Guillermo is a professional deep water free diver. his altitude (in meters relative to sea level), xxx seconds after diving, is modeled by g(x)=\dfrac{1}{20}x(x-100)g(x)= 20 1 x(x−100)g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 20, end fraction, x, left parenthesis, x, minus, 100, right parenthesis what is the lowest altitude guillermo will reach?
Answer:
-125 meters.
Step by step explanation:
We have been given that Guillermo is a professional deep water free diver. his altitude (in meters relative to sea level), x seconds after diving, is modeled by [tex]g(x)=\frac{1}{20}x(x-100)[/tex].
We have been given a quadratic function and the minimum value will occur at vertex.
First of all we will write it in standard quadratic form by using distribution property.
[tex]\frac{x^{2}}{20}-\frac{100x}{20}[/tex]
[tex]\frac{x^{2}}{20}-5x[/tex]
Now we will find vertex of our parabola using [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-5)}{2(\frac{1}{20})}[/tex]
[tex]x=\frac{5}{(\frac{2}{20})}[/tex]
[tex]x=\frac{5\times20}{2}[/tex]
[tex]x=5\times10[/tex]
[tex]x=50[/tex]
Now let us substitute x=50 in our quadratic function to find lowest altitude of Guilermo.
[tex]g(50)=\frac{50^{2}}{20}-5\times 50[/tex]
[tex]g(50)=\frac{2500}{20}-250[/tex]
[tex]g(50)=125-250[/tex]
[tex]g(50)=-125[/tex]
Therefore, the lowest altitude Guilermo will reach is -125 meters.
Given the following functions f(x) and g(x), solve (f + g)(3) and select the correct answer below:
f(x) = 2x + 21
g(x) = x − 24
A)−27
B)−21
C)6
D)48
I THINK ITS D BUT IM NOT SURE HELP ME PLEASE IM RIGHT?,
A cone-shaped hole is drilled into a solid cube of metal as shown. If the cube has sides of length 9 cm, what is the volume of the metal after the hole is drilled? Let π ≈ 3.14 and round your answer to the nearest tenth.
The abs r us bodybuilding club has an annual membership fee of $414. you plan to visit 8 times each month. how much is your cost per visit during the year?
Answer:
cost per visit during the year= $4.31
Step-by-step explanation:
The abs r us bodybuilding club has an annual membership fee of $414. you plan to visit 8 times each month
annual membership fee = $414 times each month
1 year = 12 months
Membership fee for 1 month = 414/12= 34.5
In 1 months total visit is 8
To find the cost per visit we divide the monthly fee by 8
Cost per visit = [tex]\frac{34.5}{8} =4.3125[/tex]
cost per visit during the year= $4.31
tan(x+pi/2)= negative cot x
What are the coordinates of the point? A coordinate grid with a dot placed in the second quadrant. The dot is to the left of positive 4 on the y axis and above negative 2 on the x axis
The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?
Answer:
[tex]x-4y=8[/tex]
Step-by-step explanation:
Given : (–4, –3) , (12, 1)
Solution:
[tex](x_1,y_1)=(12,1)[/tex]
[tex](x_2,y_2)=(-4,-3)[/tex]
Two point slope form : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the given values.
[tex]y-1=\frac{-3-1}{-4-12}(x-12)[/tex]
[tex]y-1=\frac{-4}{-16}(x-12)[/tex]
[tex]y-1=\frac{1}{4}(x-12)[/tex]
Now standard form of equation of line = [tex]Ax+By=C[/tex]
So, [tex]y-1=\frac{1}{4}(x-12)[/tex]
[tex]4(y-1)=(x-12)[/tex]
[tex]4y-4=(x-12)[/tex]
[tex]12-4=x-4y[/tex]
[tex]8=x-4y[/tex]
[tex]x-4y=8[/tex]
Hence the standard form of the equation for this line is [tex]x-4y=8[/tex]
I just need the answers and I promise I will give the brainliest whoever comment first
1. Vertex (1,2), Point (2,-5)
2. Vertex (-3,6), Point (1,-2)
3. Vertex (0,5), Point (1,-2)
4. Vertex (1/4, -3/2), Point (1,3)
Jon’s car averages 9 kilometers per liter of gas. How many kiloliters can Jon drive with 22 liters of gas in his car?
Final answer:
Jon can drive 198 kilometers with 22 liters of gas in his car since the car averages 9 kilometers per liter.
Explanation:
The student's question asks how many kiloliters Jon can drive with 22 liters of gas in his car, given that the car averages 9 kilometers per liter of gas. To solve this problem, we will convert liters to kiloliters and then calculate the total distance that Jon can drive.
Firstly, we must recognize that 1 kiloliter (kL) is equal to 1,000 liters (L). Therefore, to convert 22 liters to kiloliters, we simply divide 22 by 1,000, which gives us 0.022 kL.
Now, since Jon's car goes 9 kilometers per liter, to find out how far he can go with 22 liters, we multiply 9 kilometers/liter by 22 liters:
9 km/L × 22 L = 198 km
To express this distance in kiloliters, we once again need to note that 1 kL is the same as 1,000 L. Since the car's consumption is measured per liter, we don't actually need to convert kilometers to kiloliters - the initial conversion of liters to kiloliters was not required to answer this particular problem.
