]{\sf 3x + 1} = -2[/tex]

[tex]\rightarrow \sf \sf 3x + 1 = (-2)^3[/tex]

[tex]\rightarrow \sf \sf 3x + 1 = -8[/tex]

[tex]\rightarrow \sf \sf 3x = -8-1[/tex]

[tex]\rightarrow \sf \sf 3x = -9[/tex]

[tex]\rightarrow \sf \sf x = -3[/tex]

Answer:

[tex]\sqrt[3]{3x+1} =-2\\(\sqrt[3]{3x+1})^{3} =(-2)^{3} \\3x+1=-8\\3x=-9\\x=-3[/tex]

Hope it helps!

Answer:

6x = 9

Step-by-step explanation:

4x-5y  = 12

2x+5y  = -3

Add the equations together

4x-5y  = 12

2x+5y  = -3

-------------------

6x + 0y = 9

6x = 9

Answer:

B. 6x = 9

Step-by-step explanation:

4x - 5y = 12

+ 2x + 5y = -3

____________

6x + 0 = 9

Hence, option B. 6x = 9 is the correct answer.

Step-by-step explanation:

To get the angle of QPR, we subtract 90-60=30. This proves that the triangle is a 30,60,90, as angle QRP must be 60°. To get the area, we must know the length and width. These can be derived from a known relationship within 30,60,90 triangles.

[tex]qp = \frac{\sqrt{3}}{2} n[/tex]

[tex]qr = \frac{1}{2} n[/tex]

[tex]pr = n[/tex]

because half of pr is 10, we can conclude that n is 20. So we plug 20 into N for QP and QR, and get values of

[tex]qp = 5 \sqrt{3} [/tex]

[tex]qr = 5[/tex]

Now we multiply (l*w)/2 and get:

[tex] \frac{(5 \sqrt{3} \times 5)}{2} = 21.65 \: units[/tex]

Answer:

- 7x + 5y= (-11) -------(1)

-4x + 3y,= (-7) ----------(2)

Multiplying eq 1 with 3 and eq 2 with 5

3( -7x + 5y) = 3(-11)

5(- 4x + 3y) = 5(-7)

-21x + 15y = (-33)

-20x + 15y,= (-35)

Subtracting both the eq.

-x = 2

x = (-2)

Putting this value in eq. 1

- 7x + 5y= (-11)

-7(-2)+ 5y= (-11)

14 + 5y = (-11)

5y = (-11) - 14

5y= (-25)

y = (-5)

The price elasticity of demand for this product is approximately will be 1.

The price elasticity is given as

[tex]\rm PE = \dfrac{\dfrac{Q_f-Q_i}{Q_f+Q_i}}{\dfrac{P_f-P_i}{P_f+P_i}}\\\\\\[/tex]

The quantity of a good demanded rises from 1000 to 1500 units when the price falls from $1.50 to $1.00 per unit.

The price elasticity of demand for this product is approximately will be

[tex]\rm PE = \dfrac{\dfrac{1500-1000}{1500+100}}{\dfrac{1.5-1}{1.5+1}}\\[/tex]

On further solving, we have

PE = (500 / 2500) x (2.5 / 0.5)

PE = 1

The price elasticity of demand for this product is approximately will be 1.

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Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

[tex]\textsf {The function is :}[/tex]

[tex]\boxed {h(x) = 2x - 2}[/tex]

[tex]\textsf {Finding the missing values :}[/tex]

[tex]\textsf {The table :}[/tex]

[tex]\left[\begin{array}{ccc}x&f(x)\\-4&-10\\-2&-6\\1&0\\4&6\\5&8\end{array}\right][/tex]

Answer:

D

Step-by-step explanation:

You do 180-125 to find the angle (because its a straight line) and then you get 55, then you have a right angle so you have 90 and then you do:

55+90+p=180

and then you get

145 +p=180

180-145=35

p=35

Substituting in y=15,

[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]

Answer:

£8 : £12

Step-by-step explanation:

2:3 means that there are 5 parts in total. Let parts be represented as p. 5p = £20, p = £4. That meant 2 parts = £8 and 3 parts = £12. Hence to share £20 in the ratio 2:3 is £8 : £12

Answer:

9.1

Step-by-step explanation:

3(9.1)=27.3

27.3÷3=×

×=9.1

Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.

