What is the value of X

Answer:

Step-by-step explanation:

y=ax²+bx+c

x=1,y=-5

-5=a+b+c   ...(1)

x=2,y=-3

-3=4a+2b+c   ...(2)

x=3,y=3

3=9a+3b+c  ...(3)

(2)-(1) gives

2=3a+b   ...(4)

(3)-(2) gives

6=5a+b   ...(5)

(5)-(4) gives

4=2a

a=4/2=2

from (4)

6=5(2)+b

b=6-10=-4

from (1)

-5=2+(-4)+c

-5=-2+c

c=-3

y=2x²-4x-3

number of tickets for adult = 170 and number of tickets for children = 151

What is equation with two variables?

The equation that has two unknown variables and express the equality between two or more expression is called equation with two variables.

let, x denotes the number of adults went to theater.

y denotes the number of children went to theater

price of ticket for each adult = $3.50

price of tickets for each child = $2.50

if the number of total tickets = 321

x + y = 321

total cost of tickets = $3.50x + $2.50y = 972.21 dollar

we will solve the above two equations, y = 321 - x

by putting the y value in the second equation,

3.50x + 2.50 (321- x) = 972.21

3.50x + 802.5 - 2.50x = 972.21

x = 169.71

number of adults went to theater = 170

from, y = 321 -169.71

    y = 321 - 169.71

y = 151.3, y= 151

number of children went to theater = 151

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Answer:

A G.P is a sequence of numbers such that the ratio of any two consecutive terms is a constant, called the common ratio. Given the first term (3) and the common ratio (0.25) of the G.P, we can find the sum of the first 5 terms using the formula:

S_n = a(1 - r^n) / (1 - r)

Where:

S_n is the sum of the first n terms of the G.P.

a is the first term of the G.P.

r is the common ratio of the G.P.

n is the number of terms in the sum.

So, to find the sum of the first 5 terms of the G.P, we can substitute the given values into the formula:

S_5 = 3(1 - (0.25)^5) / (1 - 0.25)

S_5 = 3(1 - (0.25)^5) / (1 - 0.25) = 3(1 - 0.25^5) / (1 - 0.25) = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.

Answer:

3.996

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula to find the sum of the first 5 terms of a geometric progression whose first term is 3 and common ratio is 0.25:

[tex]\implies S_5=\dfrac{3(1-0.25^5)}{1-0.25}[/tex]

[tex]\implies S_5=\dfrac{3(1-0.00097656...)}{0.75}[/tex]

[tex]\implies S_5=\dfrac{3(0.999023437...)}{0.75}[/tex]

[tex]\implies S_5=\dfrac{2.99707031...}{0.75}[/tex]

[tex]\implies S_5=3.99609375[/tex]

[tex]\implies S_5=3.996\; \sf (4\;s.f.)[/tex]

Answer:

the answer would be están

Answer:

ln(d) = n can be rewritten in exponential form as d = e^n.

Step-by-step explanation:

The natural logarithm, denoted by ln, is the logarithm to the base e (approximately 2.718). The inverse of the natural logarithm function is the exponential function e^x. Therefore, when you take the natural logarithm of a number, you can raise e to the power of that number to get the original value.

ln(d) = n is the same as d = e^n

So, Ln(d)=n can be written as d = e^n

This is because e^n is the inverse function of Ln(d) and Ln(d)=n is the logarithm form of d = e^n

to get the y-intercept of any equation we can simply set x = 0 and solve for "y", so let's do so

[tex]y=6\left( x-\cfrac{1}{2} \right)(x+3)\implies \stackrel{\textit{setting x = 0}}{y=6\left( 0-\cfrac{1}{2} \right)(0+3)}\implies y=6\left( -\cfrac{1}{2} \right)(3) \\\\\\ y=(-3)(3)\implies y=-9\hspace{12em} {\Large \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~-9)} \end{array}}[/tex]

Answer:

[tex]\textsf{A)} \quad 5+3\sqrt{2}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{4+\sqrt{2}}{2 -\sqrt{2}}[/tex]

To rationalise the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of an expression is where we change the sign in the middle of the two terms.  Therefore, the conjugate of the denominator of the given expression is:

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\implies \dfrac{4+\sqrt{2}}{2 -\sqrt{2}} \cdot \dfrac{2 +\sqrt{2}}{2 +\sqrt{2}}[/tex]

Simplify:

