In an arithmetic series, s40 = 1900 and u40 = 106. find the value of the first term and the common difference.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

-x² + 7x + 5 is the domain of all real numbers.

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Let the two functions be f and g then f(x) = 7x + 5 and g(x) = x².

we have to calculate (g - f)(x)

Which is equivalent to:

(g - f)(x) = g(x) - f(x)

Taking the two functions and substituting them into this expression, we get,

g(x) - f(x) = (7x + 5) - (x²)

simplifying the above function, we get

g(x) - f(x) = -x² + 7x + 5

Therefore, (g - f)(x) = -x² + 7x + 5.

We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]y=7-3x-2x^2\implies \cfrac{dy}{dx}=-3-4x\implies \stackrel{\textit{setting the derivative to 5}}{5=-3-4x} \\\\\\ 8=-4x\implies \cfrac{8}{-4}=x\implies \boxed{-2=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = -2, what's "y"?}}{y=-7-3(-2)-2(-2)^2}\implies y=-7+6-8\implies \boxed{y=-9} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-2~~,~~-9)~\hfill[/tex]

No extraneous solution to the equation

The equation given is

   3[tex]\sqrt{x}[/tex] = 6

Now we have to find the value of x.

[tex]\sqrt{x}[/tex] = 2

[tex](\sqrt{x} )^{2}[/tex] = [tex]2^{2}[/tex]

x = 4

To find whether it is an extraneous solution or not put the value of x in the given equation.

3[tex]\sqrt{4}[/tex] = 6

3 × 2 = 6

6 = 6

Therefore we get to know that there is no extraneous solution.

x = 4 is the solution of the equation.

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The value of x is 5 which is option (D) .

It is given that 25/20 = x/4

On simplifying , we get

          [tex]\frac{25}{20} =\frac{x}{4} \\\\x=\frac{25\times4}{20} \\\\x=\frac{100}{20} \\\\x=5[/tex]

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The complete question is mention below :

What value of x makes this proportion true? 25/20 = x/4

A.6

B.20

C.9

D.5

simplify answers to each algebra equation

1) 9x + 13

2) 3x - 16

3) 5x + 17

4) x + 13

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.

on solving the equation we get the solution of algebra as

9x +13

3x-16

5x+17

x+13

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Answer:it’s 200 Oumou

Step-by-step explanation:203-3=200

The values for 4f(x)+2 g(x) = 2x²- 2x + 24

Given :  f(x)=2x+5

           g(x)=x²-3x+2

Solution:

          4f(x) =  8x+20

           2g(x) = 2x²-6x+4

           4f(x) + 2g(x) = 8x+20 + 2x²-6x+4

          4f(x) + 2g(x) = 2x²- 2x + 24

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Two or more expressions with equal sign in between is called as Equation. The value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.

Two or more expressions with equal sign in between is called as Equation.

The given equation is y=-2x2+4x+4

Where y=4

4=-2x2+4x+4

-2x^2+4x=0

x(-2x+4)=0

x=0 and -2x=-4

x=2

Therefore the value of x is 2 and 0 when y=4 for equation y=-2x2+4x+4.

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Comparing the price of a 50000 mercedes to the price of a 40000 lexus The absolute price difference is 10000 while the relative price difference is 20%

Absolute difference refers to the gap between the prices. This implies the amount one has more than the other.

This could be solved by subtraction an is solves as follows:

price of a mercedes -  price of a lexus

= 50 000 - 40 000

= 10 000

Here, the price difference is expressed in percentage of the reference price being checked with. This is achieved using the formula below:

( price of a mercedes -  price of a lexus ) / price of a mercedes * 100

= (( 50 000 - 40 000 ) / 50 000 ) * 100

= (( 10 000 ) / 50 000 ) * 100

= ( 0.2 ) * 100

= 20%

Hence the absolute price difference is 10 000 and the relative price difference is 20%

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The college bookstore is 40 percent off

T-shirt are usually on sale for $34.50

The price was marked down to $20.7

The price change is = 34.5 - 20.7

= 13.8

The percent off can be calculated as follows

= 13.8/34.50 × 100

= 0.4 × 100

= 40

Hence the percent off the college bookstore is 40 percent

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The best description of the given inequality is;

Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

Hence, Option B is true.

