The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the height above water and x is the horizontal distance in feet. If a beam of light is shone upward at an angle modeled by the equation x + y = 10, at what height from the water's surface will the beam of light hit the dolphin?A)2.7 feet
B)3 feet
C)5 feet
D)5.6 feet
Answers
equation 1: y = -0.4x^2 +3xequation 2: x + y = 10
We need to write equation to with y as the subject:equation 2: y = 10 - x
equation 1 = equation 2:
10 - x = -0.4x^2 + 3x0.4x^2 - 4x + 10 = 02x^2 - 20 + 50 = 0(2x - 10)(x - 5) = 0x = -10/2 or x = 5
But x >= 0 (the question says it's a height above the water), so x = 5
Substituting x = 5 into one of the equations:
y = 10 - x
y = 10 - 5
y = 5
So the answer is C
Answer:
5 feet
Step-by-step explanation:
y = 5
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A broker/dealer bought ABC stock at 8 for its inventory position. A month later when the inter-dealer market for ABC was 10.50 -- 11.25, the broker/dealer sold the stock to a customer. The basis for the dealer's markup will be:[A] 8.00[B] 8.75[C] 10.50[D] 11.25
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Find the equation of the graphed line.Thank you btw!
Answers
Answer:
Step-by-step explanation:
Answer:14.5
Step-by-step explanation:
you get on the 4th test if you want to
average a 90% for the 4 tests?
A. 94
B. 95
C. 96
D. 97
E. 98
Answers
I know this because if you go on the calculator and add up 84+82+98+96 its equals to 360 and 360 divided by four (since there are now four marks including the mark you need to get on the next test) and that equals to 90.
(in other terms)
84+82+98+96=360
360÷4=90
therefore, you need to get a score of 96 on your fourth test to receive an average of 90%
Answers
The Scientific notation of numbers is,
⇒ 4.5013 × 10⁻¹
We have to give that,
A standard form of number is,
⇒ 0.45013
Since Scientific notation is a way of writing very large or very small numbers.
For example; 230,000,000 can be written in scientific notation as
2.3 x 10⁸.
Hence, the Scientific notation of numbers is,
⇒ 0.45013
⇒ 4.5013 × 10⁻¹
To learn more about scientific notation visit:
#SPJ6
Answers
Answers
Answer:
1.) Domain X = all positive real numbers
2.) Range: F(x) > = 5450
Step-by-step explanation:
Given that
F(x) = 5,450(1.024)^x
Where the domain is the independent variable X and the range is the dependent variable Y or F(x)
Since the domain for the function represents the amount of time the money will be in the college fund, time cannot be negative, it will always be positive.
Therefore, domain x will be all positive real numbers.
The least domain x = 0
Substituting domain into the equation will give us a range of value:
F(x) = 5450 × ( 1.024 )^0
F(x) = 5450 × 1
F(x) = 5450
That is, the least value of range = 5450
Therefore, Range will be F(x) greater than or equal to 5450.
F(x) > = 5450
b- Calculate the ratio of degrees to the circumference for each circle and show that they are equal.
c- Calculate the ratio of the área to the circumference for each circle and show that they are equal.
d- Calculate the ratio of the diameter to the circumference for each and show that they are equal.
Answers
each one. Then after that, I'm going to hand you a secret that
I promise is going to knock your socks off.
a- Calculate the ratio of the diameter to the radius for each circle
and show that they are equal.
-- That won't tell you anything. The ratio of the diameter
to the radius of EVERY circle is 2 .
b- Calculate the ratio of degrees to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The circumference
of EVERY circle subtends a central angle of 360°.
c- Calculate the ratio of the área to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the area
to the circumference of EVERY circle is (radius/2).
They're only equal if the circles are the same size.
d- Calculate the ratio of the diameter to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the diameter
to the circumference of EVERY circle is 1/pi. If the ratio isn't
1/pi, then you're not looking at a circle.
None of these choices tells you whether the two circles are similar.
What are you going to do ? How can you tell ? ?
Here's the surprise I promised you.
Beware of flying socks:
All circles are similar to all other circles.
Good night.