During Christmas a book store sold 72 books. If the ratio of books to books marks sold was 9:2,how many bookmarks did the store sell

Answers

Answer 1

Answer:

16

Step-by-step explanation:

the 9 parts of the ratio is equivalent to 72 books

divide number of books by 9 to find one part of the ratio

[tex]\frac{72}{9}[/tex] = 8 ← 1 part of the ratio

2 parts = 2 × 8 = 16 ← number of bookmarks sold



Related Questions

I need help with this problem

Answers

Answer:

D

Step-by-step explanation:

Because it's saying what is the shape of the "Square" inside of the cylinder.

Answer:

C) rectangle, would be the best answer beacuse the shape of the dotted line clously resembles a rectangle

Step-by-step explanation:


Determine which system of equation has (-3,19) and (4,-23) as a solution?

Answers

Answer:

y=6x+1

Step-by-step explanation:

First you must find the slope of the two points...

[tex]\frac{4--3}{-23-19}[/tex] which then would equal 6

Then you take the slope and put into point-slope form

(y-y1)=m(x-x1)...take one of the points that is given and plug it into this formula.

so I used (-3,19).

(y-19)=6(x--3)

I would then get y-19=6x+18

Add 19 to both sides and you will get y=6x+1


A biologist is measuring growth of a frog population in a pond. She expects the number of tadpoles to grow every day by a factor of b. On day one, at the start of her experiment, the number of tadpoles is a. Which expression best predicts the number of tadpoles at the start of the nth day?

Answers

An3x=2x+1

subtract 2x from both sides

x=1 answer


Step-by-step explanation:

it will only take one day

Answer:

a * b^(n-1)

Step-by-step explanation:

I guessed and got it right :/

Glen has three pairs of shoes, five shirts, and four pairs of pants. How many outfits considering one pair of shoes, one shirt, and one pair of pants can he make?

Answers

Answer:

3

Step-by-step explanation:

To have full outfits he can only make three


Answer:

she can make 12: A

Step-by-step explanation

add up the numbers of pants, shoes , shirts you will get 12

Rectangle ABCD is similar to rectangle WXYZ. What is the value of AB if WX is & feet, AD is 12 feet, and WZ is 16 feet?

Answers

Answer:

Similar rectangles states that the corresponding sides are in proportion.

As per the statement:

Rectangle ABCD is similar to rectangle WXYZ.

WX = 8 feet, AD = 12 feet and WZ = 16 feet.

Since. Rectangle ABCD and rectangle WXYZ are similar

then;

their corresponding sides are in proportion:

[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]

To find the value of AB:

[tex]\frac{AB}{WX}=\frac{AD}{WZ}[/tex]

Substitute the given values we have;

[tex]\frac{AB}{8}=\frac{12}{16}[/tex]

Multiply both sides by 8 we have;

[tex]AB = \frac{12}{16} \times 8 = \frac{96}{16}=6[/tex]

Therefore, the value of AB is 6 units.




Final answer:

The value of AB in the similar rectangles ABCD and WXYZ, given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, is calculated as 6 feet by using the property of similar rectangles that the ratios of their corresponding sides are equal.

Explanation:

The subject in question deals with similar rectangles. Since rectangle ABCD is similar to rectangle WXYZ, the ratio of their corresponding sides will be equal. This means that the ratio of side AB to side WX should be the same as the ratio of side AD to side WZ.

Given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, we can set up the proportion as AB/WX = AD/WZ. Substituting the known values into this proportion we get AB/8 = 12/16.

To find the value of AB, we can cross multiply and solve for AB to get AB = (8 * 12) / 16 = 6 feet.

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How do the graphs of the function differ from the graph of f(x)=1.5x^3

Answers

Answer: p(x) = steeper

               q(x) = less steep and reflection

               r(x) = reflection

Step-by-step explanation:

The parent graph is: f(x) = 1.5x³

If the absolute value of the coefficient in front of x³ is greater than 1.5, then it is steeper (the graph is stretched).If the absolute value of the coefficient in front of x³ is less than 1.5, then it is less steep (the graph is shrunk/compressed).A negative sign in front of the coefficient represents a reflection over the x-axis.

p(x):  2 > 1.5 , so it is stretched (steeper).

p(x): coefficient has a positive sign, so it is NOT a reflection


q(x):  1  < 1.5 , so it is shrunk/compressed (less steep).

q(x): coefficient has a negative sign, so it is a reflection over x-axis


r(x): 1.5 = 1.5 so it is neither a stretch or a shrink

r(x): coefficient has a negative sign, so it is a reflection over x-axis



Final answer:

The graph of the function f(x) = 1.5x^3 has a steep increase or decrease, exhibits symmetry, and passes through the origin.

