Mathematics High School

What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)

Answers

Answer 1
hello : 

Hello : let  A(0,5)    B(-2,11)
the slope is :   (YB - YA)/(XB -XA)
(11-5)/(-2-0)  = 6/(-2)
the slope is : -3

the equation in point-slope form of the line is : y-11 = -3(x+2)
Answer 2

Answer: [tex]y-11=-3(x+2)[/tex]


Step-by-step explanation:

Given points :  (0, 5) and (−2, 11)

Slope of the line passing through given points .

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]

Thus, slope of line passing through given points m=-3

We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]

Thus, equation of a line passing through (−2, 11) with slope m=-3 will be

[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]

Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]

Related Questions

A mosaic is made by having 1 cm square tiles glued onto a photograph. the photograph is a 6 cm by 8 cm rectangular photo. It is enlarged by a scale factor of 1.5. how many tiles are needed to cover the enlarged photo

Answers

A scale factor is the ratio of two similar geometric figures of their corresponding sides. The scale factor is calculated by locating the corresponding sides on each figure. Enlargement of a figure would have a scale factor that is greater than 1 which is evident for the problem above. To determine how many tiles would be needed to cover the enlarged photo, we need to know the new dimension of the photo. We do as follows:

Old photo = 6 cm x 8 cm
New photo = 6 cm x 1.5 x 8 cm x 1.5
                  = 9 cm x 12 cm

Number of tiles = Area of photo / Area of tiles
             Area of photo = 9 x 12 = 108 cm^2
             Area of tiles = 1 cm x 1 cm = 1 cm^2

Number of tiles = 108 cm^2 / 1 cm^2 = 108 tiles

The x-intercept of the line x = 3.5 is . The y-intercept of the line y = -6.5 is . Enter your answer as an ordered pair such as (1, 1) or (-2, 2).

Answers

The x-intercept of the line x = 3.5 means that when y=0, and x=3.5, so the order pair for this is (3.5,0) or (3 1/2,0)
Next, The y-intercept of the line y = -6.5 means that when x=0, and y=-6.5, so the order pair for this is (0,-6.5) or (0,-6 1/2). As a result, The x-intercept of the line x = 3.5 is (3.5,0) or (3 1/2,0) . The y-intercept of the line y = -6.5 is (0,-6.5) or (0,-6 1/2). Hope it help!

two points are collinear

Answers

Collinear is when two points are on the same plane. For example: in this picture A B C and D are collinear. Two points can still be collinear if they don’t have a line in between them too, just as long as you can draw a straight line between them they are collinear.

Answer:

1. B

2. C  

3. B

4. C  

5. A

6. A

7. C  

8. A

9. D

10. C  

11. B

12. B

In triangle PQR, C is the centroid.

Answers

The centroid of a triangle divides the median PY, XR and QZ into the ratio 2:1

Question (a):

PC:CY = 2:1
If CY=10, then PC=20 and PY=20+10=30

Question (b):

QC:CZ= 2:1
If QC=10, then CZ=5 and ZQ=10+5=15

Question (c):

PX : XQ = 1 : 1
if PX = 20, then PQ = 40

The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. what is the temperature of the coldest point in the plane?

Answers

[tex] x^{2} + y^{2}-4x+2y [/tex]

can be written as follows:

[tex] x^{2} -4x+ y^{2}+2y[/tex]

[tex](x^{2} -4x+4)-4+ (y^{2}+2y+1)-1[/tex]

[tex] (x-2)^{2}+(y+1)^{2} -5[/tex]

since [tex](x-2)^{2}[/tex] and [tex](y+1)^{2}[/tex] are always positive, except for x=2 and y=-1, when they become 0,

the minimum value of this expression is when x=2, and y=-1, that is -5



Answer: -5

if acircle is inscribed in a hexagon, which of the following must be true ? Check all that apply.

A. The hexagon is circumscribed about the circle.
B. Each vertex of the hexagon lies inside the circle.
C. The circle is congruent to the hexagon.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.

Answers

A. The hexagon is circumscribed about the circle .
D. Each vertex of the hexagon lies outside the circle .
E. The circle is tangent to each side of the hexagon .

Answer:  A. The hexagon is circumscribed about the circle.

D. Each vertex of the hexagon lies outside the circle.

E. The circle is tangent to each side of the hexagon.


Step-by-step explanation:

Given: A circle is inscribed in a hexagon.

