Making connections between arithmetic sequences and linear function


Use the graph or the formula to write the equation of the line in a slope intercept form

Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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The total amount of money that Marco has that week would be = $ d + 14.55.

An allowance income is defined as the amount of money an individual earns that can be used to solve their personal needs.

Marco received double payment, an allowance from the mother and from newspaper route.

The total amount of money received from his mother for allowance for that same week = $ d

The amount of money he earned from his newspaper = $14.55

Therefore the total amount of money Marco has that week =$ d + 14.55

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Complete question:

Marco's mom gave him d dollars for his allowance one week. He also earned \$14.55$14.55dollar sign, 14, point, 55 for his newspaper route that week.

How much money does Marco have?

Write your answer as an expression.

This is because the mean is at the very center of the normal distribution. The center is at 0, with positive values on the right and negative values on the left.

Something like z = 1 means we're 1 standard deviation above the mean. As another example, z = -3 means we're 3 standard deviations below the mean.

⎆ The value of the z-score will tell how many standard deviations the person is away from the mean.

➟ If a z-score is equal to 0, then it will be on the mean. So, z-score for the mean is 0.

[tex] \\ z = \frac{(x-μ)}{σ} [/tex]

✐ Where,

On solving the provided question we can say that  by linear equation number of, Red Balls = 6x 18; Blue Balls = 3;  Yellow Balls = 6

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A bag contains 27 balls

• The ratio of red to blue to yellow balls is 6:1:2

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6X+X+2x = 27

9x = 27

x = 3

Hence the number of,

Red Balls = 6x 18

Blue Balls = 3

Yellow Balls = 6

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Answer:

Step-by-step explanation:

the first equation we konw x=-2y-1,

then -2y-1=y+5

so, y = -2, x=3

Answer:

y = -2

x = 3

Step-by-step explanation:

y + 5 + 2y = -1 (substitute)

3y + 5 = -1        (Simplify)

3y = -6            (Get rid of 5)

y = -2                 (Divide)

x = -2 + 5         (plug in y)

x = 3                 (simplify)

hope this helps :)

Answer:

64

Step-by-step explanation:

As the sequence is linear the rate of increase stays constant as we can see from the formula: [tex]S_n=mn+i[/tex] so it increases by m every term. In this all we do is subtract 13 from 28 to find the number of terms in between:

28-13=15

now we find the difference between 152 and 92

152-92=60

now we divide 60 and 15

60÷15=4

So M is 4 meaning every term has a difference of 4.

So now we can subtract 6 from 13:

13-6=7

Then multiply the difference per term (4) by 7

4×7=28

Finally we subtract 28 from 92 (13th terms value)

92-28=64

Answer:

I think he's correct

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

He has to multiply the exponents not add them.

Given :

A line passing through the point (1, 3) that has a slope of -2​.

To Find :

The equation of such line.

Solution :

Let, the equation of line is :

y = mx + c

Here, m is slope i.e m = -2 and c is y-intercept.

So,

y = -2x + c

It is also given that the line passes through (1, 3).

3 = -2× 1 + c

c = 5

Therefore, the equation of line is y = -2x + 5 .

Answer

The answer is 567

Step-by-step explanation:

189*3=567

Answer:

I'm not sure if its A or C but C sounds like it could be the right answer

Step-by-step explanation:

Answer: Planting vegations near riverbanks

Step-by-step explanation:

because everything else is harmful to the earth .-.

We have inequality. So, we have to take a test point (0,0) and as the statement is true therefore Graph will shade towards the test point (0,0).

2(0)+3(0) ≤ 30 => 0≤ 30

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.

First we make inequality according to question.

In a family number of children 3

Charge for 1 child = $y per hour

Charge for 3 children = 3y

Charge for 1 Adult = $x per hour

Charge for 2 adults = 2x

If the family does not want to spend more than $30 an hour at health club.

2x+3y≤30

Where, x and y should be greater than 0.

x≥0 and y ≥0

Now we make the graph of this inequality.

First we take equality of equation and then find x and y table.

2x+3y=30

x        y

0        10

6        6

15      0

Here we have inequality. So, we have to take a test point (0,0)

2(0)+3(0) ≤ 30 => 0≤ 30

This statement is true. So, Graph will shade towards the test point (0,0)

Please see the attachment for graph:

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Answer:

3(-2)2-9

-12-9

-21

Step-by-step explanation:

×=-2 so -2×3=-6 which is -6×2=-12

and we have -9

soo -12-9=-21

Step-by-step explanation:

1.

