Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain
restriction.
F(g(x))

Final answer:

To find the sum of the first 16 terms of the arithmetic series with a common difference of 6, use the sum formula for an arithmetic series S_n = (n/2) * (2a_1 + (n - 1)*d). By plugging in the values n = 16, a_1 = 1, and d = 6, the sum S_16 is calculated to be 736.

Explanation:

The student has presented an arithmetic series and is asking to find the sum of the first 16 terms (S16). In an arithmetic series, each term increases by a constant difference. The given sequence is 1, 7, 13, 19, and so on, showing a common difference (d) of 6.

Steps to find S16:

Identify the first term (a1) which is 1.

Determine the common difference (d), which is 6 in this case.

Use the formula for the sum of the first n terms of an arithmetic series Sn = (n/2) * (2a1 + (n - 1)*d), where n is the number of terms.

Substitute n = 16, a1 = 1, and d = 6 into the formula and calculate S16.

Now let's calculate S16:

S16 = (16/2) * (2*1 + (16 - 1)*6) = 8 * (2 + 15*6) = 8 * (2 + 90) = 8 * 92 = 736

The sum of the first 16 terms of the given arithmetic series is 736.

The figure in option B shows an example of symmetry. As we know that symmetry is when the objects on either the line of the axis are reflecting each other.

A figure is said to be in symmetry if a line can be drawn through it then the parts on either side of the line are a reflection of each other.

The line drawn between them is said to be the axis of symmetry or line of symmetry.

In the given figure,

Option (A) - the parts on either side of the line of symmetry are not reflecting each other

Option (B) - the parts on either side of the line of symmetry are reflecting each other, so they are in symmetry

Option (C) - the parts on either side of the line of symmetry are not reflecting each other

Option (D) - the parts on either side of the line of symmetry are not reflecting each other

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The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.

This means

[tex]82^\circ=m\angle 2[/tex]

[tex]\implies82=10x+12[/tex]

[tex]\implies10x=70[/tex]

[tex]\implies\boxed{x=7}[/tex]

For this case we must simplify the following expression:

[tex]\frac {\sqrt {10x ^ 3}} {\sqrt {5x}}[/tex]

We combine the expression in a single radical:

[tex]\sqrt {\frac {10x ^ 3} {5x}} =[/tex]

We eliminate common factors of the numerator and denominator:

[tex]\sqrt {\frac {2x ^ 3} {x}} =\\\sqrt {2x ^ 2} =[/tex]

By definition of power properties we have to:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

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

Answer:

Option A

Step-by-step explanation:

the circle ends(??) touches the square, so:

16 cm= diameter of the circle

area formula: (pi)r²

pi used= 22/7

16/2= 8 (radius)

22/7 x 8²

=201.143 cm2

Answer:

A. (1,2)

Step-by-step explanation:

A solution to the system of inequalities lies beyond the boundary line where the inequality is satisfied.

Hence let us assume that (yx)^2 - 4 = 0

We tried all the ordered pairs but the right answer was given by A. (1,2)

putting x = 1 and y = 2 in the expression:

(1*2)^2 - 4 = 0

0 = 0 which is true.

Answer:

A. (1,2)

Step-by-step explanation:

Answer:

Option D is correct.

Step-by-step explanation:

We need to find the quotient of the polynomials:

[tex](12x^3+14x^2 +9)\div(2x+3)\\[/tex]

The division is shown in the figure attached.

The quotient is: 6x^2-2x+3

The remainder is: 0

So, Option D is correct.

In physics, we always measure quantities and compare them with a standard. That standard defines a unit of the quantity. Suppose you want to measure the length of a car, so you use a meter stick, which is the standard for measuring distances. Then, why are units of measure important when solving real-world problems? Well, because when solving problems that involve equations, they need to be dimensionally consistent, but what does it mean? it means that you can't add two terms having different units. For instance, you can't add apples with tables!

The reasonable estimate of the probability is option A.

We know that

Probability = Number of favorable outcomes ÷ Total no of outcomes

So,

Here the number of favorable outcomes should be

= 3 + 2

= 5

And, the total no of outcomes should be

= 2 + 4 + 5 +  3 + 2

= 16

Therefore, option A is correct.

