A motor scooter travels 22 mi in the same time that a bicycle covers 8 mi. If the rate of the scooter is 6 mph more than twice the rate of the bicycle, find both rates.The scooter’s rate is ____ mph. (Type an integer or a decimal)

Answers

Answer 1

Let's use the variable x to represent the speed of the scooter and y to represent the speed of the bicycle.

For a same time t, the scooter travels 22 mi and the bicycle travels 8 mi, so we can write the following equation:

[tex]\begin{gathered} distance=speed\cdot time\\ \\ 22=x\cdot t\\ \\ t=\frac{22}{x}\\ \\ 8=y\cdot t\\ \\ t=\frac{8}{y}\\ \\ \frac{22}{x}=\frac{8}{y} \end{gathered}[/tex]

Then, if the rate of the scooter is 6 mph more than twice the rate of the bicycle, we have the following equation:

[tex]x=2y+6\\[/tex]

Using this value of x in the first equation, let's solve it for y:

[tex]\begin{gathered} \frac{22}{2y+6}=\frac{8}{y}\\ \\ 22y=8(2y+6)\\ \\ 22y=16y+48\\ \\ 6y=48\\ \\ y=8\text{ mph} \end{gathered}[/tex]

Now, calculating the value of x, we have:

[tex]\begin{gathered} x=2y+6\\ \\ x=16+6\\ \\ x=22\text{ mph} \end{gathered}[/tex]

Therefore the scooter's rate is 22 mph and the bicycle's rate is 8 mph.


Related Questions

Solve the system of two linear inequalities graphicallySysx-2y) -5x + 10Step 1 of 3: Graph the solution set of the first linear inequalityAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:10-Select the region you wish to be shaded:Submit Answer

Answers

Given:

[tex]\begin{gathered} y\leq x-2 \\ \\ y>-5x+10 \end{gathered}[/tex]

Find-: Solution set of the first linear inequality.

Sol:

Graph of first inequality is:

Graph of inequality of:

[tex]y>-5x+10[/tex]

Graph of the given inequality is:

The solution of inequality is:

[tex]\begin{gathered} x=2 \\ y=0 \end{gathered}[/tex]

Which statement about the graph below is true?

Answers

Answer:

a. The relation is a function because every input has an output.

Step-by-step explanation:

a relation in which for every input there is exactly one output (for every x there is just one y)

quizlet

Answer:

A. The relation is a function because every input has an input

Step-by-step explanation:

A relation is a function as long as there are not multiple outputs for one input. It's okay if there are multiple inputs for one output, like we can see here with points (-6, 1) and (2, 1).

Another way to test if a graphed relation is a function is the vertical line test. Draw vertical lines at multiple spots on the graph and if any of the vertical lines touches 2 points, the graphed relation is not a function.

:)

hailey is going to rent an apartment for $864 a month in addition to the first month's rent when moving in a security deposit of $216 is required what will be the total payments required when moving in

Answers

We are given that a total amount is $864, if a deposit of $216 is given, then the total amount to pay is the following:

[tex]864-216=648[/tex]

Therefore, there is $648 to pay.

Find the variance for the set of data: 22, 26, 17, 20, 20.The variance is

Answers

The variance of a given data set with size N is given by the formula:

[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}[/tex]

Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:

[tex]\begin{gathered} \mu=\frac{22+26+17+20+20}{5}=21 \\ \sigma=\sqrt{\frac{1^2+5^2+(-4)^2+(-1)^2+(-1)^2}{5}}=\sqrt{\frac{44}{5}}=2\sqrt{\frac{11}{5}} \\ \therefore Var(X)=\frac{44}{5}=8.8 \end{gathered}[/tex]

State the number of complex zeros and the possible number of real and imaginary zeros for each function. Then find all zeros. show all work

Answers

We have a cubic function

[tex]f(x)=x^3-3x^2-47x-87[/tex]

One way to find all the zeros is by factoring, we can easily find the first zero using the divisors test if we have an independent term, at our case it's -87, one of the divisors may be a zero. The divisors of -87 is 1, 3, 29 and 87.