A.Company T

B.Company A

C.At 20 minutes

2.

A.Tells you the rate of calling minutes

B.Its free.

C. Company K as it's free for the first five minutes.

Answer:

25mL

Step-by-step explanation:

15/6=2.5ml/oz

10x2.5=25mL

Answer:

y=3x+3

Step-by-step explanation:

The y-intercept is at 3.

If you do rise over run, you get 3/1. Simplify to 3. Hope this helps.

Answer:

Im guessing -2

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

The completed two column proof is presented as follows;

Statement  [tex]{}[/tex]                               Reason

1. AC bisects ∠A and ∠C [tex]{}[/tex]       1. Given

2. ∠ACB ≅ ∠ACD [tex]{}[/tex]                  2. Definition of bisector

3. ∠BAC ≅ ∠DAC     [tex]{}[/tex]              3. Definition of bisector

4. [tex]\overline {AC}[/tex] = [tex]\overline {AC}[/tex]     [tex]{}[/tex]                        4. Reflexive PE

5.  [tex]\overline {AC}[/tex] ≅ [tex]\overline {AC}[/tex]     [tex]{}[/tex]                      5. Segments with equal lengths are congruent

6. ΔABC ≅ ΔADC   [tex]{}[/tex]                6. By ASA

Step-by-step explanation:

The completed two column proof is presented as follows;

Statement  [tex]{}[/tex]                              

1. AC bisects ∠A and ∠C; The given data on the figure

2. ∠ACB ≅ ∠ACD;[tex]{}[/tex] A bisected angle is divided into two equal angles which are congruent to each other

3. ∠BAC ≅ ∠DAC     [tex]{}[/tex]              3. Definition of bisector

4. [tex]\overline {AC}[/tex] = [tex]\overline {AC}[/tex]     [tex]{}[/tex]                        4. Reflexive Property of Equality (PE)

5.  [tex]\overline {AC}[/tex] ≅ [tex]\overline {AC}[/tex]     [tex]{}[/tex]                      5. Segments with equal lengths are congruent

6. ΔABC ≅ ΔADC   [tex]{}[/tex]                6. By Angle-Side-Angle, ASA, is a condition for congruency of two triangles

Where two angles and the included side between the two angles on one triangle are equal to two angles and the included side between the two angles on another triangle, the two triangles are said to be congruent by the Angle-Side-Angle ASA rule and therefore, they each have equal measures for all corresponding angles sides.

Answer:

Step-by-step explanation:15.6

Answer:

POKEMON YEAH!

Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.

4500 - 2485 = 2015

Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:

2015/155 = 13

It will take him 13 more weeks to have enough for the Pokemon cards!

Step-by-step explanation:

Hope it helps! =D

Answer: 348

Step-by-step explanation: 12*29 = 348, which is the largest multiple less than 350.

Answer:

1/3

Step-by-step explanation:

The percentage of students who do not participate in a sport is C. 51.0%.

To find the percentage of students who do not participate in a sport, we can use the following formula:

(Number of students who do not participate in a sport) / (Total number of students) * 100%

From the table, we can see that the number of students who do not participate in a sport is 985, and the total number of students is 1930. So, plugging these values into the formula gives us:

= 985 / 1930 * 100%

= 51.03%

So, about 51.03% of students do not participate in a sport.

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Answer:

a = 5

Step-by-step explanation:

Using Pythagoras' theorem in the right triangle

a² + 12² = 13²

a² + 144 = 169 ( subtract 144 from both sides )

a² = 25 ( take the square root of both sides )

a = [tex]\sqrt{25}[/tex] = 5

Answer:

pythagoras theorem formula

h^2=p^2+b^2

here hypotenuse is 13

you can take a as either perpendicular or base

lets take it base

h^2=p^2+b^2

(13)^2=(12)^2+(a)^2

169=144+a^2

169-144=a^2

25=a^2

[tex]\sqrt{25}[/tex]=a

5=a

Step-by-step explanation:

Answer:

30 yards per minute

or

150 feet per minute

Step-by-step explanation:

450/15 = 30

can i have brainliest please?

Answer:

6z + 6x + 6y

Step-by-step explanation:

Just distribute the 6 and multiply them to all variables.