Which of the following represents a function?

Answer:

(E) (20k - 150)/(k - 10)

Step-by-step explanation:

Sum of all scores = average × number of scores = 20 × k = 20k

                   Sum of 10 scores = 15 × 10 =150

      Sum of remaining scores = 20k - 150

Number of remaining scores = k -10

Average of remaining scores = sum of remaining/no. remaining

= (20 k -150)/(k-10)

Answer:

Alex investment = $ 23,800

Step-by-step explanation:

The statement is Alex and Rachel are forming partnership. According to the agreement Alex invest $3000 more than Rachel's two-third investment and the total capital is $55,000.Find out Alex investment.

Let x be the investment of Rachel. Lets make an equation to find the value of x.

x+2/3x +$3000=$55,000

Combine the like terms:

x+2/3x = 55,000 - 3000

x+2/3x = $52000

Now take the L.C.M of L.H.S

3x+2x/3 = $52000

Now Add the values of x.

5x/3 = $52000

Multiply both the terms by 3.

5x/3 *3 = 3* $52000

5x= 156000

Now divide both the sides by 5.

5x/5 = 156000/5

x= 31200

Now calculate Alex investment. According to the statement Alex invest $3000 more than 2/3 of Rachel.

We have found the Rachel investment which is $31200. Therefore we can write 2/3 of Rachel investment as 2/3(31200).

=2/3(31200)+$3000

=2*10400+3000

=20,800+3000

=$23,800

Rachel investment = $31200

Alex investment = $ 23,800

If you want to check whether the investments are correctly determined or not. You can add both the investments and the result will be the partnership's capital amount.

$31200+$ 23,800 = $55,000 ....

Answer:

System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.

Step-by-step explanation:

We need to make system of equations of:

x^2+3x+1=2x^2+2x+3

Solving,

Adding -2x^2 on both sides

x^2+3x+1-2x^2=2x^2+2x+3-2x^2

-x^2+3x+1=2x+3

Adding -2x on both sides

-x^2+3x+1-2x=2x+3-2x

-x^2+x+1=3

Adding -3 on both sides

-x^2+x+1-3=3-3

-x^2+x-2=0

Multiplying with -1

x^2-x+2=0

System of equations of x^2+3x+1=2x^2+2x+3 is x^2-x+2=0.

can you please add the answers to choose from? I'd like to help

Answer:

B. The second graph displayed.

Step-by-step explanation:

Recieved an 100% on my test with this question!!

Hope I could help! (´⊙◞⊱​◟⊙｀)

Answer:

A'(0, -8), B'(6, 0), C'(0, 8), D'(-6, 0)

Step-by-step explanation:

Whenever you are doing a 90° clockwise rotation ABOUT THE ORIGIN, it is in the form of [y, -x], meaning you take the y and make it your x, then take your original x and put its OPPOSITE.

90° counterclockwise rotation → [-y, x]

90° clockwise rotation → [y, -x]

I hope this helps, and as always, I am joyous to assist anyone at any time.

Answer:

[tex](q \circ r)(7)=22[/tex]

[tex](r \circ q)(7)=8[/tex]

Step-by-step explanation:

1st problem:

[tex](q \circ r)(7)=q(r(7))[/tex]

r(7) means to replace x in [tex]\sqrt{x+9}[/tex] with 7.

[tex]r(7)=\sqrt{7+9}=\sqrt{16}=4[/tex]

[tex](q \circ r)(7)=q(r(7))=q(4)[/tex]

q(4) means replace x in [tex]x^2+6[/tex] with 4.

[tex]q(4)=4^2+6=16+6=22[/tex].

Therefore,

[tex](q \circ r)(7)=q(r(7))=q(4)=22[/tex]

2nd problem:

[tex](r \circ q)(7)=r(q(7))[/tex]

q(7) means replace x in [tex]x^2+6[/tex] with 7.

[tex]q(7)=7^2+6=49+6=55[/tex].

So now we have:

[tex](r \circ q)(7)=r(q(7))=r(55)[/tex].

r(55) means to replace x in [tex]\sqrt{x+9}[/tex] with 55.

[tex]r(55)=\sqrt{55+9}=\sqrt{64}=8[/tex]

Therefore,

[tex](r \circ q)(7)=r(q(7))=r(55)=8[/tex].

Step-by-step explanation:

simplify the equation

5-x(2)-3x(4x-7)/(5-x)(3x)

=10-2x-12x²+21x/15x-3x²

=-12x²-23x+10/15x-3x³

the answer is B

yes, Robot is correct but Irum is not

Answer:

simplify the equation first

5-x(2)-3x(4x-7)/(5-x)(3x)

=10-2x-12x²+21x/15x-3x²

=-12x²-23x+10/15x-3x³

the answer is B

Step-by-step explanation:

:)

Answer:

The first term of the sequence is 1/5

Step-by-step explanation:

The first term is 1/5.

