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
I am Lyosha [343]
3 years ago
10

An isosceles trapezoid ABCD with height 2 units has all its vertices on the parabola y=a(x+1)(x−5). What is the value of a, if p

oints A and D belong to the x−axis and m∠BAD=60^o?

Mathematics
1 answer:
horrorfan [7]3 years ago
8 0

Answer:

a = -0.3575

Step-by-step explanation:

The points A and D lie on the x-axis, this means that they are the x-intercepts of the parabola, and therefore we can find their location.

The points A and B are located where

y=a(x+1)(x-5)=0

This gives

x=-1

y=5

Now given the coordinates of A, we are in position to find the coordinates of the point B. Point B must have y coordinate of y=2 (because the base of the trapezoid is at y=0), and the x coordinate of B, looking at the figure, must be x coordinate of A plus horizontal distance between A and B, i.e

B_x=A_x+\frac{2}{tan(60)} =-1+\frac{2\sqrt{3} }{3}

Thus the coordinates of B are:

B=(-1+\frac{2\sqrt{3} }{3},2)

Now this point B lies on the parabola, and therefore it must satisfy the equation  y=a(x+1)(x-5).

Thus

2=a((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)

Therefore

a=\frac{2}{((-1+\frac{2\sqrt{3} }{3})+1)((-1+\frac{2\sqrt{3} }{3})-5)}

\boxed{a=-0.3575}

You might be interested in
the average weight of a baby birth is 7 pounds how many ounces is the average weight of a baby Can Y'all please help me
Savatey [412]
7 pounds converts to 112 ounces
5 0
3 years ago
Lucy is waiting for the liquid to boil in the pot. At which temperature should the liquid boil in the pot?
Alja [10]
Water boils at 212 degrees Fahrenheit (100 degrees celcius)
8 0
3 years ago
Read 2 more answers
The points(1,r) and (5,-4) lie on a line with slope 5. find the missing coordinate r. ​
Arte-miy333 [17]

The value of r is -24

Step-by-step explanation:

Given points are:

(1,r) and (5,-4)

Let the points be:

(x1,y1) = (1,r)

(x2,y2) = (5,-4)

m = 5

The slope is given by:

m = \frac{y_2-y_1}{x_2-x_1}\\5 = \frac{-4-r}{5-1}\\5 = \frac{-4-r}{4}\\5 * 4 = -4-r\\20 = -4-r\\20+4 = -4-r+4\\24 = -r\\r = -24

Hence,

The value of r is -24

Keywords: Slope, coordinates

Learn more about slope at:

  • brainly.com/question/1106840
  • brainly.com/question/10830549

#LearnwithBrainly

5 0
3 years ago
Hi do you want which is greater 0.75 x 81 or 0.9 x 81.
anygoal [31]

Answer:

0.9 x 81

Step-by-step explanation:

0.9 is actually 0.90 and 90 is greater than 75

5 0
3 years ago
Read 2 more answers
PARK is a parallelogram. Find the value of x.
jekas [21]

Answer: 40

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Mr taylor bought back 180 euros to the uk the exchange rate was €1.2 to ?1 how kuch did he get in pounds
    10·1 answer
  • How can I use models to add fractions?
    12·1 answer
  • A town has two fire engines operating independently. The probability that a specific engine is available when needed is 0.96. (a)
    15·1 answer
  • Jill is playing a game in which a number cube is rolled two times. The sum of the rolls is recorded. What is the sample space fo
    5·1 answer
  • Help help help helphelp h;i
    5·2 answers
  • Como podria la logica contribuir con la convivencia social
    5·1 answer
  • Solve this question<br> 4(5x-2)=2(9x+3)
    14·2 answers
  • Please help!! FAST!!
    13·1 answer
  • I need help ASAP!!Please explain how to do the problem
    15·1 answer
  • Camilla and Claudette offer hourly gymnastics classes. Together they can teach 14 students
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!