What is the difference between an equation with a variable and an inequality with a variable?

Answer:

aₙ = a₁ . 5⁽ⁿ⁻¹⁾

Step-by-step explanation:

The first term in the sequence is a₁ = 6.

a₂ = 30. a₃ = 150.

We see that each consecutive term is multiplies by 5 to arrive at the next term.

That is: a₂ = 30 = a₁ . [tex]$ 5^{2 - 1}  = 5 $[/tex] = 6.5 = 30.

Similarly, a₃ = 150 = 6 [tex]$ \times $[/tex] [tex]$ 5^{3 - 1} = 5^2 = 25 $[/tex]

Generalizing this, we have:

aₙ = a₁ . [tex]$ 5^{n - 1} $[/tex]

This is called the recursive formula of the sequence.

Answer:

5

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

multiply 25×6 =150

subtract 150-22 = 128

128÷4

32

Answer:

[tex]\displaystyle (3, 6)[/tex]

Step-by-step explanation:

{x -4y = −21

{8y - x = 45

_________

[tex]\displaystyle \frac{4y}{4} = \frac{24}{4} \\ \\ [/tex]

[tex]\displaystyle y = 6[/tex][Plug this back into both equations above to get the x-coordinate of 3]; [tex]\displaystyle 3 = x[/tex]

I am joyous to assist you anytime.

The kinetic energy (Ek) of the car with a mass of 1000 kg moving at a speed of 20 m/s is calculated using the formula Ek = 0.5 * m * v². Substituting the given values, we find the kinetic energy to be 2.00 x 10⁵ Joules.

To calculate the kinetic energy (Ek) of a car with a given mass and speed, you can use the formula Ek = 0.5 * m * v², where m is the mass, and v is the speed. In this case, the mass (m) of the car is 1000 kg, and the velocity (v) is 20 m/s.

Substituting the given values into the formula, we have Ek = 0.5 * (1000 kg) * (20 m/s)². This simplifies to Ek = 2.00 x 10⁵ J (Joules), which is the kinetic energy of the car.

It's important to note that kinetic energy always has units of Joules in the International System (or SI), and it represents the energy that an object has due to its motion.

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Answer:

3(x+4)=36 is the same as 3x+12=36

If 3x+12=36, that means x=8

36-12= 24

24/3=8

Answer: Explain how the distributive property can be used to solve the equation 3(x+4)=36 For this question it says to explain how the distributive property can be used to solve the equation. So instead of putting the answer to the equation 3(x+4)=36. You explain how the distributive property gets you the answer... They're not asking for the answer to the equation 3(x+4)=36

Step-by-step explanation: So to the guy that answered this question you are wrong...

Answer:

The correct answer is D. 414 in squared.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Area of the first circle = 11.5 inches ²

2. Let's calculate the area of the new circle, given that the radius of the first circle is multiplied by 6.

Area of the first circle = 11.5 inches ²

Let's find the radius:

π * r² = 11.5

r² = 11.5 / 3.1416

r² = 3.66055513

r = 1.91 inches

The first circle has a radius of 1.91 inches

So, the radius of the second circle is 1.91 * 6 = 11.48 inches

Area of the second circle = π * r²

Area of the second circle = 3.1416 * 11.48²

Area of the second circle = 3.1416 * 131.79

Area of the second circle = 414.03 inches ²

Area of the second circle = 414 inches ² (Rounded to the nearest whole number)

The correct answer is D. 414 in squared.

Answer: Y=-1 or Y=-1+4

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through a specific point, we can use the point-slope form of a linear equation.

To find the equation of a line that is parallel to the given line and passes through the point (3, 1), we need to use the fact that parallel lines have the same slope. Since the given line has a slope of 4, the parallel line will also have a slope of 4. Using the point-slope form of a linear equation, we can write the equation as:

y - y1 = m(x - x1)

Plugging in the values from the given point (3, 1) and the slope (4), we get:

y - 1 = 4(x - 3)

Simplifying the equation, we have:

y - 1 = 4x - 12

y = 4x - 11

Therefore, the equation of the line that is parallel to the given line and passes through the point (3, 1) is y = 4x - 11.

