The point on the parabola 2y = x that is closest to the point (-4,1) is (-4, -2).
How to find the point on the parabola?We have the parabola 2y = x, which can be rewritten as y = x/2.
Let P be the point on the parabola that is closest to the point (-4,1).
The distance between P and (-4,1) is minimized when the line connecting the two points is perpendicular to the tangent line of the parabola at P.
The slope of the tangent line to the parabola y = x/2 at any point (x, y) on it is given by the derivative of y with respect to x:
dy/dx = 1/2
So, the slope of the line perpendicular to the tangent line is -2.
Therefore, the equation of the line connecting (-4,1) and P is:
(y - 1) = -2(x + 4)
Simplifying, we get:
y = -2x - 7
Substituting y = x/2 from the equation of the parabola, we get:
x/2 = -2x - 7
Solving for x, we get:
x = -4
Substituting x = -4 into the equation of the parabola, we get:
2y = -4
y = -2
Therefore, the point on the parabola 2y = x that is closest to the point (-4,1) is (-4, -2).
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What is the value of the bisecting angle, x, marked on this square?
The four corners of a square are 90 degrees.
They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.
The lines form triangles, which have 3 angles that need to equal 180 degrees.
Two of the angles are 45, so 45 + 45 = 90 degrees.
X = 180 -90 = 90 degrees.
Answer:
90 degrees
By 90 * 4 is 360
Step-by-step explanation:
Please help will mark the brainaloat
Step-by-step explanation:
there is to be a stage 15m wide and 3m deep with a curved seating area as shown
Determine the area of the seating area?
PLZ JUST TELL ME IF THESE ARE RIGHT! THX
DO YOU AGREE!
Answer:
Yes, the are the right degrees.
Answer:
I do agree
Step-by-step explanation:
I know 10. is right because it is a right angle which id usually 90 degrees.
I'm pretty sure 11. is right because I know it is an obtuse angle and I think the number you gave is close if not it.
I know 12. is right because that angle looks the same as DBA which is already labeled 54 degrees.
I know 13. is right because 180 degrees is always a straight line.
Hope this helps. Plz give brainliest.
Jorge gives an equal number of marbles to 6 friends. Which could be the total number of marbles he gave to his friends?
Answer:
D. 60
Step-by-step explanation:
To find an equal number of numbers the sum has to be equal to 6*x.
Answer:
If he gave it all to his friends then its D. If it is counting him too then C.
Step-by-step explanation:
17. If a = 3b^2 and a = 27, what is one value of b?
4.5
9
1.73
3
Answer:
b = 3
Step-by-step explanation:
Given that,
→ a = 27
Forming the equation,
→ 27 = 3b²
Now the value of b will be,
→ 27 = 3b²
→ b² = 27/3
→ b = √9
→ [ b = 3 ]
Hence, the value of b is 3.
⇒Given that a=27 in the equation \(a=3b^{2} \\\) in the place of a plug in 27 and solve for b
\(27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3\)
⇒Note b can also be -3 but the only option available as the answer is 3
∴ b=3 in this case.
Find the following integrals
\(\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}\)
\( \sf x - \frac{4}{x} + C\)
Step-by-step explanation:
\( \sf \longmapsto \int \frac{ {x}^{2} + 4 }{ {x}^{2} }dx \\ \\ \\ \sf \longmapsto \int \frac{ {x}^{2} }{ {x}^{2} } dx + \int \frac{4}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto \int 1dx + 4 \int \frac{1}{ {x}^{2} } dx \\ \\ \\ \sf \longmapsto x + 4( \frac{{x}^{ -2 + 1}}{ -2 + 1} ) + C \\ \\ \\ \boxed{ \longmapsto x - \frac{4}{x} + C} \)
The following shape has 2 pairs of parallel sides.
4
4
8
2
What is the area of the shape?
units?
Answer:
28
Step-by-step explanation:
1/2xbxh=4
To find the total area of the shape, we can subtract the removed area from the larger area. 32-4=28
The ones digit is 2 less than the tens digit, and the sum of this number and its reversed number is 154.
