If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).

Answer:

-70

Step-by-step explanation:

you didn't put the function so sorry if it is wrong

Equation for the translation of y=2/x that has the given asymptotes. x=0 and y=4 is y = 4(x+7) + 6

A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.

y = 4(x+7) + 6

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Answer:

u≤25

Step-by-step explanation:

63 ≥ 3u-12

-3u    -3u

-3u+63 ≥ -12

 -63        -63

-3u ≥ -75

/-3    /-3

u≤25

The amount Nicole's mother owe her for babysitting is 9.48 dollars.

She ordered a volleyball for $9.75, a net for $29.99, and knee pads for $15.00.

Nicole's mother said that she would pay for the order on her credit card if Nicole gave her the money.

Nicole gave her mother $40.00 .

Her mother also applied the money that she owed Nicole for babysitting.

Nicole's mother then gave her back $5.26.

The amount Nicole's mother owe her for babysitting can be calculated as follows;

Therefore, the total amount for the order is

$9.75 + $29.99 + $15.00 = $54.74

let the money her mother owes her  =  x

Therefore,

x + 40 + 5.26 = 54.74

x = 54.74 - 40 - 5.26

x = 54.74 - 45.26

x = 9.48

Therefore, the amount Nicole's mother owe her for babysitting is 9.48 dollars.

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The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).

An expanded form is a method of writing a number through adding the digit values. A place value chart can help us think about the worth of a number's digits. Logarithms can be expanded by writing them as a sum as well as difference of logarithms, using the power rule if necessary. The order summation rule, product rule, as well as power rule are frequently useful.

Expanding the equation  log₂ (2 y-4)³:

log₂ (2 y-4)³

applying the log rule logₐxᵇ = b*logₐ(x)

so that

3log₂(2y -4)

The expanded form of the equation log₂ (2 y-4)³ is 3log₂(2y -4).

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The expression -2√294p³ can be simplified as -17.146 p√p using the concept of radicals.

An expression that has a root, typically a square or cube root, is referred to as a radical.

The radical form of the square root of 294 is √294 and the exponent form is [tex]294^{\frac{1}{2} }[/tex].

17.146428 is the square root of 294 when rounded to six decimal places.

Now, the square root of p³ will be

[tex]\sqrt{p^{2} .p}[/tex] = p√p

Therefore the square root of √294p³ is 17.146428p√p.

The expression -2√294p³ can be written as -17.146 p√p.

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Answer:

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

Step-by-step explanation:

If there is a pair of adjacent angles, then this pair is a linear pair if the sum of the (measures of the) two angles will be 180°. So, linear pair of angles always add up to 180°. For example, the linear pair of 30° is 150°, the linear pair of 70° is 110°, etc.

These two angles form a linear pair. We have found all four linear pairs of angles. The four linear pairs formed by the intersecting lines ←→QR Q R ↔ and ←→ST S T ↔ are ∠SOQ ∠ S O Q and ∠QOT ∠ Q O T , ∠QOT ∠ Q O T and ∠TOR ∠ T O R , ∠TOR ∠ T O R and ∠ROS ∠ R O S , and ∠ROS ∠ R O S and ∠SOQ ∠ S O Q .

The reasons in the asked situations are:

(A) E is the midpoint of AC:

(B) ∠D≅∠B:

So, (A) E is the midpoint of AC:

(B) ∠D≅∠B:

Therefore, the reasons in the asked situations are:

(A) E is the midpoint of AC:

(B) ∠D≅∠B:

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Answer:

66

Step-by-step explanation:

63% of 109 is 68.67 the closest answer is 66

points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

points of discontinuity:

In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.

points of discontinuity removable:

A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.

points of discontinuity non removable:

A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.

given that

[tex]y = \frac{ {x}^{2} + 2x}{ {x}^{2} - 7x - 18 } [/tex]

now take the denominator and find the factors of it.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

[tex] {x}^{2} - 9x + 2x - 18 = 0[/tex]

x (x -9) + 2 (x - 9) = 0

(x - 9) (x + 2) = 0

[tex]y = \frac{ {x}^{2} + 2x}{(x - 9)(x + 2)} [/tex]

now, take common on numerator

[tex]y = \frac{2(x + 2)}{(x - 9)(x + 2)} [/tex]

cancel the common factor in both numerator and denominator

[tex]y = \frac{x}{x - 9} [/tex]

now find the points of discontinuity.

x-9=0 , x+2=0

x = +9 , x = -2

now, x = +9 and x = -2

Hence the points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

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Answer:

if they have the same absolute value but different signs.

Step-by-step explanation:

Answer:

if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0

Answer:

(2/x) - 9x

Step-by-step explanation:

si una de las respuestas se ve así, elija esa.

The length of the radius DC (or EC) in units is 20 units and the coordinates of the center C of the circle is (19, 17) using concept of Coordinate Geometry and Lines.

