Round 228 to the nearest 100

The correct expansion of  (3x + 2)(3x² + 4) will be 9x³ + 12x + 6x² +8.

In order to expand any factor, we need to multiply the first term with all two-term with another bracket.

similarly, multiply the second term with all two-term with another bracket.

Since given that (3x + 2)(3x² + 4)

multiply 3x by (3x² + 4)

⇒   9x³ + 12x

Now multiply 2 with (3x² + 4)

⇒  6x² +8

By adding these two we get  9x³ + 12x + 6x² +8 which is the correct expansion of the (3x + 2)(3x² + 4).

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Final answer:

The correct expansion of the expression (3x + 2)(3x² + 4) is found by multiplying each term of the first binomial by each term of the second polynomial, resulting in the expanded form 9x³ + 12x + 6x² + 8.

Explanation:

The student's question refers to the process of expanding a binomial multiplied by a polynomial using the distributive property (also known as the FOIL method for binomials). To expand it, each term in the first binomial is multiplied by each term in the second polynomial and the results are then added together. Applying this method:

Adding all these products together gives the expanded form: 9x³ + 12x + 6x² + 8. It is important to also combine like terms if there are any; however, in this expansion, there are no like terms to combine.

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points A(-4, 0) and B(2, -3). Substitute:

[tex]m=\dfrac{-3-0}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]

C(-2, 2).

The point on the x-axis D(x , 0).

The slope:

[tex]m=\dfrac{0-2}{x-(-2)}=\dfrac{-2}{x+2}[/tex]

Put the value of the slope:

[tex]\dfrac{-2}{x+2}=\dfrac{-1}{2}[/tex]           change the signs

[tex]\dfrac{2}{x+2}=\dfrac{1}{2}[/tex]           cross multiply

[tex]x+2=(2)(2)[/tex]

[tex]x+2=4[/tex]            subtract 2 from both sides

[tex]x=2[/tex]

Final answer:

To find the probability of choosing a random non-honor student who is an athlete, subtract the number of non-honor students who are athletes but not in the 3 honor athletes group from the total non-honor students.

Explanation:

The question: A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

Step-by-step explanation:

Answer:

y+13 = 5(x+2)

Step-by-step explanation:

y = 5x-3

The slope is 5 since it is in the form y= mx +b where m is the slope

The point slope form of the equation of a line is

y-y1 = m(x-x1)  where (x1,y1) is the point

y--13 = 5(x--2)

y+13 = 5(x+2)

Answer:

B or y + 13 = 5(x + 2)

Step-by-step explanation:

Answer:

.05

Step-by-step explanation:

See The attachment for explanation

Hope it helps you...☺

Answer:

x = 6

Step-by-step explanation:

First, write the proportion, using a letter to stand for the missing term. We find the cross products by multiplying 8 times x, and 2 times 24. Then divide to find x. Study this step closely, because this is a technique we will use often in algebra. We are trying to get our unknown number, x, on the left side of the equation, all by itself. Since x is multiplied by 8, we can use the "inverse" of multiplying, which is dividing, to get rid of the 8. We can divide both sides of the equation by the same number, without changing the meaning of the equation. When we divide both sides by 8, we find that the x would equal 6.

Hope this helped!

The answer is B) x = 12.

Here are the steps I did. 1. Simplify 2/8 to 1/4 ( 1/4 = x/48)2. Multiply both sides by 48 ( 1/4 x 48 = x)3. Simplify 1/4 x 48 to 48/4 ( 48/4 = x)4. Simplify 48/4 to 12 ( 12 = x)5. Now reverse it ( x = 12)

Answer:

927 Cubic Inches.

Answer:

Area of the prism = 927 in²

Step-by-step explanation:

Area of the prism is defined by A = Area of the base × height

Since base of the prism is an octagon with side length = 4 inches

and apothem = 4.83 inches

Now area of the octagonal base = [tex]\frac{1}{2}(\text{Perimeter})(\text{Apothem})[/tex]

= [tex]\frac{1}{2}(4)(8)(4.83)[/tex]

= 77.28 inch²

Now area of the prism = 12×77.28 = 927.36 inch²

Therefore, area of the prism having base in the shape of an octagon is 927 inch²

The correct option is B.

The probability [tex]\( P(A \cap B \cap C) \)[/tex] from the Venn diagram is [tex]\( \frac{2}{25} \)[/tex], as 4 out of 50 elements overlap.

To find [tex]\( P(A \cap B \cap C) \)[/tex] from the given Venn diagram, we need to identify the part of the diagram where all three sets A, B, and C overlap, and then calculate the probability of landing in that part of the diagram.