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In mathematics, notation like V(x) generally represents a function. Whether it is indeed a function depends on its definition and if every input x corresponds to exactly one output.

In mathematics, V(x) can indeed be a function. The notation V(x) generally represents a function named 'V' that takes an input 'x'. Whether it represents a function in a particular context depends on how it is defined. For a relationship to be a function, every input x must correspond to exactly one output in the function V. For instance, if V(x) is defined as x², then it IS a function, because each input x yields a specific output, which is the square of x.

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Answer:

0.1 or 1/10

Step-by-step explanation:

100% --> 1

9/10 --> 0.9

1 - 0.9 = 0.1

Answer:

120

Step-by-step explanation:

A: D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

B: D: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

C: D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

D: D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

W(b) = 12b.

he has enough to build 10 birdhouses, he doesn't have for more than that, he can either build no birdhouses or build 10 birdhouses, since "b" is the independent variable and thus the domain will come from it, what values can "b" safely take?   "b" can be either 0 or more than 0 but nor more than 10, because Owen doesn't have enough for more than that, 0 ≤ b ≤ 10.

let's say owen chooses to build 0 birdhouses, then W(0) = 12(0) => W(0) = 0.

let's say owen chooses to build 10 birdhouses, then W(10) = 12(10) => W(10) = 120.

so the amount of wood needed for those birdhouses, namely the range, can be either 0, if he chooses to build none, or 120 if he chooses to build 10, 0 ≤ W(b) ≤ 120.

Answer:

(13, -8, 5)

Step-by-step explanation:

Given

[tex]u = (5,-2,3)\\and\\v = (1,1,2)[/tex]

We have to find 3u-2v

So,

[tex]3u = 3(5,-2,3)\\3u= (15,-6,9)\\\\And\\\\2v= 2(1,1,2)\\2v= (2,2,4)\\\\3u-2v = (15,-6,9) - (2,2,4)\\= (15-2, -6-2 , 9-4)\\= (13, -8, 5)[/tex]

The ordered triple that represents 3u-2v is:

(13, -8, 5) ..

Answer:

C on edge

Step-by-step explanation:

Did the practice :)

Answer:

The value of b is 28.28

Step-by-step explanation:

We would use Law of sines to find the value of b

The law of sines is:

[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]

We are given

a= 20

A = 30°

B = 45°

b=?

Putting values in the formula:

[tex]\frac{20}{sin(30)}=\frac{b}{sin(45)}\\\frac{20}{0.5}=\frac{b}{0.707}\\b = \frac{20}{0.5} * 0.707\\b = 40 * 0.707\\b= 28.28\\[/tex]

The value of b is 28.28

Answer:

[tex]\boxed{\text{8.7 gal}}[/tex]

Step-by-step explanation:

The volume V of a prism is the area of the base b times the height h.

V=bh

Step 1. Calculate the volume of the prism.

Data:

b = 100 in²

h = 20 in

Calculation:

V = 100 in² × 20 in =2000 in³

Step 2. Convert cubic inches to gallons

1 gal = 231 in³

[tex]V = \text{2000 in}^{3} \times \dfrac{\text{1 gal}}{\text{231 in}^{3}}} = \textbf{8.7 gal}\\\\\text{The water jug will hold } \boxed{\textbf{8.7 gal}}[/tex]

Answer:

8.7gal

Step-by-step explanation

I uhm need points please

the associative property of addition. Try and memorize the different properties. youll need to know them later on. I hope this helped!

Answer:

side of the pool = 11 m

Step-by-step explanation:

Square Plot:

side = 35 m

Area = 35 * 35 = 1225 sq.m

Area of  lawn = 1104 sq.m

Swimming pool:

Area of the Swimming pool = 1225 - 1104 = 121 sq.m

 side * side = 121 = 11 * 11

side = √11 * 11

side of the pool = 11 m

Final answer:

The linear equation is solved by distributing the number outside the parentheses, combining like terms, and then isolating the variable x. The final answer is x = 1/4.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, let's follow the standard steps for solving a linear equation.