[tex]\implies \dfrac{(4+\sqrt{2})(2 +\sqrt{2})}{(2 -\sqrt{2})(2 +\sqrt{2})}[/tex]

[tex]\implies \dfrac{8+4\sqrt{2}+2\sqrt{2}+\sqrt{2}\sqrt{2}}{4+2\sqrt{2}-2\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]

[tex]\implies \dfrac{8+6\sqrt{2}+2}{4-2}[/tex]

[tex]\implies \dfrac{10+6\sqrt{2}}{2}[/tex]

Reduce to its simplest form by dividing the numerator and the denominator by 2:

[tex]\implies 5+3\sqrt{2}[/tex]

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }[/tex]

If he walks up the moving escalator at a speed of 25 meters per minute,

the person will reach the top in six minutes.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A person standing on an escalator reaches the top in 3 minutes.

The escalator is 150 meters long.

He walks up the moving escalator at a speed of 25 meters per minute.

So, the time taken = divide 150 by 25

The time taken = 150/25

The time taken = 6 minutes.

Therefore, he will reach the top in six minutes.

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The quantity of additive which Belle put in each can as required is; 1/8 pint.

It follows from the task content that the quantity of additive which Belle put in each can be determined if 1/2 of a pint of special paint additive is shared among 4 cans of paint.

The resulting expression which given the required quantity is;

1/2 ÷ 4

= 1/2 × 1/4

= 1/8.

On this note, the quantity of additive in each can of paint is 1/8 pint of special paint additive.

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The value of n(AxB) is mathematically given as

n(A x B)  = 18

Generally, It is possible to extend the formula for calculating the magnitude of a vector to any number of dimensions. For instance, the magnitude of a four-dimensional vector denoted by

a=(a1,a2,a3,a4) may be calculated using the following formula: a=a21+a22+a23+a24.

The question "how much of a quantity" is what's meant to be answered when one asks about magnitude.

For instance, the magnitude may be used to provide an explanation for why the speeds of a vehicle and a bicycle cannot be compared directly to one another. It is also possible to use it to describe the distance traveled by an item or the quantity of an object in terms of its magnitude. Both of these applications need the usage of magnitude.

n(A x B) = |A| x |B|

= 6 x 3

n(A x B)  = 18

Where

The product of these two values is the total number of ordered pairs that can be formed from the elements of A and B, which is 18.

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Answer:

38[tex]\sqrt{3}[/tex]

Step-by-step explanation:

6[tex]\sqrt{5x5x3}[/tex] + 4[tex]\sqrt{2x2x3}[/tex]  We can pull out a pair of 5's and 2's

6(5) [tex]\sqrt{3}[/tex] + 4(2)[tex]\sqrt{3}[/tex]

30[tex]\sqrt{3}[/tex] + 8[tex]\sqrt{3}[/tex]

38[tex]\sqrt{3}[/tex]

Answer:

synthetic division method use it

The solution of the system of equations by using substitution method is x = 1 and y = 3

The substitution method is a method for solving systems of equations. It involves solving for one variable in one of the equations and then substituting that value into the other equation to find the value of the other variable.

We have the equations 4x + 4y = 16 and y = x+2

Substitute y = x +2 into  4x + 4y = 16:

4x + 4y = 16

4x + 4(x +2) = 16

Clear the parenthesis:

4x + 4x + 8 = 16

8x + 8 = 16

8x = 16-8

8x = 8

x = 8/8

x = 1

put x = 1 into  y = x+2:

y = x+2

y = 1 + 2

y = 3

Therefore, the solution of the system of equations is x = 1 and y = 3

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Answer:

x+2 domain: (-infiniy, +infinity) or -infinity<x<infinity

1/x +2 domain: (-infinity, 0) and (0, infinity) or 0<x<0

Answer:

Step-by-step explanation:

To find the solutions to f(x) = g(x), we need to find the values of x that make the two sides of the equation equal.The function f(x) = −|x−4| + 4 is a piecewise function. For x≤4, f(x) = −(x−4) + 4 = 4−x and for x>4, f(x) = (x−4) + 4 = x.The function g(x) = 1/2x − 4 is a linear function.When we graph these two functions in the same coordinate plane, we can see that they intersect at the point (4, 4) this point is the only solution where f(x) = g(x)so the solution of x = 4

x = 4

Answer:

Step-by-step explanation:

Distance formula is as follows.