What is inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

The inequality is given as;

⇒ 120 ≤ 12 k + 29

It can be written as;

12k + 29 ≥ 120

Now, We have;

A constant term = 29

And, Variable with number = 12k

Which is multiple of the number of buttons collected and the number of years k.

The sign is ''greater than equal'' to with 120, that's mean 'at least 120'

So, The best description of the given inequality is;

Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

Hence, Option B is true.

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The complete question is this;

Which situation can be represented by this inequality? 120 ≤ 12 k + 29

(A)Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

(B)Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

(C)Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

(D)Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

Answer: The question is not clear.

Step-by-step explanation:

Answer:

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian axes in the plane or in space. The plural of "axis" is "axes," pronounced "ax-ees."

Step-by-step explanation:

that

The value of subtraction will be equal to 723,862.58.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 2 is subtracted from the number 724,062.58. The value of the subtraction is calculated as:-

Subtraction = 724,062.58  -  200

If we write 2 at the hundredth place it will become 200.

Subtraction = 724,062.58  -  200 = 723,862.58

Therefore, the value of subtraction will be equal to 723,862.58.

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The x-coordinate of the solution is -0.22

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

5x - 4y =8

10x + 3y = -9

Next, we graph the equations

From the graph, we have the x-coordinate of the intersection to be

x = -0.22

Hence, the x-coordinate of the solution is -0.22

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Answer:

x<-27/4

​

Step-by-step explanation:

−4(2−x)1<−35

Multiply −4 and 1 to get −4.

−4(2−x) <−35

Use the distributive property to multiply −4 by 2−x.

−8+4x<−35

Add 8 to both sides.

4x<−35+8

Add −35 and 8 to get −27.

4x<−27

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

The slope of the line is -5 / 4.

The slope of a line is a measure of its steepness.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

Therefore,

slope = change in y / change in x

slope = y₂ - y₁ / x₂ - x₁

Using (1, -3)(-3, 2)

x₁ = 1

x₂ = -3

y₁ = -3

y₂ = 2

Therefore,

slope = 2 - (-3) / -3 - 1

slope = 2 + 3 / -4

slope = - 5 / 4

Therefore, the slope of the line is -5 / 4.

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The complete table is shown in the attachment.

1. 4.8 gallons of water

2. 25 mins

3. The constant of proportionality = 1.6

An example of a proportional relationship is the relationship between time taken and the number of gallons of water that fills the tank which is at a constant rate.

Constant rate is the same as constant of proportionality. It is calculated as, k = y/x.

The equation of a proportional relationship is expressed as y = kx.

Using the pair, (0.5, 0.8), find the constant rate/constant of proportionality (k):

k = y/x = 0.8/0.5

k = 1.6 gallon/min

Substitute k = 1.6 into y = kx

y = 1.6x

Fill the table using the equation, y = 1.6x

For 1 min (x):

y = 1.6(1) = 1.6

1.6 gallon

For 3 mins (x):

y = 1.6(3) = 4.8

4.8 gallons

For 40 gallons (y):

40 = 1.6x

40/1.6 = x

x = 25

25 mins.

The complete table is shown in the attachment.

1. 4.8 gallons of water will be in the tank after 3 mins

2. It will take 25 mins to fill the tank with 40 gallons of water.

3. The constant of proportionality = 1.6

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Solution of exponential equation 5²x=130 is , [tex]x = \frac{26}{5}[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa is also possible . The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

Mathematically, if  [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as    [tex]a^n = x[/tex] .

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

According to given statement,

5²x=130

divide both side by 5² , the equation becomes :

[tex]= > x = \frac{130}{(5^2)} \\\\= > x = \frac{26 (5)}{(5^2)}\\\\= > x = \frac{26}{5}\\\\[/tex]

Thus solution for this equation is  [tex]x = \frac{26}{5}[/tex]

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The cubic polynomial equation has three real roots. Simplify the expression to a linear factor and a quadratic expression. The linear factor is obtained by taking values for x and substituting in f(x) to get f(x) = 0. If a value of x gives f(p) = 0, then x-p is a linear factor. By algebraic long  division, obtain the quadratic equation and solve it to obtain the real roots.

f(x) = x³-7 x²+13 x-4

x = 4,

f(x) = 4³-7 (4)²+13 (4)-4 = 0

Thus, x-4 is a linear factor.  

x³-7 x²+13 x-4/ x-4.

