An abundant number is a positive integer N such that the sum of the factors of N (not including N) is greater than N. What is the smallest abundant number?

Answer:

x = 8

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Sum the exterior angles and equate to 360

62 + 66 + 77 + 59 + 12x = 360, that is

264 + 12x = 360 ( subtract 264 from both sides )

12x = 96 ( divide both sides by 12 )

x = 8

Answer:

A= 706.85m^2

Step-by-step explanation:

A= 4• Pi•r^2

= 4•Pi•15^2

=2827.43/4

=706.8575m^2

For this case we have that by definition, the area of a circular sector is given by:

[tex]A = \frac {a * r ^ 2} {2}[/tex]

Where:

r: It's the radio

a: It is the angle of the sector

We have to:

a = 90 degrees

[tex]90\ degrees = \frac {\pi} {2}[/tex]

Then, replacing:

[tex]A = \frac {\frac {\pi} {2} * 15 ^ 2} {2} = \frac {225 \pi} {4}[/tex]

Answer:

Option A

Answer:

I'm pretty sure its A

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Option: A is the correct answer:

                     [tex]A.\ y=-3x[/tex]

The equation of a line passing through two points (a,b) and (c,d) is calculated with the help of a two-point formula:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Based on the graph we observe that the line passes through:

(0,0) and (3,-9)

i.e. we have: (a,b)=(0,0) and (c,d)=(3,-9)

i.e. the equation of line is given by:

[tex]y-0=\dfrac{-9-0}{3-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-9}{3}\times x\\\\i.e.\\\\y=-3x[/tex]

          The answer is: Option: A

Answer:

C. (-2,2π/3)

Step-by-step explanation:

Given:

In the given plane, each line represents angles and the circles shows the radii. Now as full circle is of 360 degrees or 2π and there are 12 straight lines that means

every angle is π/6 apart (30 degrees).

As the given red point is on circle 2, this means the radii, r=2

and Ф=300 degrees or 5π/3

r=(2,5π/3)

but above is not given in the options.

Polar coordinates can have positive or negative theta and also have positive or negative radii. In case of negative radii the polar coordinate moves in opposite direction of the pole.

if we consider r=-2 then we have to move in opposite direction of pole of  Ф=300 degrees or 5π/3 is 120 degrees or 2π/3.

hence r=-2 andФ=2π/3

Correct option is C:(-2,2π/3)!

Midpoint has form of,

[tex]M(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

We can insert the data,

[tex]M(\dfrac{4+3}{2},\dfrac{-1+2}{2})[/tex]

Which simplifies to,

[tex]\boxed{M(3.5, 0.5)}[/tex]

Hope this helps.

r3t40

B, because every prime number greater than 2 is odd, and the product of two odd numbers is odd.

Answer: I'm pretty sure its B

Step-by-step explanation:

..

Answer:

See explanation

Step-by-step explanation:

1. [tex]JK\cong LM[/tex] - given

2.  [tex]JL\cong LN[/tex] - definition of midpoint (the midpoint of the segment divides the segment into two congruent segments)

3. [tex]\angle LJK\cong \angle NLM[/tex] - corresponding angles theorem (corresponding angles theorem states: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.)

4. [tex]\triangle JLK\cong \triangle LNM[/tex] - SAS (SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent).

Answer:

LARGEST ANGLE= 96 DEGREES

Step-by-step explanation:

MEASURE OF LARGEST ANGLE= 3A

SMALLEST ANGLE= A

THIRD ANGLE= 20+A

3A+A+20+A=180(SUM OF INTERIOR ANGLES OF TRAINGLE IS 180 DEGREES)

TRANSPOSE 20 TO RHS.

5A=180-20=160

A=160/5

=32

MEASURE OF SMALLEST ANGLE=32

LARGEST ANGLE=3A=3*32=96 DEGREES

THIRD ANGLE=32+20=52 DEGREES

Answer:

The largest angle has a measure of 96 degrees.

Step-by-step explanation:

In order to solve this problem, we have to know the fact that the sumatory of the internal angles of any triangle is 180 degrees.

With this statement in mind, and looking at the image, we can say:

180 = A + B + C (eq. 1)

Before continue any further, let's affirmt that B is the smallest angle.