Distribute the 3 to both terms inside the parentheses: 3 × (−4x) + 3 × 5 = 12, which simplifies to −12x + 15 = 12.

Subtract 15 from both sides of the equation to get the x term by itself: −12x + 15 − 15 = 12 − 15, which simplifies to −12x = −3.

Finally, divide both sides of the equation by −12 to solve for x: −12x / −12 = −3 / −12, which simplifies to x = 1/4.

By following these steps, we've found that the value that satisfies the equation is x = 1/4.

Final answer:

To solve the equation 3(−4x + 5) = 12, distribute the 3, subtract 15 from both sides, and then divide by −12, yielding the solution x = 1/4 or 0.25.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, we'll start by expanding the equation and then isolating x.

Therefore, the solution to the equation 3(−4x + 5) = 12 is x = 0.25.

The answer is:

The option that represents the matrix is the option D:

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

From the statement we know that the matrix is formed with the information obtained from a system of equations:

Being the values of the first column the values of the variable "x"

Being the values of the second column the values of the variable "y"

Being the values of the third column the values of the variable "z"

Being the values of the fourth column the values of the constant numbers (after the equality)

Knowing that, we are looking for a system equation that contains the following equations:

First equation:

[tex]3x+6y-z=8[/tex]

Second equation:

[tex]-2x+3y=4[/tex]

Third equation:

[tex]4x+5y+4z=-2[/tex]

Hence, we can see that the option that matches with the matrix is the option D.

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

Have a nice day!

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=0.25(x+5)^2\implies y=0.25[x-(\stackrel{h}{-5})]^2+\stackrel{k}{0}~\hfill \stackrel{\textit{vertex}}{(-5,0)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{the y-intercept occurs when x =0}~\hfill }{y=0.25(0+5)^2\implies y=0.25(5)^2}\implies y=6.25~\hfill \stackrel{\textit{y-intercept}}{(0, 6.25)}[/tex]

To identify the vertex and the y-intercept for the function \( y = 0.25(x + 5)^2 \), we will use our knowledge of quadratic functions and their properties.
Vertex:
The given function is in the form of \( y = a(x - h)^2 + k \), where (h, k) is the vertex of the parabola. This form is commonly referred to as the vertex form.
For the given function, \( y = 0.25(x + 5)^2 \), we can see that it is equivalent to \( y = 0.25(x - (-5))^2 + 0 \), indicating that the vertex (h, k) is at (-5, 0). This means the parabola opens upwards (because the coefficient of \( (x + 5)^2 \) is positive) and has its vertex point at x = -5 and y = 0.
Y-intercept:
The y-intercept of a function is found by evaluating the function when x = 0.
So we'll substitute x = 0 into the function to find the y-coordinate of the y-intercept:
\( y = 0.25(0 + 5)^2 \)
Now, we'll calculate the value inside the parentheses:
\( 0 + 5 = 5 \)
Then, we raise it to the power of 2:
\( 5^2 = 25 \)
Finally, we multiply by 0.25:
\( y = 0.25 \times 25 = 6.25 \)
Therefore, the y-intercept where the graph crosses the y-axis is at the point (0, 6.25), where the x-coordinate is 0 and the y-coordinate is the value we just calculated, 6.25.
In summary, the vertex of the function \( y = 0.25(x + 5)^2 \) is (-5, 0), and the y-intercept is at (0, 6.25).

Answer:

C.1/16

Step-by-step explanation:

When a coin is tossed 4 times, the number of outcomes are:

2^4 = 16

So,

From the outcomes, only one outcome will be when there will be all heads

So, the probability will be:

One out of the 16 outcomes

Hence, the probability of a coin landing on heads all 4 times is:

C.1/16

Answer:

768

Step-by-step explanation:

3 x (-2^8) = 768

Answer: 3x4 - 13x3 + 28x2 - 23x + 10

Step-by-step explanation:

(3x2 - 4x + 5)(x2 - 3x + 2)

(3x4 - 9x3 + 6x2)

+       (-4x3 + 12x2 - 8x)

                    (10x2 - 15x + 10)

3x4 - 13x3 + 28x2 - 23x + 10

Answer: 3x^4 - 13x^3 + 23x^2 -23x + 10

For me at least

Step-by-step explanation: Good luck! :)

For this case we have that by definition, a quadratic expression is of the form:

[tex]ax ^ 2 + bx + c[/tex]

Where "c" represents the constant term.