The reason is that there is a common ratio between each term. In this case multiplying the previous term in the sequence by 5 would give the next term.

So in this case 1/5 is the first term.

If we multiply 1/5 by 5, it will give the next term which is 1.

1/5*5=1

Thus the first term in the sequence = 1/5....

Answer:

Step-by-step explanation:

When you divide by 100, the decimal moves 2 places to the left.

847.8

When you have moved the decimal 3 places to the left, you have divided by 1000

To reverse the effects of 847.8 by dividing by 10000 you need to multiply by 10000

847.8 * 10000 = 8478000 Try this on your calculator to confirm it.

Same with the last one. To get 847.8 when you have divided by 1 million, you movie the decimal in the answer 6 places.

847.8 * 1000000 = 847800000

[tex](f-g)(x)=2x-6-(3x+9)=2x-6-3x-9=-x-15[/tex]

Answer:

The correct option is C.

Step-by-step explanation:

The correct option is C.

We have given:

f(x) = 2x - 6 and g(x) = 3x + 9

Now we have to find (f-g)(x)

(f-g)(x) = f(x)- g(x)

Now subtract g(x) from f(x)

(2x - 6) - (3x + 9)

Open the parenthesis. When we open the parenthesis the signs of second bracket will become negative because there is a negative sign outside the bracket.

(f-g)(x)= 2x-6-3x-9

Now solve the like terms:

(f-g)(x)= -x-15

Thus the correct option is C....

Answer:

A.

Step-by-step explanation:

Now since the degree is odd (3 in this case) and the leading coefficient is positive (1), then the end behavior is going to be:

for left-end behavior, it is down

for right-end behavior, it is up

We are going to definitely have some increasing action going on because it goes from down to up reading from left to right.

Let's graph it in our ti-84's or whatever you have.

This is a very rough graph but you can see it is just increasing on the entire domain.  This means reading the graph from left to right, there is only rise.

I can give you an answer with calculus in it if you prefer.

Answer:[tex]\large\boxed{C.\ (x-5)^2}[/tex]Step-by-step explanation:

[tex]f(x)=x-5,\ g(x)=x^2\\\\g\bigg(f(x)\bigg)-\text{put}\ x-5\ \text{expression instead of}\ x\ \text{in}\ g(x):\\\\g\bigg(f(x)\bigg)=(x-5)^2[/tex]

Answer:

Step-by-step explanation:

(x^3 + 2x − 3)(x^4 − 3x^2 + x)

Multiply each value of 2nd bracket with 1st bracket:

=x^4(x^3 + 2x − 3) - 3x^2(x^3 + 2x − 3) +x(x^3 + 2x − 3)

=x^7+2x^5-3x^4-3x^5-6x^3+9x^2+x^4+2x^2-3x

Now combine the terms with same power:

=x^7-x^5-2x^4-6x^3+11x^2-3x

You can also  take the common from the expression:

x(x^6-x^4-2x^3-6x^2+11x-3)....

The product of (x^3 + 2x − 3)(x^4 − 3x^2 + x) is x(x^6-x^4-2x^3-6x^2+11x-3)....

Answer:

the cost of each notebook is $4.8

Step-by-step explanation:

Cost of each notebook= ?

Cost of a poster = $6

Total amount she spent = $20.40

If we subtract the cost of poster from total amount we get the cost of 3 notebooks.

$20.40-$6

=$ 14.4

It means the cost of 3 notebooks = $14.4

To find the cost of each notebook divide the cost of 3 notebooks by the number of books.

=14.4/3

=$4.8

Thus the cost of each notebook is $4.8....

Answer:

2 /√3 or  2√3 / 3.

Step-by-step explanation:

Referring to the 30-60-90 triangle: hypotenuse = 2 , smaller leg = 1 and longer leg = √3 and the shorter side is opposite the 30 degree angle.

So cos 30 = √3/2

Sec 30 = 1 / cos 30

= 2 /√3

or  2√3 / 3.

The exact value of sec(30º) using trigonometric identity for secant is 2.

To find the exact value of sec(30º), use the trigonometric identity for secant:

sec(θ) = 1/cos(θ)

Using the special right triangle with angles 30º, 60º, and 90º, it is known that the side lengths are in the ratio 1:√3:2.

The cosine is defined as the adjacent side divided by the hypotenuse.

For a 30º angle, the adjacent side = 1 and the hypotenuse = 2.