Explanation:

When comparing the graphs of different functions, it's important to analyze their key characteristics. In the case of the function f(x) = 1.5x^3, the graph will be a cubic function. Here are three significant differences between the graph of f(x) = 1.5x^3 and other functions:

The graph will have a steep increase if x > 0 and a steep decrease if x < 0, due to the positive coefficient of the x^3 term.The graph will exhibit symmetry with respect to the y-axis because the power of x is odd.The graph will pass through the origin (0, 0) since there is no constant term in the function.

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Identify the sequence that lists the angles of △JKW in order from largest to smallest. THE ANSWER WITH THE RED ARROW IS WRONG!!

Answers

i think that its is w,k,j. i could be wrong though


Calculate s24 for the arithmetic sequence in which a13=1.9 and the common difference is d=3.7.

Answers

Answer:

The correct answer option is 42.6.

Step-by-step explanation:

We know that in a arithmetic sequence, [tex]a_{13}=1.9[/tex] and the common difference is [tex](d)=3.7[/tex].

The standard form of an arithmetic sequence is given by:

[tex]a_n=a_1+(n-1)d[/tex]

So we will substitute the given values in this formula to find the value of [tex]a_1[/tex].

[tex]a_{13}=a_1+(13-1)3.7[/tex]

[tex]1.9=a_1+(12)3.7[/tex]

[tex]1.9=a_1+44.4[/tex]

[tex]a_1=-42.5[/tex]

Now finding the 24th term"

[tex]S_{24}=a_1+(n-1)d\\\\S_{24}=-42.5+(24-1)3.7\\\\\\S_{24}=42.6[/tex].

Therefore, the 24th term of the given arithmetic sequence is 42.6.


Answer:

Just took this test the correct answer is 1.2


Use the equation below to answer these questions.
[tex]x+2=\sqrt{3x+10}[/tex]

1.) What is the solution to the equation?

2.) What is the extraneous solution? Why?

3.) In general, what is an extraneous solution?

Answers

1) [tex]x+2=\sqrt{3x+10}[/tex]

Square both sides to get

[tex](x+2)^2=(\sqrt{3x+10})^2\implies x^2+4x+4=3x+10\implies x^2+x-6=0[/tex]

Factorize and solve:

[tex]x^2+x-6=(x+3)(x-2)=0\implies x=-3,x=2[/tex]

2) I assume we take [tex]\sqrt x[/tex] to be defined only for [tex]x\ge0[/tex]. Under this condition, a solution would be extraneous if [tex]\sqrt{3x+10}[/tex] is undefined, which happens if [tex]3x+10<0[/tex].

If [tex]x=-3[/tex], then [tex]3x+10=-9+10=1[/tex], so it is not extraneous.

If [tex]x=2[/tex], then [tex]3x+10=6+10=16[/tex], so it is not extraneous.

So there are not extraneous solutions to this equation.

3) Lots of information on this on the web...

Final answer:

The solution for the given equation is x=2. -3 is an extraneous solution caused by the squaring operation and it doesn't satisfy the original equation. An extraneous solution is a solution that does not satisfy the original equation.

Explanation:

To find the solution of the equation x+2=√(3x+10), we first square both sides to eliminate the square root: (x+2)2=3x+10.

This simplifies down to x2 + 4x + 4=3x+10. Rearranging terms then gives us x2 + x - 6=0. The solutions of this quadratic equation are x=2 and x=-3.

However, if we substitute x=-3 back into the original equation, it does not hold true. Thus, -3 is an extraneous solution. This extraneous solution arises in this case because we applied the squaring operation, which is not a reversible process. An extraneous solution, generally, is a solution to a transformed equation that does not satisfy the original equation.

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Colby and Danielle clean pools for extra money over the summer. Colby's income is determined by f(x) = 3x + 12, where x is the number of hours. Danielle's income is g(x) = 5x + 10. If Colby and Danielle were to combine their efforts, their income would be h(x) = f(x) + g(x). Create the new function h(x). If Colby works 4 hours and Danielle works 4 hours, and if they each get half of the money when they work together, will Colby make more money working alone or by teaming with Danielle?