Therefore, Jon can drive a total of 198 kilometers with his 22 liters of gas.
Jon's car with fuel efficiency of 9 km/l can drive 198 kilometers with 22 liters of gas. The distance in volume terms is 0.022 kiloliters, illustrating that 22 liters of gasoline would be used on such a trip.
Explanation:The student's question is how many kiloliters Jon can drive with 22 liters of gas if his car averages 9 kilometers per liter of gas. To answer this question, we need to perform a simple multiplication. Given that Jon's car has a fuel efficiency of 9 kilometers per liter, we multiply this rate by the amount of fuel he has, which is 22 liters, to determine the distance he can drive:
9 kilometers/liter × 22 liters = 198 kilometersTo convert kilometers to kiloliters (assuming the question intends to ask for the distance in kilometers rather than 'kiloliters'), we note that kiloliters is not a unit of distance, but rather a volume. Therefore, it is likely that the question contains a typo and should ask how many kilometers can Jon drive. To find out how many kiloliters that distance amounts to, we remember that 1 kiloliter equals 1,000 liters, so:
198 kilometers × (1 liter/9 kilometers) = 22 liters22 liters / 1,000 = 0.022 kilolitersTherefore, Jon can drive 198 kilometers with 22 liters of gas, which equals 0.022 kiloliters of gasoline consumed.
Select the locations on the number line to plot the points 9/2 and −7/2 .
The locations of the given numbers on the number line are needed.
The locations have been shown in the figure attached.
The numbers are [tex]\dfrac{9}{2}[/tex] and [tex]-\dfrac{7}{2}[/tex]
The numbers can be written as
[tex]\dfrac{9}{2}=4.5[/tex]
[tex]-\dfrac{7}{2}=-3.5[/tex]
In the given number line it can be seen that the longer vertical lines are whole numbers which are positive and negative.
The smaller vertical lines are an increment of [tex]0.5[/tex].
As the extreme ends are [tex]+5[/tex] and [tex]-5[/tex] the center longer vertical line will be [tex]0[/tex].
So, [tex]4.5[/tex] will be the smaller vertical line to the left of [tex]+5[/tex].
[tex]-3.5[/tex] will be the smaller vertical line to the right of [tex]-4[/tex].
The locations have been shown in the figure attached.
Learn more:
https://brainly.com/question/13425491
https://brainly.com/question/18611090
Three coins are in a bag. the first coin flips heads with probability 50%, the second coin flips heads with probability 60%, and the third coin flips heads with probability 70%. i pull out a coin and flip heads. if i flip this coin again, what is the probability i will get heads?
Final answer:
The probability of flipping heads again after already flipping heads once is 50%
Explanation:
The probability of getting heads when flipping a coin twice can be calculated by multiplying the probabilities of getting heads each time. Let's calculate the probability step by step:
Pick a coin: Each coin has a probability of being picked, so the probability of picking any of the three coins is 1/3.The probability of picking a coin that flips heads is 50%, since the first coin has a 50% probability of flipping heads.Flip the coin: Since we know the coin flips heads, the probability of getting heads on the second flip is still 50%, regardless of which coin was picked.Therefore, the probability of getting heads on the second flip is 50%.
Which expression is equivalent to (x - 6) (2x2 - 3x + 4)? 2x2 - 2x - 2 2x2 - 2x + 4 2x3 - 3x2 + 4x - 6 2x3 - 15x2 + 22x - 24
The U.S. government borrows money by _____.
A. asking banks or foreign investors
B. printing money
C. issuing stocks
D. issuing Treasury bonds and other government-backed securities
Answer:
D. issuing Treasury bonds and other government-backed securities
Step-by-step explanation:
Governments create debt by issuing government bonds and bills. Less creditworthy countries sometimes borrow directly from a supranational organization (e.g. the World Bank) or international financial institutions.
Treasury bonds are how the US - and all governments for that matter - borrow hard cash: they issue government securities, which other countries and institutions buy. So, the US national debt is owned mostly in the US - but the $5.4tn foreign-owned debt is owned predominantly by Asian economies.
A man wants to make up 100 one-pound jars of nuts to sell for 66 cents a jar. He plans to use 40 pounds of nuts worth 75 cents a pound. What should be the price of the other type of nuts he uses? Answer:
60 cents a pounds is needed.
From the question, we are given that:
100 one pound of nut to sell for 66 percent a jar 40 pound of nuts worth 75 cents a poundSince the question says he plans to use 40 pounds and he wants to make up 100 pounds jar of nut, therefore you should know that 60 pounds of the nuts is needed.
Further ExplanationLet Y be the price of 60 pounds of nuts
Therefore, the equations should as follows:
(40 x 75) + (60 x y) = 66 x 100
= 3000 + 60y = 6600
60y = 6600 – 3000
60y = 3600 (divide both side by 60)
60y/60 = 3600/60 (60 cross out 60)
Y = 3600/60
Y = 60
Therefore, 60 cents a pounds is needed.