The numbers within each section of the Venn diagram represent the number of elements in that section. The overlapping section of A, B, and C is the center where all three circles intersect, which has the number 4 in it. This means there are 4 elements that are in all three sets A, B, and C.

To calculate the probability [tex]\( P(A \cap B \cap C) \)[/tex], we need to divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space. The sample space in this case is all the numbers within the Venn diagram.

The total number of elements in the Venn diagram is the sum of all the numbers inside the circles.

Let's calculate it step by step.

The probability [tex]\( P(A \cap B \cap C) \)[/tex] is [tex]\( \frac{4}{50} \)[/tex], which simplifies to [tex]\( \frac{2}{25} \)[/tex]. Therefore, the answer is 2/25. Here is the step-by-step calculation:

1. Count the number of elements in the intersection of A, B, and C, which is 4.

2. Count the total number of elements in the sample space, which is 50.

3. Divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space to find the probability:

[tex]\[ P(A \cap B \cap C) = \frac{4}{50} = \frac{2}{25} \][/tex]

This is the required probability.

The complete question is here:

Options

A.2/25

B.3/25

C.4/25

D.1/25

Answer: On APEX it’s 2/25

Step-by-step explanation:

Answer:

g(- 8) = - 62

Step-by-step explanation:

Equate 8x + 2 to - 62

8x + 2 = - 62 ( subtract 2 from both sides )

8x = - 64 ( divide both sides by 8 )

x = - 8

Hence g(- 8) = - 62

Answer:

10%

Step-by-step explanation:

The difference between 86 and 77 is 9.

Divide 9 by 86

[tex]\frac{9}{86} = .1046511[/tex]

Multiply by 100

[tex].1046511 * 100 = 10.46511[/tex]

Round to the nearest percent

[tex]10.46511 \rightarrow 10 \textrm{ percent}[/tex]

Answer:

The probability of the spinner landing on an even number or a multiple of 3 is 0.6667 .

The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is 0.7778 .

Step-by-step explanation:

Be the events

A = even number

B = Multiple of 3

C = Odd Number

D = Number between 4 and 15, both numbers excluded

The sets are as follows:

A = {2,4,6,8,10,12,14,16,18}

B = {3,6,9,12,15,18}

C = {1,3,5,7,9,11,13,15,17}

D = {5,6,7,8,9,10,11,12,13,14}

To calculate the probability that the roulette lands in an even number or in a multiple of 3, we make the union of A and B:

A U B = {2,3,4,6,8,9,10,12,14,15,16,18} = 12 numbers of 18

P (A U B) = 12/18 = 2/3 = 0.6667

To calculate the probability that roulette lands on an odd number or a number between 4 and 15 (both numbers excluded), we make the union of C and D:

C U D = {1,3,5,6,7,8,9,10,11,12,13,14,15,17} = 14 numbers of 18

P (C U D) = 14/18 = 7/9 = 0.7778

The first answer is 0.6667

The second answer is 0.7778

Hope this helps!

Answer:

first one: 2/3

second one: 7/9

Step-by-step explanation:

PLATO

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-4)]^2+[5-0]^2}\implies d=\sqrt{(2+4)^2+(5-0)^2} \\\\\\ d=\sqrt{36+25}\implies d=\sqrt{61}\implies d\approx 7.81[/tex]

Answer:

    All values of x are solutions

Step-by-step explanation:

−15x+4 ≤ 109  OR −6x + 70 > −2

-15x ≤ 105       OR -6x  > -72

  -x ≤ 7            OR    -x > - 12

   x ≥ -7           OR     x < 12

Answer

       x ≥ -7           OR     x < 12

       All values of x are solutions

Answer:

(x + 4)(x + 5)

Step-by-step explanation:

Given

x² + 9x + 20

Consider the factors of the constant term (+ 20) which sum to give the coefficient of the x- term (+ 9)

The factors are + 4 and + 5, since

4 × 5 = 20 and 5 + 4 = 9, hence

x² + 9x + 20 = (x + 4)(x + 5)

Answer:

[ -8 , 9 ]

Step-by-step explanation:

You are looking at where f(t), the function, is on its y values.

Please mark for Brainliest!! :D Thanks!!

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Answer:

the axis of symmetry is x = 4

Step-by-step explanation:

The three coefficients of the polynomial f(x) = 2x^2 - 16x + 27 are a= 2, b = -16 and c = 27.                                                     -b

The formula for the axis of symmetry is  x = ------------

                                                                             2a

                               -(-16)

which here is x = ------------ = 4

                                2(2)

The equation of the axis of symmetry is x = 4.