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Answer:

Procedure in option C only works.

Step-by-step explanation:

We have to select the process in which Mrs. Smith can help her to work 30 divided by 3.

(A) (27 divided by 9) + (9 divided by 3) = 3 + 3 = 6  

But (30 ÷ 3) = 10 ≠ 6

(B) (24 divided by 4) + (4 divided by 4) = 6 + 1 = 7 ≠ 10

(C) (21 divided by 3) + (9 divided by 3) = 7 + 3 = 10

(D) (20 divided by 4) + (10 divided by 4) = 5 + 2.5 = 7.5 ≠ 10

So, procedure in option C only works. (Answer)

Again, we can prove the procedure in the following way:

[tex]\frac{30}{3} = \frac{21 + 9}{3} = \frac{21}{3} + \frac{9}{3}[/tex]  

{Which is the distributive property of division}

Answer:

Each dog toy costs $1.75.

Step-by-step explanation:

6x=10.5

x=10.5/6

x=1.75

Answer:

Step-by-step explanation:

- Predicting the gender of an arbitrarily picked craftsmanship educator if 1 of 3 workmanship / art instructors is female .

- Predicting the gender of a haphazardly picked science / biology instructor if 8 of 12 biology educators are female .

- Predicting the gender of a haphazardly picked health educator if 2 of 4 health instructors are female .

Answer:

1/3 8/12 2/4

Step-by-step explanation:

Because they involve 6

Good evening ,

Answer:

The set of solutions is IR

Step-by-step explanation:

-2(2x+8)>-16-4x ⇌ -4x-16>-16-4x

Any x∈IR verify the inequality

then The set of solutions is IR.

:)

Answer: The tip is $17. The total amount he paid is $102.

Step-by-step explanation: 85 times .2 gets the tip, then you add that sum to the subtotal.

If the item is 80% off than the sale price is only 20% of the original price.

So, 20% x $50 = $10

Answer:

NOT PROPORTIONAL

Step-by-step explanation:

The given two fractions are: [tex]$ \frac{5}{8} $[/tex] and [tex]$ \frac{8}{10} $[/tex].

Proportional fractions are those which have the same value when to reduced to the simplest form.

Consider two fractions [tex]$ \frac{p}{q} $[/tex] and [tex]$ \frac{x}{y} $[/tex].

We say they are proportional if [tex]$ p : q = x : y $[/tex].

Or, if [tex]$ py = qx $[/tex] then we can say the fractions are proportional.

Here the fractions are:  [tex]$ \frac{5}{8} $[/tex] and [tex]$ \frac{8}{10} $[/tex].

LHS: 5 X 10 = 50.

RHS: 8 X 8 = 64.

Clearly they are not equal. So, we can say these two fractions are not proportional.

Answer:

30 miles

Step-by-step explanation:

We know

D = RT

Where

D is the distance

R is the rate

T is the time

Towards Island:

R = 15

Let time be x

So, we can write:

D = 15x

Return from Island:

R = 10

Let time be y

So, we can write:

D = 10y

Also, total time is 5 hours, so we can write:

x + y = 5   [equation 2]

Now, since the distance for both legs of the journey is equal, we can write:

Distance 1 = Distance 2

15x = 10y

Now we replace this equation with equation 2, so we get:

Equation 2: x + y = 5 or x = 5 - y

15x = 10y

15(5 - y) = 10y

75 - 15y = 10y

75 = 25y

y = 75/25

y = 3

Distance 2 = D = 10y

Replacing y with 3, we get:

D = 10y

D = 10(3)

D = 30

So, the distance to island is 30 miles

Answer:

42 years, 9 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n)^(nt)

where Accrued amount (A) which is quadruple the initial deposit

A = 4 x 500 = $2000

P = principal; $500

r = 3.25% = 0.0325

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

2000 = 500 (1 + 0.0325/12)^(12t)

Therefore

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

finding the log of both sides

12t x log 1.002708 = log 4

12t x 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

which is estimated as 42 years, (0.7 x 12 = 9) months

hence it takes about 43 years to quadruple the deposit

The number of years it will take to be the amount by quadruple will be 42.7 years.

