F(x, y) = (2x - 3y)i + (-3x + 4y - 8)j is a conservative vector field.
Answers
The vector field is conservative and calculates its potential function does not exist as a function f F = ∇f.
To determine whether or not F is a conservative vector field, we need to check if the mixed partial derivatives of its components are equal. The vector field F can be written as F(x,y) = (2x - 3y)i + (-3x + 4y - 8)j.
To compute the mixed partial derivatives, we take the partial derivative of the y-component with respect to x, and the partial derivative of the x-component with respect to y. Doing so, we get:
∂Fy/∂x = -3
∂Fx/∂y = -3
Since these partial derivatives are not equal, we can conclude that F is not a conservative vector field.
Therefore, there does not exist a function f such that F = ∇f.
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Related Questions
Tom reads books that he borrows from the library. After borrowing books for a while, he began recording at the beginning of each month the total number of books he has borrowed so far. The data for the first 5 months he recorded are shown below.
Answers
43 days are required on average to read 5 pages daily.
What will be the number of days?Given that the total number of pages is 300 and Tom has read 85 pages this means he has 300-85=215 pages unread. We are told that if he reads 5 pages per day how many days would he be done with the 215 pages left.
To solve for the number of days left, we have to divide 215 by 5
= 215 / 5
= 43 days
So Tom needs 43 days to read the 215 pages left and return the book to the Library.
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solve the liner equation 3(2x-14)+x=15-(-9x-5)
PLEASE HELP! DO NOT PUT A SILLY AWSER I WILL REPORT YOU!
Answers
Answer:
x= -31
Step-by-step explanation:
Let's solve your equation step-by-step.
3(2x−14)+x=15−(−9x−5)
Step 1: Simplify both sides of the equation.
3(2x−14)+x=15−(−9x−5)
3(2x−14)+x=15+−1(−9x−5)(Distribute the Negative Sign)
3(2x−14)+x=15+−1(−9x)+(−1)(−5)
3(2x−14)+x=15+9x+5
(3)(2x)+(3)(−14)+x=15+9x+5(Distribute)
6x+−42+x=15+9x+5
(6x+x)+(−42)=(9x)+(15+5)(Combine Like Terms)
7x+−42=9x+20
7x−42=9x+20
Step 2: Subtract 9x from both sides.
7x−42−9x=9x+20−9x
−2x−42=20
Step 3: Add 42 to both sides.
−2x−42+42=20+42
−2x=62
Step 4: Divide both sides by -2.
−2x
−2
=
62
−2
x=−31
Answer:
give her brainliest
Step-by-step explanation:
Castel spent half of his weekly allowance playing mini-golf. To earn more money his parents let him clean the gutters for $5.46. What is his weekly allowance if he ended with $12.66? His weekly allowance was $ ______
Answers
Answer:
18.12
Step-by-step explanation:
Not very clear what you mean. I added 5.46 and 12.66.
if 0 subtracted from a number the difference is the
Answers
If 0 is subtracted from any number, then the result is the Number itself.
Example :-
25 - 0 = 2510 - 0 = 101 - 0 = 115 - 0 = 15. Luego de perder en forma sucesiva 1/3 y 2/5 de lo que le iba quedando, Alfredo gana en forma consecutiva sus 3 últimos juegos: 1/2, 1/4 y 1/6 de la cantidad que iba acumulando retirándose con s/. 70. ¿Cuánto tenía al inicio?
Answers
Answer:
Alfredo tenía 80 soles peruanos al inicio.
Step-by-step explanation:
La descripción del problema puede traducirse a las siguientes ecuaciones matemáticas:
Luego de perder en forma sucesiva 1/3 y 2/5 de lo que le iba quedando:
\(y = \left(1 - \frac{1}{3}\right)\cdot x\)
\(z = \left(1 - \frac{2}{5}\right)\cdot y\)
Donde:
\(x\) - Monto inicial, medido en soles peruanos.
\(y\), \(z\) - Montos remanentes después de pérdidas, medidos en soles peruanos.
