The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?

[tex]\lim \limits_{n \to \infty} ~\dfrac{8n}{3n^2 +5} \\\\\\=8\lim \limits_{n \to \infty} ~ \dfrac{\tfrac n{n^2}}{\tfrac{3n^2}{n^2} + \tfrac 5{n^2}}\\\\\\=8 \lim \limits_{n \to \infty} ~\dfrac{ \tfrac 1n}{ 3 + \tfrac 5{n^2}}}\\\\\\=8 \cdot \dfrac{ 0}{3 +0} = 8 \cdot 0 = 0[/tex]

We want to evaluate the limit of [tex]\frac{8n}{3n^{2}+5}[/tex] as n tends toward infinity (+∞)

The limit of this expression is the same as the limit of [tex]\frac{8n}{3n^{2}}[/tex]

But this last expression can be simplified, we can remove one n up and down which gives us : [tex]\frac{8}{3n}[/tex]

We know the limit of this one, it is simply Zero 0, by definition of the class lesson.

So to conclude the limit of [tex]\frac{8n}{3n^{2}+5}[/tex] as n tends toward infinity is 0.

Good Luck

Answer:

Part A would be C because divided 30 by 5 to get the unit rate.

Part B would be B

Answer:

C). −30÷5

B). –$6

Step-by-step explanation:

Line m and line l are parallel as m∠2 = m∠3

An equation is an expression that shows the relationship between two or more variables and numbers.

Two angles are said to be supplementary if they add up to 180 degrees.

m∠1 + m∠2 = 180° (Given)

m∠1 + m∠3 = 180° (sum of angles on a straight line)

Hence:

m∠1 + m∠2 = m∠1 + m∠3

m∠2 = m∠3

Line m and line l are parallel as m∠2 = m∠3

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Answer:

42

Step-by-step explanation:

168 factors into

2•2•2•3•7

two of the 2's make a perfect square

(2•2)•2•3•7

   2²•2•3•7

as none of the product of the remaining factors makes a perfect square

2•3 = 6,  2•7 = 14,  3•7 = 21

we need to multiply the remaining factors together to find another perfect square

   2²•(2•3•7)²

2•3•7 = 42

42(168) = 7056 = 84²

Answer:

Step-by-step explanation:

3 = 2w

=> 2w = 3

[tex] = > w = \frac{3}{2} [/tex]

=> w = 1.5 (Ans)

[tex]2v - 3u\\\\=2<3,7> - 3<-5,4>\\\\=<6,14>-<-15,12>\\\\=<6+15, 14-12>\\\\=<21,2>[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf y= -7x -30}}[/tex]

Step-by-step explanation:

We are asked to find the equation of a line,  given a point and a slope.

We can use the point-slope formula:

[tex]y-y_1= m(x-x_1)[/tex]

In this formula, (x₁, y₁) is the point and m is the slope. This line has a slope of -7 and passes through the point (-5,5). Therefore:

Substitute the values into the formula.

[tex]y-5= -7 (x- -5)[/tex]

[tex]y-5= -7(x+5)[/tex]

We want to give the answer in slope-intercept form, or y=mx+b. We must isolate the variable y.

First, distribute the -7 on the right side of the equation. Multiply each term inside the parentheses by -7.

[tex]y-5= (-7*x) + (-7*5)\\y-5 = (-7x) + (-35) \\y-5= -7x -35[/tex]

5 is being subtracted from y. The inverse operation of subtraction is addition. Add 5 to both sides of the equation.

[tex]y-5+5 =-7x -35 +5 \\y= -7x -35 +5 \\y= -7x +30[/tex]

The equation of the line is y= -7x+30.