Answer:
Step-by-step explanation:
the answer is 86
hope it helps!
(-_-)
1/8x-5/6=2x solve for X
Answer:
x= -4/9
Step-by-step explanation:
HOPE THIS HELPS!!!! :)
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If a hospital patient is given 50 milligrams of medicine which leaves the bloodstream at 10% per hour, how many milligrams of medicine will remain in the system after 6 hours? Use the function A(t) = Iert. 12. 39 mg 27. 44 mg 45. 24 mg 91. 11 mg.
The amount of medicine that will remain in the system after 6 hours is 27.44 milligrams.
Given to usInitial condition = 50 milligrams of medicine,
Rate at which medicine will be disposed = 10% = 0.1
function = \(A(t) = I \times e^{rt}\)
To findMedicine remains in the system after 6 hours
As the function is already given to us, substituting the values in the function we get,
\(A(t) = I \times e^{rt}\)
\(A(t) = (50) \times e^{(-0.1\times 6)}\)
the value of r is -0.1(10%) because the medicine is leaving the system, therefore, the value of medicine will be reduced.
Solving the function further,
\(A(t) = (50) \times e^{(-0.1\times 6)}\\A(t) = 27.44\ milligrams\)
Hence, the amount of medicine that will remain in the system after 6 hours is 27.44 milligrams.
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for the region rr below, write ∬rfda∬rfda as an iterated integral in polar coordinates.
No function f(r,θ) is given, we cannot evaluate the integral further.
To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.
Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:
r ≤ 3
To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:
0 ≤ θ ≤ π
Now, we can write the iterated integral as:
∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr
where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.
In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.
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if an ice block 10 centimeters wide, 10 centimeters high, and 20 centimeters long was melted, how much would it raise the water level in a tank that is 100 centimeters long by 40 centimeters wide?
Step-by-step explanation:
Volume of ice = 10 X 10 X 20 = 2000 cm^3
tank volume increase will be the same
100 x 40 x HEIGHT = 2000
Height = 2000/ ( 100 X 40) = .5 cm height increase
The melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters. This can be answered by the concept of Volume
To calculate the amount of water that would be displaced by the ice block, we need to first find its volume, which is 10 x 10 x 20 = 2000 cubic centimeters. Since 1 cubic centimeter of water has a mass of 1 gram, the mass of the ice block would be 2000 grams or 2 kilograms.
When the ice block melts, it will turn into water and occupy the same volume, which would displace an equal amount of water in the tank. The volume of the tank is 100 x 40 x h, where h is the increase in water level. Setting the volume of the ice block equal to the increase in the water level, we get:
2000 = 100 x 40 x h
h = 0.5 centimeters
Therefore, the melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters.
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2,914 rounded to the thousand and to nearest hundred
Answer: 2194.00 and 2194.000
Step-by-step explanation: rounded to the nearest 1000= 2194.000
rounded to the nearest 100 = 2194.00
simplify -4(-9p + -3) -2(-2p + 6)
Answer:
-32p
hope this helps!!:)
Step-by-step explanation:
Answer:
-32p
Step-by-step explanation:
-4(-9p+ -3) -2(-2p+6)
-36p+12 4p+-12
-32p
Je m'entraîne
41
x désigne un nombre positif.
On note A la fonction qui, à
une longueur x en cm, associe x
l'aire, en cm?, du triangle
rectangle représenté ci-contre.
a. Calculer A(3).
b. Donner l'expression de A(x).
C. Est-il vrai que 5 est un antécédent de 17,5 par la
fonction A?
Answer:
what what what what what what what what
math help pls answer
Answer:
-7 -4 0 1 7
Step-by-step explanation:
x=0
x²-49=0
x²=49
x=±7
x²+3x-4= ² + 4 − − 4= ( + 4 ) − 1 ( + 4 )=(x+4)(x-1)=0
x+4=0
x=-4
x=1
Answers with the reasons
Answer:
hope this will help you more...good luck
A scale drawing of Elizabeth's rectangular room is 4 inches by 7 inches. The scale is 1 inch = 3 feet. What is the area, in square feet, of Elizabeth's room?