Se reduce el sistema de ecuaciones:
\(z = \left(1-\frac{2}{5}\right)\cdot \left(1-\frac{1}{3} \right)\cdot x\)
\(z = \frac{2}{5}\cdot x\)
Gana en forma consecutiva sus 3 últimos juegos:
\(u = \left(1+\frac{1}{2} \right)\cdot z\)
\(v = \left(1 + \frac{1}{4} \right)\cdot u\)
\(w = \left(1+\frac{1}{6} \right)\cdot v\)
Donde:
\(z\) - Monto inicial, medido en soles peruanos.
\(u\), \(v\), \(w\) - Montos remanentes después de ganancias, medidos en soles peruanos. (Donde w es el monto final).
Se reduce el sistema de ecuaciones:
\(w = \left(1+\frac{1}{2} \right)\cdot \left(1+\frac{1}{4} \right)\cdot \left(1+\frac{1}{6} \right)\cdot z\)
\(w = \frac{35}{16}\cdot z\)
Si \(w = 70\), el monto inicial es:
\(z = \frac{16}{35}\cdot w\)
\(z = \frac{16}{35} \cdot (70)\)
\(z = 32\)
Ahora,
\(x = \frac{5}{2} \cdot z\)
\(x = \frac{5}{2}\cdot (32)\)
\(x = 80\)
Alfredo tenía 80 soles peruanos al inicio.
Al inicio Alfredo tenía $80.
Determinación de cantidadesDado que, luego de perder en forma sucesiva 1/3 y 2/5 de lo que le iba quedando, Alfredo gana en forma consecutiva en sus 3 últimos juegos 1/2, 1/4 y 1/6 de la cantidad que iba acumulando retirándose con $70, para determinar cuánto tenía al inicio se debe realizar el siguiente cálculo:
((((0.66X) x 0.6) x 1.5) x 1.25) x 1.16 = 70((((0.66X) x 0.6) x 1.5) x 1.25) = 70 / 1.16(((0.66X) x 0.6) x 1.5) = 60 / 1.25(((0.66X) x 0.6) x 1.5) = 60 / 1.25((0.66X) x 0.6) = 48 / 1.50.66X = 32 / 0.6X = 53.333 / 0.66 X = 80Por lo tanto, al inicio Alfredo tenía $80.
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z →z . f(x)=x 3. select the correct description of the function f.
Answers
The correct description of the function f: Z → Z, given by f(x) = x + 3, is "Neither one-to-one nor onto."
To determine if the function f is one-to-one, we need to check if each input value (x) has a unique output value (f(x)). In this case, for any integer x, f(x) = x + 3. Since the value of f(x) depends solely on the input value x, different input values can yield the same output value. For example, f(1) = 4 and f(2) = 5, indicating that the function is not one-to-one.
To determine if the function f is onto, we need to check if every possible output value has a corresponding input value. In this case, since f(x) = x + 3, any integer y can be obtained as an output value by choosing x = y - 3. Therefore, every possible integer output has a corresponding input value, making the function onto.
As a result, the function f: Z → Z, defined by f(x) = x + 3, is neither one-to-one nor onto.
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f:Z→Z.f(x)=x+3f:Z→Z.f(x)=x+3
Select the correct description of the function f.
One-to-one and onto
One-to-one but not onto
Onto but not one-to-one
(rimts) . fat circular plate of 1.25 {~m} diameter is immersed in water such that its greatest and least depths are 1.5 {~m} and 0.6 {~m}, respectively. Determin
Answers
For the flat circular plate of 1.25 {~m} diameter immersed in water,
1. The force exerted on one face by the water pressure is 2708.7032N.
2. The position of the center of pressure is 2.689 m.
We need to determine the force exerted on one face by the water pressure and the position of the center of pressure.
A circular plate of 1.25m diameter is immersed in water such that its greatest and least depths are 1.5m and 0.6m, respectively.
