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Answer: 9

Step-by-step explanation: The common denominator will be the least common multiple for the two denominators.

To find the least common multiple or lcm of 3 and 9, begin by listing the first few multiples for each number.

Multiples of 6

1 × 9 = 9

2 × 9 = 18

3 × 9 = 27

Notice that we skipped 0 × 9 in our list of multiples. That's because 0 × 6 is 0 according to the zero property of multiplication and our least common multiple can't be 0.

When listing the multiples of 3, it's a good idea to keep an eye on the list of multiples for 9 so that we will notice when we find a least common multiple.

Multiples of 3

1 × 3 = 3

2 × 3 = 6

3 × 3 = 9

Notice that in both lists, we have the least common multiple which is 9.

Therefore, the least common denominator of 9 and 3 is 9.

Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

[tex]F=P(1+r)^t[/tex]

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]

To solve exponentials, we can take Natural Log (Ln) of both sides:

[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]

Using the rule shown below we can simplify and solve:

[tex]Ln(a^b)=bLn(a)[/tex]

We can write:

[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]

To the nearest year, that would be about 9 years

Answer:

[tex]a_n=2n+5[/tex]

Step-by-step explanation:

we have the sequence

[tex]7,9,11,...[/tex]

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant and this term is called a common difference

Let

[tex]a_1=7\\a_2=9\\a_3=11[/tex]

we know that

[tex]a_2-a_1=9-7=2[/tex] ----> [tex]a_2=a_1+2[/tex]

[tex]a_3-a_2=11-9=2[/tex] ----> [tex]a_3=a_2+2[/tex]

The common difference is 2

This is an arithmetic sequence

The general formula for an arithmetic sequence is

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

where

d is the common difference

n is the number of terms

substitute the given values

[tex]a_n=7+2(n-1)[/tex]

[tex]a_n=7+2n-2[/tex]

[tex]a_n=2n+5[/tex]

Answer:

(3,6)

Step-by-step explanation:

the x input cannot repeat in order for it to be a function

Answer:

The answer is 16.4%

Step-by-step explanation:

The total decrease of price percentage is 16.4% when the price was decreased by 12% .

Evaluating decrease price :

The first discount reduces the price to (100 - 12)%

                                  = 88%  which is 0.88 times the original price.

The second discount reduces the already discounted price to

                                    (100 - 5)% =

                    95% of the discounted price

(0.95 times the discounted price). Get 2 discounts combined

Final Price = (0.95)(0.88) x (Original Price)

                            = 0.836 x (Original Price)

This is 83.6% of the original price, so the total discount rate is

                               (100 - 83.6)%

                                     = 16.4%.

a) He will earn $584 for working 36 hours.

b) He will earn $656 for working 39 hours.

c) He will earn $728 for working 42 hours.

Step-by-step explanation:

Amount per hour = $16

Time and a half means 1.5 times more than the original payment.

Therefore, above 35 hours, the earning for one hour,

Extra time per hour = 16*1.5 = $24

A) 36 h

For the first 35 hours, he will get $16 per hour, therefore,

Amount of 35 hours = [tex]35*16= \$560[/tex]

Amount of one hour = $24 (as calculated above)

Total = 560+24 = $584

He will earn $584 for working 36 hours.

B) 39 h

39 h = 35h + 4h

Amount of 35 hours = $560

Amount of extra 4 hours = $24*4 = $96

Total = 560+72 = $656

He will earn $656 for working 39 hours.

C) 42 h

42 h = 35h + 7h

Amount of 35 hours = $560

Amount of extra 7 hours = 24*7 = $168

Total = 560+168 = $728

He will earn $728 for working 42 hours.

Keywords: addition, multiplication

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Final answer:

The balance in the savings account after 5 years, with quarterly compounded interest, will be $2,699.80.

Explanation:

To find the balance after 5 years when the interest is compounded quarterly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

Where:
- A is the final amount
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years

Plugging in the given values:

[tex]A = $2,000(1 + 0.06/4)^(4*5)[/tex]

[tex]A = $2,000(1.015)^20[/tex]

A = $2,000 * 1.3499

A ≈ $2,699.80

After 5 years, the balance in the savings account will be approximately $2,699.80.

