There is a point $A$ with positive coordinates such that the sum of the coordinates of $A$ is $14$. If the $x$-coordinate of $A$ is $a$, then point $P$ is at $(3a, a^2+13a-11)$. If the slope of a line passing through $A$ and $P$ is $7$, find $a$.

Answers

Answer 1

Answer:

The x-coordinate of A is:

a = 6.1

Step-by-step explanation:

For point A:

x-coordinate = a

x-coordinate + y-coordinate = 14

y-coordinate = 14 - x-coordinate

y-coordinate = 14 - a

So point A can be written as (a, 14-a)

Let (a,14) be (x₁,y₁)

Point P can be written as (3a, a²+13a-11)

Let P be (x₂,y₂)

Slope of a line passing through 2 point is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where m=7

Substitute all values

[tex]7=\frac{(a^2+13a-11)-(14-a)}{3a-a}\\7=\frac{a^2+13a-a-11-14}{3a-a}\\7=\frac{a^2+12a-25}{2a}\\14a=a^2+12a-25\\a^2-2a-25=0\\a=6.1,a=-4.1[/tex]

As A has only positive coordinates

a = 6.1


Related Questions

What is the formula for the circumference using the radius below? // ANSWER IF POSSIBLE !!! //

Answers

Answer:

the answer is 2(pi)5

Step-by-step explanation:

the formula for circumfrence is 2(pi)r, and r in this case is 5

Answer:

The formula for circumference is 2πr, and r is 5 in this problem. Therefore, the circumference can be expressed using the expression 2π5, or 10π. Hope this helped!

please help with clear explanation

Answers

Answer:

102

Step-by-step explanation:

You can split that shape up into 2 rectangles to make it easier get the area of each rectangle and add them together.

Step 1

Identify the width and height

Step 2

Multiply the sides to get the answer

For example if we split the shape we will have 9,10 and 2,6

9 times 10 is 90

and 2 times 6 is 12

Add the 2 and get 102

Hopefully this helped.

Which graph represents 2x - 3y less than or equal to 9?

Answers

Answer:

answer is c

Step-by-step explanation:

34 + 2 ⋅ 5 = ____. (Input only whole numbers.) Numerical Answers Expected! Answer for Blank 1: i will give brainliest plese

Answers

Answer:

44

Step-by-step explanation:

The answer is 44 because of order of operations we do multiplication fist so it would be

2 * 5 = 10

34 + 10

44

Answer:

44

Step-by-step explanation:

the first step is to multiply (which is what the ⋅ is) and I get 10. After I multiply I add 34 which is 10 + 34 = 44 and that is the answer.

The least common denominator of 5/6, 2/3, and 3/5 is:



Answers

Answer:

30

Step-by-step explanation:

List the factors

6 = 2*3

3 =3

5 = 5

The least common multiple is 2*3*5 = 30

The least common denominator is 30

Answer:

30

Step-by-step explanation:

6= 6,12,18,24,30

3= 3,6,9,12,15,18,21,24,27,30

5= 5,10,15,20,25,30

Solve the following equations: 24 1/14 +8 3/7 =(x÷1 1/9 )·5 5/12

Answers

Answer:

x=21978/35

Step-by-step explanation:

Steps:

1: Step 1: Simplify both sides of the equation

241 14 + 83 7 = x 11 9 (55) 12 241 14 + 83 7 = 5 108 x ( 241 14 + 83 7 )= 5 108 x(Combine Like Terms) 407 14 = 5 108 x 407 14 = 5 108 x

2: Step 2: Flip the equation

5/108x=407/14

3:  Step 3: Multiply both sides by 108/5.

(1085)*(5108x)=(1085)*(40714)

Answer: x=21978/35

Plz mark brainliest

Hope this helps.

SOMEONE PLEASE HELP ME ASAP PLEASE!!!​

Answers

Answer:

120

Step-by-step explanation:

You add the angles up and the angles add up to 120.  61+59=120

What is the value of x/5

Answers

Answer:

2

Step-by-step explanation:

Since this is a right triangle we can use trig functions

cos theta = adj / hypotenuse

cos 60 = 5/x

.5 = 5/x

Flip each side

1 / .5 = x/5

2 = x/5

Must find the slope of the hill

Answers

Answer: Option no. C 486/11

The requried slope of the hill which is 11 yd tall and 486 yd long is 11/486. Option D is correct.

To find the slope of a hill, we can use the formula: slope = rise/run.

In this case, the rise refers to the vertical change, which is the height of the hill, given as 11 yd. The run refers to the horizontal change, which is the length of the hill, given as 486 yd.

