A direct variation function contains the points (-9, -3) and (-12, 4). Which equation represents the function"
y=-3x
0 y=-
Oy
y = 3x

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:

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:

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

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

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

For this case we must factor the following expression:

[tex]d ^ 4-81[/tex]

Rewriting the expression:

[tex](d ^ 2) ^ 2-9 ^ 2[/tex]

We factor using the formula of the square difference:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

Where:

[tex]a = d ^ 2\\b = 9[/tex]

So:

[tex](d ^ 2 + 9) (d ^ 2-9)[/tex]

From the second term we have:

[tex]d ^ 2-3 ^ 2 = (d-3) (d + 3)[/tex]

Finally, the factored expression is:

[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]

Answer:

[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]

The complete factorization of the term:

              [tex]d^4-81[/tex] is:

        [tex](d-3)(d+3)(d^2+9)[/tex]

To factor a term means to express is as a product of distinct factors i.e. multiples.

We are asked to factor the algebraic expression which is given by:

[tex]d^4-81[/tex]

We could write this expression as:

[tex](d^2)^2-(3^2)^2=(d^2)^2-(9)^2[/tex]

We know that:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

i.e.

[tex]d^4-81=(d^2-9)(d^2+9)\\\\i.e.\\\\d^4-81=(d^2-3^2)(d^2+9)\\\\i.e.\\\\d^4-81=(d-3)(d+3)(d^2+9)[/tex]

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

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:

(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:

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:

    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 = 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:

x = 2

Step-by-step explanation:

x+3 = -x + 7

x = -x + 4

(2) = -(2) + 4

2 = 2

Answer:

The correct answer is x = 2.

Step-by-step explanation:

To solve this equation, we must get all of the variables (x's) to one side of the equation and get all of the constant terms (numbers only) to the other side.

Starting with this equation, we are going to add x to both sides of the equation.  This will cancel out the -x on the right side of the equation, thereby moving all of the variable x's to the left side of the equation.

x + x + 3 = -x + x + 7

If we simplify by combining like terms, or adding the x's together, we get:

2x + 3 = 7

Next, we should subtract 3 from both sides of the equation in order to move all of the constant terms to the right side of the equation.

2x + 3 -3 = 7 - 3

If we simplify, we get:

2x = 4

Finally, we should divide both sides by 2 in order to get the variable x alone on the left side of the equation, solving it.

x = 2

Therefore, your answer is x = 2.

Hope this helps!

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:

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

[tex]\bf (\stackrel{x_1}{7}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-(-5)}{3-7}\implies \cfrac{-9+5}{-4}\implies \cfrac{-4}{-4}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=1(x-7) \\\\\\ y+5=x-7\implies y=x-12[/tex]

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:

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:

i^88 =  1

Step-by-step explanation:

i^88 = i^ 4*22 = 1    { i^4k = 1 ; i^4k+1 =i ; i^4k+2 = (-1); i^4k+3 = (-i)  }

The equivalent expression for i^88 is 1 as the powers of i cycle every 4. Hence (i^4)^22 which is same as 1^22 ends up being 1.

In complex numbers, i is the imaginary unit with the property i^2 = -1. The powers of i repeat in a cycle: i^1=i, i^2=-1, i^3=-i, and i^4=1. To find the equivalent expression for i^88, we will the fact that i^4=1 and i^88 would be equivalent to (i^4)^22, because 4*22 = 88.

Therefore, (i^4)^22 = 1^22. The equivalent expression for i^88 is 1.

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49 out of 50 drinks were lemonade.

Divide the number of lemonade drinks by total drinks:

49 / 50 = 0.98 = 98%

98% of the drinks were lemonade, so there would be a 98% chance the next drink was lemonade.

[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:

A. 60°

Step-by-step explanation:

From the diagram, in triangle ABC,

AB=BC=CA=15 units.

This means triangle ABC is an equilateral triangle.

All angles in equilateral triangle are congruent. The sum of all interior angles in triangle is always 180°, so one angle of equilateral triangle is equal to 60°. Thus,

∠A=∠B=∠C=60°

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).

Learn more about the expansion of factors.

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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.

[tex]|x|+5\leq1\\|x|\leq-4\\x\in\emptyset[/tex]

C

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:

B

Step-by-step explanation:

A graph skewed right would have LESS dots on the right side

Hope this helped!

Answer:

The correct option is B.  

Step-by-step explanation:

Consider the provided graph.

A skewed right: If the distribution has a long right tail then it is know as skewed right. It is also called the positive-skew distributions. Due to a lengthy tail on the number line in the positive direction. The mean is on the right of the peak as well. See figure 1.

Now, consider the provided graph.

Option A is skewed left, so it is not the correct option.

Option B is skewed right, which is the correct option.

Whereas C and D are neither skewed left or right.

Therefore, the correct option is B.

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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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