determine whether the following graph represent a function.

1. one to one function
2. function but not one to one
3. not a function

The slope of the line containing (-6,-11) and (-12,-10) is  (-1/6).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .

On substituting the values of variables in equation1, we will get

m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).

As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (-6,-11) and (-12,-10) is  (-1/6).

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It should be noted that Zahraa saying that the first division to perform is determining how many whole times 289 divides into 5,437 is incorrect.

It should be noted that based on the information, Zahraa is calculating the quotient of 54,379÷289 and she set up the long division with the numbers in the correct places.

She said that first division to perform is determining how many whole times 289 divides into 5,437. This is incorrect.

It should be noted that the first thing to do is to find the number of times that 28 will go in 54 and then bring the remainder down and solve till she gets the final value.

In this case, 54,379÷289 will be 188 47/289

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Answer: 6 and 27

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x+8= 4(x+2) and that should be the answer if not then i don't know what to do

Algebraic expression (C) p - 125 represents the reduced price.

So, if p is the mountain bike's original price.

Therefore, algebraic expression (C) p - 125 represents the reduced price.

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Myra's distance is increasing as time increases.

Given table showing the time (in minutes) and distance (in miles) :

Time (in minutes)    Distance (in miles)

 0                                        0.0

 2                                        0.4

 4                                        0.8

 6                                        1.2

 8                                        1.6

As we can see from the table, when there is an increase of 2 minutes in time, the distance is increasing by 0.4 miles.

So the distance covered by Myra is increasing with increase in time.

The question is incomplete. Find the complete question below:

The table shows the total distance that Myra runs over different time periods. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0. 0, 0. 4, 0. 8, 1. 2, 1. 6. Which describes Myra's distance as time increases? increasing decreasing zero constant.

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Two isosceles triangles are not necessarily similar triangles.

Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.

Analyzing each statements:

F. two right triangles with one angle measuring 30°

- these two triangles have angles measuring 90°, 30°, and 60°

- they both have equal angle measurements

∴ they are similar triangles

G. two right triangles with one angle measuring 45°

- these two triangles have angles measuring 90°, 45°, and 45°

- they both have equal angle measurements

∴ they are similar triangles

H. two isosceles triangles

- isosceles triangles are triangles that have two sides of equal lengths

- two isosceles triangles are similar if the angle of one is congruent to the corresponding angle of the other

∴ they are not necessarily similar, unless stated that their corresponding angles are equal

J. two equilateral triangles

- all equilateral triangles of any side lengths are considered similar triangles as each of its corresponding sides are proportional

∴ they are similar triangles

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The required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

Given that,
Osslyn is thinking of a number, n.
Her first clue is that eight less than two times her number is between two and six (inclusive).
To write a compound inequality that shows the range of numbers that Josslyn might be thinking of.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number be x,
According to the question,
Gusset number = 2x - 8,   where x is between 2 and 8 implies
2 < x < 6

Thus, the required number that is guessed  is 2x - 8 where inequality  2 < x < 6.

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Step-by-step explanation:

Hope the pictures will help you

Answer:

Below in bold.

Step-by-step explanation:

The time you were driving = distance / average speed

= 1500/42

= 35.714 hours.

Required equation is

t = 42 - d/s          where t = time not driving, d = distance and s = average speed

Time not driving :

t = 42 - 35.714

 = 6.286 hours

That is about 6 hours 17 minutes.

Using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

Given,

The points =  O(-12,0) and P(-8,3)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance [tex]=\sqrt{(-8--12)^{2}+(3-0)^{2} }[/tex]

[tex]=\sqrt{4^{2}+3^{2} } \\=\sqrt{16+9} \\=\sqrt{25}[/tex]

= 5 units

Hence, using the distance formula, the distance between the pair of points O(-12,0) and P(-8,3) is 5 units  

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Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

The term triangular coordinates can refer to at least three related systems of coordinates in the Euclidean plane: a special case of barycentric coordinates for a triangle, also known as a ternary plot or areal coordinates, among other things.

Because this is a right triangle, two of its sides can be found on the axes. Placing the triangle's right angle at the origin will allow the two legs to be parallel to the x- and y-axis.

Insert the triangle into the first quadrant. Z's y-coordinate is 0 because it is on the x-axis. Because the leg is 3b units long, its x-coordinate is 3b. Y's X-coordinate is 0 because it is on the y-axis. Because the leg is b units long, its y-coordinate is b.