So, cos(30º) = 1/2

Substituting this into the formula for secant:

sec(30º) = 1/cos(30º)

               = 1/(1/2)

               = 2

Therefore, the exact value of sec(30º) is 2.

Learn more about Trigonometry here:

https://brainly.com/question/12068045

#SPJ6

Answer:

D. (x+8)^2

Step-by-step explanation:

x^2 + 16x  + 64

We are factoring a quadratic trinomial in which the first term is x^2.

We need to find two numbers whose product is 64 and whose sum is 8.

8 * 8 = 64

8 + 8 = 16

The numbers are 8 and 8.

x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2

Check: If (x + 8)^2 is indeed the correct factorization of x^2 + 16x + 64, then if you multiply out (x + 8)^2, you must get x^2 + 16x + 64.

(x + 8)^2 =

= (x + 8)(x + 8)

= x^2 + 8x + 64

= x^2 + 16x + 64

We get the correct product, so our factorization is correct.

Answer:

The graph of g(x) is a translation of f(x) 3 units down.

Step-by-step explanation:

The given function is

[tex]g(x) = f(x) - 3[/tex]

The parent function now is f(x).

The -3 tells us that there is a vertical translation of the parent function 3 units down.

Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.

Answer:

The value of x is 4

Step-by-step explanation:

we know taht

The intersecting chords theorem  states that the products of the lengths of the line segments on each chord are equal.

so

In this problem

[tex](12)(x)=(8)(x+2)[/tex]

solve for x

[tex]12x=8x+16[/tex]

[tex]12x-8x=16[/tex]

[tex]4x=16[/tex]

[tex]x=4[/tex]

To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.

Original equation:

y = 4x + 5

Switched:

x = 4y + 5

Solve for y by isolating it:

x - 5 = 4y + 5 - 5

x - 5 = 4y

(x - 5)/4 = 4y/4

[tex]\frac{1}{4}x-\frac{5}{4} = y[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

a) The equation of the total cost is d = a + bc

   The equation for calculating the total is d = 60 + 4(50)

b) The total cost for the job is $260

Step-by-step explanation:

* Lets explain how to solve the problem

- Mr. Gomez owns a carpet cleaning business

- The situation of the job;

# a represents the initial charge (in dollar) for coming to the house

# b represents the number of hours the job takes

# c represents the charge (in dollars) for each hour the  job takes

# d represents the total cost (in dollars) of the job

* Lets make the equation of the total cost

∵ The initial amount of the job is a dollars

∵ The number of hours the job takes is b

∵ The charge per hour is c dollars

∵ The total cost of the job is d

- The total cost is the sum of the initial amount and the product of

 the number of hours the job takes and the charge per hour

∵ The total cost = initial amount + the number of hours × charge

   per hour

∴ d = a + b × c

∴ d = a + bc

a)

* The equation of the total cost is d = a + bc

∵ a = $60 , b = 4 hours , c = $50

∴ d = 60 + 4(50)

* The equation for calculating the total is d = 60 + 4(50)

b)

∵ d = 60 + 4(50)

∴ d = 60 + 200

∴ d = 260

* The total cost for the job is $260

Answer:

B. 3.64 to the nearest hundredth.

Step-by-step explanation:

3tan1/3theta=8

tan1/3theta = 8/3

1/3 theta =  1.212 radians, 1.212 + π radians.

theta = 1.212 * 3 = 3.636 radians,    3(1.212 + π) radians.

The second value is greater than 2π radians.

The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.

To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]

[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]

Next, we take the inverse tangent (arctan) of both sides to solve for

[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]

Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:

[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]

Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.

The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]

[tex]\[ \theta \approx 1.21 + k\pi \][/tex]

where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]

For[tex]\( k = 0 \):[/tex]

[tex]\[ \theta \approx 1.21 \][/tex]

For [tex]\( k = 1 \):[/tex]

[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]

For[tex]\( k = 2 \):[/tex]

[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]

However, this value is outside our interval, so we do not include it.

For[tex]\( k = 3 \):[/tex]

[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]

This value is also outside our interval, so we do not include it.

Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]

For [tex]\( k = 0 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]

For [tex]\( k = 1 \)[/tex]:

[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]

This value is outside our interval, so we do not include it.

Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]

Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.

[tex]a_1=1\\d=2\\a_n=1+(n-1)\cdot 2=1+2n-2=2n-1[/tex]

Answer:

We know that sec(x) = 1/cos(x). Therefore:

7sec(2x) = 7/cos(2x).

The function won't be define at the points where the denomitator equals zero, which is when x=(2n+1)π/2.

Using a graphing calculator, we get that the graph of the function is the one attached.