(x³-7 x²+13 x-4)/ x-4 =  x²-3 x+1

x²-3 x+1  = 0

By quadratic formula: x = (-b±√(b²-4ac))/(2a)

x =  (--3±√((-3)²-4(1x1))/(2)

x = (3±√(9-4))/(2)

x  = (3±√5)/(2)  

x  = (3±2.24)/(2)  

x = (3+ 2.24)/2 = 2.62

x = (3- 2.24)/2 = 0.38

The real roots are x = 0.38, 2.62 and 4

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The given expression is equivalent to [tex]\frac{l}{m}[/tex]. The  correct option is C. None of the above

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex]- \frac{l}{-m}[/tex]

This expression can be written as

[tex]\frac{-l}{-m}[/tex]

Multiplying the numerator and the denominator by -1

[tex]\frac{-l \times -1 }{-m \times -1 }[/tex]

= [tex]\frac{l}{m}[/tex]

Hence, the given expression is equivalent to [tex]\frac{l}{m}[/tex]. The  correct option is C. None of the above

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Point Q will be located at 27 / 7.

We are given the points:

P = - 26

R = - 5

Let Q = x

Now, we also have the ratio as:

PQ : QR = 5 : 2

PQ = Q - P

PQ = x - ( - 26 )

PQ = x + 26

QR = R - Q

QR = - 5 - x

Now, we know that:

PQ / QR = 5 / 2

2 PQ = 5 QR

2 ( x + 26 ) = 5 ( - 5 - x )

2 x + 52 = - 25 - 5 x

2 x + 5 x = 52 - 25

7 x = 27

x = 27 / 7

Therefore, point Q will be located at 27 / 7.

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Using proportions, it is found that the conservationist would expect there to be 310 trouts in the lake.

A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.

Direct relations, which are the most usual, are when both variable behave similarly(both increase or both decrease), while for inverse relations, they behave differently.

For this problem, we have that from the fact that out of the 26 trout, 13 were tagged, the proportion of tagged trouts is:

p = 13/26 = 0.5.

Hence, if 155 trouts were tagged, the expected amount is given by:

0.5n = 155

n = 155/0.5

n = 155 x 2

n = 310.

The conservationist would expect there to be 310 trouts in the lake.

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The cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

Based on the information, the appropriate equation will be:

6g + 9y = 144

9g + 7y = 151

where g = grass sod

o = ornamental grass

Multiply equation I by 9

Multiply equation ii by 6

54g + 81y = 1296

54g + 42y = 906

Subtract

39y = 390

y = 390/39

y = 10

From 9g + 7y = 151

9g + 7(10) = 151

9g = 151 - 70

9g = 81

g = 81/9

g = 9

Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

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After solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.

So,

Then,

Therefore, after solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.

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The inverse of the function will be y = x/2 + 3/2. Yes, inverse is a function as well.

Functions that "undo" one another are known as inverse functions. In other words, f(g(x)) = g(f(x)) = x if g(x) is the inverse of f(x). We have a great approach we can use to achieve this given an equation for which we wish to get the inverse.

Not all functions have their opposite. It is simple to see that f(x) will never take on the same value again if f(x) has an inverse. We give this asset a unique name.

If each member of the range corresponds to precisely one element of the domain, a function is said to be one-to-one (f(x)).

Given,

We have a function,

y=2 x-3

Add 3 to each side.

⇒ y + 3 = 2x

Divide by 2 and then either

⇒ x = y/2 + 3/2 or y/2 + 3/2

Just change the labels now, x to y.

⇒ y = x/2 + 3/2

So, the inverse of given function is y = x/2 + 3/2

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Answer: B is correct answer

It should be noted that in order to measure the value, the measurement have to be in the same unit.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Measurement is crucial in establishing connections across different branches of mathematics. For instance, it gives the use of math abilities and spatial concepts a rich and meaningful context. Measurement also establishes connections between mathematics and other academic disciplines.

From the information, it was illustrated that the boys all had measurement of trees taken. Therefore, it should be noted that since they are in different units, it cannot be done.

In this case, the reason is that in order to measure the value, the measurement has to be in the same unit. This will make it easier to do the calculation.

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Answer:

about 42%

Step-by-step explanation:

3/7 = 0.41857... =  42%