Answers

Answer:

Colby makes more money by teaming with Danielle

Step-by-step explanation:

Colby's income =f(x) = 3x+12

and Danielle's income = g(x) = 5x+10

If they combine their efforts the combined income would be

h(x) = 3x+12+5x+10 = 8x +22

If shared equally between them

Colby would get 1/2(8x+22) = 4x+11  and

Danielle would get  1/2(8x+22) = 4x+11

Since given they worked each for 4 hours

Colby income = Danielle income= 4(4) +11 = 27

If not combined, then

Colby income 3(4) + 12=24 and

Danielle income= 5(4) +10 = 30

Because of combining Colby makes more money by teaming with Danielle.

The difference is 3 for 4 hours work.

Answer:

B

Step-by-step explanation:

team with Danielle , h(x)=8x+22

Which expression is equivalent to [tex]\frac{4-2}{2^{2}}[/tex]?

A: −16

B: −8

C: 8

D: 16

Answers

Answer:

1/2

Step-by-step explanation:

(4-2)

----------

2^2

The numerator is 4-2 = 2

The denominator is 2^2 = 4

2

------

4

1/2

Please help!!!!
Leonard wants to restrict the domain of the tangent function so that its inverse is a function. Which description best describes how he could restrict the domain?

A) Choose any interval between consecutive asymptotes.
B) Choose any interval that includes two asymptotes.
C) Choose any interval of length 2π radians.
D) Choose any interval of length π radians.

Answers

Answer:

Correct choice is A

Step-by-step explanation:

If a function has an inverse, then there is at most one x-value for each y-value.

The tangent function is periodic with period [tex]\pi.[/tex] Hence, at each value for which [tex]f(x)=\tan x[/tex] is defined, [tex]f(x+n\pi )=\tan x[/tex] for each integer n. Therefore, the function [tex]f(x)=\tan x[/tex] does not have an inverse. Since tangent is not a one-to-one function, the domain must be limited. From examining the graph of the tangent function, we see that in each interval of the form

[tex]\left((2k−1)\dfrac{\pi}{2},(2k+1)\dfrac{\pi}{2}\right)[/tex]

where k is an integer, the tangent function assumes every value in its range. Moreover, in each such interval, each y-value is achieved exactly once. Hence, we can create an invertible function by restricting the domain tangent function to one such interval. Such interval is an interval between two consecutive vertical asymptotes [tex]x=(2k−1)\dfrac{\pi}{2}[/tex] and [tex]x=(2k+1)\dfrac{\pi}{2}.[/tex]

Jack has $55 and Emily has $28. Jack is saving $4 per day, and Emily is saving $13 per day. After how many days will Jack and Emily have the same amount of money.

Answers

Answer:

About 4

Step-by-step explanation:


Answer: B: 3 Days

Step-by-step explanation:

Let x be the number of days when Jack and Emily have the same amount of money.

Then, the total amount saved by Jack =4x+55

The total amount saved by Emily  = 13x+28

According to the question,

13x + 28 = 4x + 55

13x - 4x = 55 - 28

9x = 27

x = 3

Brainiest PLZ

Samantha is saving to buy a new computer. the first month she saves $100. each of the following months she plans to save 10%more than the previous month. how much money will she have saved after 6 months

Answers


She saves $100.She saves 10% more.They want to know how much they will save after 6 months. Multiply 10% by 6months and you get 60%.Then you multiply the answer of .60 (60%) by 100 and you get 60. Lastly, since you wanna know how much you saved,subtract $100-60 and your final answer you get is that she saves $40.Hope that helped!

What is the answer a factory adds three red drops an two blue drops of coloring to white paint to make each pint of purple paint the factory will make 50 gallons of this purple paint how many drops of red and blue coloring will the factory need the 50 gallon batch of purple paint

Answers

Answer:

Red = 30 drops

Blue = 20 drops

Step-by-step explanation:

The ratio red to blue is 3 : 2

Sum of ratios = 3 + 2 = 5

Required purple paint = 50 gallons

So,

[tex]Multiplier = \frac{50}{5} = 10[/tex]

Now, Red drops = 3×10 = 30

Blue drops = 2×10 = 20


Answer:

Step-by-step

Bryan and Seth are both members of the same private social networking site. Bryan’s membership plan can be expressed with the function y = 9.50x + 22, where x is the number of months that he is a member and y is the total cost. Seth’s membership fees are shown in the graph.

If x represents the number of months that they are members of the social networking site, how much will Bryan and Seth each pay after 15 months of membership?