Answer:
84 feet
Step-by-step explanation:
4 inches× 7 inches=28inches
28 inches×3feet=84feet
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:
"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."
The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.
Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.
In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.
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a
1
Jazmine had a bag of 24 jellybeans. If of the
5
jellybeans are white, how many jelly beans are
white?
Answer:
im sorry but can you be more specific? your question is not complete, and I think you either wrote it wrong or copy and pasted it wrong. Judging by the way you asked it I think it would be 5?
Step-by-step explanation:
Answer:
5 jelly beans
Step-by-step explanation:
Hope this helps!!
what is the difference between a bar graph and a histogram? a. there is no difference between a bar graph and a histogram. b. a bar graph displays categorical data, while a histogram displays quantitative data. c. a bar graph has no spaces between the bars, while a histogram must have space between the bars. d. a bar graph displays quantitative data, while a histogram displays categorical data.
The difference between a bar graph and a histogram is that of b. a bar graph displays categorical data, while a histogram displays quantitative data.
A bar graph is majorly used to compare different categories or groups of data. It displays data in separate bars, each representing a different category. A histogram, on the other hand, is used to display the distribution of a continuous quantitative variable. It shows the frequency of different values within a range of values by using bars of different heights. The bars in a histogram are also adjacent to each other, with no space between them.
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Set up the partial fraction decomposition for a given function. Do not evaluate the coefficients. f(x) = 16x3 + 12x2 + 10x + 2 / (x4 – 4x2)(x2 + x + 1)2(x2 – 3x + 2)(x4 + 3x2 + 2)
We can decompose the given rational function as follows:
f(x) = (16x^3 + 12x^2 + 10x + 2) / [(x^4 – 4x^2)(x^2 + x + 1)^2(x^2 – 3x + 2)(x^4 + 3x^2 + 2)]
To find the partial fraction decomposition, we first factor the denominator completely:
x^4 – 4x^2 = x^2(x^2 – 4) = x^2(x – 2)(x + 2)
x^2 + x + 1 = (x + 1/2)^2 + 3/4
x^2 – 3x + 2 = (x – 1)(x – 2)
x^4 + 3x^2 + 2 = (x^2 + 1)(x^2 + 2)
Substituting these factorizations into the denominator, we get:
f(x) = (16x^3 + 12x^2 + 10x + 2) / [x^2(x – 2)(x + 2)(x + 1/2)^2(3/4)^2(x – 1)(x – 2)(x^2 + 1)(x^2 + 2)]
We can now write the partial fraction decomposition as:
f(x) = A/x + Bx + C/(x – 2) + D/(x + 2) + E/(x + 1/2) + F/(x + 1/2)^2 + G/(x – 1) + H/(x^2 + 1) + I/(x^2 + 2)
where A, B, C, D, E, F, G, H, and I are constants to be determined.
Note that the term E/(x + 1/2) has a repeated linear factor (x + 1/2)^2, so we need to include a second term F/(x + 1/2)^2 in the decomposition.
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Find all critical points of the function f(x) = xin(4x). (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. If the function does not have any critical points, enter DNE.) critical points:
The critical points of f(x) = xin(4x) are x = 0, pi/4, and 3pi/4.
To find the critical points of f(x), we need to find the values of x where the derivative is zero. The derivative of f(x) is f'(x) = (1 - 4x^2)in(4x). Setting this equal to zero and solving for x, we get x = 0, pi/4, and 3pi/4. These are the only values of x where the derivative is zero, so they are the only critical points of f(x).
At x = 0, the function f(x) is undefined. At x = pi/4 and x = 3pi/4, the function f(x) has a local maximum and a local minimum, respectively.
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Need help solving! I got 4x+17 with a remainder of 42 not sure if it is correct!