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Answer:

32,14 minutes

Step-by-step explanation:

5.6 calories per hour = 5.6 x 60 = 336 calories per hour
So in 1 hour, that person will lose 336 calories

To lose only 180 calories time he should walk = 180/336 hour = 180/336 x 60 = 32,14 minutes

We can figure out our answer is in the ballpark by noting that 336/2 = 168

So to lose 168 calories, the person should walk for 1/2 hour so since 180 is slightly greater than 168, the person should walk for slightly more than half-hour

Answer:

n – p

x= –––––

m

Hope that helps! Have a good day :)

The probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

In this question,

We have been given a standard deck of 52 cards.

Three cards are selected from a standard deck of 52 cards.

Sample space n(S) = 52

We need to find the probability that all three cards are diamonds if neither the first nor the second card is replaced.

We know that, in a standard deck of 52 cards, there are 13 diamond cards.

The probability that the first card is diamond,

P1 = 13/52

The card is not replaced, so the total number of cards in a standard deck = 51

And the number of diamonds = 12

Now the probability that second card would be diamond,

P2 = 12/51

Similarly the probability that the third card is diamond,

P3 = 11/50

So, the probability that all three cards are diamonds if neither the first nor the second card is replaced:

⇒ P = P1 × P2 × P3

⇒ P = 13/52 × 12/51 × 11/50

⇒ P = 0.25 × 0.24 × 0.22

⇒ P = 0.0132

Therefore, the probability that all three cards are diamonds if neither the first nor the second card is replaced: 0.0132

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There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.

When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.

The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.

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The correct question is-

Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵​? ​Why?

Area of base:

3 * 9 = 27

So, 243 is the answer.

The amount in the savings account after 2 years, 5 years and 8 years is respectively $13.6, $34, $54.4.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't really compound, therefore the creditor only has to pay more interest on the principal sum and the borrower never has to pay interest on the interest that has already accrued.

Principle=3400

Rate of interest=0.2

Time period=2, 5 and 8 years

To calculate simple interest I= PRT/100

=> To find the amount in the savings account after 2 years

=(3400×0.2×2)/100

=13.6

So the amount in the savings account after 2 years is $13.6.

=> To find the amount in the savings account after 5 years

=(3400×0.2×5)/100

=34

Therefore the amount in the savings account after 5 years is $34.

=> To find the amount in the savings account after 8 years

=(3400×0.2×8)/100

=54.4

Hence the amount in the savings account after 8 years is $54.4.

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Answer:

2 years: 3413.60 or 3,413.60

5 years: 3434, 3,434.00, 3,434, or 3434.00

8 years: 3454.40 or 3,454.40

(the other persons is wrong)

Answer:

add the like terms if there's no like the answer will be 3x+2y-3z=-1

Answer:

y = 4x - 4

Step-by-step explanation:

Slope intercept follows the form y = mx + b

m represents the slope

b represents the y intercept

To find the slope of a table you can find the constant change in y over the constant change in x. The y values 0, 4, 8, 12 are increasing by 4 every point meaning the change in y is 4. The x values 1, 2, 3, 4 are increasing by 1 every point meaning the change in x is 1. Making the slope 4/1 or just 4.

Now use what you know: y = 4x + b to find b, we can use any of the coordinate points to substitute. I'm going to use point (1,0) where 1 is the x value and 0 is the y value.

y = 4x + b

0 = 4(1) + b

Solve for b

b = -4

:)

The expression can be simplified as follows:

a. (-4)(-2) -6(2 - 5) = 26

b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43

c. 23 - (17 - 3.4)² +  6 = -155.96

The expressions can be solved using PEMDAS rule,

P = Parenthesis

E = Exponential

M = Multiplication

D = division

A = addition

S = Subtraction

Hence,

a.

(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26

b.

12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43

c.

23 - (17 - 3.4)² +  6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96

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Answer:

384, 576

Step-by-step explanation:

The surface area is

[tex]2(12 \cdot 6+12 \cdot 6+6\cdot 8)=384[/tex]

The volume is

[tex](12)(8)(6)=576[/tex]

The value of the variable 'x' shown in th the geometrical figure is equal to 2cm

What is line bisector?

A line bisector divides the line into two equal parts. For a line of length ' L ', the bisector divides the line into two equal parts of length L/2 each.

Given is a geometrical figure in which RS is bisector of AB at point T and RS = 36.