Then the hexagon is circumscribed about the circle.

Each vertex of hexagon lies outside the circle.

As each side of hexagon is just attached to the circle not passing through the circle, thus the circle is tangent to each side of the hexagon.

Since circle is a closed curve and hexagon is regular polygon with 6 sides, they cannot be congruent because they have different shapes.

What is the slope of a line that is perpendicular to the line v= 3/4x-6?

A. 3/4
B. -4/3
C. -3/4
D. 1/6

Answers

A perpendicular slope is equal to the negative reciprocal of the given slope, which is 3/4.

The reciprocal of 3/4 is 4/3. The negative of that is -4/3.

Final answer: B

The slope of line which is given to be perpendicular to the line represented by equation "v = (3/4)x - 6" is : (b) -4/3.

To determine the slope of a line that is perpendicular to the given line v = (3/4)x - 6, we use the property that perpendicular lines have slopes that are "negative-reciprocals" of each other.

The slope of the given line is 3/4. To find the slope of the perpendicular line, we take the negative reciprocal of 3/4.

The negative reciprocal of 3/4 is -4/3. So, the slope of the line that is perpendicular to the given-line v = (3/4)x - 6 is -4/3.

Therefore, the correct answer is (b) -4/3.

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You flip a coin eight times. find the number of possible outcomes in the sample space.

Answers

2( coin faces) 8( number of times)

Find the least common multiple of these two expressions. 14x^2y^4 and 21x^3u^7y^8

Answers

LCM of 14 and 21:-

14 = 2 * 7
21 = 3*7

LCM = 2*3*7 = 42

answer is 42x^3u^7y^8

Two minor league baseball players got a total of 292 292 hits. washington had 18 18 more hits than sanchez. find the number of hits for each player

Answers

Let number of hits by Sanchez be x.

Number of hits by Washington = 18 + x

Total number of hits = 292

x + 18 + x = 292

2x + 18 = 292

2x = 274

x = 137

Hence, Sanchez has 137 hits and Washington has 155 hits.

The area of a rectangle is 28 ft2 , and the length of the rectangle is 1 ft more than twice the width. find the dimensions of the rectangle.

Answers

W=x
L=2x+1
Area=(2x+1)x=28
2x²+x=28
2x²+x-28=0

(2x-7)(x+4)=0
x=3.5, -4. (3.5 makes more sense)
2x+1=8
area = 28 ft²
width = 3.5 feet | length = 8 feet.

The length is 8feet and the width of the rectangle is 3.5feet

Let the width of the rectangle be represented by w

Let the length of the rectangle be represented by = 2w + 1

Therefore, based on the information given, the equation to solve the question will be:

w(2w + 1) = 28

2w² + w = 28

2w² + w - 28 = 0

2w² + 8w - 7w - 28 = 0

2w(w + 4) - 7(w + 4) = 0

2w - 7 = 0

2w = 0 + 7

2w = 7

w = 7/2

w = 3.5

The width is 3.5 feet

The length will be:

= 2w + 1

= 2(3.5) + 1

= 7 + 1

= 8

The length is 8feet and the width is 3.5feet

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The screen on Lawrence's new phone is 3.15 centimeters long.What mixed number represent the lenght of the phone screen?

Answers

A mixed number is written in a form of [tex]a \frac{b}{c} [/tex], where 'a' is a whole number.

One example of mixed number is [tex]3 \frac{1}{4} [/tex], read as 'three and one quarter'. As decimal fraction, [tex]3 \frac{1}{4} [/tex] equals to 3.25

We are given the value of 3.15 and to change this into a mixed number, first note the whole number, which is 3.

We then change the decimal value 0.15 into a fraction and it is [tex] \frac{15}{100}= \frac{3}{20} [/tex] 

Hence, 3.15 = [tex]3 \frac{3}{20} [/tex] 

The graph of a line goes down and to the right when

Answers

It is a negative slope!

it goes down and to the right when the graph is negative.

Chase answers 3/4 of his math questions correctly. There were 40 questions on the test.

a. How many did he get right?

b. How many did he miss?

Answers

multiply 40 by 3/4

40 x 3/4 = 40*3 = 120, 120/4 = 30

 he answered 30 correctly

40-30 = 10, he missed 10

Which of the following is an identity?