Given:
\(\frac{4x^2+5x-9}{x-3}\)Using synthetic division we get,
Hence, the answer is,
\(4x+17+\frac{42}{x-3}\)An office building has three air conditioning units, one for each office. Each unit runs only when employees are
working. The tables below show the number of hours employees worked at each office over a three-month period
and the total air conditioning electric costs for the entire office for each month.
June
July
August
Number of Hours Worked
Unit A
Unit B
184
207
174
198
168
189
Unit C
276
264
242
w
Total Air Conditioning Electric Costs
June
$142.60
July
$135.96
August
$128.30
How much does it cost to run Unit A per hour?
Answer:0.22
Step-by-step explanation:
Answer:$0.22
Step-by-step explanation:
EDGE
Question 2 options:VOCAB: Use the three terms below to fill in the blanks: (Be careful to spell them correctly!) mean median modeTo find the____________, put all the number in order and find the middle number, or if there are two middle numbers, average them by adding them and dividing by two. To find the ________________, find the number or numbers which appear with the highest frequency in the list. To find the ________________________add all the numbers and then divide by how many numbers there are.
Given:
Mean , median and mode are given.
Median: Put all the number in order and find the middle number, or if there are two middle numbers, average them by adding them and dividing by two.
Mode: The number or numbers which appear with the highest frequency in the list.
Mean: Add all the numbers and then divide by how many numbers there are.
It is a six-digit whole number.
Half of its digits are 2's.
Half of its digits are 1's.
It is divisible by 3.
It is an odd number
It is divisible by 9.
Its digits alternate.
It is greater than 200,000.
Its hundreds digit is less
than 2
Its tens digit is 2.
Please help ASAP!!
Answer:
212121.
Step-by-step explanation:
It is odd number so it ends in 1.
There are 3 2's and 3 1's which alternate.
Diivisible by 3 and 9
It is 212121.
calcula el interés simple sobre un préstamo de 5000 al 9% en 36 meses interés simple = principal X tasa interés X tiempo).
$16,200
1) Coletando los datos
Valor presente: 5,000
rate: 9%
Tiempo: 36 meses
2) Escribindo la formula y despues aplicando los datos, tienemos:
\(\begin{gathered} A=P(1+r\cdot n) \\ A=5000(1+0.09\times36) \\ A=5000(1\text{ +3.24)} \\ A=\text{ 21,200} \\ I=21,200-5000 \\ I=16200 \end{gathered}\)Mira que subtraemos de lo Valor Futuro, el Principal. A -P = i
3) Entonces el interés simple és $16,200
Construct a 90% confidence interval for the population mean you. Assume the population has a normal distribution a sample of 15 randomly selected math majors had mean grade point average 2.86 with a standard deviation of 0.78
The 90% confidence interval is: (2.51, 3.22)
Confidence interval :It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.
We have the following information :
Number of students randomly selected, n = 15.Sample mean, x(bar) = 2.86Sample standard deviation, s = 0.78Degree of confidence, c = 90% or 0.90The level of significance is calculated as:
\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)
The degrees of freedom for the case is:
df = n - 1
df = 15 - 1
df = 14
The 90% confidence interval is calculated as:
=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)
= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 0.3547
= (2.51, 3.22)
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Need help, will be giving points
Answer:
189 in³------------------------------
Volume equation of the pyramid:
V = 1/3 a²h, where a- side of the base, h - height f the pyramidSubstitute values a = 9 in, h = 7 in:
V = 9²*7/3 = 189 in³Answer:
Volume of pyramid = 189 in³
Step-by-step explanation:
Now we have to,
→ find the volume of the pyramid.
Formula we use,
→ Volume = (1/3)a² × h
Then the volume of pyramid is,
→ (1/3)a² × h
→ (1/3) × (9)² × 7
→ (1/3) × 81 × 7
→ (81/3) × 7
→ 27 × 7
→ 189 in³
Hence, the volume is 189 in³.