answer.
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
Keith_Richards [23]
1 year ago
14

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:
ch4aika [34]1 year ago
6 0

Answer:

  5

Step-by-step explanation:

<u>Given</u>:

  A = (a, 14-a)

  P = (3a, a^2 +13a -11)

  the slope of AP is 7

  a > 0

<u>Find</u>:

  a

<u>Solution</u>:

The slope of AP is ...

  m = (Py -Ay)/(Px -Ax)

  7 = (a^2 +13a -11 -(14 -a))/(3a -a)

  14a = a^2 +14a -25

  25 = a^2

  a = √25 = 5 . . . . . the positive solution

The value of 'a' is 5.

_____

<em>Check</em>

The point A is (a, 14-a) = (5, 9).

The point P is (3a, a^2 +13a -11) = (15, 79)

The slope of AP is (79 -9)/(15 -5) = 70/10 = 7.

You might be interested in
An employee compiled sales data for a company once each month. The scatter plot below shows the sales (in multiples of $1000) fo
ss7ja [257]

Answer:

$50,100

Step-by-step explanation:

Given the scatter plot and the linear model, we can estimate that the total sales for the company after 40 months will be close to $50,000.  However, in order to get a more precise answer, we can solve for the total sales, 'y', based on the number of months, 'x', in the given linear model:

y = 0.94(40) + 12.5  = 37.6 + 12.5 = 50.1

Since the amount of sales is in multiples of $1000:

50.1 * 1,000 = $50,100

3 0
2 years ago
Read 2 more answers
The high temperatures in Montana are recorded for a week. High Temperatures Sunday 46°F Monday 52°F Tuesday 51°F Wednesday 54°F
Elan Coil [88]

Answer:


Step-by-step explanation:

to get the mean you need to add up all the numbers

46+52+51+54+49+51+61=364

then divide that sum by the amount of numbers you have

364 divided by 7=52

so the mean you have is 52 degrees

5 0
1 year ago
Read 2 more answers
A geometry teacher asked Charlene to define “acute triangle.” Charlene said that an acute triangle is a triangle whose three int
Slav-nsk [51]
By definition we have to:
 Acute triangle - It is a triangle that has all acute angles. An acute angle is one whose degree of measurement is less than 90.
 Therefore, Charlene's definition is correct.
 Charlene said:
 triangle is a triangle whose three interior angles have measures less than 90 °
 Answer:
 C.Yes, because this definition fits all acute triangles and does not fit triangles that are not acute.
4 0
2 years ago
Which option lists an expression that is not equivalent to 4 2/3?
I am Lyosha [343]

Answer:

Option A and Option B are not equivalent to the given expression.

Step-by-step explanation:

We are given the following expression:

4^{\frac{2}{3}}

Applying properties of exponents and base:

(a^x)^y = a^{xy}\\a^{-x}= (\frac{1}{a})^x\\

A. Using the exponential property a^{-x}= (\frac{1}{a})^x\\, we can write:

0.25^{\frac{3}{2}} = (\frac{1}{0.25})^{\frac{-3}{2}} = (4)^{\frac{-3}{2}}

which is not equal to the given expression.

B. Using the exponential property a^{-x}= (\frac{1}{a})^x\\, we can write:

(0.25)^{\frac{-3}{2}} = (\frac{1}{0.25})^{\frac{3}{2}} = (4)^{\frac{3}{2}}

which is not equal to the given expression.

C. First we convert the radical form into exponent form. Then by using the property (a^x)^y = a^{xy} of exponent, we can write the following:

^3\sqrt{16} = (16)^{\frac{1}{3}} = (4^2)^{\frac{1}{3}} = 4^{\frac{2}{3}}

which is equal to the given expression.

D. First we convert the radical form into exponent form. Then by using the property (a^x)^y = a^{xy} of exponent, we can write the following:

(^3\sqrt{4})^2 = (4^{\frac{1}{3}})^2 = 4^{\frac{2}{3}}

which is equal to the given expression.

Option D and Option C are equivalent to the given expression.

7 0
2 years ago
Read 2 more answers
What is the GCF of x2 and x9?​
zepelin [54]

Answer:

x²

Step-by-step explanation:

Given the values x² and x^9

The greatest common factor is the factors common to two or more compared values :

Factors of :

x² = x * x

x^9 = x * x * x * x * x * x * x * x * x

Multiplying the Factors in both are : x * x = x²

Similarly :

___|x² | x^9

_ x | x | x^8

_ x | 1 | x^7

There is no factor which can reduce both further simultaneously, Hence the G. C. F = (x * x) = x²

3 0
1 year ago
Other questions:
  • How would u find 4 1\5 divided by 2 1\3
    14·2 answers
  • Eric has challenged himself to walk 24,000 steps in 4 days. If Eric walks the same number of steps each day, which function repr
    5·1 answer
  • Convert the decimal expansion 0.1777 into a rational number.
    15·2 answers
  • What is the sum of 14 and the opposite of 12
    7·1 answer
  • The Green family is a family of six people. They have used 4,885.78 gallons of water so far this month. They cannot exceed 9,750
    15·2 answers
  • Samuel wants to buy at least twice as many graphic novels as comic books, Comic books sell for $7 each, and graphic
    11·2 answers
  • A worker is paid rs. 2130 for 6 days .if his total wage during a month is rs. 9230 find the number of days he worked in the mont
    13·1 answer
  • A child wanders slowly down a circular staircase from the top of a tower. With x,y,zx,y,z in feet and the origin at the base of
    14·1 answer
  • Quiz 3
    10·1 answer
  • At the Yogurt Pump, all flavors of frozen yogurt are $1.75 per scoop. If a customer buys v vanilla scoops and c chocolate scoops
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!