A. csc^2 x + cot^2 x = 1
B. (cscx + cotx)^2 = 1
C. sec^2 x sec^2 x + 1 = tan^2 x csc^2 x
D. sin^2 x - cos^2 x = 1

Answers

I am not sure at all but I think the answer is C.
there is an identity  csc^2 x = 1 + cot^2x  so it cant be A

Nor D  because sin^2 x + cos^2 x = 1

I think Its C 

converting to sin's and cos's 

1 / cos^4 x  + 1    =   sin^2 x / cos^2x  *   1 / sin^2 x   = 1 / cos^2 x

I dont think any are identities
You sure you have  the question correct?


When a meteorologist says that there is a 30% chance of showers, what type of probability is the person using?

Answers

Empirical and Subjective probability

A customer calls and says that they are upset because they just received their bill and it is for two months service plus a $20 late fee. They have never had a late payment before. They explain that they moved last month and never received their bill. What would you tell them?

Answers

I would tell them that I apologize for the misunderstanding for the bill not being delivered to the proper person but it was out of my hands

Answer with explanation:

The Customer , is irked due to the reason that,he or She hasn't got the last month bill and now they have to pay the bill for two months service plus $ 20 late fee.

Also, the customer is Saying that they moved from that place last month where they were Residing.

I will start Querying with the customer  in the following way

Sir, or Madam

1. Have you checked , or asked your Neighbor or Landlord, after leaving that place ,whether they have got this kind of bill ?

2. Secondly , we have your email-ID as well as Mobile number.We message every month about your bill,through email as well as Messaging tool of your mobile.Haven't you Checked your Mail as well as  Messaging.

it Shows that Customer is Lying.

So, Sir or Madam

  Please , pay the Bill along with late fee.

the lines shown below are parallel. if the green line has a slope of -1/11, what is the slope of the red line?
a)-1/11
b)1/11
c)-11
d)11

Answers

Parallel lines must have the same slope and a different y-intercept.  So if one line has a slope of -1/11, any possible parallel line will also have a slope of -1/11.

Answer:

-1/11

Step-by-step explanation:

I just did it

A veterinarian surveys her clients and finds that 32 percent of the households have dogs, 25 percent have cats, and 11 percent have both dogs and cats. Let event C be choosing a client who has cats and let event D be choosing a client who has dogs. Which statements are true? Check all that apply.
1.P(C | D) = 0.78
2.P(D | C) = 0.44
3.P(C ∩ D) = 0.11
4.P(C ∩ D) = P(D ∩ C)
5.P(C | D) = P(D | C)

Answers

check the venn diagram of the problem.

let the total number of the clients be 100.

since there are 11 clients with both cats and dogs, 

there are 32-11=21 clients with dogs but not cats

and 25-11=14 clients with cat but not dogs.

The number of clients with neither dogs nor cats is given by:

100-(21+11+14)=100-46=54


so we have the following:

P(C)=25/100=0.25
P(D)=32/100=0.32
P(C∩D)=P(D∩C)=11/100=0.11

we also have the formula P(A|B)=P(A∩B)/P(B), the formula of conditional probability

now we check each choice:

1. P(C|D)=P(C∩D)/P(D)=0.11/0.32=0.34
2. P(D|C)=P(D∩C)/P(C)=0.11/0.25=0.44
3  and  4 are already checked, and they are true
5. by 1 and 2, not true



Answer: 2, 3, 4 are True

The statements which are true based on the given sets of data are:

2.P(D | C) = 0.443.P(C ∩ D) = 0.114.P(C ∩ D) = P(D ∩ C)

What is a Set?

This refers to the grouping of data between different types of data within a range.

Based on the given information, we can see that

32% have dogs

25% have cats

11% has both cats and dogs

We can see that using a Venn diagram, we can make the graphical representation where there would be the intersection and Union of the data.

With this, we can see that options B, C and D are true because they satisfy the choosing events about the given set of data.


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(04.01 LC)

Which of the tables represents a function?
Table A


Input

Output

3 1
3 4
2 3

Table B


Input

Output

2 7
5 6
2 9

Table C


Input

Output

1 5
7 2
7 3

Table D


Input

Output

3 4
1 5
8 5


Table A
Table B
Table C
Table D

Answers

Only table D is a function.  All of the others fail the "vertical line test."  The definition of a function is for each input there is only one unique output.  So for example, any given input value of x, there can only be one unique output value for y.

