(x+5)-(x - 5)² for x = 3

Answer:352

Step-by-step explanation:

The value of the expression -5(-6k-6)-(-9k-10) in simplest terms is 39k + 40

An algebraic expression can be described as an expression that is made up of terms, variables, coefficients, factors and constants.

These expressions are also known to be composed of certain mathematical operations, such as;

We have the expression;

-5(-6k-6)-(-9k-10)

expand the bracket

-5(-6k - 6) + 9k + 10

collect like terms

30k + 30 + 9k + 10

Add the like terms

39k + 40

Hence, the value is 39k + 40

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Answer:A=72

B=108

Step-by-step explanation:

The solution is, angle a = 72 & b = 108

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

from the given figure we get,

∠ABC = 180

∠BCD = 180

so, we have,

∠ABC + ∠BCD = 180 + 180

ABE + EBC + a + b = 360

again, we know that,

EBC + a = 180 - 38 = 142

[we know, from property of triangle's angle]

now, we get,

ABE + 142 + b = 360

or, 110 + 142 + b = 360

or, b = 108

so, we get,

a = 180 - 108 = 72

Hence, The solution is, angle a = 72 & b = 108.

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The inverse function is given as s⁻¹ = [tex]\frac{t^2+4t-12}{t^2-9t+14}[/tex] and the equation represents the average sales each day for the real estate company would be [tex]s^{-1}=\frac{t+6}{t-7}[/tex].

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

A real estate company balances the books for its business on the first day of each month.

It hopes to sell houses every other day of the month.

The average number of houses, S, the company sells each day, t is represented by the inverse of the function given below.

               [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}[/tex]

Then the inverse function can be written as

                   [tex]s^{-1}=\frac{t^2+4t-12}{t^2-9t+14}\\\\s^{-1}=\frac{t^2+6t-2t-12}{t^2-7t-2t+14}\\\\s^{-1}=\frac{(t+6)(t-2)}{(t-7)(t-2)}\\\\s^{-1}=\frac{t+6}{t-7}[/tex]

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Answer:

C. [tex]S=\frac{7t+6}{t-1}[/tex]

Step-by-step explanation:

I got it right on the exam.

First, take the equation and inverse it, replace and t with y and the y with t

[tex]y=\frac{t^{2}+4t-12}{t^{2}-9t+14} \\\\t=\frac{y^{2} +4y-12}{y^{2}-9y+14}[/tex]

Then, factor both the top and bottom

[tex]t=\frac{(y+6)(y-2)}{(y-7)(y-2)}[/tex]

You see that there is a duplicate of the (y-2) in the numerator and denominator, so they cancel out,

[tex]t=\frac{(y+6)}{(y-7)}[/tex]

Now you can start getting the y alone to make an equation,

[tex]t(y-7)=\frac{(y+6)}{(y-7)} (y-7)\\t(y-7)=(y+6)[/tex]

[tex]ty-7t=y+6\\ty-7t-y+7t=y+6-y+7t\\ty-y=7t-6\\y(t-1)=7t-6\\\frac{y(t-1)}{(t-1)} =\frac{7t-6}{t-1} \\y=\frac{7t-6}{t-1}[/tex]

The probability is 0.6 that if randomly choosen none of them are senior.

acc to our question-

Hence,the probability is 0.6 that if randomly choosen none of them are senior.

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The "Poisson distribution" is the probability distribution that comes the closest to accurately describing that many dog bite patients visit this hospital across any given day.

For the given data of,

An average of two dog bite victims show up at Carver Memorial Hospital each day.

A probability distribution that most accurately predicts the number of dog bite victims who visit this hospital on any given day is characterized as the "Poisson distribution."

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Answer:

 50 people

Step-by-step explanation:

Solution

25% as a fraction is 25/100 which reduces down to 1/4. What this tells you is that 1/4 of the people asked want the hotel

1/4 * 200 = 50

50 people want the hotel.

Step-by-step explanation:

that simply means we use one equation to express one variable by the other, and then we use that identity in the second equation (substituting one variable by the expression of the other variable. and then we solve for that remaining variable.

finally we use one of the original equations to solve for the second variable.

4x + y = 19

so, that gives us

y = 19 - 4x

we use that now in the second equation :

6x + 7(19 - 4x) = 1

6x + 133 - 28x = 1

-22x + 133 = 1

-22x = -132

22x = 132

x = 6

now, let's use e.g.

