What is the image point of (1, -1) after a translation left 4 units and down 5 units?

The height of the tunnel at the center is 35ft, and the vertical clearance must be 21 ft at a point of 8ft from the center. Find

Zinaida [17]

Answer:

y=-0.215x^2+35

Step by Step:

Let, $h=0$ , $k=35$ , $x=8$ , $y=21$

We know that, the general equation of the parabola.

$y-k = a(x-h)^2$

$\Rightarrow y=a(x-h)^2+k .........(i)$

Substitute the value of $h, k, x, y$ in equation $(i)$ and find the value of $a.$

$21=a(8-0)^2+35$

$\Rightarrow 21=a\times 8^2+35$

$\Rightarrow 21=64a+35$

$\Rightarrow 64a=21-35$

$\Rightarrow 64a=-14$

$\Rightarrow a=\frac{-14}{65}$

$\Rightarrow a=-0.215$

Hence, the equation of the parabola is:

$y=-0.215x^2+35$

8 0

2 years ago

An employee’s wages are directly proportional to the time worked.If an employee earns $105 for 7 hours how much will the employe

stich3 [128]

Answer:

600

Step-by-step explanation:

105/7 * x/40

7x=4,200

x=600

8 0

2 years ago

I need help with answering the following questions. :/ :)

s344n2d4d5 [400]

Answer:

a) (0, ∞)

b) (-∞, ∞)

c) x = 0

Step-by-step explanation:

It helps to have some idea what the log function is.

__

a) The domain is all positive numbers: (0, ∞).

b) The range is all real numbers: (-∞, ∞). (The vertical translation downward by 5 units does not change that.)

c) There is a vertical asymptote where the argument of the log function is zero: at x=0.

3 0

3 years ago

Answer choice <br> D) A worker with 15 years of service gets 5 weeks of vacation and each year.

otez555 [7]

Answer: it seems to be D, but the equation makes practically no sense!

The value of the factor changes for the different amounts of service years and vacation weeks.

Step-by-step explanation: The equation means that the employee is trying to figure out the value of the "v-factor" for how vacation time is earned.

If you substitute the number of service years into the left side of the "formula" and vacation weeks on the right side, then solve for "v", v(15)=5 you get v= 1/3 or 0.33

If you substitute other numbers, like v(2)=2, so v= 1 then v(30) = 8, v = 4/15 or 0.2667. You see the factor's value decreases. The company is much more generous to to employees with one or two years of service than with the older ones.

7 0

2 years ago

In triangle ABC, AB=10, BC=8, and angle B=30. In triangle KLJ, LJ=20, JK=16, and angle L=30. State whether the triangles are sim

Margaret [11]

Answer:

They are not similar.

Step-by-step explanation:

In triangle ABC, the angle we are given is in between the two defined sides(AB and BC with angle B). If these triangles were similar, we would see this with the SAS postulate.

In triangle KLJ, the angle is not in between the two sides, so they are not similar according to any of these two postulates.

6 0

7 months ago