Translate the sentence to an equation x minus 6 is 7

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

horrorfan [7]

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

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

$\boxed{a=-0.3575}$

8 0

3 years ago

Find the length of side X in simplest radical form with a rational denominator.<br> X

german

Answer:

given in the figure an isosceles right triangle

hence

x = √3

√3 is a <u>surd</u> it can't be simplified further

7 0

3 years ago

An engineer stands 200 feet from a tower and sights the top of the tower at a 45° angle of elevation. Find the height of the tow

Alik [6]

Drawing a diagram of a triangle may be helpful. The hypotenuse is irrelevant, but the vertical leg and the horizontal leg are useful. Since we know the engineer is looking up at a 45 degree angle from a distance of 200 feet, we can label the vertical leg the "opposite", since it is on the opposite side of the angle we are given. The horizontal leg then becomes the "adjacent". You can then use trigonometry to solve for the opposite.
The options are:
sin(theta)= opposite/hypotenuse
cos(theta)= adjacent/hypotenuse
tan(theta)= opposite/adjacent
Since we don't care about the hypotenuse, the last equation is the one to use. The angle we are given can be substituted in for theta:
tan(45)= x/200
1.61977519= x/200
x= 323.955038 feet

6 0

3 years ago

20% percent tip on 8 dollar

sesenic [268]

Answer:

9.60 dollars tip is $1.60

Step-by-step explanation:

8 0

2 years ago

Pls help! given: -2(x-4)=2x+12 Prove: x=-1

nata0808 [166]

Answer:

X= -1

Step-by-step explanation:

In pic

(hope this helps can I pls have brainlist (crown) ☺️)

7 0

3 years ago