If we check for all of the divisors we will see that -3 is a zero. (Check with both signals).

If -3 is a zero, the D'Alembert theorem tells us that f(x) is divisible by (x+3), if we do that division we'll have a quadratic function where we can just apply the quadratic formula, then

There's a theorem that says that, if f(a) is a zero, i.e f(a) = 0, and f(x) is a polynomial, then f(x) is divisible by (x-a), in other words, we can divide f(x) by (x-a) and the rest of the division will be 0.

Therefore, let's divide our function by (x+3)

Then we can write our function as

[tex]f(x)=(x+3)(x^2-6x-29)[/tex]

Look that now we have a quadratic function, and we can easily find its zeros, applying the quadratic formula

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

We have a = 1, b = -6 and c = -29. Then

[tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36+4\cdot29}}{2} \\ \\ x=\frac{6\pm\sqrt[]{156}}{2} \\ \\ x=\frac{6\pm2\sqrt[]{38}}{2} \\ \\ x=3\pm\sqrt[]{38} \end{gathered}[/tex]

Now we have all the zeros of f(x), it's

[tex]\begin{gathered} x=-3 \\ \\ x=3+\sqrt[]{38} \\ \\ x=3-\sqrt[]{38} \end{gathered}[/tex]

As we can see there's no complex zero, all the zeros are real numbers.

The max number of complex zeros is 2 because the complex zeros always come in pairs, so if we have 1 complex zero, automatically we have another, for a 3-degree equation, there's a maximum of 2 complex zeros and 1 real zero, or all the of them are real.

Then the correct answer is A)

Is my answer correct help please

Answers

Answer:

Yes your answer is right !

Step-by-step explanation:

steps

X= 3 and y = 7

So first replace [tex]2^{x}[/tex] with [tex]2^{3}[/tex] an that will give you 8

Then 8-Y and so you replace y with 7 and so it becomes

8-7 = 1

So the correct answer is D (1)

Hope this helps

~~Wdfads~~

URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!

Answers

Answer:

option 3

Step-by-step explanation:

As long as both lines are rotated the same direction and the same angle, then the angle between the two lines will not change.

An electronics store sends an email survey to all customers who bought tablets. The previous month, 570 people bought tablets. Surveys were sent to 300 of these people, chosen at random, and 138 people responded to the survey. Identify the population and the sample. (4 points)The population is 570. The sample is 138.The population is 570. The sample is 300.The population is 300. The sample is 138.The population is 138. The sample is 570.The population is 138. The sample is 300.

Answers

Answer:

The population is 300. The sample is 138.

Explanation:

In statistics, population refers to the entire group of persons or things that a study is to be carried out on. Looking at the given question, we can see that, even though there were 570 people that bought tablets, the surveys were only sent to 300 people chosen at random. It shows that only 300 of the 570 people are to be surveyed, therefore, the population is 300.

A sample is the particular/specific group of persons or things that data is to be received from.

Looking at the given question, we can see that, out of the 300 people that the surveys were sent to, only 138 people responded to the survey. So the sample is 138.

What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2

Answers

[tex]x-3y=6[/tex]

Let's make y the subject of the equation.

[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]

The correct option is A

You live 3 miles from collage and 2 miles from the business where you work.Let d represent the distance between your work and the collage write an inequality involving d.

Answers

The inequality involving the distance is 3 > d > 2.

What is an inequality?

An inequality is simply used to illustrate the expressions that aren't equal. This can be illustrated through the use of greater than, less than, etc.

When you live live 3 miles from collage and 2 miles from the business where you work. This will be expressed thus

Let d represent the distance between your work and the collage and the inequality is 3 > d > 2.