Answer:

3.3

bc jamal is standing on a platform 1.5 meters high but the trout is under by 4.8

so

4.8-1.5=3.3

Step-by-step explanation:

Answer:

3.3 meters below surface

Step-by-step explanation:

Jamal dude and the distance between surface of water is 1.5 meters

----------------------------------------------------------/ <- the surface of water

                                                                     \

                                                                      I

    trout                                                       /   below jamal by 4.8

equation is 1.5- 4.8 so its - 3.3 or 3.3 meters below surface

Answer:

Let the number of packets be x and the number of boxes be y.

Then, the formula is 6x + 15y

Step-by-step explanation:

The formula for the total number of buttons Nomusa buys, represented by t, in terms of the number of packets, p, and boxes, b, she buys is: t = 6p + 15b.

In this mathematical context, let's suppose that Nomusa buys p packets and b boxes of buttons. The total number of buttons can be represented by the letter t. Since there are 6 buttons in a packet and 15 buttons in a box, the total number of buttons Nomusa buys will be the sum of all buttons in the packets and boxes she buys. Thus, the formula in terms of p (packets) and b (boxes) will be: t = 6p + 15b.

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Answer:7

Step-by-step explanation:

Because it’s the place value of 5

Answer:

$34781.78

Step-by-step explanation:

$33,284 * 1.045 = $34781.78

The new salary will be $34781.78

Last year salary = $33284

Annual raise = 4.5%

Therefore, based on the above figures the new salary will be:

= $33284 + (4.5% × $33284)

= $33284 + (0.045 × $33284)

= $33284 + $1497.78

= $34781.78

Based on the calculation above, the new salary will be $34781.78

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Answer:

-1 91/200, -1.45, -7/5, -1 5/11

Step-by-step explanation:

Lowest Common Denominator:

LCD = 2200

Equivalent Fractions with the LCD

-7/5 = -3080/2200  (-7/5)

-15/11 = -3000/2200  (-1 5/11)

-145/100 = -3190/2200  (-1.45)

-291/200 = -3201/2200  (-1 91/200)

Answer:

810

Step-by-step explanation:

90/100=729/x

100×729= 90x

72900=90x

810 = x

Answer:

£810

Step-by-step explanation:

100% - 10% = 90%

£729 is 90 % after the price was decreased by 10%. Therefore, Divide £729 by 90% to get the original price.

£729/90% = £810

it's either 2/3 or 66.6 (neverending 6s)

Answer:it changed from $100

Step-by-step explanation:

18 km apart

You subtract 33 and 15

Answer:

16/24 which can then be simplified to 2/3

Answer:

8/24 = 1/3

Step-by-step explanation:

Answer:

The point (9,5) is on the graph of the equation

The graph of the equation is the set of all points that are solutions to the equation

Step-by-step explanation:

we have the linear equation

[tex]y=\frac{1}{3}x+2[/tex]

This is the equation of the line in point slope form

where

the slope is [tex]m=\frac{1}{3}[/tex]

the y-intercept is [tex]b=2[/tex]

Remember that

If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation

The graph of the equation is the set of all points that are solutions to the equation

Verify each statement

case 1) The graph of the equation is a single point representing one solution to the equation

The statement is false

Because the graph of the equation is the set of all points that are solutions to the equation

case 2) The point (9,5) is on the graph of the equation

The statement is true

Because

For x=9, y=5

substitute the value of x and the value of y in the linear equation

[tex]5=\frac{1}{3}(9)+2[/tex]

[tex]5=3+2[/tex]

[tex]5=5[/tex] ----> is true

so

the ordered pair satisfy the linear equation

therefore

The point is on the graph of the equation

case 3) The graph of the equation is the set of all points that are solutions to the equation

The statement is true

case 4) The point (-3,-1) is on the graph of the equation

The statement is false

Because

For x=-3, y=-1

substitute the value of x and the value of y in the linear equation

[tex]-1=\frac{1}{3}(-3)+2[/tex]

[tex]-1=-1+2[/tex]

[tex]-1=1[/tex] ----> is not true

so

the ordered pair not satisfy the linear equation

therefore

The point is not on the graph of the equation

Answer:

you can qualify for more jobs and make more money

Step-by-step explanation:

Final answer:

One benefit of getting an Associate Degree is gaining specialized knowledge and skills, which can increase job prospects. Additionally, it can be a stepping stone towards earning a higher degree, leading to more opportunities. Lastly, earning an Associate Degree can provide personal fulfillment and a sense of accomplishment.