Answer:

c :)

Step-by-step explanation:

i guessed and got it right <3

Answer:

Area= 18 x 18=324 sq.cm

Step-by-step explanation:

p=36 x2=72 (as it is twice that of the original paper)

since it is a square, length of 1 side = 72/4= 18

so, the area = l x l= 18 x 18= 324 sq.cm

Answer:

Area= 18 x 18=324 sq.cm

Step-by-step explanation:

p=36 x2=72 (as it is twice that of the original paper)

Since it is a square, length of 1 side = 72/4= 18

Therefore, the area = l x l= 18 x 18= 324 sq.cm

Hope this helps :)

Answer:     3 :3 :3

                 $8.88

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

shaded area = 2/4

shaded area as a percentage ;

     2 / 4 x 100

  = 1 / 2 x 100

  = 1 / 1 x 50

  = 50%

Step-by-step explanation:

Camilla started her collection with 20 buttons, meaning that this number is a constant, and that it will not change: (+20)

She then collects 5 buttons per month. Month is represented by the variable, x (given by the question), and there are 5 per month (so you multiply).

Set the equation:

Total pins = Amount of pins per month x amount of months + Amount of pins started.

y = 5x + 20

In this case, plug in the amount of months (x) to obtain your total (y):

When x = 0, y = 20

y = 5(0) + 20

y = 0 + 20

y = 20

When x = 1 , y = 25

y = 5(1) + 20

y = 5 + 20

y = 25

When x = 2, y = 30

y = 5(2) + 20

y = 10 + 20

y = 30

When x = 3, y = 35

y = 5(3) + 20

y = 15 + 20

y = 35

When x = 4, y = 40

y = 5(4) + 20

y = 20 + 20

y = 40

~

Note: This is a linear graph, so you can choose any of these given points (and more if you want to plot more). I would choose two that aren't too close to each other, unless you want a really small graph size.

Answer:

The answer is 24 with remainder of 1

Step-by-step explanation:

First, solve the problem by seeing what number gives you 4 when multiplied by 2. That would be 2 (2x2=4)

you subtract 4 by 4 to get zero and bring down the nine

Then you see which number would get you close to nine without overlapping when multiplied by two. That would be 4 (2x4=8)

your answer would be 24 then you subtract 9 by 8 to get a remainder of 1

Answer:

c. x=65

f. Alternate Exterior Angles

Step-by-step explanation:

2x+2=3x-63

2x=3x-65

-x=-65

x=65

They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles

Answer:

Range: {-5, 19, 31}

Step-by-step explanation:

Given the linear function, f(x) = 2x + 1, and the domain, {-3, 9, 15}.

In order to determine the range of the given linear function, simply substitute each domain value as inputs into the function.

f(x) = 2x + 1

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

f(-3) = -6 + 1

f(-3) = -5

f(9) = 2x + 1

f(9) = 2(9) + 1

f(9) = 18 + 1

f(9) = 19

f(15) = 2x + 1

f(15) = 2(15) + 1

f(15) = 30 + 1

f(15) = 31

Therfore, the range of the function is: {-5, 19, 31}.

Answer:

Step-by-step explanation:

Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):

[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to

[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to

[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and

[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex]  Bring up the lower fraction and flip it and multiply:

[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex]  In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:

[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:

[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]

Answer:

(-1,1)

Step-by-step explanation:

Im pretty sure the answer to A'' would be the inverse of A, as the triangle was mirrored on the opposite quadrant of the graph. (The inverse or opposite  of (1,-1) would be (-1,1) ).

Hope this helped!

Length of larger piece be x

x=12m

[tex]\\ \sf\longmapsto 4x+5=4(12)+5=60+5=65m[/tex]

Total length=65+12=77m

The length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.

Given that length of the smaller piece is 12 meters.

The length of the smaller piece is 5 meters greater than 4 times the length of the larger piece.

Let's represent the length of the larger piece as "x."

Length of the smaller piece = 4 times the length of the larger piece + 5

12 = 4x + 5

Subtracting 5 from both sides:

12 - 5 = 4x

7 = 4x

Dividing both sides by 4:

7/4 = x

1.75 = x

So, the length of the bigger piece is 1.75 meters.

To calculate the total length of the carpet, we add the length of the smaller piece and the length of the bigger piece:

Total length of the carpet = Length of the smaller piece + Length of the bigger piece

Total length of the carpet = 12 + 1.75

Total length of the carpet is approximately 13.75 meters.