Answer:

I believe the answer is table D.

Step-by-step explanation:

Each input can only have one output. The other tables have multiple outputs for each input. Therefore they get "cut off," and table D is the answer.

Helper's Message:

I hope this answer helped you! I wouldn't mind if you hit the 5-star rating or gave me a thank you. :)

-ChocoChocoCho

I'm in desperate need of help please !!

Answers

8a)

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\qquad \begin{cases} year\ 0\\ -----\\ t=0\\ A=42679 \end{cases} \\\\\\ 42679=Ie^{k0}\implies 42679=I\cdot 1\implies 42679=I\qquad thus \\\\\\ \boxed{A=42679e^{rt}}[/tex]

now, let's fast-forward 8 years later, t = 8, the population has dropped  to 33247, so A = 33247, what's "r", or in your paper, it uses "k", anyhow, is just the rate.

[tex]\bf A=42679e^{rt}\qquad \begin{cases} t=8\\ A=33247 \end{cases}\implies 33247=42679e^{r8} \\\\\\ \cfrac{33247}{42679}=e^{8r}\impliedby \textit{let's now take \underline{ln} to both sides} \\\\\\ ln\left( \frac{33247}{42679} \right)=ln(e^{8r})\implies ln\left( \frac{33247}{42679} \right)=8r\implies \cfrac{ln\left( \frac{33247}{42679} \right)}{8}=r \\\\\\ -0.0312178\approx r\qquad now\ 100\cdot r\approx -3.1\%[/tex]

is a negative rate, because, the population is decreasing.

-------------------------------------------------------------------

8)

how many days does it take for 60% of the population to know about the crime?  well, what's 60% of 1,150,000? well (60/100) * 1,150,000, or 69000.

[tex]\bf P(t)=1150000e^{-0.03t}\implies 690000=1150000e^{-0.03t} \\\\\\ \cfrac{690000}{1150000}=e^{-0.03t}\implies \cfrac{3}{5}=e^{-0.03t} \\\\\\ \textit{again, we take \underline{ln} to both sides} \\\\\\ ln\left( \frac{3}{5} \right)=ln(e^{-0.03t})\implies ln\left( \frac{3}{5} \right)=-0.03t \\\\\\ \cfrac{ln\left( \frac{3}{5} \right)}{-0.03}=t\implies 17.0275\approx t[/tex]

so.. roughly about 17 days.

Write a function max that has two c string parameters and returns the larger of the two.

Answers

char max(char number1, char *number2){
if (strcmp(number1, number2) > 0)
return number1;
else
return number2;
}

Final answer:

To determine the larger of two C strings, a function named max uses strcmp to compare them, returning the one considered greater in alphabetical order.

Explanation:

To write a function named max that returns the larger of two C strings, one must compare the two strings alphabetically. Here is an example implementation in C:

#include  // Include the header file for string functions

// Function declaration
const char* max(const char* str1, const char* str2) {
   // Compare the two strings
   int result = strcmp(str1, str2);

   // If str1 is greater than or equal to str2
   if(result >= 0)
       return str1;
   else
       return str2;
}

The strcmp function from the string.h library is used to perform the comparison. If the first string (str1) is greater than or equal to the second string (str2), str1 is returned; otherwise, str2 is returned. Note that the comparison is based on the ASCII values of the characters, effectively ordering them alphabetically.

A student claims that a figure has rotational symmetry and that the angle of rotational symmetry is 360 degrees. Critique the student's statement.

Answers

Remember rotational symmetry means if you turn it you end up with the same figure you started with. This happens with regular polygons since each angle is congruent. To find the angle of rotation you divide 360 by the number of angles. So if you rotated 360 degrees, that means 360/360=1. Your figure only had one angle, so it can't even be a polynomial! Also, every figure in the world will look exactly like it started if rotated 360 degrees, so this would not be logical. 