Explanation:

One benefit of getting an Associate Degree is that it provides students with the opportunity to gain specialized knowledge and skills in a specific field. This can make them more competitive in the job market and increase their chances of finding employment. For example, someone with an Associate Degree in Business Administration may have a better understanding of business operations and management principles, which can be valuable in entry-level positions or when starting their own business.

Another benefit is that an Associate Degree can serve as a stepping stone towards earning a higher degree. Many universities and colleges accept transfer credits from associate degree programs, allowing students to continue their education and earn a bachelor's degree or beyond. This can open up more career opportunities and potentially lead to higher salaries.

Lastly, getting an Associate Degree can also provide personal fulfillment and a sense of accomplishment. It shows that you have successfully completed a program of study and have attained a certain level of expertise in a subject area. This can boost self-confidence and motivate you to pursue further education or career goals.

The width and length of the rectangle are 7 meters and 10 meters, respectively, as determined by using algebraic expressions to relate the given perimeter with the width and length formulas.

To solve for the length and width of a rectangle given the perimeter, we can use algebra. Since we know the length (L) is 4 meters less than twice the width (W), we can write this relationship as L = 2W - 4. The formula for the perimeter (P) of a rectangular shape is P = 2L + 2W. We are given that the perimeter is 34 meters.

Substituting the expression for L into the perimeter formula gives us:

Since the perimeter is 34 meters, we set 6W - 8 = 34.

Now, we find the length using the expression L = 2W - 4:

Therefore, the width is 7 meters and the length is 10 meters.

Answer:

y=2x+9

Step-by-step explanation:

Answer:

212.9 days

Step-by-step explanation:

The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P(t).

Using growth formula:

P(t) = Po ( 1 + r)^t where r is rate in percent and t is time in days

r = 1.28%, P(t) = 375, and Po = 25

substituting this values into the equation above yields

375 = 25 (1 + 1.28/100)^t

375÷25 = ( 1 + 0.0128)^t

15 = (1.0128)^t

take logarithm of both sides

log 15 = log (1.0128)^t remember the law log a^b = b log a

applying the same law gives

log 15 = t log 1.0128

divide both side by log 1.0128

log 15 ÷ log 1.0128 = t log 1.0128 ÷ log 1.0128

t = 212.9 days

Answer:

211 days

Step-by-step explanation:

The system of equations are p = 150 + 5n and p = 15n

Solution:

Given that, The Parks and recreation department in your town offers a season pass for $150.  

With the season pass you pay $5 per session to use the town's tennis courts.  

Without the season pass you pay $15 per session to use the tennis courts.

We have to write a system of equations to represent the situation

Now, let the number of sessions be "n" and total paying amount be "p"

Then in case of taking season pass  

total amount = season pass cost + $5 per session

p = 150 + 5 x n  

p = 150 + 5n  

And in case of no season pass

total amount = 15 per session

p = 15 x n  

p  = 15n

Hence, the system of equations are p = 150 + 5n and p = 15n

Final answer:

To represent the cost of using the town's tennis courts with and without a season pass, we use two equations: C = 150 + 5x for with a pass, and C = 15x for without a pass, where C is the total cost and x is the number of sessions.

Explanation:

The Parks and Recreation Department offers two options for using the town's tennis courts: with a season pass and without a season pass. We need to write a system of equations to represent the cost for each option depending on the number of sessions a person attends.

Equations

With Season Pass: C = 150 + 5x

Without Season Pass: C = 15x

In these equations, C represents the total cost of using the tennis courts for a given number of x sessions. For the pass option, there is an upfront cost of $150 plus $5 per session. Without the pass, each session costs $15.

These equations can help determine the point at which purchasing a season pass becomes more cost-effective than paying per session.

Answer:

First Option.

Step-by-step explanation:

I recommend using the app Photomath for these types of math problems. It gives a detailed explanation as to how you should solve them.

