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forsale [732]
2 years ago
8

The graph shows the rate at which the depth of the water in a pond is changing over time. On a coordinate plane, a graph titled

Depth of Pond Water has Minutes on the x-axis and Feet on the y-axis. A line goes through points (2, 4) and (4, 8). The depth of the water is increasing by feet each minute.
Mathematics
1 answer:
lawyer [7]2 years ago
4 0

Answer:

Step-by-step explanation:

The key to solving this question is to find the distance bwtween the two points given

distance=y2-y1/x2-x1

(2,4)(4,8)

2=x1,4=y1

4=x2

8=y2

8-4/4-2

4/2=2

The depth of the water is increasing by 2 ft each minute

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A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is lo
vodomira [7]

Answer: x^2=32y


Step-by-step explanation:

Given:  A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

The pipe is located 8 inches from the vertex of the mirror.

Assume the vertex is at the origin.

If the parabola opens upwards

then the coordinates of focus= (0,8)

We know that equation of parabola with focus (0,a) and open upards is of the form (vertex=(0,0)) is

x^2=4ay

Substitute the value of a=8 in equation, we get

x^2=4\times8y

\Rightarrow\ x^2=32y

Therefore, equation of the parabola that models the cross section of the mirror is x^2=32y

3 0
2 years ago
Avon Edwards worked 45.5 hours at $5 per hour. He made $100 in tips but no bonuses. Anything over 40 hours is paid time-and-a-ha
posledela

Answer:

1. D

2. B


Step-by-step explanation:

<u>Question 1:</u>

We can get Avon's earnings using the equation  W=HR+1.5VR+B+T

Where W is his earnings

HR is the regular hours (40 hours in this case)

V is overtime hours (hours over 40, 45.5 - 40 = 5.5 hours)

B is bonus (no bonus)

T is tips ( $100 tips, given)

and R is the rate (which is $5 per hour)


<em>Substituting the given info into the equation, we get:</em>

<em>W=HR+1.5VR+B+T\\W=(40)(5)+1.5(5.5)(5)+0+100\\W=341.25</em>


<em>So avon's earnings are $341.25</em>

<em>Answer choice D is right.</em>


<u>Question 2:</u>

The other employee needs to work x hours @ $15 per hour to equate or surpass $428. So we can set up the equation shown below and solve for x:

(15)(x)=428\\x=\frac{428}{15}\\x=28.53

Rounded to 1 decimal place, this is about 28.5 hours

Answer choice B is right.


6 0
2 years ago
Read 2 more answers
5.63x10^-5 in standard form
NemiM [27]

Answer:

the correct anser is 0.0000563

Step-by-step explanation:

you move the decimal point to the left 5 spaces because it is negative

5 0
2 years ago
In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.
pshichka [43]

Answer:

The answer is:

\bold{c\approx 20.2\ units}

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

Putting all the values.

cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units

The answer is:

\bold{c\approx 20.2\ units}

4 0
2 years ago
Using the standard normal table, the probability that Seth’s light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is abo
lana66690 [7]

Answer:

How many standard deviations above the mean is 14,500 hours? 1.25 1.5 2.5 Using the standard normal table, the probability that Seth's light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about ✔ 89% .

5 0
1 year ago
Read 2 more answers
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