Answers

Answer:

After 15 month of membership, Brian will pay $164.5 and Seth will pay $100.

Step-by-step explanation:

Brian

y=9.50(15)+22

y=142.5+22

y=164.5

Seth

(15,100)

Jaz was 43 inches tall. Eighteen months later she was 52 inches tall. Find the constant rate of change of jaz's height

Answers

Answer:

.5 inches a month


Step-by-step explanation:

52 - 43 = 9 inches


9/18 = .5



Answer:

0.5 inches a month

Step-by-step explanation:

subtract 43 from 52 and divide that answer by 18

52-43=9 9÷18=0.5

please mark me brainliest

Can someone please please help me?? :(

A driver descends to a location of -50 1/4 meters relative to the surface of the water.

He then descends another 10 1/2 meters. What is the driver’s final location relative to the surface of the water?

Enter your answer as a simplified mixed number in the box.

_________ meter's.

Answers

Answer:

-60 3/4m

Step-by-step explanation:

The diver first dives down 50 1/4m, which is represented by the -50 1/4m. He then descends another 10 1/2m down. So -50 1/4m - 10 1/2m.

-50-10=-60

-(1/4)-(1/2)= (1/4)+(1/2)

(1/4+1/2)=(2/8+4/8) you can only add with the same denominators.

=6/8 (simplifies down to 3/4)

The sales tax rate is 7.25%. How much tax in dollars is added on an item that costs $56.00?

Answers

Hi there! :)

Answer:

$4.06 of taxes is added on an item that costs $56.00 is the sales tax rate is 7.25%.


Step-by-step explanation:

You are looking for 7.25% of $56.00

7.25% is the same thing as 7.25/100, which is the same thing as 7.25 ÷ 100

7.25 ÷ 100 = 0.0725

The word "of" is the same thing as a multiplication sign (×).

SO, 7.25% of $56.00 = 0.0725 × 56


0.0725 × 56 = 4.06 ⇒ YOUR ANSWER


There you go! I really hope this helped, if there's anything just let me know! :)

The tax on that item will be 4.06$.

What is tax?

A tax is a necessary fee or financial charge imposed by a government on an individual or an organization in order to raise funds for public works projects that provide the greatest services and infrastructure. The gathered funds are subsequently utilized to finance other government activities.

Given, The sales tax rate is 7.25%. for an item whose cost is 56.00$.

Tax added on that item  = 56* 7.25%

Tax added on that item  = 4.06$

Therefore, the total tax added on the item whose total value is 56 will be 4.06$.

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the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days what is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days


a.0.2981


b.0.7019


c.0.8186


d.0.1814

Answers

Answer:

a. 0.2981

Step-by-step explanation:

We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Let us find z-score for 260 days.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]x[/tex] = Sample score,

[tex]\mu[/tex] = Mean  

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{260-268}{15}[/tex]    

[tex]z=\frac{-8}{15}[/tex]  

[tex]z=-0.53[/tex]  

Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.  

From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.

Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.

A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you? need?

Answers

Answer:

[tex]13\frac{1}{3}[/tex] cups

Step-by-step explanation:

We are told that a recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B.      

To find the number of cups of ingredient B we will use proportions.

[tex]1\frac{2}{3}=\frac{5}{3}[/tex]

[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{\frac{1}{2}}{\frac{5}{3}}[/tex]

[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]  

Now let us substitute our amount of Ingredient A =4 in our proportions.

[tex]\frac{4}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]

[tex]\frac{\text{Number of cups of ingredient B}}{4}=\frac{10}{3}[/tex]

Multiplying both sides of our equation by 4.

[tex]4*\frac{\text{Number of cups of ingredient B}}{4}=4*\frac{10}{3}[/tex]

[tex]\text{Number of cups of ingredient B}=\frac{40}{3}[/tex]

[tex]\text{Number of cups of ingredient B}=13\frac{1}{3}[/tex]

Therefore, we need [tex]13\frac{1}{3}[/tex] cups of ingredient B to make our recipe.

Answer:

Proportion states that the  two ratios are equal.

Given statement: A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A.