Now the enunciate says "One angle in a triangle has a measure that is three times as large as the smallest angle"; This can be express as:

A = 3B (eq. 2)

The other enunciate is "The measure of the third angle is 20 degrees more than that of the smallest angle" This can be express as:

C = B + 20 (eq. 3)

Now, replacing equations 2 and 3 into 1:

(eq. 1) 180 = 3B + B + B + 20

And clearing B:

B = 32.

By knowing B, we can clear A and C from equations 2 and 3 respectively:

(eq. 2) A = 3B,  so A= 96

(eq. 3) C = B + 20, so C =52

Answer:

its B and the next one is C

Step-by-step explanation:

Formula for the sequence based on term number is

[tex]a_{n} =(4)(2)^{n-1}[/tex].

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given

First term [tex]a[/tex] = 4

Common ratio r = -2

It is a geometric sequence because we have common ratio

Formula for the sequence based on term number is

[tex]a_{n} =ar^{n-1}[/tex]

[tex]a_{n} =(4)(2)^{n-1}[/tex]

Hence, Formula for the sequence based on term number is

[tex]a_{n} =(4)(2)^{n-1}[/tex].

Find out more information about geometric sequence here

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Answer:

x^2+7x if you are asked to find the difference of a function f and function g

Step-by-step explanation:

We are asked to A-B or f(x)-g(x).

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

4x^2+6x-3x^2+x

The like terms I'm going to pair up.

4x^2-3x^2+6x+x

1x^2          +7x

x^2            +7x

The answer is x^2+7x

Answer:

OPTION D: [tex]h(x)=x^2+7x[/tex]

Step-by-step explanation:

You know that the area of Rectangle A is given by :

[tex]f(x)= 4x^2+6x[/tex]

And the area of Rectangle B is given by:

[tex]g(x)=3x^2-x[/tex]

Therefore, in otder to find the function that represents the difference, you need to subtract the functions f(x) and g(x).

Then, you get this function h(x):

 [tex]h(x)=f(x)-g(x)\\\\h(x)= (4x^2+6x)-(3x^2-x)\\\\h(x)=4x^2+6x-3x^2+x\\\\h(x)=x^2+7x[/tex]

Step-by-step explanation:

[tex]-\sqrt5-3\sqrt5=-1\sqrt5-3\sqrt5=(-1-3)\sqrt5=-4\sqrt5[/tex]

Answer:

930

Step-by-step explanation:

To use the division method

Write the given numbers in a horizontal row separated by commas.

Divide them by a suitable prime number

Place the quotient under the numbers in the next row. If a number is not divided exactly then bring it down to the next row.

Repeat the process until only co prime numbers are left in the last row.

Multiply all the prime numbers used as divisors.

The product is the LCM

Given 30 and 62, then

2 | 30, 62

3 | 15, 31

5 | 5, 31

31 | 1, 31

    | 1, 1 ← co primes left

Hence LCM = 2 × 3 × 5 × 31 = 930

Answer:

1/110

Step-by-step explanation:

Her chance of originally grabbing a pink marker is 1/11. Her chance of grabbing a blue marker after the pink marker is taken out is 1/10. When you multiply 1/11 by 1/10, you get a 1/110 chance of getting the colored markers in this series

Answer:

The probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Step-by-step explanation:

Hello, this is a great question and one that many people struggle with in school. Hopefully I can help you understand it more clearly. Kelly has 11 markers in total within her backpack and needs to randomly pick out the pink marker. since there is only 1 that would mean her probability of picking out the pink marker is 1/11 .

Now there are 10 markers inside the backpack and she needs to randomly pick out the blue marker. since there is only 1 blue marker that would mean her probability of picking that one out is 1/10.

So now we have the following probabilities

Now if we want to find the probability of her getting the pink marker and the blue marker one after another we would need to multiply both fractions together

[tex]\frac{1}{11} * \frac{1}{10} = \frac{1}{110}[/tex]

So the probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Answer:

[tex]\Huge \boxed{20}[/tex]

Step-by-step explanation:

This question is about order of operations. It stands for parenthesis, exponent, multiply, divide, add, and subtract from left to right.

First thing you do is parenthesis.

[tex]\displaystyle [2-6]=-4[/tex]

[tex]\displaystyle -4-[-24][/tex]

Then, add and subtract numbers from left to right to find the answer.

[tex]\displaystyle -4-[-24][/tex]

[tex]\displaystyle -4-[-24]=-4+24=20[/tex]

20, which is our answer.