Compound interest is applicable when there will be a change in the principal amount after the given time period.

As per the given,

The total amount will be,

A = 4 × 500 = $2000

Principle amount P = $500
Rate of interest r =  3.25% = 0.0325

The time period is t.

n = number of times interest is compounded

n = 12

By compound interest formula,

2000 = 500 [tex](1 + 0.0325/12)^{12t}[/tex]

(1.002708)^12t = 2000/500

(1.002708)^12t = 4

Take logs on both sides,

12t × log 1.002708 = log 4

12t × 0.001174 = 0.6021

12t = 0.6021/0.001174

12t = 512.83

t = 512.83/12

t = 42.7

Thus, the time period will be 42.7 years.

Hence "The number of years it will take to be the amount by quadruple will be 42.7 years.".

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1.) 7+5 > 6+2

2.) g ≥ 8

3.) s = -2, -8

4.) from the middle and beyond (best way i can answer)

5.)

b < 11 = The board is shorter than 11 cm

b > 11 = The box contains more than 11 books

b < 12 = There are fewer 12 beetles in a jar

b > 12 = The building is taller than 12 ft.

Answer:

1. 6 times 5

2. 7/6 simplified

3. 4 times 13

4. 45 divided by 1 1/6

5. 10 as a proporation

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

7-3 pretty much

Answer: x=-10

Step-by-step explanation:

let x be that number

so, 7+x=-3

subtract 7 on both sides and...

x=-10

[A] 23w + 35 = 150 ; Sal will have enough money in 5 weeks.

We can see 35 as the starting value since he already has that amount when he started saving up money. We can subtract it (150 - 35 = 115). Then we can divide (115 / 23 = 5). It took Sal 5 weeks to save enough money for the bike. The first option makes the most sense because the expression can be solve to find how many weeks he save up his money.

_______

Best Regards,

Wolfyy :)

Answer:

-88/85

Step-by-step explanation:

2 14/49=112/49

7 3/85=598/85

3 35/49=182/49

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

112/49-(598/85-182/49)

112/49-1976/595

-88/85

To find the perimeter of the bedroom floor, subtract the rug's length and width from the floor's length and width. Then, use the formula 2(length + width) to calculate the perimeter. The perimeter of the bedroom floor is 64 ft.

To find the perimeter of the bedroom floor, we need to subtract the length and width of the rug from the length and width of the floor. The length of the floor is 10 ft and the rug leaves 1 ft exposed on each side, so the length of the rug is 8 ft. Similarly, the width of the floor is 8 ft and the rug leaves 1 ft exposed on each side, so the width of the rug is 6 ft. Therefore, the perimeter of the bedroom floor is 2(10 ft + 8 ft) + 2(8 ft + 6 ft) = 2(18 ft) + 2(14 ft) = 36 ft + 28 ft = 64 ft.

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Answer:

Option A. [tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]

Step-by-step explanation:

we know that

Applying the law of sines in the triangle ABC

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]

substitute the given values

[tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]

[tex]b=\frac{7}{sin(45\°)}sin(40\°)\\\\b=6.4\ units[/tex]

Answer:a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February:

y=(1/3)x

b. What is the meaning of the slope as a rate of change for this line of best fit?

For each three days of the month of february the number of golf carts repaired was 1; that means each three days of the month of february was repaired one golf cart.

Step-by-step explanation:

a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February:

y=(1/3)x

b. What is the meaning of the slope as a rate of change for this line of best fit?

For each three days of the month of february the number of golf carts repaired was 1; that means each three days of the month of february was repaired one golf cart.

Let:

x: Day of the month

y: Number of golf carts repaired

a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February.