By using proportion definition to find ingredients B;


[tex]\frac{\frac{1}{2} }{1\frac{2}{3} } = \frac{4}{B}[/tex]

Simplify:

[tex]\frac{\frac{1}{2} }{\frac{5}{3}} = \frac{4}{B}[/tex]

By cross multiply we get;

[tex]B \cdot \frac{1}{2} = 4 \cdot \frac{5}{3}[/tex]

or

[tex]\frac{B}{2} = \frac{20}{3}[/tex]

Multiply both sides by 2 we get;

[tex]B = \frac{20}{3} \times 2 = \frac{40}{3} = 13\frac{1}{3}[/tex]

Therefore, [tex]13\frac{1}{3}[/tex] cups of ingredients B needs.

jason is training for a marathon bike ride. His average speed increase from 3 miles per hour to 6 miles per hour in 3 months find the rate of change in the miles per hour that jason bikes

Answers

Answer:

The rate of change is 1 mile per hour per month

Step-by-step explanation:

We are given

initial speed = 3 mph

final speed =6 mph

total number of months =3

now, we can use rate of change formula

we know that

rate of change = ( final speed - initial speed)/(total number of months)

now, we can plug values

and we get

Rate of change is

[tex]=\frac{6-3}{3}[/tex] mph per month

=1 mph per month

Jason's rate of change in biking speed is 1 mile per hour per month.

Jason is training for a marathon bike ride. His average speed increases from 3 miles per hour to 6 miles per hour in 3 months. To find the rate of change in the miles per hour that Jason bikes, we use the formula:

Rate of Change = (Final Speed - Initial Speed) / Time Period

The final speed is 6 miles per hour, the initial speed is 3 miles per hour, and the time period is 3 months. Therefore:

Rate of Change = (6 - 3) mph / 3 months

Rate of Change = 3 mph / 3 months

Rate of Change = 1 mph per month

Therefore, Jason's rate of change in biking speed is 1 mile per hour per month.

please help on this one? :)

Answers

The answer is A:62 kg

Answer:

62 kg: A

Step-by-step explanation:

The black line is called line of best fit. This line shows the points plotted and how they compare to the predicted amounts. The reason why A is the correct answer is because all of the other blue points line up with the line of best fit. Since the point 62kg is NOT on the line of best fit, that is the point where experimental error may have occurred.

At the movie theatre 30% of the audience members were children. If the number of children at the movie theatre was 210, what was the total number of people at the movie theatre?

Answers

Answer:

The total number of people at the movie theatre is 700.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

At the movie theatre 30% of the audience members were children.

If the number of children at the movie theatre was 210.

Percentage = 30%

Part value =  210

Put in the formula

[tex]30 = \frac{210\times 100}{Total\ value}[/tex]

[tex]Total\ value = \frac{21000}{30}[/tex]

Total value = 700

Therefore the total number of people at the movie theatre is 700.



Elvie can type 4,200 words in 30 minutes givr the ratio of the time in minutes to the number of words

Answers

Answer:

1 : 140

Step-by-step explanation:

Ratio is 30 : 4200

Divide both numbers by 30:-

= 1 : 140   (answer)

Final answer:

To calculate the ratio of time to words, divide the minutes by the number of words, resulting in a 30:4200 ratio. This ratio highlights the efficiency of typing, useful for productivity analysis.

Explanation:

The question involves calculating the ratio of time in minutes to the number of words typed. Elvie can type 4,200 words in 30 minutes. To find the ratio of time in minutes to the number of words, we divide the number of minutes by the number of words.


First, express both quantities in their simplest forms: 30 minutes and 4,200 words. Then, create the ratio as follows:



Time in minutes : Number of words = 30 : 4,200


For easier comparison or further calculations, the ratio can be simplified by dividing both terms by the greatest common divisor. However, in this case, presenting the ratio in its initial form already communicates the relationship clearly, showing how many words are typed in a given amount of time. The ratio can be crucial for understanding productivity and efficiency in typing or other time-bound tasks.

The population of the town was 25,000 people.Then 3,200 people moved away.What was the percent of increase?

Answers

There was no increase. There was actually a decrease of people in the population. If you are asking for the percent of decrease, the answer is 3200/25000=0.128 0.128*100=12.8%.


which shows the reflection of the figure over the line

Answers

Answer:

The answer is B, I just took the test.

Step-by-step explanation:


Answer:

hello there the answer is b hope this helps

Step-by-step explanation:


Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}{cb} = \dfrac{1}{2}$ and the point $d$ is such that $\dfrac{da}{ba} = 3$ and $\dfrac{db}{ba} = 2.$ if $c = (0, 4),$ $d = (4, 0),$ and $a = (x, y),$ what is the value of $2x + y$?

