Trixie exclaimed , “hey! Arithmetic sequences are just name for linear functions.” What do you think ? justify your idea based on multiple representations

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

The rate of change will be 3/4.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function. Here, a stands for the line's gradient, and b for the y-axis intercept (which is sometimes called the vertical intercept).

The rate of change of y with respect to x, can be calculated utilizing any two of the pairs of values of the table, say, (3, -5) and (7, -2).

Rate of change [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]

Let, (3, -5) = (x1, y1) and (7, -2) = (x1, y1).

Rate of change [tex]$=\frac{(-5)-(-2)}{7-3}$[/tex]

Rate of change = 3/4.

Therefore, the correct answer is option c) 3/4.

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The 95% confidence interval will be more extensive than the 90% confidence interval

In measurements, the probability that a population boundary will fall between a bunch of values for a specific level of the time is alluded to as a certainty stretch. Investigators every now and again utilize certainty goes that incorporate 95% or the vast majority of expected perceptions. Thus, it could be presumed that there is a 95% probability that the genuine worth falls inside that reach assuming that a point gauge of 10.00 with a 95% certainty time frame - 10.50 is determined utilizing a factual model.

The degree of conviction or vulnerability in a testing cycle is estimated by certainty spans.

Also, they are utilized in relapse examination and speculation testing.

To decide measurable importance, analysts often join certainty spans with p-values.

95% or almost 100% certainty levels are most often utilized in their development.

The actual distance between city c and city d represented by 2.38 feet on the map as required in the task content is; 700 miles.

It follows from the task content that the actual distance between city c and city d be determined according to the map's scale factor given.

It follows from the task content that the distance between cities a and b which is 500 miles is represented by 1.7 feet on the map;

1.7 feet ===== 500 miles

Hence, let x = the actual distance between the cities c and d represented by 2.38 on the map is; so that we have;

1.7 feet ====== 500 miles

2.38 feet ====== x miles.

x = (500 × 2.38)/1.7

x = 700 miles.

Therefore, the actual distance between the two cities c and d is; 700 miles.

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The equivalent expressions to (9 7/8 + 2 4/5) - 1/2 are given as follows:

a) 9 7/8 + (2 4/5) - 1/2.

b) 9 7/8 + 2 4/5 + (-1/2).

Equivalent expressions are expressions that have the same result.

In this problem, the expression a is equivalent to the given expression, as the only difference is the order of the operations being applied, as the subtraction of 2 4/5 and -1/2 is applied before the addition of 9 7/8 + 2 4/5.

Expression b is also equivalent to the given expression, as an addition with the negative number in the fraction is made. However, the addition sign means that the sign inside the parenthesis is kept, which is negative, hence no change is made to the expression.

The remaining expressions involve changes to the signals of each term, hence they are not equivalent to the presented expressions.

The problem is given by the image at the end of the answer.

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It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.

Recall that we are given:
approximate distance from the sun for a few different planets.  

Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.

Recall that
Planet             approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance of Saturn form the sun and Venus is given as

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 * 10⁸  [Multiply 1.4 x 10 and we've got]

= 14 x 10⁸  - 1.1 * 10⁸  

= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]

= 12.9  x 10⁸  [Revert back to the power of 9 and we have]

=  1.29 x 10⁹ km

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Full Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus?  Express your answer in scientific notation.

Planet                                  Approximate distance from the Sun (in km)

Mercury                                        5.8 x 10⁷

Venus                                           1.1 x 10⁸

Earth                                             1.5 x 10⁸

Saturn                                           1.4 x 10⁹

It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.

The number is written in the form  [tex]a \times 10^b[/tex] where we have  [tex]1 \leq a < 10[/tex]

We have been given that the approximate distance from the sun for a few different planets.  

Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;

Planet             the approximate distance from the sun ( km)

Mercury          5.8 x 10⁷

Venus             1.1 x 10⁸

Earth               1.5 x 10⁸

Saturn             1.4 x 10⁹

The distance between Saturn from the sun and Venus can be calculated as;

= Distance of Saturn from Sun - Distance of Venus from Sun

= 1.4 x 10⁹  - 1.1 x 10⁸

= 14 x 10⁸  - 1.1 x 10⁸  

= (14 - 1.1) x 10⁸

= 12.9  x 10⁸

=  1.29 x 10⁹ km

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Answer:

-1

Step-by-step explanation:

BEDMAS

[tex]\frac{4+(5-11)}{2^{4}-14 }\\\frac{4+(-6)}{16-14 }\\\frac{-2}{2}\\-1[/tex]

Hope that helps

Answer:

f(x) = 0

px^2 + qx - 4p = 0

abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)

x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)

x = (-q ± √(q^2 + 4^2·p^2))/(2·p)

Because q^2 + 4^2·p^2 > 0 there are two roots.

Answer:

13

Step-by-step explanation:

y^2 = 169

y = [tex]\sqrt{169}[/tex]

y = 13

Answer: a) [tex]y = \frac{2}5x} - \frac{4}{5}[/tex]  b) y = -2x + 4

Step-by-step explanation:

2x - 5y = 4

2x - 4 = 5y

[tex]y = \frac{2}5x} - \frac{4}{5}[/tex]

6x + 3y = 12

3y = -6x + 12

y = -2x + 4

The amount of money Landon will make in 1 hour is $12 and he needs to work for 13 hours to make $156.

The amount of money he will make in 1 hour can be calculated by using division.

It can be determined by dividing the total amount earned by him by the total number of hours he worked yesterday. Therefore;

money earned in 1 hour = total amount earned ÷ total number of hours

money earned in 1 hour = 48 ÷ 4

money earned in 1 hour = $12

Now we can calculate the number of hours he needs to work at the movie theater to make $156 by dividing the desired amount by the amount earned in one hour. Therefore;

number of hours required = 156 / 12

number of hours required = 13

Hence, Landon will make $12 in one hour and he will need to work 13 hours to make $156

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Answer:

The answer is -18

Step-by-step explanation:

- [tex](-3)^{2}[/tex] + 3(-3)

-9 + -9 = -18

Answer:

short piece = 20

Longer piece = 40

Step-by-step explanation:

Comment

Let the shorter piece be x

Then the longer piece is 2x

Givens

The rope is 60 meters long

Equation

x + 2x = 60 meters               Combine like terms

Solution

3x = 60                                  Divide by 3

3x/3=60/3

x = 20

Answer:

3A+B+2a+4b

Step-by-step explanation:

Explanation

Question 23

To get the value of x, let us get y as shown below

Next, we will make use of the fact tha y and (x+85 ) are vertical angles so that

For question 23, x = -5

For question 24

The total angle in a circle is 360 degrees so that

solving for x

For question 24, x =-3

The perimeter of the triangle is computed adding the length of each side. That is,

P = (2x - 2) + (2x - 2) + x

P = (2x + 2x + x) + (-2 - 2)

P = 5x - 4

Substituting with P =56 and solving for x:

56 = 5x - 4

56 + 4 = 5x

60 = 5x

60/5 = x

12 = x

The sloth speed of running is 10/3 meters per minute

Distance travelled = 1/3 meters

Time taken to travel the distance = 1/10 minute

The formula for speed is given:

The distance travelled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction. A faster rate of movement is indicated by a higher speed. It is travelling more slowly if the speed is lower.

Speed = Distance/ Time

Speed of the sloth = (1/3)/(1/10)

= 1/3*10/1

= 10/3 meters per minute

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Answer:

Explanation:

The standard form of an equation is expressed as y = mx+b

m is the slope

Given the equation x - y = 6

Rewrite in standard form;

-y = -x + 6

Multiply through by -1

-(-y) = -(-x) - 6

y = x - 6

Compare with the standard equation

mx = 1x

mx+b

m is the slope

Given

Answer:

8.9 is larger

Step-by-step explanation:

7/8 is 0.875 in decimal form

8/9 is 0.88 or 0.89 if you round up.

7/8 < 8/9

Hope this helps! Please have a great day :)

Given:

Because the dividend is the same for all three expressions the larger the divisor the__the quotient

the answer will be: smaller or least

1. Common ratio of the G.P is 50

2. First term of the G.P is -100

3. Sum of the 8th term is 250.

Given,

In a Geometric progression,

7th term is 16 times the 3rd term

Sum of 2nd and 6th term is 102

Common ratio is positive.