Hope this helps!

Answer:

Sample Response: A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.

Step-by-step explanation:

trust me

To prove a projectile's trajectory is parabolic, we start with the horizontal motion equation, solve for time, and substitute into the vertical motion equation, ending up with a quadratic equation in the form of y = ax + bx², showing parabolic motion.

To prove that the trajectory of a projectile is parabolic, we start with the two separate equations for horizontal and vertical motion. The horizontal motion equation is given by x = Voxt, where Vox is the horizontal velocity component. We solve this for time t to get t = x / Vox. We then substitute this expression for t into the vertical motion equation y = Voyt - 1/2gt2, where Voy is the vertical velocity component and g is the acceleration due to gravity.

Substituting t = x / Vox into the vertical equation, we get y = Voy(x / Vox) - (1/2)g(x / Vox)2. This simplifies to y = (Voy/ Vox)x - (g / 2Vox2)x2, which is of the form y = ax + bx2, proving that the trajectory is parabolic with a and b as constants.

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Answer:

D. of any age

Step-by-step explanation:

A driver  can be charged with Driving While Intoxicated of any age.

It doesn't matter how old you are because a crime is a crime. If you are younger there will most likely be less of a punishment as adults.

Answer: x = 10  y = 6

Step-by-step explanation:

0.1X + 5 = y

0.2X + 4 = y

0.1X + 5 = 0.2X  + 4

-0.1X - 4 = -0.1X - 4

1 = .1X

x = 10

0.1(10) + 5 = y

1 +5 = y

6 = y

Question 7

Answers:

Jane's Uber business has the function f(x) = 0.10x+5

Joe's Uber business has the function f(x) = 0.20x+4

x is the number of miles, f(x) is the total cost for the customer

-------------------------

Explanation:

Jane charges $5 no matter how many miles are driven. This is the base fee. On top of this base fee, an additional price is charged based on the number of miles driven. If Jane drives 1 mile, then an additional 0.10*1 = 0.10 dollars is added on. If 2 miles are driven, then 0.10*2 = 0.20 dollars is added on. And so on.

In general, an additional 0.10*x dollars is added on the base fee to get the total cost to be 5 + 0.10x which rearranges to 0.10x + 5. That's how I ended up with f(x) = 0.10x + 5

Joe's equation will be constructed in a similar way. His base fee is $4 and you add on 0.20x dollars (since it costs $0.20 per mile for Joe's company). Overall, we get f(x) = 0.20x + 4 for Joe's company.

Note how your teacher is not asking you to solve for x or f(x). If you want, you can replace f(x) with y; however, this isn't in function notation.

=============================================================

Question 8

Answers:

Function for Joseph's plan is: f(x) = 0.10x + 20

Function for Micki's plan is: f(x) = 0.15x + 10

The plans cost the same when 200 text messages are sent

-------------------------

Explanation:

We'll set up the equations in a similar way done in problem 7. We start with $20 as the base fee for Joseph's plan and then add on 0.10x dollars because $0.10 is charged per text message. We have x represent the number of text messages. Joseph's function is therefore f(x) = 0.10x + 20. Similarly, Micki's function is f(x) = 0.15x + 10

Let's replace f(x) with y and we have these two equations: y = 0.10x + 20 and y = 0.15x + 10

Now use substitution to solve for x and y

y = 0.10x + 20

0.15x + 10 = 0.10x + 20 ... y replaced with 0.15x+10

0.15x-0.10x = 20-10

0.05x = 10

x = 10/0.05

x = 200

This means that the two plans cost the same when 200 messages are sent.

Note plugging x = 200 into each f(x) function leads to

f(x) = 0.10x + 20

f(200) = 0.10*200 + 20

f(200) = 20 + 20

f(200) = 40 <<--- it costs Joseph $40 to send 200 messages

and

f(x) = 0.15x + 10

f(200) = 0.15*200 + 10

f(200) = 30 + 10

f(200) = 40 <<--- it costs Micki $40 to send 200 messages

Answer:

Second one

Step-by-step explanation:

Second choice.

Second one is growing by a factor of 2 because the exponent on 2 tells me that 2 is is being repeated as a factor.

If x=0 then 15*2^0=15(1)=15 which is what we have initially.