A ship traveled for 4 hours heading west and for 5 hours heading north. If the total distance traveled was 119 miles, and the ship traveled 5 miles per hour faster west, at what speed was the ship traveling west

Answers

let speed that ship travelled west be x mph

then distance travelled west =  time * speed =  4x

speed going North was x - 5 mph   and distance = 5(x - 5)

so we have
4x + 5x -25 = 119


9x = 119+25  = 144
x = 144/9 =  16 mph <------ answer


A swimming pool is 15 by 30 feet and a consistent 5 feet deep. you are painting the walls and floor of the pool. if a gallon can of paint covers 250 square feet, how many gallon cans would you need to buy

Answers

the bottom of the pool is 15 x 30 = 450 sq feet.

 you the have 2 walls that are 30 x 5 = 150 x 2 = 300 square feet

 then 2 walls that are 15 x 5 = 75 x 2 = 150 square feet

 for a total of 450 +300 +150 = 900 square feet

 1 can covers 250 sq ft

so 900/250 = 3.6

 so you would need 4 cans of paint

In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ?x - 49

Answers

We are asked to find unknown or the missing number to complete the polynomial given in the problem which is x² + ?x -49. First, let us equate the number to be equal to zero such as it would become x² + ?x - 49 = 0. Next, we need to find the factors such that it would produce a difference of squares and these two factors are a = +7 and b = -7. Hence, the complete solution is shown below:
(x + 7) (x-7) = 0
perform distribution and multiplication of terms such as shown below:
x² + 7x - 7x - 49 = 0
Combine the same term such as we can either add or subtract +7x to -7x and the result will be equal to 0x.
 x² + 0x - 49 = 0

Therefore, the missing number is 0. The answer is 0 which will result to x² +0x - 49.

Answer:

0

Step-by-step explanation:

PLEASE PLEASE IM RUNNING OUT OF TIME AND NEED YOUR HELP!!!!!
hope i wrote these correctly!
Simplify: ^3√108c^17

My Choics are...
:
a. 6c^8√3c

b. 3^3√4c^17

c. 3c^5 ^3√4c^2

d. 18c^8√3c

Answers

∛ 108c^17 = 3c^5 ∛4c^2

answer

c. 3c^5 ∛4c^2

simplify
 27 2/3
----------
27 4/3

Answers

Hey!

We can write it like this,
[tex]\frac{27\frac{2}{3}}{27\frac{4}{3}}[/tex]
Let's convert them to improper fractions,
[tex]=\frac{\frac{83}{3}}{\frac{85}{3}}[/tex]
Let's divide them, but to do that we have to take the reciprocal of the second fraction,
[tex]=\frac{83\cdot \:3}{3\cdot \:85}[/tex]
Since our common factor is 3, we can cancel them out.
[tex]=\frac{83}{85}[/tex]
That would be our final answer.

Thanks
-TetraFish

Answer:

It would be 9

Step-by-step explanation:

for edgen 2020

A building is 60 ft tall and another is 80 ft tall. A model of the 60 ft building is made at 1 ft. tall. How tall is the model of the 80 ft tall building?

Answers

1 foot = 60 feet

80/60 = 1.333

 80 foot building is made 1.33 feet tall (16 inches, 1 foot 4 inches)

15,000 loses value by 20% each year. What is the value after 3 years

Answers

So you have 15,000, which decreases in value by 20% each year. The question asks, what is the value after 3 years. So you would have 15,000(1-0.2)^3 and that is your equation. The reason for this is because you have your initial value 15,000, and when it is a percent decrease, you use the formula i(1-d)^x, where i represents the initial value, d represents the percent decrease, and x represents the number of years. We can convert 20% into a decimal as 0.2. So our initial value is 15000, our percent decrease is 0.2, and number of years we can see is 3. That is why the equation is 15,000(1-0.2)^3. I would solve this using PEMDAS, meaning that Parenthesis comes first, Exponents come second, and then Multiplication comes after both of those. I stopped here because these are the only three things we need to do to solve. When I solve this, I do (1-0.2) = 0.8, and (0.8)^3 = 0.512. Then I multiply 15,000 with 0.512, which gives me 7680. Therefore the value of 15000 after 3 years is $7680. Hope this helps. Feel free to ask me questions about my explanation, and feel free to post more questions.

Answer:

Step-by-step explanation: 7680

After losing 20% we have 80% remaining

∴ value after three years = 15,000 × [tex]\frac{80}{100}[/tex] × [tex]\frac{80}{100}[/tex] ×[tex]\frac{80}{100}[/tex]

                                            = 15,000 × [tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex]

                                           = 7680

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