As per the question statement, The diameter of a circle has endpoints D(7, 33) and E(31, 1). The center of the circle denoted by C, is the midpoint of the diameter. We are supposed to find the length of the radius DC (or EC) in units and the coordinates of the center C of the circle

Now using the distance formula in Line concept and coordinate geometry,

Distance between two points is given by d = √{(x2-x1)^2+(y2-y1)^2}

Given coordinates of D are (7, 33) and E are (31, 1)

Therefore Distance DE = √{(31-7)^2 + (1-33)^2}

DE = √{(576)+(1024)}

DE = √1600

DE = 40 units

Therefore, length of diameter DE is 40 units so length of radius DC (or EC)  will DE/2 = 40/2 = 20 units

Now using Mid Point Formula of  Line concept and coordinate geometry,

Mid Point of line joining two points is given by

C = ({x1 + x2}/2, {y1 + y2}/2)

C = ( {31+7}/2 , {1+33}/2)

C = (19, 17)

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Answer:

1

Step-by-step explanation:

1 / 3-x

x - 2/x - 3

(x - 2)/x - 3

-3/x - 3

(x - 2) + -1/x - 3

= x - 3/x - 3

Cancel

= 1

Answer:

24

Step-by-step explanation:

24 - 19 = 5

5 * -3 = -15

Answer:

answer is 5

Step-by-step explanation:

[tex] - 3(x - 19) = - 15[/tex]

cancel out both sides by -3, therefore -15 will become positive

[tex] \frac{ - 3(x - 19)}{ - 3} = \frac{ - 15}{ - 3} [/tex]

then add 19 to both sides

[tex]x - 19 +19= 5 + 19[/tex]

then X will add up to 24

From the given triangular sail, it is found that:

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.

Considering that 1 ft = 12 inches, the outer edges for this triangle are given as follows:

14.5833 ft, 13.3333 ft, 13.3333 ft.

Hence the perimeter is given by:

P = 14.5833 + 13.3333 + 13.3333 = 41.25 ft = 41 ft 3 in.

The area of a triangle is given by half the multiplication of the base and the height of the triangle.

For this triangle, we have that:

Hence the area is:

A = 0.5 x 14.5833 x 11.1667 = 81.4 ft².

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Answer:

100%

Step-by-step explanation:

Answer:

-1/5

Step-by-step explanation:

First:

Calculate the rise:

On this graph we go down 1 meaning our rise will be -1.

Second:

Calculate the run:

On the graph we go right 5 so the run would be 5.

Third:

We put the rise and run together to get the slope.

Hence, the answer is -1/5

Notes:

Rise means how many units you move up or down from point to point.

Run means how far left or right you move from point to point.

Up and Right= + outcome

Down and Left= - outcome

Also if your rise over run is the same number but two negative number the slope would turn into a positive.

Example:

-5/-5=1

The length of one side of the pool is 12 feet

The shape of the pool is a square

A square is a 2-dimensional quadrilateral with sides of equal lengths.

Characteristics of a square

The angles in the square are right angles

The sum of angles equal 360 degrees

Diagonals are equal in length

Area of a square = length²

144 = length²

In order to determine the length of a side, determine the square root of the area

√144 = 12 feet

therefore the area of a gym is 12 feet.

dimension, in common parlance, the measure of the size of an object, such as a box, usually given as length, width, and height. In mathematics, the notion of dimension is an extension of the idea that a line is one-dimensional, a plane is two-dimensional, and space is three-dimensional.

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[tex] \large \bf \longrightarrow{(3, - 8)}[/tex]

Step 1) : Write the midpoint formula

[tex] \large \implies \bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

Step 2) : Substitute (-1 , -9) and (7 , -7) into [tex]\bf(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )[/tex]

[tex]\large \implies \bf(\frac{ - 1 + 7}{2}, \frac{ - 9 - 7}{2} )[/tex]

Step 3) : Calculate

[tex]\large \implies \bf(\frac{6}{2}, \frac{ - 16}{2} )[/tex]

Step 4) : Cross out the common factor

[tex]{\large \implies \bf(\frac{ \cancel{6}}{ \cancel{2}}3, \frac{ \cancel{ - 16}}{ \cancel{2}}} \bf - 8)[/tex]

Step 5) : We have got the answer

[tex]\large \bf \implies{(3, - 8)}[/tex]

The best function to model this data is a linear function.

We have the data:

x             y

0            -1

1           -0.5

2             0

3           0.5

4               1

From the table, we see that,

The slope of the points are given by:

(- 0.5 + 1) / (1 - 0) = 0.5 / 1 = 0.5

(0 + 0.5) / (2 - 1) = 0.5

(0.5 - 0 ) / (3 - 2) = 0.5

(1 - 0.5) / ( 4 - 3 ) = 0.5

Thus, the equation of the function is, y = 0.5 x - 1

So, the best function for this model is a linear function.

Therefore, we get that, the best function to model this data is a linear function.

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Your question was incomplete. Please refer the content below:

Which kind of function best models the data in the table? use differences or ratios.

x             y

0            -1

1           -0.5

2             0

3           0.5

4               1

a)liner

b)quadratic

c)exponential

d)none of these

Answer: put 32x over 9 as a fraction and it would be a negative so put a - in front

Step-by-step explanation:

Answer:

the answer is 49

Step-by-step explanation:

Using linear function concepts, it is found that:

Bob's function is missing, and is given by:

f(t) = 7.2t.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, the linear functions for the distances are given as follows:

The rate of change of a linear function is given by it's slope, hence they are given as follows for the functions in this problem:

The difference between the rates is given by:

7.2 - 5.9 = 1.3.