Using the formula, we can calculate the slope:

slope = rise/run

slope = 11 yd / 486 yd

To simplify the slope, we can divide both the numerator and the denominator by the greatest common divisor, which is 1 in this case:

slope = 11 / 486

Therefore, the slope of the hill is 11/486.

Learn more about slope here:

https://brainly.com/question/28567972

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Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15? Question 4 options: A) x = 14∕2 B) –1 – 6x + 15 = x – 15 + 15 C) –1 – 6x = x – 15 D) 23 – 6x – 24 = x – 15

Answers

Answer:

B) -1-6 x +15 = x - 15 +15

Step-by-step explanation:

Explanation:-

Given equation is  –1 – 6 x = x – 15

By addition property of equality

                       ⇒     - 1 - 6 x + 15 = x - 15 +15

                      ⇒      - 6 x + 14  = x

subtracting 'x' on both sides ,we get

                       ⇒      - 6 x -x +14 =0

                        ⇒      - 7 x +14 =0

                         ⇒      -7 x = - 14

   Dividing '-7'  on both sides , we get

                                 x  = 2

The solution of given equation is    x  = 2

Answer:

-1-6x+15=x-15+15

Step-by-step explanation:I took the test

Work must be shown for this problem! The figure shown below is a rectangle. Make sure to solve for x and BD. Give both answers below.

Answers

Answer:

x = 10

BD = 74

Step-by-step explanation:

Find x by setting 3x+7 equal to 37. Solve for x by subtracting 7 on both sides then divide by 3 to get x=10.

Since 37 is half of AC, multiply that by 2 to find AC or BD, which are the exact same length of 74.

Answer:

x=10 and BD=74

Step-by-step explanation:

In a rectangle, the two parts of the diagonals are always equal to each other. This means that AE=CE=BE=ED.

So, if AE is 3x+7, this means DE and BE are also 3x+7, so BD is twice that, or 2(3x+7) which when you multiply it is 6x+14.

Oh, also, since it says CE=37, this means that 3x+7=37

3x+7=37

    -7   -7

3x=30

x=10

Now that you know that BD is 6x+14, and x is 10, simply multiply it.

6(10)+14=BD

60+14=BD

74=BD

Which is the graph of y = [x] - 2?
5
2

Answers

Answer:

2

Step-by-step explanation:

slope=1

intercept=2

Can someone help me with this quick ??

Answers

Hi there!

The graph that represents the equation d = 4t is the first one.

Hope this helps !

f(x)=x^2 what is g(x)

Answers

Answer: A. g(x) = -x^2-4

Step-by-step explanation:

y-intercept is -4

You can determine if the slope of the graph is negative or positive based on if it is going up or down

example: x^2 going up, -x^2 going down.

Answer:

A

Step-by-step explanation:

A reflection maps the point (2, 3) to the point (-2, 3).
It is a reflection over the
O X-axis
O y-axis
O line y = x

Answers

it reflects over the x axis :)
It reflects over the y axis not the x.

A Shop sells two different bags of rice .
Rice A 500 g plus 25% extra free rice .
Rice B 750 g plus 1/5 extra free rice . Which bag gives you more free rice ? A or B



Pls help me :)

Answers

Answer:

b gives you more free rice

Step-by-step explanation:

....hope it helps

inform if wrong!!

Plz help if you know

Answers

Answer: the first one y<=1/2x+2

Step-by-step explanation:

It intercepts at 2

It’s less than because the solution area is at the bottom part of the graph

1/2 because from the y-intercept you can go up 1& over 2

Find the difference.
5wх² - 2wх²
А. 3
В. 2wx²
С. Зwх²
D. 4wх²​

Answers


the answer is 3wx^2
The answer is C. Hello

what is the equation of a line that passes through the point (-3,1) and is parallel to a line with a slope of 2?

Answers

Answer:

Step-by-step explanation:

y - 1 = 2(x + 3)

y - 1 = 2x + 6

y = 2x + 7

The answer is y=2x+7

Since the line is parallel to a line that has a slope of 2, the slope of the line is also 2. Since parallel lines have the same slope.