Taking two points of the right line, for example:

P1=(0,0)=(x1,y1)→x1=0, y1=0

P2=(3,1)=(x2,y2)→x2=3, y2=1

Slope: m=(y2-y1)/(x2-x1)

Replacing the known values:

m=(1-0)/(3-0)

m=1/3

Equation of the right line, using the form point-slope:

y-y1=m(x-x1)

Replacing the known values:

y-0=(1/3)(x-0)

y=(1/3)x

Answer:

A). f(x) = (-5)x + 90

Step-by-step explanation:

A). As shown in the graph, line of best fit is passing through two points (0, 90) and (18, 0).

Equation of this line will be in the form of y = mx + b.

Here m = slope of the line

b = y-intercept

Since slope of a line passing through two points (x, y) and (x', y') is represented by,

m = [tex]\frac{y-y'}{x-x'}[/tex]

So slope of the line of best fit from the given graph,

'm' = [tex]\frac{90-0}{0-18}[/tex]

m = (-5)

y-intercept 'b' = 90

When we plug in these values in the equation,

y = (-5)x + 90

Function representing this situation,

f(x) = -5x + 90

B). Slope of the line of best fit shows the change in sales per day in the month of Feb that is "5 golf carts per day".

Negative notation of the slope shows the decrease in the sales day by day.

 Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 x the number of children's tickets sold on Friday.

                                      =  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938

Answer:

The total amount of money Alex spends on 5 DVD = $ 35.

Step-by-step explanation:

Total number of DVD purchased by Alex = 5

The cost of each DVD = $9

So, the total cost of purchasing 5 DVD = 5 x ( csot of 1 DVD)

= 5 x ( $ 9) = $ 45

Now , the discount if 1 DVD = $ 2

So, the total discount of 5 DVD = 5 x ( Discount on1 DVD)

= 5 x ($ 2) = $ 10

⇒ The total amount Alex spends

= Total cost of 5 DVD - Discount on 5 DVD

= $ 45 - $ 10 = $ 35

Hence, the total amount of money Alex spends on 5 DVD = $ 35.

Answer:

g+4-5

Step-by-step explanation:

because the plus would go first anyways.

Answer:

3. irrational

4. rational

5. rational

6. natural, whole, integer, rational

Step-by-step explanation:

Answer:

12:30PM

Step-by-step explanation:

Known information:

There are 4 classes.

Each class is 1 hour.

There are 10 minutes between classes, like a break.

Draw a diagram:

start-CLASS1, break, CLASS2, break, CLASS3, break, CLASS4-end

There are 3 breaks because there are no breaks before and after the first  and last classes.

Multiply the number of classes by the time length for class.

Multiply the number of breaks by the time length for breaks.

Add the two numbers together to get the total school time:

Classes: 4*1h = 4h

Breaks: 3*10min = 30min

4h + 30min = 4h 30min

Calculate 4h and 30min after 8:00 AM.

Add 4 hours and 30 minutes to 8.

.    8:00

+   4:30

.    12:30

In the AM/PM clock (not 24 hour clock) there are 12 hours. After 12:59, it becomes 1:00, not 13:00.

Since "12:30" is possible on the AM/PM, we do not need to fix it.

The AM/PM clock changes at 12:00.

This means that after 11:59PM it becomes 12:00AM.

After 11:59AM it becomes 12:00PM.  (Usually lunch)

Since 12:30 passed 11:59, the AM/PM sign changes.

The fourth class ends at 12:30PM.

Answer:

The number of terms of the G.P. is 6

Step-by-step explanation:

Let the G.P. has first term a, common ratio r and the number of terms n.

The G.P. has first term 2, so a = 2.

Now, the fourth term is 54 i.e. ar³ = 54

⇒ 2r³ = 54

⇒ r³ = 27

⇒ r = 3

Now, the last term i.e. the nth term is= [tex]ar^{n - 1} = 486[/tex]

⇒ [tex]2 \times 3^{n - 1} = 486[/tex]

⇒ [tex]3^{n - 1} = 243 = 3^{5}[/tex]

Hence, (n - 1) = 5

⇒ n = 6

So the number of terms of the G.P. is 6 (Answer)

Answer:

-65/64

Step-by-step explanation:

1 5/8/(-1 3/5)

1 5/8=13/8

-1 3/5=-8/5

(13/8)/(-8/5)

(13/8)(-5/8)

-65/64