Final answer:

The correct option is f(x)=15⋅2^x. The function that best models the cell growth after x hours is f(x) = 15⋅ 2^x, illustrating the exponential nature of cell division starting with 15 cells.

Explanation:

The amount of cells in the laboratory after x hours, when the number of cells doubles every hour, is best represented by the function f(x) = 15⋅ 2^x. This is because the cell population increases exponentially, starting with 15 cells and doubling each hour. The formula represents exponential growth where the original amount of cells (15) is multiplied by two raised to the power of the number of hours elapsed (x).

c.10/18 and 45/81

10/18=.5555555555555555555555

45/81=.5555555555555555555555

Answer:

D 5/6 and 5/24

step by step explanation  :

when you multiply 6 times 4 it equals 24

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case m is 1/2 and b is 2.

This means that the slope of this line is 1/2 and the y-intercept is (0, 2) or simply 2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

y = [tex]\frac{1}{2}[/tex] x + 2 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = 2

Answer:

3 like vegetables but do not like fruit

Step-by-step explanation:

We have 11 total members

There are 5 members that like fruit

11-5=6

That means there are 6 members that do not like fruit

Of those 6 members ,3 do not like vegetables

6-3 =3

That means we have 3 members who do not like fruit who like vegetables

Answer:

3

Step-by-step explanation:

Answer:

80

Explanation:

46 + 37 = 83 so 83 rounded to the nearest 10 is 80

Answer:

80

Step-by-step explanation:

46+37 = 83

Rounding to the nearest ten

80

Answer:

93%

Step-by-step explanation:

Formula for calculating average = sum of data/ total number of data

Step 1: Add all percentages

Let the percentage on the last test be x

82% + 75% + 90% + x = 247% + x

Step 2: Apply the formula

Average = sum of percentages/ total number of tests

85 = 247 + x /4

340 = 247 + x

x = 340 - 247

x = 93%

Therefore, Briana must receive 93% on her final test to maintain an average of 85%.

!!

Answer:

$29,000

Step-by-step explanation:

Given:

Receivable draw per week= $11,00

Commission on all sales= 12%

Sale for the month= $205,000

weeks in a month= 4

Jim's commission after the draw=?

total draws= 11,00 (4)

                  = 44,00

Commission on the sale= 205000(0.12)

                                        =24600

Jim's commission after the draw= 4400 +24600

                                                     =29,000 !

Jim Smith's commission after the draw is calculated by determining his total commission from sales and then subtracting the draw he receives weekly. For a month where he made $205,000 in sales, his commission after the draw is $20,200.

The subject of this question is Jim Smith's commission after the draw, who works as a salesman and receives a draw of $1,100 per week plus a 12% commission on all sales. Considering that Jim made $205,000 in sales for the month, we would first calculate his total commission by multiplying the sales amount by the commission percentage. Next, we deduct the total draw for the month from the total commission to find Jim's commission after the draw.

To calculate the total commission earned, you would use the formula: Commission = Sales x Commission Rate. Therefore, for a sales amount of $205,000 and a commission rate of 12%, the total commission would be $205,000  x 0.12, which equals $24,600. Since a month is considered to have four weeks, Jim's total draw for the month would be $1,100 x 4, totaling $4,400.

To find out how much commission Jim has after accounting for the draw, we subtract the draw from the total commission: Commission after Draw = Total Commission - Total Draw, or $24,600 - $4,400, which equals $20,200.

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\==============================[/tex]

[tex]\text{We have the equation:}\ y=5x-4\to m_1=5.\\\\\text{Therefore}\ m_2=5.\\\\\text{We have the equation:}\ y=5x+b.\\\\\text{Put the coordinates of the given point (3, 4) to the equation:}\\\\4=5(3)+b\\\\4=15+b\qquad\text{subtract 15 from both sides}\\\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=5x-11[/tex]

Answer:

A

Step-by-step explanation:

The table of values is linear so we can express the function as

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 4) and (x₂, y₂ ) = (- 3, - 2) ← ordered pairs from the table

m = [tex]\frac{-2+4}{-3+6}[/tex] = [tex]\frac{2}{3}[/tex]

Note the ordered pair (0, 0) ⇒ c = 0

y = [tex]\frac{2}{3}[/tex] x → A

Answer:

24.4444

Step-by-step explanation:

76 degrees faherheit = 24.4444 degrees Celsius

(76°F − 32) × 5/9 = 24.444°C

Answer:

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