The distance between two co-ordinates, say, (x₁ , y₁) and (x₂,y₂), is equal to

√((x₁ - x₂)² + (y₁ - y₂)²)

Just substitute the values here.

√((1 - (-7) )² + ( - 3 - 2)²)

= √((1 + 7)² + ( - 3 - 2)²)

= √(8² + -5²)

= √(65 + 25)

= √90  ≈9.5 units

Pls mark as brainliest. I really need for no apparent reason. Cheers

Answer:

1 is p

2 is np

3 is p

4 is np

(should be right)

Step-by-step explanation:

The number of seats of each bus is given as follows:

The number of seats of each bus is obtained applying the proportions in the context of the problem.

One bus has 3 rows of seats with 9 seats in each row, hence the number of seats of the first bus is given as follows:

3 x 9 = 27.

The other bus has four times as many seat as the first bus, hence the number of seats of the second bus is given as follows:

4 x 27 = 108.

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Answer:

1) The vertex is the maximum value.

2) The axis of symmetry is x = negative one-half.

3) The domain is all real numbers.    

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 cups of lemon per 4 cups water

in 6 cups of lemonade, 2 cups lemon (2/6)

simplified 1/3

Answer:

x = 10 (yes)

x = 14 (yes)

x = 6 (no)

x = 4 (no)

Step-by-step explanation:

Plug in each x value into the function and determine if it is true or not.

44 [tex]\leq[/tex] 35 + x

44 [tex]\leq[/tex] 35 + (10)

44 [tex]\leq[/tex] 45

45 is greater than or equal to 44, so it is a solution

44 [tex]\leq[/tex] 35 + (14)

44 [tex]\leq[/tex] 49

49 is greater than or equal to 44, so it is a solution

44 [tex]\leq[/tex] 35 + (6)

44 [tex]\leq[/tex] 41

41 is not greater than or equal to 44, so it is not a solution

44 [tex]\leq[/tex] 35 + (4)

44 [tex]\leq[/tex] 39

39 is not greater than or equal to 44, so it is not a solution

I hope this helps! :)

Answer:

There are two terms in the expression

Step-by-step explanation:

2b is one term since it is multiplied together, and 6 is by itself and is the second term

When the function, m ( x)  = x + 1 is graphed, the result is shown attached.

When graphing a function, you need to remember that x is the independent variable. This means that you need to come up with the values of x and then use these values to come up with the corresponding values of y or m (x ) using the function.

Assuming you have values of x which are -3, -2, -1, 0, 1, 2, 3, the values of y would be:

x = - 3:
= x + 1

= - 3 + 1

= -2

x = - 2

= - 2 + 1

= - 1

x = - 1

= - 1 + 1

= 0

x = 0:

= 0 + 1

= 1

x = 1 :

= 1 + 1

= 2

x = 2 :

= 2 + 1

= 3

x = 3 :

= 3 + 1

= 4

The points would then be:
( - 3, - 2) , ( - 2, - 1) , ( - 1 , 0 ) ( 0, 1 ) ( 1, 2 ) ( 2, 3 ) ( 3, 4 )

The graph would be shown as attached.

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Answer:

y = -3

Step-by-step explanation:

The midline of a sinusoidal function is y = a where "a" is halfway between the minimum and maximum y-values of the function.

From inspection of the given graph:

Therefore, the y-value that is halfway between the minimum and maximum points is:

[tex]\implies y=\dfrac{y_2+y_1}{2}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3[/tex]

Therefore, the equation of the midline of the given sinusoidal function is:

The collateral for the loan that Jordan signed the finance agreement, is nothing. There was no collateral.

A loan that doesn't require any sort of collateral is known as an unsecured loan. Lenders approve unsecured loans based on a borrower's creditworthiness rather than their assets as collateral. Personal loans, school loans, and credit cards are a few examples of unsecured loans.

Since secured loans are safer for lenders to approve than unsecured loans, unsecured loans need better credit scores.

Jordan most likely made a purchase with her credit card and so the finance agreement she signed would therefore likely be an unsecured loan with no collateral.

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Answer:

f(8) = - 1

Step-by-step explanation:

f(8) has x = 8 which is in the interval x > 0 , then f(x) = - 1 , so

f(8) = - 1

Explanation:

First we solve for y.

x + 2y = -14

2y = -14 - x

2y = -x - 14

y = (-x - 14)/2

y = -x/2 - 14/2

y = (-1/2)x - 7

The equation is in slope intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2

For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.