From the difference between the rates, Bob is 1.3 kilometer an hour faster than Alice.

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Since their dot product is equal to zero,  then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.

Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.

These two vectors are also called orthogonal to each other.

Let u = (u₁, u₂) and  v = (v₁, v₂), then the dot product u . v is defined as:

u . v = u₁v₁ + u₂v₂

To check whether the vectors are normal to each other, let us check their dot product.

The given vectors are: (0.8, -0.6) and (0.3, 0.4).

Let u = ((0.8, -0.6) and  v = (0.3, 0.4), then,

u . v = 0.8 . 0.3 + (-0.6) . 0.4

      = 2.4 + (-2.4) = 0

Since u.v = 0, then vectors (0.8, -0.6) and (0.3, 0.4) are normal to each other.

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The height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.

The statement indicates the dimensions of a triangle, where the base and the height of the figure are expressed by exponential numbers with positive integer base and negative integer exponents and each of which must be rewritten with positive exponents, this can be done by using the following power property:

a⁻ⁿ = 1 / aⁿ

Then, if the height of the triangle has a measure of 2⁻⁴ units, that is equivalent to a measure of 1 / 2⁴ units.

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Answer: Select all the equations you can use to find the number of basketball courts, c is = 4.

Step-by-step explanation:

Given data,

Number of players on the basketball court in a city = 40

Number of teams on each court = 2

Number of players on each team = 5

Find all the equations you can use to find the number of basketball courts, 'c'.

So, we can solve it all equations,

Then,

We select equation A :
Equation A is : c times 2 times 5= 40

We can write,

Equation A is : cx2x5 = 40

simplify equation,

 c x 2 teams x 5 players = 40players

We can write,

                             cx2x5 = 40

                              cx10 = 40

                               c = 40/10

                                c = 4

Therefore, equation A use the number of basket ball courts c is = 4.

We select equation B :
Equation B is : 40 divided by c = 2 times 5

We can write,

Equation B is : 40/c = 2x5

simplify equation,

 40 players / c = 2 teams x 5 players

We can write,

                             40/c = 2x5

                              40/c = 10

                              40 = 10c

                               c = 40/10

                               c = 4

Therefore, equation B use the number of basket ball courts c is = 4.

We select equation C :
Equation C is : 2 times 5 times 40= c

We can write,

Equation C is : (2 x 5) 40 = c

simplify equation,

 (2 teams x 5 players ) 40 players = c

  (2 teams x 5 players ) = 40 players divided by c

We can write,

                             ( 2 x 5 ) = 40/c

                               10 = 40/c

                                c = 40/10

                                c = 4

Therefore, equation C use the number of basket ball courts c is = 4.

We select equation D :
Equation D is : 40 divided by 5 times 2= c

We can write,

Equation D is : 40/5x2 = c

simplify equation,

 40 players / 5 players x 2teams = c

We can write,

                              40/5x2 = c

                              40/10 = c

                              4 = c

                              c = 4

Therefore, equation D use the number of basket ball courts c is = 4.

We select equation E :
Equation E is : 40 divided by (5 times 2)= c

We can write,

Equation E is : 40/5x2 = c

simplify equation,

 40 players /  5 players x 2 teams = c

We can write,

                             40/5x2 = c

                              40/10 = c

                              4 = c

                               c = 4

Therefore, equation E use the number of basket ball courts c is = 4.

Therefore,

select all the equations you can use to find the number of basketball courts, c is = 4.

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Answer:

In standard form 7.4 × 10^-2

Step-by-step explanation:

Answer:

7.4×10^-2

Step-by-step explanation:

Firstly, to convert 0.074 to standard form you will bring the first significant figure and make it the first I.e 7.4 then count how many times you took it backwards to make it 7.4 then put a negative sign in front of it because you took it backwards

Answer:

Step-by-step explanation:

The area of shaded region is 3.6077 cm²

The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle.

A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l x w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.

Given:

rectangle:

Length = 4 cm

width= [tex]3 \frac{1}{2}[/tex] cm

So, area of rectangle

= length x width

=4 x  [tex]3 \frac{1}{2}[/tex]

= 4 x 7/2

=14 cm²

Now, area of Hexagon

= 3√3/2 x a²

= 3√3/2 x 2²

= 3√3/2 x 4

= 3√3 x 2

= 10.3923 cm²

Then, area of shaded region

= 14 - 10.3923

=3.6077 cm²

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Correct answer is B. We can rewrite the expression in the form of 39 - 80i

Any function that goes from complex numbers to complex numbers is said to as complex. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain. A nonempty open subset of the complex plane is typically found in the domain of complex functions.

Using (a-b)²= a²-2ab+b²

(8-5i)² = 8²-2(8)(5i)+(5i)²

= 64 - 80i + 25i²

We know that i²=-1

So

= 64 - 80i + 25(-1)

=64 - 25 - 80i

= 39 - 80i

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