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Sally Sue had spent all day preparing for the prom. All the glitz and the glamour of the evening fell apart as she stepped out of the limousine and her heel broke and she fell to the ground. Within minutes, news of her crashing fall had spread to the 550 people already at the prom. The function, p(t) = 550(1-e^-0.039t) where t represents the number of minutes after the fall, models the number of people who were already at the prom who heard the news.How many minutes does it take before all 550 people already at the prom hear the news ofthe great fall? Show your work.

Answers

We have the function

[tex]p(t)=550(1-e^{-0.039t})[/tex]

Therefore we want to determine when we have

[tex]p(t_0)=550[/tex]

It means that the term

[tex]e^{-0.039t}[/tex]

Must go to zero, then let's forget the rest of the function for a sec and focus only on this term

[tex]e^{-0.039t}\rightarrow0[/tex]

But for which value of t? When we have a decreasing exponential, it's interesting to input values that are multiples of the exponential coefficient, if we have 0.039 in the exponential, let's define that

[tex]\alpha=\frac{1}{0.039}[/tex]

The inverse of the number, but why do that? look what happens when we do t = α

[tex]e^{-0.039t}\Rightarrow e^{-0.039\alpha}\Rightarrow e^{-1}=\frac{1}{e}[/tex]

And when t = 2α

[tex]e^{-0.039t}\Rightarrow e^{-0.039\cdot2\alpha}\Rightarrow e^{-2}=\frac{1}{e^2}[/tex]

We can write it in terms of e only.

And we can find for which value of α we have a small value that satisfies

[tex]e^{-0.039t}\approx0[/tex]

Only using powers of e

Let's write some inverse powers of e:

[tex]\begin{gathered} \frac{1}{e}=0.368 \\ \\ \frac{1}{e^2}=0.135 \\ \\ \frac{1}{e^3}=0.05 \\ \\ \frac{1}{e^4}=0.02 \\ \\ \frac{1}{e^5}=0.006 \end{gathered}[/tex]

See that at t = 5α we have a small value already, then if we input p(5α) we can get

[tex]\begin{gathered} p(5\alpha)=550(1-e^{-0.039\cdot5\alpha}) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550\cdot0.994 \\ \\ p(5\alpha)\approx547 \end{gathered}[/tex]

That's already very close to 550, if we want a better approximation we can use t = 8α, which will result in 549.81, which is basically 550.

Therefore, we can use t = 5α and say that 3 people are not important for our case, and say that it's basically 550, or use t = 8α and get a very close value.

In both cases, the decimal answers would be

[tex]\begin{gathered} 5\alpha=\frac{5}{0.039}=128.2\text{ minutes (good approx)} \\ \\ 8\alpha=\frac{8}{0.039}=205.13\text{ minutes (even better approx)} \end{gathered}[/tex]

Solve the following addition and subtraction problems.3 km9hm9dam19 m+7km2 dam5sq km95 ha8,994sq m+11sq km11 ha9,010sq m44m−5dm72km47hm2dam−11 km55hm

Answers

As a well accepted rule to solve this problem, we would transform all values to the lower units.

so for the first question:

3 km 9hm 9 dam 19 m + 7 km 2 dam

3,000 m 900 m 90 m 19 m + 7,000 m 20 m

= 4,009 + 7,020

= 11,029 m

The second question:

5 sq.km 95 ha 8,994 sq.m + 11 sq.km 11 ha 9,010 sq.m

5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq 9,010 sq m

= 5,103,994 sq m + 11,119,010 sq m

= 16,223,004 sq m

The third question:

44 m - 5 dm

44 m - 0.5 dm

= 43.5 m

The fourth question:

72 km 47 hm 2 dam - 11 km 55 hm

72,000 m 4,700 m 20 m - 11,000 m 5,500 m

= 76,720 m - 16, 500 m

= 60,220 m

7(x+2)=

4(x+4)=

9(x+6)=

Answers

14

16

54

Multiply each term in the parentheses by 9 and you should get something like this: 9x+9x6 and then multiply the numbers and you should get 9x+54