Therefore, the length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.

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Answer:

10.446

Step-by-step explanation:

Answer:

B= (-1,0,1)

Step-by-step explanation:

because -1 is not a whole number.

Answer:

B = {-1, 0, 1)

Step-by-step explanation:

The answer is B = {-1, 0, 1) because -1 is not a whole number.

Hope this helps :)

Answer:

All ordered pairs with the same x value

Step-by-step explanation:

A vertical line can be represented by the equation x=k for some value k. So any pair with x value equal to k satisfies the equation and is thus in the set

Step-by-step explanation:

13.

oh, come on !

you never had and solved the situation "one piece costs that much, how much will be 2 or 5 or 10 of them ?"

it is a simple multiplication.

and hence the answer B.

the first hint is already in the table with 1 pizza costing $5.25.

2 pizzas are then 2×$5.25, 3 pizzas 3×$5.25, ...

so, the cost c = number of pizzas × $5.25

or short

c = p×5.25 or 5.25p

14.

the domain is the interval or set of valid values for the input variable (x) of a function/relation.

and the range is the interval or set of valid values for the result variable (y) of a function/relation.

so, the domain is the set {-3, -1, 0, 1, 3}.

and the range is the set {-4, 0, 2, 4}.

In mathematics, a function is a binary relation between two intervals or sets that associates each element of the first interval/set (domain) to exactly one element of the second interval/set (range).

and that's what is done here.

it is a function.

each value of x is associated exactly with 1 result value of y.

a y value can be associated with more than one x value - no problem.

but no x value can have more than one associated y value - otherwise that would break the principle of a function.

=====================================================

Explanation:

Refer to the dice chart below. It represents all possible ways to roll two dice and sum up the face values.

According to the table, there are...

There are A+B+C+D = 1+2+3+4 = 10 instances where we get a sum between 2 and 5. The table shows 6*6 = 36 sums total. This means there are 36-10 = 26 sums where they are between 6 and 12, aka "the sum being greater than 5".

Those 26 sums are what we focus on. Out of those 26 items, four of them are sums of "9".

The probability we want is therefore 4/26 = 2/13

The probability that the sum of the dice is 9, given that the sum is greater than 5 is 0.154

See attachment for the sample space of a roll of two dice.

From the attached sample space,

Represent the events that a sum is greater than 5 with A, and a sum is greater than 5 is 9 with B.

So, we have:

[tex]n(A) = 26[/tex]

[tex]n(A\ n\ B) = 4[/tex]

The probability that the sum of the dice is 9, given that the sum is greater than 5 is then calculated using:

[tex]Pr = \frac{n(A\ n\ B)}{n(A)}[/tex]

This gives

[tex]Pr = \frac{4}{26}[/tex]

[tex]Pr = 0.154[/tex]

Hence, the probability is 0.154

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Answer:

y = -1/4x + 2

Step-by-step explanation:

1. First you find m. Because the line is slanting downwards, you know it is negative. Then you can find the number by looking at the rise over run (rise/run). We can go up 1 (rise) and then to the side 4 (run). We go to the right side 4 because that is where the line intersects with up 1. So because the rise goes over the run, the number would be 1/4. But remember that it is negative so m = -1/4

2. Now we have to find c. For this you just have to go up or down the y-axis until you find the point where it intersects with the line. On this graph it intersects on positive 2. So c = + 2

Answer:

1/4 in decimal form is 0.25. You can convert any fraction into a decimal by just diving the numerator by the denominator.

Every time you see a fraction sign basically “—“ it jsut means divide by.

Now you can just divide. 1/4= 0.25

now we Increase which just means add

2.75+0.25 =3

Answer:

3 lbs

Step-by-step explanation:

20 mins is 1/4 lb (4oz)

1 hr is 3/4 lb (12 oz)

4 hrs= 3/4 lb or 12 oz × 4

4 hrs= 3 lbs or 48 oz