A linear function is modeled by:

y = mx + b

In which:

The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:

They will be equal when:

A(t) = H(t).

Hence:

30000 - 1000t = 500t

1500t = 30000

t = 30000/1500

t = 20 minutes.

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The correct classification for √18 is an irrational number, non-repeating decimal.

The correct classification of √18 is an irrational number.An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and cannot be written as a terminating or repeating decimal.

√18 cannot be simplified to a fraction, and when expressed as a decimal, it is a non-repeating decimal that continues indefinitely without a pattern.

Therefore, the correct classification for √18 is an irrational number, non-repeating decimal.The number √18 is the square root of 18. An irrational number is a number that cannot be expressed as a fraction of two integers (a/b) where a and b are integers and b is not equal to zero.

When we calculate the square root of 18, we find that it is approximately 4.24264. However, this decimal representation continues indefinitely without repeating or terminating. It does not settle into a pattern of digits that repeats infinitely like a rational number or terminate after a finite number of decimal places.

Since √18 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating, it falls under the category of an irrational number.

Therefore, the correct classification of √18 is an irrational number, specifically a non-repeating decimal.

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Here you go! please make sure you read it all too understand it, and make sure you try work before asking for help :D Have a awesome day/night

Answer:735

Step-by-step explanation:I was hoping you’d have another. Dv/dt=d/dt((7+5t)^3)=3x5x((7+5t)^2)=15x49. Does this work?

A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. The shape can be completed as shown below.

A balanced and proportionate likeness observed in two sides of an item is characterized as symmetry. It signifies that one side is a mirror image of the other. The line of symmetry is the imaginary line or axis along which you can fold a figure to produce the symmetrical halves.

The shape can be completed as shown below, so that the complete shape is symmetrical about the given axis.

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The percentage decrease would be 70 percent.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The price of an item has dropped to 27$ today. Yesterday it was 90.

90 - 27 = 63

The percentage decrease;

63 / 90 x 100= 70%

Hence, The percentage decrease would be 70 percent.

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We have that the ways 5-person committee such that exactly 2 local business owners are represented is mathematically given as

N=5940

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The Probability that 2 local business owners are represented on the committee is given by finding the ways they can be seated amongst the 5

Generally, 2 local business owners are represented is mathematically given as

N=11C3 x 9C2

Therefore

N=165 x 36

N=5940

Therefore the way 5-person committee such that exactly 2 local business owners are represented is mathematically given as

N=5940

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Answer:

26.2 feet

Step-by-step explanation:

tan(50°) = h/22

h = 22 × tan(50°) = 26.2 feet

Answer:

8

Step-by-step explanation:

8*25=2.00

2.00+.90=2.90

Answer:

1256 cm

Step-by-step explanation:

First we must find the perimeter, because the perimeter is equal to 1 revolution.

The perimeter of any circle is Pi(Diameter)

3.14*20

62.8 cm is the perimeter of the bike wheel.

Because the perimeter is basically a revolution, we can multiply 62.8 by 20 to get:

1256 cm

The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].

The question can't be solved because we can't have negative sign under square root

Answer:

 -5 +6i

Step-by-step explanation:

Square roots of negative numbers are imaginary. This is asking for the difference of two complex numbers. A suitable calculator can show you what that is.

__

We know that √(-1) ≜ i. This means the radicals can be simplified to ...

  [tex]\sqrt{-81}=\sqrt{9^2(-1)}=9\sqrt{-1}=9i\\\\\sqrt{-9}=\sqrt{3^2(-1)}=3\sqrt{-1}=3i[/tex]

So the expression becomes ...

  (4 +9i) -(9 +3i)

Like terms can be combined in the usual way. For the purpose here, i can be treated as though it were a variable.

  (4 +9i) -(9 +3i) = 4 +9i -9 -3i

  = (4 -9) +(9 -3)i

  = -5 +6i