Answer:

[tex]\frac{15}{61}+\frac{18}{61}i[/tex]

Step-by-step explanation:

[tex]\frac{3}{5-6i}[/tex]

To simplify or to write in the form a+bi, you will need multiply the top and bottom by the bottom's conjugate like so:

[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}[/tex]

Keep in mind when multiplying conjugates you only have to multiply first and last.

That is the product of (a+b) and (a-b) is (a+b)(a-b)=a^2-b^2.

(a+b) and (a-b) are conjugates

Let's multiply now:

[tex]\frac{3}{5-6i} \cdot \frac{5+6i}{5+6i}=\frac{3(5+6i)}{25-36i^2}[/tex]

i^2=-1

[tex]\frac{15+18i}{25-36(-1)}[/tex]

[tex]\frac{15+18i}{25+36}[/tex]

[tex]\frac{15+18i}{61}[/tex]

[tex]\frac{15}{61}+\frac{18}{61}i[/tex]

For this case we must simplify the following expression:

[tex]\frac {3} {5-6i}[/tex]

We multiply by:

[tex]\frac {5 + 6i} {5 + 6i}\\\frac {3} {5-6i} * \frac {5 + 6i} {5 + 6i} =\\\frac {3 (5 + 6i)} {(5-6i) (5 + 6i)} =\\\frac {3 (5 + 6i)} {5 * 5 + 5 * 6i-6i * 5- (6i) ^ 2} =\\\frac {3 (5 + 6i)} {25-36i ^ 2} =\\\frac {3 (5 + 6i)} {25-36 (-1)} =\\\frac {3 (5 + 6i)} {25 + 36} =\\\frac {3 (5 + 6i)} {61} =\\\frac {15 + 18i} {61}[/tex]

Answer:

[tex]\frac {15 + 18i} {61}[/tex]

Answer:

=1/40

Step-by-step explanation:

=1/8/5

=1/40

Answer:

Option B

center (3,2)

radius 3

Step-by-step explanation:

Given:

x^2+y^2-6x+4y+4=0

x^2+y^2-6x+4y=-4

Now completing square of x^2-6x by introducing +9 on both sides:

x^2-6x+9+y^2+4y=-4+9

(x-3)^2+y^2+4y=5

Now completing square of y^2+4y by introducing +4 on both sides:

(x-3)^2+y^2+4y+4=5+4

(x-3)^2 + (y-2)^2= 9

Now comparing with the circle equation:

(x-h)^2 + (y-k)^2= r^2

where

r= radius of circle

h= x-offset from origin

k= y-offset from origin

In given case

r=3

h=3

k=2

Hence, option B is correct with radius =3 and center =(3,2)!

Answer:

Center (3,-2); radius 3

Answer:

The area (probability) is: 0.6864.

Step-by-step explanation:

According to the statement, we are in front of a normal distribution with the following parameters:

µ (mean) = 0

σ (Standard deviation) = 1.

Then we need to find the area of the shaded region, which is the area between the points -1.21 < z < 0.84.

And the area (probability) is: 0.6864.

Answer:

A. 0.6864

Step-by-step explanation:

The area of the shaded region between the two z-scores indicated in the diagram is 0.6864.

mean = 0

Standard deviation = 1

Answer:

Answer is x>3

Step-by-step explanation:

The last step is: divide -2 to both sides and since the 2 is negative the sign flips so it would be x>3.

Hope my answer has helped you and if not i'm sorry.

Answer:

b. 10x^3 - 6x^2 - 9x + 12

Step-by-step explanation:

A cubic expression has the highest power of the variable to the third power

x^3

b. 10x^3 - 6x^2 - 9x + 12

is the only expression that has the highest power as x^3

a  has x^4  and c and d do not have an x^3 term

Final answer:

The expression that represents a cubic expression is (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex], as it is the only option where the highest power of x is three.

Explanation:

The expression that represents a cubic expression is option (b) [tex]10x^3 - 6x^2 - 9x + 12[/tex]. A cubic expression is one in which the highest degree of any term is three, which means the variable (most commonly x) is raised to the third power. Looking at the options provided:

(a) [tex]19x^4 + 18x^3 - 16x^2 - 12x + 1[/tex] is not a cubic expression because it contains a term with x to the fourth power.

(b) [tex]10x^3 - 6x^2 - 9x + 12[/tex] is a cubic expression because the highest power of x is three.

(c)[tex]-9x^2 - 3x + 4[/tex] is not a cubic expression; it's a quadratic expression since the highest power of x is two.

(d) 4x + 3 is also not a cubic expression; it's linear as the highest power of x is one.