6 times the sum of a number and 5

The recursive formula for the given sequence is a(n) = 2 a(n-1) - a(n-2) + 1

A recursive formula is an equation that express the nth term as a function of preceding term(s), i.e. as function of (n-1)th term, (n-2)th terms, and so on. Mathematically it can be written as:

a(n) = f(a(n-1), a(n-2), ..., a(1))

The given sequence: 1,3,6,10, . . .

Here a(1) = 1. Notice that:

a(2) = 3 = 1 + 2

a(3) = 6 = 3 + 3

a(4) = 10 = 6 + 4

Notice that the differences between terms increase by 1.

Further, we can write:

a(2) = 3 = 1 + (1 - 0) + 1

             = a(1) + a(1) + 1

             = 2a(1) + 1  

a(3) = 6 = 3 + (3 -1) + 1

             = a(2) + a(2) - a(1) + 1

             = 2a(2) - a(1) + 1

a(4) = 10 = 6 + (6 - 3) + 1

               = a(3) + a(3) - a(2) + 1

               = 2 a(3) - a(2) + 1

We can continue this recursive pattern to find a(n),

a(n) = 2 a(n-1) - a(n-2) + 1

We can find next term for n = 5:

a(5) = 2a(4) - a(3) + 1

       = 2. 10 - 6 + 1 = 15

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Answer: x=1

Step-by-step explanation:

x-5=2x-6

x-5+6=2x-6+6

x+1=2x

x-x+1=2x-x

2x-x=1

x=1

Answer: x = 1

Step-by-step explanation:

fewer or less than means minus -

difference of x and 5 = x - 5

6 fewer = - 6

twice the number of x = 2x

x - 5 = 2x - 6

x = 2x - 6 + 5

x -2x = - 6 + 5

- x = - 1

x = 1

checking

1 - 5 = 2(1) - 6

4 = 2 - 6

4 = 4

Answer:

perimeter: 14.5

Step-by-step explanation:

The ordering of the number is 6.286  , 6.628 , 6.826

According to the question we have been given three numbers which are

     6.826 , 6.628 and 6.286

We need to arrange in ascending order that is from least number to the greatest number.

when we arrange number in ascending order for decimal number we first look at the number before the decimal point then if they are all same then we look at the number after the decimal point. After the decimal point the first number is compared which is closest to the decimal point.

If we look into this question the number before decimal points are all same thus we will look the numbers after the decimal point. Therefore we will arrange according to the first  number after the decimal that is 8 , 6 and 2

Hence the ordering the number we get:

      6.286  , 6.628 , 6.826

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Answer:

x =7

Step-by-step explanation:

hope it helped

Answer:

x=7

Step-by-step explanation:

i just saw that this has been answered but i want to give an explanation incase it is needed:

•3x+4=5x-10

first move the like terms to one side of the = sign. (its best to move the smaller x value to the bigger one.

•4+10=5x-3x

then you just solve the equation on both sides:

• 14=2x

then you have to being the 2 over the = sign so that x is by itself. when you bring a divide value over the = sign it will turn into the opposite operation.

so basically you are dividing 14 by 2

•14/2 = x or 14÷2=x

which finally gives you :

x=7

hope that makes sense...

Answer:

48

Step-by-step explanation:

The right-angle triangle on the coordinate plane will be drawn. Then the third length of the right triangle will be 2√(a² - b²) units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The right triangle ΔABC with legs AC and AB so that AC is 2a units long and leg AB is 2b units long.

We know that the angle ABC is a right angle which means 90°.

Then the third length of the right triangle will be

H² = P² + B²

(2a)² = (2b)² + B²

B² = 4a² - 4b²

B² = 4(a - b²)

B = 2√(a² - b²)

The right-angle triangle on the coordinate plane will be drawn.

The diagram is attached below.

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Using it's concept, there is a 0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A standard deck is given by 4 suits of 13 cards, each with either a number from 1 to 10 or one letter from A, Q or K, hence:

Hence the probability is given by:

p = 48/51 x 45/50 x 42/49 = 0.726.

0.726 = 72.6% probability that all 4 cards have distinct characters (letters or numbers).

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Answer:

ue7e7373777 is is and 88877376363778

When Olga turns 18, she will have $3032.89 in her account, which earned a monthly compound interest rate of 1.75%.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula of monthly compound interest is:

B = P(1 + r)^t

where B is the ending balance, P is the principal amount or original balance, r is the monthly interest rate in decimal form, and t is the number of months.

If Olga's uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly, using the formula, solve for the ending balance after 2 years.

B = P(1 + r)^t

B = 2000(1+ 0.0175)^24

B = $3032.89

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The value of A in the 4-digit number is 5.

Given the information provided in the question, the 4-digit number is a multiple of 15. A multiple of a number is the product of an integer and that number.

The multiple of a number is divisible by that number. For example, a multiple of 2 is 20. This is because 2 multiplied by 10 is equal to 20 and 20 is divisible by 2 to yield a value of 10.

The multiplies of 15 either have a unit value of 5 or 0.

If A is 5, the number becomes 3555.

3555 / 15 = 237

If A is 0, the number becomes 3050

3050 / 15 = 203.333

Thus, the value of A is 5 because 3555 is divisible by 15.