LEARN MORE:
A man wants to make up 100 one-pound jars of nuts to sell for 66 cents a jar. https://brainly.com/question/8565795A grocer mixed nuts worth 80 cents per pound with nuts worth 50 cents per pound. https://brainly.com/question/8080590KEYWORDS:
66 cents jar40 pounds of nut100 one-pound60 cents75 cents a poundEasy Math Problem....
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
Incorrect answers will be reported!
Which equation is in standard form and represents a line with slope 5 through the point (0, 2)?
Choose all that are correct.
An inscribed angle measures 80° with an arc measurement of 160°.
An inscribed angle measures 30° with an arc measurement of 15°.
A central angle measures 50° with an arc measurement of 25°.
An arc measures 40° with an inscribed angle is 20°.
Answer: Second and third options are correct.
Step-by-step explanation:
As we know that
Angle at the center is the double the angle formed at the circumference of the circle.
So, An inscribed angle measure 30° if the angle formed at the circumference ( an arc measurement is of 15°)
Similarly, A central angle measures 50° with an arc measurement of 25°.
Hence, Second and third options are correct.
Answer:
The answer is the first one and the last one.
An inscribed angle measures 80° with an arc measurement of 160°.
and
An arc measures 40° with an inscribed angle is 20°.
the guy above is wrong do not do his answers
If Thomas wants a volume of 12 in3, what size does the cutout need to be? What would be the dimensions of this box?
The expression sin x (cos x cot x - sin x) simplifies to?
Write the quadratic equation y= x^2 -6x + 7 in vertex form
What’s the answer to this?
What is the value of 238 - 3x^2 when x=4??
Given f(x)=4x^2−5 and g(x)=x+3 . What is (fg)(x) ?
The Main answer is [tex](fg)(x)=4x^{3} +12x^{2} -5x-15.[/tex] Given [tex]f(x)=4x^{2} -5[/tex] and [tex]g(x)=x+3[/tex] the value of [tex](fg)(x)[/tex] is [tex](fg)(x)=4x^{3} +12x^{2} -5x-15.[/tex]
To find the product of two functions [tex]f(x)[/tex] and [tex]g(x),[/tex] denoted as [tex](fg)(x)[/tex], we simply multiply the two functions together.
Given [tex]f(x)=4x^{2} -5[/tex] and [tex]g(x)=x+3[/tex], we multiply them to get [tex](fg)(x)[/tex]:
[tex](fg)(x)=f(x)*g(x)=(4x^{2} -5)*(x+3).[/tex]
Now, we distribute [tex]4x^{2} -5[/tex] across [tex](x+3)[/tex]:
[tex](fg)(x)=4x^{2} *(x+3)-5*(x+3).[/tex]
Expanding further:
[tex]=4x^{3} +12x^{2} -5x-15.[/tex]
So, [tex](fg)(x)=4x^{3} +12x^{2} -5x-15.[/tex]
COMPLETE QUESTION:
Given [tex]f(x)=4x^{2} -5[/tex] and [tex]g(x)=x+3[/tex]. What is [tex](fg)(x)[/tex]?
Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour
ABCD∼EFGH
AD=45 in. , EH=75 in. , and AB=30 in.
What is EF ?
Enter your answer in the box.
EF =
in.
What is the value of X?
The number of adults who attend a county fair (measured in hundreds of people) is represented by the function a(d)=−0.3d2+4d+9 , where d is the number of days since the fair opened. The number of children who attend the same county fair (measured in hundreds of people) is represented by the function c(d)=−0.2d2+5d+11 , where d is the number of days since the fair opened. What function, f(d) , can be used to determine how many more children than adults attend the fair on any day?
Given is the function for number of adults who visit fair at day 'd' after its opening, a(d) = −0.3d² + 4d + 9.
Given is the function for number of children who visit fair at day 'd' after its opening, c(d) = −0.2d² + 5d + 11.
Any function f(d) to find excess of children more than adults can be written as follows :-
f(d) = c(d) - a(d).
⇒ f(d) = (−0.2d² + 5d + 11) - (−0.3d² + 4d + 9)
⇒ f(d) = -0.2d² + 0.3d² + 5d - 4d + 11 - 9
⇒ f(d) = 0.1d² + d + 2
What is the perimeter of 10 and 12?
draw and label a figure that has 4 points, 2 rays, and 1 right angle.
Answer:
Figure attached below.
Step-by-step explanation:
To draw and label - A figure that has 4 points, 2 rays, and 1 right angle.
Image is attached below.
This image has 4 points, 2 rays, and 1 right angle.
The point is a dot from which a line form.
The point s are: A, B, C, D.
A ray is starts out at a point and continues off to infinity.
The rays are: BA, BF, BD, CD, and CE
An angle is the angle formed between two rays .
The right angle is at B i.e, 90°
BRAINLIEST ANSWER!!!!!!!!!!!!!!!!!!!!!!! HELP PLZ!!!!!! Use the net to determine the lateral surface area.
The net of a triangular prism with the height of 4 inches, and each leg of the triangular base is 6 inches and its height is 5.2 inches is laid flat.
**i can't paste the picture, so this is all I have. If you can please help, i would appreciate it so much. plz help, ty!