Answer:

right

Step-by-step explanation:

there is a right angle in the triangle

Answer:

Right

Step-by-step explanation:

Right... the giveaway was the right angle  in the pic

[tex]f(g(x))=x[/tex] when [tex]g(x)=f^{-1}(x)[/tex]

So [tex]f(g(2))=2[/tex]

The value of f(g(2)) is 2 since g(x) is the inverse of f(x).

An inverse function that does the opposite operation of the actual function. It is denoted by f⁻¹(x).

The given function is f(x) and g(x) is the inverse of f(x) i..e, g(x) = f⁻¹(x).

Then,

f(g(x)) = f(f⁻¹(x))

         = x

Thus,

f(g(2)) = 2 (since x=2)

Therefore, the value of f(g(2)) = 2.

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Answer:

A

Step-by-step explanation:

To evaluate h(6) substitute x = 6 into h(x), that is

h(6) = (3 × 6) - 4 = 18 - 4 = 14 → A

The answer is:

The ordered pair satisfies the following system of equations since it satisfies both equations.

If we need to know if the ordered pair (-11/3,2/3) satisfies the system of equations we need to evaluate it and check if it satisfies both equations, we must remember that the condition that determines if the system of equations is satisfied is that both equations must be satisfied.

So, evaluating the ordered pair, we have:

First equation:

[tex]-x+5y=7\\\\-(\frac{-11}{3})+5*\frac{2}{3}=7\\\\\frac{11}{3}+\frac{10}{3}=7\\\\\frac{11+10}{3}=7\\\\\frac{21}{3}=7\\\\7=7[/tex]

We have that the equation is satisfied.

Second equation:

[tex]-x-7y=-1\\\\-(\frac{-11}{3})-7*\frac{2}{3}=-1\\\\\frac{11}{3}-\frac{14}{3}=-1\\\\\frac{11-14}{3}=7\\\\\frac{-3}{3}=-1\\\\-1=-1[/tex]

We have that the equation is satisfied.

Hence, we have that the ordered pair satisfies the system of equations since it satisfies both equations

Have a nice day!

Final answer:

The ordered pair (-11/3, 2/3) satisfies both equations in the given system, making it a solution to the system of equations.

Explanation:

To determine if the ordered pair (-11/3, 2/3) satisfies the given system of equations, we substitute x with -11/3 and y with 2/3 into both equations.

For the first equation -x + 5y = 7, we get:
-(-11/3) + 5(2/3) = 7
11/3 + 10/3 = 7
21/3 = 7
7 = 7
This confirms that the ordered pair satisfies the first equation.

For the second equation -x - 7y = -1, we calculate:
-(-11/3) - 7(2/3) = -1
11/3 - 14/3 = -1
-3/3 = -1
-1 = -1
The ordered pair also satisfies the second equation.

Since the ordered pair satisfies both equations, it is a solution to the system.

Answer:

The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]

Step-by-step explanation:

Let

x -----> the length of the rectangle

y -----> the width of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(x+y)[/tex]

[tex]P=56\ m[/tex]

so

[tex]56=2(x+y)[/tex]

[tex]28=(x+y)[/tex] ------> equation A

[tex]x=y+8[/tex] -----> equation B

Substitute equation B in equation A and solve for y

[tex]28=(y+8+y)[/tex]

[tex]28=2y+8[/tex]

[tex]2y=20[/tex]

[tex]y=10\ m[/tex]

Find the value of x

[tex]x=10+8=18\ m[/tex]

therefore

The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]

Answer:

20 by 20

Step-by-step explanation:

the new dimensions have to be 12 because 12×12 =144 so you would add 8 to 12 and get 20 for each side

Answer:

D) 20 feet by 20 feet

Step-by-step explanation:

Given:

The area of the original grass lawn reduced by 8 feet on each side.

The smaller lawn's area = 144 square feet which is represented by the equation

[tex](x - 8)^2 = 144[/tex], where "x" is the side of the original lawn.

To find the original dimension of the lawn, we need to solve for x from the above equation.

To solve follow the steps.

Step 1:

To get rid of square on the right hand side, we need to take square root on both sides.

Taking the square root on both sides, we get

[tex]\sqrt{(x - 8)^2} = \sqrt{144}[/tex]

[tex](x - 8) = 12[/tex]

Step 2:

Now add 8 on both sides, we get

x - 8 + 8 = 12 + 8

x = 20

Therefore, the original dimensions of the lawn is 20 feet by 20 feet.