What’s the correct answer answer asap for brainlist

Answers

Answer: 3 years it started in Europe in 1914 and the USA got involved in 1917

Step-by-step explanation:

Rearrange the formula y = a-bx² to make x the subject.​

Answers

Answer:

x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]

Step-by-step explanation:

y = a - bx² ( subtract a from both sides )

y - a = - bx² ( multiply through by - 1 )

bx² = a - y ( divide both sides by b )

x² = [tex]\frac{a-y}{b}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]

Approximate when the function is positive, negative, increasing, or decreasing.

Describe the end behavior of the function.

Answers

The function y = - | x | + 1 is increasing on ( - ∞, 0 ) and decreases on ( 0, ∞ ).

A relationship between a group of inputs with each output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Consider the function,

y = - | x | + 1

The non-negative value of a real number x, represented by the symbol |x|, is the absolute value or modulus of x, regardless of its sign.

From the graph, we can approximate that the function is increasing from negative infinity to zero and the function decreases from zero to infinity.

Increasing on: ( - ∞, 0 )

Decreasing on: ( 0, ∞ )

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What happens to F(x) when x is negative but approaches zero for the functionF(x) = 1/x, whose graph is shown below?

Answers

Given: The graph of the function below

[tex]F(x)=\frac{1}{x}[/tex]

To Determine: What happens to F(x) when x is negative but approaches zero

Solution:

It can be observed from the given graph that when x is negative but approaches zero, F(x) approaches negative infinity

This is as shown below

From the options provided, the best answer is F(x) is a negative number, OPTION C

Solve by applying the zero product property.m^2= 27-6m

Answers

To apply the zero product property we first need to write all the terms of the equation on side:

[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]

Now we need to factorise the expression on the right:

[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]

The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:

[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]

Therefore, the solutions of the equation are m=-9 and m=3

Suppose you are in a restaurant and the menu is as follows: 5 beverages, 11 appetizers, 9 main courses, and 3 desserts. Impose the condition that exactly one choice must be made from each category. How many
distinguishable meals can be created?

Answers

Answer:

1485

Step-by-step explanation:

The answer is found by multiplying how many of each of the categories there are;

5 × 11 × 9 × 3 = 1485

PLEASE ANSWER ASAP1. The length of a bookshelf is 5 ft. The length of a model of this bookshelf is 3 ft. Find the scale of the model to the bookshelf. Enter your answer in the box.2. A rectangular garden has a length of 8 ft and a width of 4 ft. A smaller garden was made, using a scale of 3:4 . Find the dimensions of the smaller garden. Enter your answers in the boxes.

Answers

1.

The scale factor would be:

[tex]3\colon5[/tex]

2.

Divide each original dimension by 4 and then multiply by 3, as following:

[tex]\begin{gathered} \frac{8ft}{4}\cdot3=6ft \\ \\ \frac{4ft}{4}\cdot3=3ft \end{gathered}[/tex]

The smaller garden has a length of 6 ft and a widht of 3 ft

Classify the following conic section from its standard equation: 4y2 - 6x +16y - 21 = 0.My

Answers

it is a parabolla because only variable is quadratic and the other is linear.

Find all x-intercepts of the following function. Write your answer or answers as
coordinate points. Be sure to select the appropriate number of x-intercepts.
f(x)
3x + 30
25x2 - 49

Answers

Given: The function below

[tex]f(x)=\frac{3x+30}{25x^2-49}[/tex]

To determine: All x-intercepts of the given function

The x-intercept is a point where the graph crosses the x-axis

We would substitute the function equal to zero and find the value of x

[tex]\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}[/tex][tex]\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}[/tex]

Therefore, the coordinate of the x-intercept is (-10, 0)

Need help finding the volume and rounding to nearest whole number.