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Answer:

b=v

Step-by-step explanation:

Answer:

I got b=v so it would be 0

Step-by-step explanation:

I'm sorry if I'm wrong

Answer:

Pon tu tarea aquí para que podamos ayudarte con ella :)

Answer:

860.9 m³

Step-by-step explanation:

We can obtain the volume of the composite figure by subtracting the volume of cylinder from the volume of cuboid.

     l = 10 m

     w = 10 m

    h = 12 m

[tex]\sf \boxed{\text{ \bf Volume of cuboid = l *w * h}}[/tex]

                                    = 10 * 10 * 12

                                    = 1200 m³

      r = 3 m

      h = height of the cuboid = 12 m

    [tex]\sf \boxed{\text{\bf Volume of cylinder = $\pi r^2h$}}[/tex]

                                         = 3.14 * 3 * 3 * 12

                                         = 339.1 m³

Volume of composite figure = 1200 - 339.1

                                                = 860.9 m³

ANSWER:

19.54

Step-by-step explanation:

23.7-8.3

=15.4

15.4+4.14

=18.54

Answer:

k <−33

Step-by-step explanation:

The knowledge of  how many more minutes m you can use during the rest of the month is given by the linear inequality 648 + m ≤700, where 'm' is the minutes on the cell phone or simply m ≤ 52

It is given that the  monthly minutes on your cell phone can add up to no more than 700 minutes so the highest limit is 700

And You have already used 648 minutes so this is our base for the formation of linear inequality

We are provided to use 'm' for rest of  the minutes on the cell phone

Hence, we can form a linear inequality using the three points as the sum of already used minutes and the maximum minutes that can be used in this month is at most  700 minutes is given by 648 + m ≤700

This can also be simplified as

m ≤ 700 - 648

m≤52

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The value of b is b=p-a.

Given the equation is p=a+b.

A pair of inverse operations is defined as two operations to be performed on a number or. variable,  always returns the original number or variable And inverse means opposite.

equation means a mathematical statement with the symbol "equal" between two expressions of equal value. This is represented by '='.

The given equation is p=a+b.

Now, we will apply the inverse operations on both sides.

Subtract a from both sides, we get

p-a=a+b-a

Now, we will simplify the above equation, we get

p-a=b

Hence, the value of b from the given equation p=a+b is b=p-a.

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If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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Answer:

d = 13

Step-by-step explanation:

19d - 16d - d - d - 1 = 12

19d + (-16 - 1d - 1d) - 1 = 12

19d + (--18d) - 1 = 12

19d - 18d - 1 = 12

1d = 12 + 1

d = 13

Check:

19*13 - 16*13 - 13 - 13 - 1 = 12

247 - 208 - 26 - 1 = 12

39 - 27 = 12

For the given parabola, we have that:

a) The equation is: f(x) = -16(x - 0.75)² + 18.

b) The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (0.75,18), hence:

h = 0.75, k = 18.

f(x) = a(x - 0.75)² + 18.

When x = 0, y = 9, hence:

9 = 0.5625a + 18

a = -9/0.5625

a = -16.

Hence:

f(x) = -16(x - 0.75)² + 18.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

It is increasing between x = 0 and x = 0.75, in which f(0) = 9, f(0.75) = 18, hence:

r = 9/0.75 = 12.

The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

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The student walked 58.58 meters more than the total displacement from the starting point.

Given that a student walked 100 meters north, then 100 meters west.

We are required to find the number of meters, the student travelled more as compared to the total displacement from the starting point.

We have to find the distance from the starting point to ending point. We have to apply pythagoras theorem to find that distance.

Pythagoras theorem basically says that the square of hypotenuse of right angled triangle is equal to the sum of squares of base and perpendicular.

[tex]H^{2} =P^{2} +B^{2}[/tex]

In our case P is 100 meters and B is 100 meters and we have to find H from the formula given above.

[tex]H^{2} =100^{2} +100^{2}[/tex]

H=[tex]\sqrt{10000+10000}[/tex]

H=[tex]\sqrt{20000}[/tex]

H=141.42 meters

Difference=100+100-141.42

=200-141.42

=58.58 meters

Hence the student walked 58.58 meters more than the total displacement from the starting point.

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The two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

It should be noted that decimals simply means.the numbers that aren't whole numbers.

It should be noted that this is a straight forward question.

Here, the two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

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Answer/Step-by-step explanation:

2.

5x + 3y = 15

3y = -5x + 15

÷3   ÷3    ÷3

y = (-5/3)x + 5

* = coordinate: (0, 5), (3, 0)

                5  *

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----*----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

4.

10x + 8y = -40

8y = -10x - 40

÷8     ÷8    ÷8

y = (-5/4)x - 5

* coordinate: (0, -5), (4, -10)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 *

                 -6 -

                 -7 -

                 -8 -

                 -9 -

                 -10 -                    *

6.

-3x + 6y = 12

6y = 3x + 12

÷6   ÷6   ÷6

y = (1/2)x + 2

* coordinate: (0, 2), (2, 3)

                5   -

                4   -

                3   -          *

                2   *

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

8. x - y = 5

-y = -x + 5

÷-1   ÷-1  ÷-1

y = x - 5

* coordinate: (0, -5), (1, -4)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -     *

                 -5 *

I hope this helps!

Answer:

value of k is 3 to make it perfectly

The translated and reflected function is:

g(x) = f(-x) - 3 = 3x + 1.

Here we want to transform a function f(x)=  -3x + 4.

First, remember that a vertical translation is written as:

g(x) = f(x) + N

Then a translation of 3 units down is written as:

g(x) = f(x) - 3

Now we want to do a reflection across the y-axis, this just changes the sign of the variable, so we get:

g(x) = f(-x) - 3

Now we replace the actual function f(x) by -3x + 4, we will get:

g(x) = -3*(-x) - 3 + 4 = 3x + 1

g(x) = 3x + 1

We conclude that the transformed function is 3x + 1.

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How is the Additive Identity Property similar to the Multiplicative Identity Property?

How is it different?

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