Answer:

width =5m

length=18m

Step-by-step explanation:

w=x

l=3x+3

perimeter =2(l+w)

46=2(x+3x+3)

46=2(4x+3)

46=8x+6

46-6=8x

40=8x

x=40/8

x=5

l=3x+3=3*5+3=15+3=18

Final answer:

To find the length and width of a rectangle with a given perimeter, use algebra to solve for the width first, then use that value to find the length. The width is 5 meters and the length is 18 meters based on the given perimeter and the relationship between length and width.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. According to the problem, the perimeter is 46 meters, and the length is 3 meters more than 3 times the width. Therefore, we can express the length as l = 3w + 3. Let's set up the equation using the perimeter formula:

Now that we've found the width to be 5 meters, we can find the length:

The width of the rectangle is 5 meters and the length is 18 meters.

The starting point is (0 , 210) and the rate of change is 1.12

Step-by-step explanation:

The form of the exponential function is [tex]f(x)=a(b)^{x}[/tex] , where

∵ The function is [tex]a(x)=210(1.12)^{x}[/tex]

∵ At the starting point x = 0

- Substitute x in the function by 0

∴ [tex]a(0)=210(1.12)^{0}[/tex]

- Remember any number to power of zero = 1 except 0

∴ [tex](1.12)^{0}=1[/tex]

∴ a(0) = 210(1) = 210

∵ a(x) = y

∴ The starting point is (0 , 210)

∵ The from of the exponential equation is [tex]f(x)=a(b)^{x}[/tex]

∵ [tex]a(x)=210(1.12)^{x}[/tex]

- Compare the two function

∴ b = 1.12

∵ b is the rate of change of the function

∴ The rate of change of the function is 1.12

The starting point is (0 , 210) and the rate of change is 1.12

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Answer:

[tex]3+3i[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two complex numbers (a+bi) and (c+di) points is equal to

[tex](\frac{a+c}{2})+(\frac{b+d}{2})i[/tex]

we have

(1+9i) and (5-3i)

substitute the given values

[tex](\frac{1+5}{2})+(\frac{9-3}{2})i[/tex]

[tex]3+3i[/tex]

Final answer:

The midpoint of the complex numbers 1+9i and 5-3i is calculated using the average of their real and imaginary parts, resulting in the midpoint of 3 + 3i.

Explanation:

To find the midpoint of two complex numbers, 1+9i and 5-3i, we use the midpoint formula for complex numbers which is the average of the real parts and the average of the imaginary parts separately. The formula for the midpoint M is given by:

M = ½(x1 + x2) + ½(y1 + y2)i

For our complex numbers, the real parts are 1 and 5, and the imaginary parts are 9 and -3. Applying the midpoint formula, we get:

M = ½(1 + 5) + ½(9 - 3)i = ½(6) + ½(6)i = 3 + 3i

Therefore, the midpoint of the complex numbers 1+9i and 5-3i is 3 + 3i.

Answer:

x = 7

Step-by-step explanation:

The segment joining the midpoints of the 2 sides of the triangle is one half the length of the third side, that is

2x - 6 = 8 ( add 6 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7

Answer:

2.84

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

Part 1) Record the coordinates of the given triangle

Looking at the graph

Let

A(-4,2)

B(-2,5)

C(3,2)

Part 2) Translate the given triangle down 2 units and right 5 units. Graph the translation

we know that

A translation of 5 units at right means (x+5)

A translation of 2 units down means (y-2)

so

The rule of the translation is equal to

(x,y) -----> (x+5,y-2)

Apply the rule of the translation at each vertices

A(-4,2) ----->A'(-4+5,2-2)

A(-4,2) ----->A'(1,0)

B(-2,5) -----> B'(-2+5,5-2)

B(-2,5) -----> B'(3,3)

C(3,2) -----> C'(3+5,2-2)

C(3,2) -----> C'(8,0)

using a graphing tool

The graph in the attached figure

Answer:

i think it is the second answer

Step-by-step explanation:

i think this because the  upside down ? is reflecting the ?

Answer:

One figure is a reflection of the other.

Step-by-step explanation:

Each point of the shape of one figure is equidistant to the equivalent point of the other, observing a symmetry line which perpendicular to the distance between each corresponding pair of points.