Answers

Start with a line segment connecting two points, A and B. [tex]\dfrac{DA}{BA}=3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\dfrac{DB}{BA}=2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\dfrac{AB}{CB}=\dfrac12[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let [tex]d[/tex] be the length of AB. Then the length of CD in terms of [tex]d[/tex] is [tex]4d[/tex]. We have the coordinates of C and D, and the distance between them is [tex]\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2[/tex]. So

[tex]4d=4\sqrt2\implies d=\sqrt2[/tex]

The slope of the line through C and D is

[tex]\dfrac{0-4}{4-0}=-1[/tex]

and so the equation of the line through these points is

[tex]y-4=-(x-0)\implies x+y=4[/tex]

So the coordinates of A are [tex](x,y)=(x,4-x)[/tex]. The distance between C and A is [tex]d=\sqrt2[/tex], so we have

[tex]\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1[/tex]

Since A falls to the right of C (in the [tex]x,y[/tex] plane, not just in the sketch), we know to take the positive value [tex]x=1[/tex]. Then the [tex]y[/tex] coordinate is [tex]y=4-1=3[/tex].

All this to say that A is the point (1, 3), so

[tex]2x+y=2+3=5[/tex]

The value 2x + y of  is 5.

Start with a line segment connecting two points, A and B. [tex]\frac{DA}{BA} =3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\frac{DB}{BA} =2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\frac{AB}{CB} =\frac{1}{2}[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let  be the length of AB. Then the length of CD in terms of  is . We have the coordinates of C and D, and the distance between them is

[tex]\sqrt{(4-0)^2+ (4-0)^2} =4\sqrt{2}[/tex]

So

4d= 4√2 = d= √2

The slope of the line through C and D is

[tex]\frac{0- 4}{4-0} = -1[/tex]

and so the equation of the line through these points is

y- 4 = -(x- 0) =x + y =0

So the coordinates of A are (x, y) = (x,4 -x). The distance between C and A is d= √2, so we have

[tex]\sqrt{(x-0)^2+(4- x - 4)^2} = \sqrt{2x^3} = |x| \sqrt{2} = \sqrt{2} = |x| = 1[/tex]

Since A falls to the right of C (in the x, y plane, not just in the sketch), we know to take the positive value . Then the  coordinate is .

All this to say that A is the point (1, 3), so 2x + y= 2+3=5

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Question

Let us have four distinct collinear points a, b, c, and d on the cartesian plane. the point c is such that [tex]\dfrac{ab}{cb} = \dfrac{1}{2}[/tex] and the point d is such that [tex]\dfrac{da}{ba} = 3[/tex] and [tex]\dfrac{db}{ba} = 2[/tex] c = (0, 4), d = (4, 0), and a = (x, y), what is the value of 2x + y?

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

Answers

Answer:

The vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].

Step-by-step explanation:

The given function is

[tex]f(x)=4+x^2-2x[/tex]

The vertex form is

[tex]f(x)=(x-h)^2+k[/tex]

Rewrite the given function

[tex]f(x)=(x^2-2x)+4[/tex]

[tex]-\frac{b}{2a}=-\frac{-2}{2(1)}=1[/tex]

Add and Subtract [tex](-\frac{b}{2a})^2[/tex].

[tex]f(x)=(x^2-2x+1)+4-1[/tex]

Use [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]f(x)=(x-1)^2+3[/tex]

Therefore the vertex form of the function is [tex]f(x)=(x-1)^2+3[/tex].

Answer: A on Edge 2020

Step-by-step explanation:

what is the factorization of the polynomial below? x^2-x-42

Answers

Answer:

(x-7)(x+6)

Step-by-step explanation:


The solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].

How to factorize any given polynomial ?

Given equation :-   [tex]x^{2} - x - 42[/tex]

For finding factors of the equation, we have equate the given polynomial with zero.

∴    [tex]x^{2} - x - 42 = 0[/tex]

Factorizing the above equation,

⇒   [tex]x^{2} - 7x + 6x - 42 = 0[/tex]

⇒   [tex]x (x -7) + 6(x - 7) = 0[/tex]

⇒   [tex](x + 6)(x - 7) = 0[/tex]  

∴ Either x + 6 = 0  or  x - 7 = 0  

x1 = -6  and  x2 = 7

Where x1 and x2 are the respective factors of the given polynomial in the question.

Thus, the solution of the equation is -6 and 7 for factorization of the given polynomial [tex]x^{2} - x - 42[/tex].

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