1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vilka [71]
3 years ago
9

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 $a$.
Mathematics
1 answer:
andre [41]3 years ago
5 0

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:

m=\frac{y_2-y_1}{x_2-x_1}

where m=7

Substitute all values

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

As A has only positive coordinates

a = 6.1

You might be interested in
Find the value of x<br><br> Please help
zloy xaker [14]
80/60 = (80 + 2x)/(60 + 27)
80/60 = (80 + 2x)/87
4/3 = (80 + 2x)/87
3 . (80 + 2x) = 4 . 87
240 + 6x = 348
6x = 348 - 240
6x = 108
x = 18
4 0
3 years ago
Read 2 more answers
The sum of three consecutive integers is 267. What is the largest integer?
OverLord2011 [107]
3 consecutive integers : x, x + 1, x + 2

x + (x + 1) + ( x + 2) = 267...combine like terms
3x + 3 = 267...subtract 3 from both sides
3x = 267 - 3
3x = 264
x = 264/3
x = 88

x + 1 = 88 + 1 = 89
x + 2 = 88 + 2 = 90

the largest will be 90
5 0
3 years ago
Read 2 more answers
Tessellations
Misha Larkins [42]

Answer:

A. Yes; measure of interior angle = 90

Step-by-step explanation:

I calculated it logically

8 0
3 years ago
What is one cubic centimeter equivalent to?
vazorg [7]

Answer:

1 Millimeter

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Is it a linear? <br><br> 2x + 3y = 7
garri49 [273]
Yes this equation is a linear equation in two variables. Because for every value of “x” there is an alternate value for “y”
7 0
3 years ago
Read 2 more answers
Other questions:
  • A cylindrical glass holds 3768 cubic centimeters of water. It has a height of 12 cm. Find the radius.
    6·2 answers
  • Wesley sailed his boat north for 18 miles then due east for another 18 miles approximately how far is Wesley from where he began
    11·2 answers
  • Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?
    10·1 answer
  • A person is training for a cross country and manages to run 2 miles in a time of 12 mins what was the runners average velocity i
    10·2 answers
  • marinas bill for dinner totals 38.65 including tax. she leaves a 20% tip. if she pays with a $100, how much change will she reci
    12·1 answer
  • When does the confirmation bias occur?
    15·1 answer
  • Ray earns 17.75 per hour. How many hours per week must he work if he wants to earn approximately $682 a week? Round to the neare
    10·1 answer
  • Building a has 7,500 ft of an office space for 320 employees building b has 9,500 square feet of office space for 370 employees
    9·1 answer
  • Write the equation of the line in fully simplified slope-intercept form.
    7·1 answer
  • Help please!<br><br> Find the length of AB:
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!