Now,

Take a as first term.

r as common ratio

Then,

2nd term = a + r

6th term = a + 5r

So,

a + r + a + 5r = 102

Then,

2a + 6r = 102

2a = 102 - 6r

a = (102 - 6r) / 2

Now,

1. Common ratio:

Consider any term,

Here, 3rd term = a + 2r

Substitute a here.

a + 2r =  (102 - 6r) / 2 + 2r

102 - 6r + 4r = 2

102 - 2 = 6r - 4r

100 = 2r

r = 100/2 = 50

That is,

The common ratio of the G.P is 50.

2. First term:

Consider,

7th term is 16 times the 3rd term

That is,

3rd term = a + 2r

7th term = 16(a + 2r)

r = 50

Then,

a + 50 × 2 = 16(a + 50 × 2)

a + 100 = 16(a + 100)

a + 100 = 16a + 1600

100 - 1600 = 16a - a

15a = -1500

a = -1500/15

a = -100

Therefore,

The first term of the G.P is -100

3. Sum of the 8th term.

8th term = a + 7r = -100 + 7 × 50 = -100 + 350 = 250

That is,

The sum of the 8th term is 250.

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Answer: -7, -11

Step-by-step explanation:

[tex]5|x+9| \leq 10\\\\|x+9| \leq 2\\\\-2 \leq x+9 \leq 2\\\\-11 \leq x \leq -7[/tex]

Answer:

x∈(−11,−7)

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer:

its 7!!!!

Step-by-step explanation: i just got it right im in 8th grade also!

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

If the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex] then simplifying we get the value of t exists 7.61 x [tex]10^{-6}[/tex].

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Let the equation be 125000 = 45000( 1 + 0.021/365[tex]$) ^{365t[/tex]

simplifying the above equation, we get

t = [tex]$\frac{125000}{ 45000( 1+ \frac{0.021}{365} ) 365}[/tex]

t = 7.61 x [tex]10^{-6}[/tex].

Therefore, the value of t exists 7.61 x [tex]10^{-6}[/tex].

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The final term  after following the steps is  ( 42 + 6x ).

We are provided with some steps that we have to follow to reach the final answer or expression. The steps we have to follow to reach the final answer or expression are mentioned below;

Step 1: Add 7 to x

In the first steps we need to add 7 to the x. Mathematically this can be written as,

7 + x

Step 2: Multiply by 6

In the second step we need to multiply the entire term obtained in step 1 by 6 .  Mathematically this can be written as,

( 7 + x ) × 6

= 42 + 6x

Thus, the final term is  ( 42 + 6x ).

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An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

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The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.

in the question ,

it is given that ,

On the map  [tex]1\frac{1}{2}[/tex]  miles is equal to  [tex]1\frac{7}{8}[/tex] inches  .

we first convert the mixed fraction to normal fractions ,

we get

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

and

[tex]1\frac{7}{8}[/tex] inches = (8+7)/8 = 15/8 inches

So, the statement becomes

On the map  3/2  miles is equal to  15/8 inches .

So  1 mile = (15/8)/(3/2) = (15*2)/(8*3) = 30/24 = 5/4

so , the unite rate is 5/4 inches per mile .

given the road B is 15 miles long .

and the unit rate is 5/4 .

so 15 miles = 15 *(5/4) = 75/4 = 18.75 inches

Therefore , The unit rate per inch on the map is 5/4 , and the length of road B is 18.75 miles.

The given question is incomplete , the complete question is

A certain map shows two roads. Road A is [tex]1\frac{1}{2}[/tex] miles long but is [tex]1\frac{7}{8}[/tex] inches long on the map. What is the unit rate for inches per mile on this map​? If road B is 8 miles ​long, how long is road B on the map​?

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We are given a trapezoid and we are asked to determine one of its angles. To do that we need to have into account that the following angles are equal:

Also, the sum of two different angles must be equal to 180, therefore, we have the following relationship:

Replacing the value of angle W:

Subtracting 112 to both sides:

Therefore, the measure of angle Z is 68.