To find the y-intercept, you have to substitute the point into the slope intercept form.

y=mx+b

(-3,1)

1=2(-3)+b

1=-6+b

Add 6 to both sides

7=b



find the volume of the rectangular prism 4.5cm,2.5cm 3cm

Answers

Answer: 31.25

Step-by-step explanation:

4.5 x 3 = 12.5

12.5 x 2.5 = 31.25

Suppose N is between M and P. Use the Segment Addition Postulate to solve for the variable. MN = 7y - 4 NP= y + 6 MP = 29 Select one: a. 3.735 b. 3.75 c. 3.375 d. -3.75

Answers

Answer:

C

Step-by-step explanation:

29 = 7y -4 +y+6

29 = 8y+2

8y = 27

y = 27/8

y =. 3.375

The midpoint of a line is the middle of the distance between two points. The value of y if  is the midpoint of AC is 3.375

Midpoint of a segment

The midpoint of a line is the middle of the distance between two points. Given the following parameters

MN = 7y - 4, and;

NP= y + 6

MP = 29

If N is between M and P.  hence;

MN + NP = MP

Substitute

7y-4 + y + 6 = 29

8y + 2 = 29
8y = 27

y = 27/8

y = 3.375

Hence the value of y if   N is between M and P is 3.375

Learn more on midpoint here: https://brainly.com/question/5566419

#SPJ9

Please help !! (Simplify)

Answers

Answer:

The first one

A line passes through (2,9) and has a zero slope

Answers

Answer:

d

Step-by-step explanation:

y = 9

Find the distance between the points (0, –3) and (4, 0). answers :A) 1 B) 25 C) 5 D) 7

Answers

Answer:The answer is C)5 if you need help understanding how I got this answer let me know and I'll gladly explain!

Answer: C) 5

Step-by-step explanation: Use distance formula: [tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^2 }[/tex]

Plug in respected values [tex](0,-3) = (x_{1},y_{1})[/tex] and [tex](4,0) = (x_{2},y_{2})[/tex]

Then Solve

what's the y intercept and the x intercept?​

Answers

Answer:

y-intercept is at (0, 0.4)

x-intercept is at (0.3,0)

Step-by-step explanation:

y-intercept is where the line intercepts the y axis and x-intercept is where the line intercepts the x axis.

As of mid-2016, the world's population was about 7.4 billion people. The population of the United States was 324 million.

The land area of a certain state is about 261,787 square miles. If in mid-2016 all of the world's people were put into that state, how many people would there be in each square mile? (Round your answer to the nearest whole number.)

Answers

Answer:

There would be approximately 28,267 per square mile.

Step-by-step explanation:

There are 7,400,000,000 people in the world. The state is 261,787 square miles.

7,400,000,000/261,787 = 28,267.2554 → 28,267

Someone please help me with this question??

Examine the following table that represents some points on a line.
Which equations in point-slope form represents this line?

y + 10 = 2(x + 6)

y + 9 = 1/2(x + 4)

y + 10 = 1/2(x + 6)

y + 4 = 1/2(x — 6)

y + 4 = 2 (x — 6)

y — 9 = 2(x — 4)

Answers

Answer:

Option (2), (3) and (4)

Step-by-step explanation:

Let the equation of the line representing the given table is,

y - y' = m(x - x')

where 'm' = slope of the line

(x', y') is the point lying on the line.

Let the two points (-6, -10) and (-4, -9) lie on the line

Slope 'm' = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

               = [tex]\frac{-9+10}{-4+6}[/tex]

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

Equation of the line passing through (-4, -9) with slope [tex]\frac{1}{2}[/tex] will be

y - (-9) = [tex]\frac{1}{2}(x+4)[/tex]

y + 9 = [tex]\frac{1}{2}(x+4)[/tex]

Equation of the line passing through (-6, -10) with slope = [tex]\frac{1}{2}[/tex]

y - (-10) = [tex]\frac{1}{2}(x+6)[/tex]

y + 10 = [tex]\frac{1}{2}(x+6)[/tex]

Equation of the line passing through (6, -4) and slope =  [tex]\frac{1}{2}[/tex]

y + 4 = [tex]\frac{1}{2}(x-6)[/tex]

Therefore, Options (2), (3) and (4) will be the answer.

What is the equation, in point-slope form, of the line that is
parallel to the given line and passes through the point (-3,
1)?
2.2)
1
34
y-1==3(x + 3)
y-l=-(x + 3)
y-1= f (x + 3)
y-1= (x + 3)

Answers

Answer:

1 1/2x - 1

Step-by-step explanation:

The slope is (2--4)/(2--2)=3/2.

The y-intercept is -1

the answers are not so clear, i'll edit to give you an option if you make it clearer

please help! ill mark you as brainleist if you get it correct!​

Answers

Answer:

7.96

Step-by-step explanation:

50/3.14

15.92

15.92/2

7.96

Answer:

7.96

Step-by-step explanation:

50/2 = 25

25/3.14 = 7.96

Find the central angle of a sector of a circle if the area of the sector and the area of the remaining part of the circle are in the proportion 4 : 5 ( with explanation )

Answers

Answer:

288

Step-by-step explanation:

360/5 = 72

72x4 = 288

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