Based on data in the two way table which statement is true

The cost of a student ticket to the school play is $7. Write an equation that correctly relates the total cost, c, for a particu

Mazyrski [523]

C = $7s
independent variable ie the changing variable is s
dependent variable ie the non changing variable is c

8 0

3 years ago

Read 2 more answers

PLEASE HELP ME WITH THIS

Vedmedyk [2.9K]

Let's start with the drawing. (See the drawing at the bottom of this answer.)

Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.

Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.

The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.

Now we use trigonometry to find the measure of angle A.

For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.

$\sin A = \dfrac{opp}{hyp}$

$\sin A = \dfrac{11.8}{12}$

$\sin A = 0.98333$

Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.

$A = \sin^{-1} 0.98333$

$A = 79.5^\circ$

Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.

           |\
     | \
     |    \
       |    \
opp = |    \ hyp = 12
= 11.8 |    \
     |       \
     |_______\ A

3 0

3 years ago

Answer ASAP. Please give correct answer. (Involves a bunch of circles and trig identities)

iren [92.7K]

Answer:

45.40

Step-by-step explanation:

First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:

y=acoshxa

You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:

a+30=acoshd2a(1)

The lenght of the catenary is given by the following formula (which can be proved easily):

s=asinhx2a−asinhx1a

where x1,x2 are x-cooridanates of ending points. In our case:

80=2asinhd2a

40=asinhd2a(2)

You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.

Square (1) and (2) and subtract. You will get:

(a+30)2−402=a2

Calculate a from this equation, replace that value into (1) or (2) to evaluate d.

My calculation:

a=353≈11.67

d=703arccosh257≈45.40

7 0

3 years ago

What is the factored form of y^2+6y-16

Vlada [557]

<h2><em>y 2 + 6 y − 16 = ( y + 8 ) ( y − 2 ) </em></h2><h2 /><h2><em>Explanation: </em></h2><h2><em>Note that in general: </em></h2><h2 /><h2><em>( y + a ) (y − b ) = y 2 + ( a − b ) y − a b </em></h2><h2 /><h2><em>So we want to find a pair of factors a and b of 16 which differ by 6 . </em></h2><h2><em>The pair 8 , 2 works in that 8− 2 = 6 and 8 ⋅ 2= 16 . </em></h2><h2 /><h2><em>Hence: </em></h2><h2><em> y 2 + 6 y − 16 = ( y+ 8 ) ( y − 2 )</em></h2><h2><em>y=2,-8</em></h2>

6 0

3 years ago

Read 2 more answers

find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a +

hodyreva [135]

Answer:

a= 5 and b=1

Step-by-step explanation:

To solve, we will follow the steps below:

2x + 3y = 7

(a-b)x + (a+b)y = 3a + b - 2

We should note that since it has infinitely many solutions then,

$\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

Hence

2/a-b = 3/a+b = 7/3a +b-2

2/a-b = 3/a+b

cross-multiply

3(a-b) = 2( a+b)

open the bracket

3a - 3b = 2a + 2b

collect like term

3a - 2a = 2b + 3b

a = 5b -------------------------------------------(1)

Similarly

3/a+b = 7/3a +b-2

cross-multiply

7(a+b) = 3(3a+b -2)

7a + 7b = 9a + 3b -6

take all the variables to the left-hand side of the equation

7a - 9a+ 7b-3b = -6

-2a + 4b = -6 ---------------------------------(2)

but a = 5b

substitute a= 5b in equation (2) and solve for b

-2(5) + 4b = -6

-10 + 4b = -6

add 10 to both-side of the equation

-10 + 10+ 4b = -6+10

4b = 4

divide both-side of the equation by 4

b = 1

substitute b= 1 in equation (1)

a = 5b

a =5(1)

a=5

Therefore, a= 5 and b=1

8 0

3 years ago