RS bisects AB at point T. Therefore, we can say that T is the mid-point of AB. So, we can write -

AT = TB

25 - 3x = 2y - 5

- 3x - 2y = - 5 - 25

-(3x + 2y) = - 30

3x + 2y = 30             ...[1]

RS = 36

RT + TS = 36

2y - 6 + 18 = 36

2y + 12 = 36

2y = 24

y = 12

Substitute y = 12 in [1], we get -

3x + 2 x 12 = 30

3x + 24 = 30

3x = 6

x = 2

Therefore, the value of x = 2

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The algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

Given

The word phrase

"The quotient of the sum of 2 and a number b and 3"

Sum off 2 and a number b = 2+b

Then the quotient of the sum of 2 and a number b and 3 = [tex]\frac{2+b}{3}[/tex]

Hence ,the algebraic expression of the word phrase "The quotient of the sum of 2 and a number b and 3" is [tex]\frac{2+b}{3}[/tex]

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The equation of the circle (x + 5)^2 + y^2 = 18 has a radius of 3√2 and a center located at (-5 , 0).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 5)^2 + y^2 = 18, is in standard form, then

h = -5

k = 0

r = 3√2

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The four Quantities are a1 , r, n , [tex]S_{n}[/tex]

What is a Series:

A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.

Arithmetic progression

     an = a1 + ( n-1) d

     a1 is the first term

    d =common difference

    an is the nth term

   an can be found out if we know the a1 , d and n

b)  Arithmetic progression

         a1 is the first term

        an is the nth term

        sn is the sum of the n terms of the series

        Sn = n/2 ( a1 + an)

       we can calculate sn if we know a1 , an and n

c)Geometric progression

  an = a1rn-1

a1 is the first term

an is the nth term

r is the common ratio

we can calculate an if we know a1 , r and n

d)Geometric progression

  Sn = a1( 1- rn) / 1 - r

 a1 is the first term

r is the common ratio

sn is the sum of the n terms of the series

If we know a1 , r and n we can calculate [tex]S_{n}[/tex].

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The sum of the given finite series is -1

The given series is:

     [tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]

The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.

Let us expand this summation notation:

n = 1  ⇒ a(1) = (-1)¹ = -1

n = 2  ⇒ a(2) = (-1)² = 1

n = 3  ⇒ a(3) = (-1)³ = -1

We can continue to expand until n = 9, but we can see the pattern. The series can be written as:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]

We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:

    [tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]

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The 8th term of the sequence 310 is closest to the term 300.

An arithmetic progression is a series of numbers that have a set common difference in between two consecutive numbers (A.P.).

Each term in an arithmetic sequence increases or decreases by adding or subtracting a constant term.

a = 30 for the first term

d = 40, common difference

We solve in what term is closest to 300 in this manner;

300 / 40 = 7.5

Thus, find the 7th and 8th term.

7th is solved by verifying for;

a₇ = a + ( n - 1 ) d

a₇ = 30 + ( 7 - 1 ) 40

a₇ = 30 + 240

a₇ = 270

The 8th term to certify the closest;

a₈ = T7 + d

a₈ = T7 + 40

a₈ = 270 + 40

a₈ = 310

As a result, the 8th term is the closest, with a value of 310.

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The complete question is-

The numbers in this sequence increase by 40 each time 30, 70, 110,The sequence is continued with the same rule. Which number in the sequence will be closest to 300?

The simplification by combining like terms of 0.5g + g is 1.5g.

According to the given question.

We have an expression 0.5g + g .

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 0.5g + g.

Here 0.5g, and g both are the like terms.

So, we add coeffcients of g to simplify the given expression.

Therefore, the simplification of 0.5g + g  is given by

0.5g + g

= 1.5g

Hence, the simplification by combining like terms of 0.5g + g is 1.5g.

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The characteristic that justifies each assertion Property of substitution

The substitution property asserts that if a=b, then one can of replacing b in quite an expression or equation.

X Y+20=Y W and X Y+20=D T

then Y W=D T

The replacement property of equality states that "If a variable x is equal towards another variable y, then x may be substituted in place of y in whatsoever equation/expression and y can indeed be substituted throughout the place of x in any equation/expression."

Substitution connects many aspects of mathematics and hence aids in viewing mathematics as an entire discipline.

Three phases are involved in the substitution method: Solve this equation for a single of the variables. Substitute (plug-inin) this equation into a different equation and solve. Replace the value inside this original equation to obtain the equivalent variable.

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The given infinite geometric series 150+30+6+ . . . is convergent and the sum is 187.5

The given geometric series is:

  150 + 30 + 6 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 150

a(2) = 30

a(3) = 6

Hence, the common ratio is

   r = a(2) / a(1) = 30/150 = 1/5

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 1/5, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 150 and r = 1/5 into the formula:

S = 150 / (1 - 1/5)

   = 150 / (4/5)

   =  187.5

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