4x + y = 19

4×6 + y = 19

24 + y = 19

y = -5

Answer:

Step-by-step explanation:

One example is a=-6 and b=3

-6/3=-2

-6*3=-18

-2 is greater than -18; the quotient is greater than the product in this case.

Another example is a=6 and b=3

6/3=2

6*3=18

2 is smaller than 18; the quotient is smaller than the product in this case.

The rationalization of the denominator of the given fraction gives 8 -2√3

From the question, we are to rationalize the denominator of the given fraction

The given fraction is

26 / (4+√3)

To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.

The denominator is 4+√3

Thus,

The conjugate of the denominator is 4-√3

Now, multiply the numerator and the denominator by the conjugate.

That is,

(26 × (4-√3)) / ((4+√3) × (4-√3))

(104 - 26√3) / (16 - 3)

(104 - 26√3) / 13

= 104/13 - (26√3)/13

= 8 - 2√3

Hence,

The result of rationalizing is 8 -2√3

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]

[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]

[tex]{ \red{ \sf{7x = 14}}}[/tex]

[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]

From the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

As given in the question,

Table which represents the system of linear function are as follow:

table 1:

x:      -4       -2        0       2

y:     26       18       10     2

table 2:

x:      -4       -2        0       2

y:     14       8         2      -4

For table1 :

System of linear function:

(x₁ , y₁) = (0,10)

(x₂ , y₂) = (2, 2)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -10)/ (x-0) =(2-10)/(2-0)

⇒y-10 =-4(x)

⇒ y = -4x +10     __(1)

For table2 :

System of linear function:

(x₁ , y₁) = (0,2)

(x₂ , y₂) = (2, -4)

Equation of linear function:

(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)

⇒(y -2)/ (x-0) =(-4-2)/(2-0)

⇒y-2 =-3(x)

⇒ y = -3x +2     __(2)

Solve system of linear function (1) and (2) we get,

-4x +10 = -3x +2

⇒4x -3x =10 -2

⇒x =8

⇒y = -4(8) +10

     = -22

(x, y) = (8 ,-22)

Therefore, from the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).

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Answer:

D

Step-by-step explanation:

trust

The number of hours it is suggested to study is 8.5 hours using the concept of the equation.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. The value of an unknown variable, or unknown quantity, can be determined by solving equations.

Given,

The given linear equation P = 6.31H + 41.5, is used to predict the points earned P.

Also P = 95,

Now, we will find the value of H by using LHS=RHS

95 = 6.31H+41.5

Subtract 41.5 from both sides,

53.5 = 6.31H

Now, divide both sides by 6.31,

8.5 = H

Therefore, the number of hours it is suggested to study is 8.5 hours.

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There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.

In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:

x + 2 · y + 8 = 0

2 · y = - x - 8

y = - (1 / 2) · x - 4

Then, the resulting line has a slope of - 1 / 2.

Second, determine the intercept of the resulting line:

y = m · x + b

b = y - m · x

b = - 3 - (- 1 / 2) · (- 2)

b = - 3 - 1

b = - 4

The intercept of the resulting line is - 4.

Third, transform the equation of the resulting line into standard form:

y = - (1 / 2) · x - 4

- 2 · y = x + 8

x + 2 · y + 8 = 0

There is no parallel line for the point (x, y) = (- 2, 3).

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The relation accepts reflexive, symmetry, and transitive.

Recall that a relation R is reflexive if the element (x, x) belongs to R for all elements X in the domain of R.

If (x, y) belongs to R, then follows that (y, x) must likewise belong to R, making the situation symmetric.

And it is transitive if (x, y) and (y, z) belongs to R necessarily implies that (x, z) belongs to R.

Given r is a relation on the set of all nonnegative integers R(a,b)

Reflexive - YES. A given number a will always have the same remainder when divided by 5.

Symmetric - YES. If a and b have the same remainder when divided by 5, then b and a are the same pair, so again they will have the same remainder.

Transitive - YES. If a and b as well as b and c have the same remainder when divided by 5, this is possible if both a and c also have the same remainder when divided by 5.

Therefore the relation accepts reflexive, symmetry, and transitive.

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The possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

We need to find the four possible pairs of integers that has product -18

Let x and y be two required integers.