Answers

For a cylinder, the volume can be calculated using the formula:

[tex]V=\pi r^2h[/tex]

Where r is the radius of the base and h is the height. From the problem, we identify:

[tex]\begin{gathered} r=\frac{16}{2}=8\text{ yd} \\ \\ h=10\text{ yd} \end{gathered}[/tex]

Then, using these values to calculate the volume of the cylinder:

[tex]\begin{gathered} V=\pi(8)^2(10)=\pi(64)(10)=640\pi \\ \\ \therefore V=2011\text{ yd}^3 \end{gathered}[/tex]

The triangles are similar, solve for the question mark. A Z с ? 15 10 12 B X D E 8 8 18 12.5 0 24

Answers

Answer:

18

Explanation:

The triangles are similar if their sides are proportional. It meant that the ratio of AB to CD is equal to the ratio of AE to CE, so we can write the following equation:

[tex]\begin{gathered} \frac{AB}{CD}=\frac{AE}{CE} \\ \frac{15}{10}=\frac{AE}{12} \end{gathered}[/tex]

So, we can solve for AE as:

[tex]\begin{gathered} \frac{15}{10}\cdot12=\frac{AE}{12}\cdot12 \\ 18=AE \end{gathered}[/tex]

Therefore, the measure of AE is 18

determine the orderd pair (8,-3)is a solytion to the linear pair

Answers

To answer this question, we need to evaluate if the ordered pair forms an identity with both equations. We need to substitute the values for x = 8, and y = -3 in both equations:

[tex]\frac{x}{2}+5y=-11\Rightarrow\frac{8}{2}+5(-3)=-11\Rightarrow4-15=-11\Rightarrow-11=-11[/tex]

These values result in an equality in this equation. We need to evaluate the other equation:

[tex]6x-\frac{y}{6}=40\Rightarrow6\cdot(8)-(\frac{-3}{6})=40\Rightarrow48+\frac{1}{2}=\frac{97}{2}\ne-11[/tex]

In this case, the values do not result in an equality in one of both equations.

Therefore, we have that the correct answer is the option B:

No, the proposed solution does not result in an equality in one of the two equations.

With the information given, find the lenght of the prism

Answers

Answer:

The lenght of the prism is 22 cm.

Step-by-step explanation:

From the given drawing, we can conclude that a one-unit line measures 2 cm. Since the prism is 11 unit lines long, we can conclude that it is 22 cm.

Slove this equation 19=n+22

Answers

Step-by-step explanation:

I think it helps you

please mark me as brainlist

Answer:

greyehahhsh[tex]5.5723[/tex]

the circle below is centered at the point (2,-1 ) and had a radius of length 3 what is its equation

Answers

The standard equation for a circle is

[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where} \\ a=2 \\ b=-1 \\ r=\text{radius}=3 \\ (x-2)^2+(y-(-1))^2=3^2 \\ (x-2)^2+(y+1)^2=3^2 \\ \end{gathered}[/tex]

Options for this are: 20 of the best selling cameras, same photographer, 100 pictures with each camera, consistent across all cameras 10 point scale, two were from companies who are major advertisers

Answers

It is given that:

A writer for a magazine recently did a test to determine which mid-range digital camera takes the best pictures. Her method is described below.

Which part of the method describes an area of potential bias?

She gathered 20 of the best.selling cameras and used the same photographer to take 100 pictures with each camera .She ensured that the environment and the subject of each picture were consistent across all cameras and used a 10.point scale to determine picture quality. Of the cameras tested, two were from companies who are major advertisers in the magazine.

Now if the reading is done carefully, it can be concluded that the information given by:

"Of the cameras tested, two were from companies who are major advertisers in the magazine." can be considered for a potential bias since the magazine may be pressured by these two companies to give them a higher rating than they deserve.

So the option:two were from companies who are major advertisers is correct.

Select all the correct locations on the image.Which statements are logically equivalent to (p q)?

Answers

-(p ∧ q ) is logically equivalent to

-pv-q

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