Then, given the following expression:

[tex]4h ^ 7- \frac {h} {3} + \frac {1} {2}[/tex]

The constant term is given by:

[tex]\frac {1} {2}[/tex]

Answer:

Option D

Answer:

5^-7

Step-by-step explanation:

5^-4 over 5^3   : 5^-4/ 5^3 = 5^-4 × 5^-3 = 5^-7

Answer:

2

Step-by-step explanation:

The equation of the fourth side of the considered parallelogram is y = 2x + 10

Parallel lines have same slope, since slope is like measure of steepness and since parallel lines are of same steepness, thus, are of same slope.

Since given parallel line has equation [tex]y = 2x + 2[/tex], thus its slope is 2 and thus, the slope of the needed line is 2 too.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx + c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

A parallelogram is a four sided polygon, whose opposite sides are parallel to each other.

The slopes of y = 0 and y = 2 is same. (being 0)

Therefore the fourth side would've same slope as that of y = 2x.

The slope of y = 2x is 2 (the coefficient of x)

Thus, the equation of fourth side would be:

y = 2x + c for some real number c

Let we find the coordinates of four vertices. These are intersections of the equations of the adjacent sides.

Intersection of y = 0:

Putting y = 0 gives 0 = 2x, or x = 0

Thus, the intersection is on (0,0)

Putting y = 0 gives 0 = 2x + c, or x = -c/2

Thus, the intersection is on (-c/2, 0)

Intersection of y = 2:

Putting y = 2 gives 2 = 2x, or x = 1
Thus, the intersection is on (1,2)

Putting y = 2 gives 2 = 2x + c, or x = (2-c)/2

Thus, the intersection is on ((2-c)/2, 2)

Thus, the four vertices' coordinates are:

(0,0), (1,2), (-c/2, 0), and ( (2-c)/2, 0)

Let we name these points, as:

A(0,0), B(-c/2, 0),  C( (2-c)/2, 2) and D(1,2),

AB is line y = 0 (known from the y-coordinates of A and B)

Similarly, CD is line y = 2 (known from the y-coordinates of C and D)

AD and BC are parallel. (these are going to be other pair of parallel sides).

The length of AD is:

[tex]\sqrt{(1-0)^2 + (2-0)^2} = \sqrt{5} \: \rm units[/tex]

A parallelogram has its parallel sides of equal length.

Thus, length of BC is of √5 units too.

Since this parallelogram has two side lengths of 5 units, adn as AD and BC are not those sides, so we must have:

|AB| = |CD| = 5 units.

Length of AB is:

[tex]|AB| = \sqrt{(-c/2 - 0)^2 + (0 - 0)^2 } = c/2 = 5\\c = 10[/tex]

Thus, the equation of the fourth line is:

[tex]y = 2x + 10[/tex]

The graph of the considered parallelogram is given below.

Thus, the equation of the fourth side of the considered parallelogram is y = 2x + 10

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Answer:

95.1893

Step-by-step explanation:

The distance between points (16, -43) and (1, 51) is 95.1893

Answer:

k = 29

Step-by-step explanation:

(5k -3) + (9+k) = 180

5k-3+9+k = 180

6k + 6 = 180

6k = 180 - 6 = 174

k = 29

The value of k is:

                     k = 29

We know that when two angles lie on a straight line then the sum of the two angles is equal to 180 degree.

Here we have two angles on a straight line as:

first angle = (5k-3)°

and second angle= (9+k)°

Hence, we have:

(5k-3)°+(9+k)°=180°

i.e.

5k-3+9+k=180

on combining the like terms on the left hand side of the equation we have:

5k+k+9-3=180

6k+6=180

6k=180-6

6k=174

i.e.

k=174/6

i.e.

k=29