Since the product is negative, one of the integer must be negative integer.

x      y          x*y

9    -2          -18

2     -9         -18

18    -1         -18

-1     18        -18

6      -3        -18

3      -6        -18

Therefore, the possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

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-68 as a quotient of integers is -680/10.

The given integer is -68.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, -68/1

Multiply 10 to both the numerator and denominator, we get

= -680/10

= -68

Therefore, -68 as a quotient of integers is -680/10.

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The Maximum and Minimum values of x is  = (3,30)

The maximum of a quadratic function occurs at

x = − b/2a

If  a is negative, the maximum value of the function is

f ( − b/2a).

f max x  =ax^2+bx+c occurs at

x = −b/2a

Finding the value of

x = −b/2a

Substitute in the values of a and b.

x = − 18/2(3)

Simplify

x = -3

Replace the variable x with -3 in the expression

f (-3) = -3(-3)^2+18(-3)+3

f(-3) = - 27 +54 +3

f(-3) = -30

f(3) = 30

The maximum   of -3x^2+18x+3 = (3,30)

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Step-by-step explanation:

the slow of a line is the factor of x in a "y = ..." firm of equation.

the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).

(B) and (C) are out, because there is no line with slope 3 (only -3).

the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).

(A) is out, as there is no line with the slope -2 (only +2).

so, (D) is the correct answer.

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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The equation of the line is y=3x+1 when the line is on the graph of the given picture.

Given that,

In the picture we have a graph.

We have to find the equation of the line.

We know that,

From the graph we can see the points,

(1,4) and (0,1)

We know that the equation of the line is y=mx +b

The y and x value are from the points and the m is the slope that is rise by run and b is the y intercept.

m is rise/run

m= 1-4/0-1

m=-3/-1

m=3

b is 4=3(1)+b

4=3+b

b=4-3

b=1

The equation of the line is y=3x+1

Therefore, The equation of the line is y=3x+1 when the line is on the graph of the given picture.

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The number problems solved by the little Monsters  of Beast Academy in March's meet is 15.

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the number of questions solved by little Monsters  of Beast Academy in

In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5

In March's Math Meet, they solved $\frac23$ of the problems = 2x/3

Hence:

y/5 + 2x/3 = 12

x + y = 30

solving the equation gives

x = y = 15

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Considering the figure the required angle is solved using the vertical angle theorem. The values are

The problem is solved considering this theorems

vertical angle theorem

According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.

solution for the missing angle

x + 70 + 60 = 180 sum of angles of a triangle

x = 50

Using vertical angle theorem

? + 88 + 50  = 180 sum of angles of a triangle

? = 180 - 88 - 50

? =  42

solution for the missing angle

x + 75 + 30 = 180 sum of angles of a triangle

x = 75

Using vertical angle theorem

? + 88 + 75  = 180 sum of angles of a triangle

? = 180 - 85 - 75

? =  20

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Answer: I'm pretty sure this is the same question. https://brainly.com/question/16428516

Answer:

Step-by-step explanation:

Dibuja una diagrama de cinta dividido en 3 y pinta 2 de los espacios

De nada :>

The presense of a midpoint will result in congruent segments.

Congruent segments are just equal-length line segments. Congruent means similar. Congruent line segments are typically represented by drawing the same number of little tic lines perpendicular to the segments in the middle of the segments.

A congruent line segment is any line segment with equal measure. Congruent line segments, for example, are the sides of an equilateral triangle since they all have the same length.

When we insert a midpoint to a line segment, it divides the line into two equal portions. Because equal segments are congruent, we can say that congruent segments are generated.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(x) = 2x^{2} + 5x - 7\\\\g(x) = x^{2} -2\\ \\f(g(x)) = 2(x^{2}-2) + 5(x^{2} -2) - 7\\ \\= 2x^{2} - 4 +5x^{2} -10 - 7\\= 2x^{2} + 5x^{2} -4-10-7\\\\\\f(g(x)) = 7x^{2} -21[/tex]

The input value x in the function j(x) = 3-x as j(x) equals -5 is 8.

A function is simply a relationship that maps one input to one output.

Given the function in the question;

To determine the value x or input value, equate the function to -5 and solve for x.

j( x ) = 3 - x

j( x ) = -5

-5 = 3 - x

Add 5 to both sides

-5 + 5 = 3 + 5 - x

0 = 8 - x

Add x to both sides

0 + x = 8 - x + x

x = 8 - x + x

x = 8

Therefore, the value of x is 8.

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