Answer:

c

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( where m is the slope and c the y- intercept )

Given y = 2x - 3 ← in slope- intercept form

with m = 2

• Parallel lines have equal slopes, hence

y = 2x + c ← is the partial equation of the parallel line

To find c substitute (- 1, 2) into the partial equation

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = 2x + 4 → c

Answer:

F(4) = G(4) and F(12) = G(12) ⇒ answer B

Step-by-step explanation:

* Lets explain the meaning of the common solutions of two equation

- If two equations intersect at one point, (x , y) where x and y have the

 same values for both equations

- The point (x , y) belongs to the two graphs

- Ex: If (2 , 3) is a common solution of f(x) and g(x) , then the graphs of

 f(x) and g(x) meet each other at the point (2 , 3) that means f(2) = 3

 and g(2) = 3

- So f(2) = g(2)

* Lets solve the problem

∵ F(x) = Ix - 6I

∵ G(x) = 0.5 x

∵ The two graphs intersected at points (4 , 2) and (12 , 6)

- That means the two points (4 , 2) and (2 , 6) on the two graphs

∴ F(4) = 2 and G(4) = 2

∴ F(12) = 6 and G(12) = 6

- That means the two points are common solutions for both equations

∴ The solutions of the equation |x - 6|= 0.5 x are x = 4 and x = 12

∴ F(4) = G(4) and F(12) = G(12)

∴ The  best reasons which justifies Kiana's conclusion is;

   F(4) = G(4) and F(12) = G(12)

- Look to the attached graph to more understanding

- The red graph is F(x)

- The blue graph is G(x)

The best justification of Kiana's conclusion is ; F(4) = G(4) and F(12) = G(12) Option B

The justification for Kiana's conclusion is that the values of x and y at the points of intersection are the same for both equations.

This means that the point (x, y) belongs to both graphs.

For example, if (2, 3) is a common solution of f(x) and g(x), then the graphs of f(x) and g(x) intersect at the point (2, 3), which implies that f(2) = 3 and g(2) = 3. Therefore, f(2) = g(2).

To solve the problem at hand, we have

F(x) = |x - 6| and G(x)

= 0.5x.

Given that the two graphs intersect at the points (4, 2) and (12, 6),

Consequently, F(4) = 2 and G(4) = 2, as well as

F(12) = 6 and

G(12) = 6.

These common solutions indicate that the solutions of the equation

|x - 6| = 0.5x are

x = 4 and x = 12.

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Final answer:

To order the relative frequencies from least to greatest, calculate the relative frequency for each data value by dividing the frequency by the total number of data values. Then, determine the cumulative relative frequency by adding all previous relative frequencies to the relative frequency for the current row. Finally, list the data values in increasing order of their relative frequencies.

Explanation:

The given data is:

114,950; 158,000; 230,500; 387,000; 389,950; 479,000; 488,800; 529,000; 575,000; 639,000; 659,000; 1,095,000; 5,500,000

To order the relative frequencies from least to greatest, we need to determine the relative frequency for each data value. The relative frequency is found by dividing the frequency by the total number of data values. The cumulative relative frequency is the sum of all previous relative frequencies. Here are the calculations:

Relative Frequency:
114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100

Now we can order the relative frequencies from least to greatest:

114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100

Final answer:

To convert 720° to radians, multiply by π/180 to get 4π rad. This shows that 720° is equivalent to 4π radians.

Explanation:

To convert 720° to radians, we use the relationship that 1 revolution equals 360° or 2π radians. Therefore, to convert degrees to radians, you multiply the number of degrees by π/180. In this case:

720° × (π rad / 180°) = 4π rad

Thus, 720° is equal to 4π radians. The concept of angular velocity is related to radians as it is the rate of change of an angle with time, and using radians can be especially useful in calculations involving angular motion.

The statements which are true are:

In Trigonometry, the Law of Sine relates the length of sides of a triangle to the angle of a triangle.

According to this law if a,b and c are the sides of a triangle and A,B and C  respectively are opposite angles to the side.

Hence, we have:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

i.e. we have:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]

This could also be given by:

[tex]a\sin B=b\sin A[/tex]

[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

Answer:its all of them

Step-by-step explanation:

e2020

Answer:

I believe the answer is 12 • (x + 11) .

if the diameter is 14, then its radius must be half that, or 7.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=7 \end{cases}\implies V=\cfrac{4\pi (7)^3}{3}\implies \stackrel{\pi =3.14}{V=1436.03} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=7\\ h=14 \end{cases}\implies V=\pi (7)^2(14)\implies \stackrel{\pi =3.14}{V=2154.04}[/tex]