1. The force exerted on one face by the water pressure
Water pressure is given by the formula, P = ρgh
where P = Pressure
ρ = density of the fluid
g = acceleration due to gravity
h = depth of the object submerged
Therefore, the pressure on the circular plate can be given by, P = ρgh
P = (1000)(9.81)(1.5 - 0.6)
P = 8829 N/m²
The force exerted on one face by the water pressure can be given by F = PA
where P = Pressure & A = Area
F = 8829 x (π/4) (0.625²)
F = 2708.7032 N
Therefore, the force exerted on one face by the water pressure is 2708.7032N.
2. The position of the center of pressure
The position of the center of pressure can be determined by the formula, XCP = (I2 / I1) x d
where XCP = position of the center of pressure
I1 = moment of inertia of the area about its centroid
d = depth of the centroid from the surface
I2 = moment of inertia of the area about a horizontal axis passing through the centroid
Therefore, let's calculate I1 and I2
I1 = (π/4) (0.625)⁴
I1 = 0.1198m⁴
I2 = (π/4) (0.625)²
I2 = 0.3068m⁴
d= (greatest depth + least depth)/2
d= (1.5+0.6)/2 = 1.05m
Thus,XCP = (I2 / I1) x d
XCP = (0.3068 / 0.1198) x 1.05
XCP = 2.689m
Therefore, the position of the center of pressure is 2.689 m.
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The given question is incomplete. The complete question is
A flat circular plate of 1.25 m diameter is immersed in water such that its greatest and least depths are 1.5 m and 0.6 m, respectively. Determine
1. The force exerted on one face by the water pressure
2. The position of the center of pressure
Bo is buying a board game that usually costs B dollars. The game is on sale, and the price has been reduced by 18%, percent.Which of the following expressions could represent how much Bo pays for the game? 2 awnsers
Answers
Answer:
\(0.82B\)
or
\(B-0.18B\)
Step-by-step explanation:
When the price has been reduced by 18%, you can either say that the price is 82% of the original price (100-18), or that you've subtracted 18% of the original price from the original price.
Option A. 82% of the original price
Reduction: \(18\%\)
% of original price: \(100\% - 18\% = 82\% = 0.82\)
Since the original price is B, the on-sale price can be expressed as:
\(0.82 * B = 0.82B\)
Option B. Subtracting 18%:
Reduction: 18% of B = \(0.18 * B\)
Original price is B.
Original price minus the reduction:
\(B - 0.18 * B\)
Answer:
what the Dino said
Step-by-step explanation:
b) Arya spins both spinners.
What is the probability that Arya gets blue on both spinners?
Give your answer as a fraction.
b)
+
Submit Answer
Answers
Arya getting blue on both spinners has a 2/16 chance of happening.
What is the probability?A possibility that deals with the occurrence of random occurrences is referred to as probability.
All occurrences must have a chance of occuring at least once, or 1.
P(E) = The proportion of positive outcomes to all outcomes.
Since there are 2 spinners and the total number on them is 8, 8 + 8 equals 16, and the blue one has 1.
we get 1 + 1 = 2.
The likelihood that Arya spins both reels in blue
= desired odds/total odds
=2/16
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2 apples cost 2 dabloons.
How much does 1 apple cost
Answers
Using your formulas, predict what the wavelength will be if we set the wave speed to 150 cm/s.
Answers
wavelength = ?
speed = 150 cm/s
But the question is incomplete, I need the frecuency.
suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. how many customers should the company survey in order to be 95% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
Answers
The company should survey at least 601 customers to be 95% confident that the estimated proportion is within 4 percentage points of the true population proportion.
To determine the sample size needed, we can use the formula:
n = (z^2 * p * (1-p)) / E^2
where:
n is the sample size needed
z is the z-score for the desired confidence level (in this case, 1.96 for 95% confidence)
p is the estimated population proportion (we don't have an estimate, so we'll use 0.5, which gives the largest possible sample size)
E is the maximum margin of error (4 percentage points in this case, or 0.04)
Plugging in the values, we get:
n = (1.96^2 * 0.5 * 0.5) / 0.04^2
n = 600.25
We round up to the nearest whole number to get a sample size of 601.
This means that if the company surveys 601 randomly selected customers and finds that, for example, 60% of them keep up with regular vehicle maintenance, we can be 95% confident that the true proportion of all customers who keep up with regular vehicle maintenance is between 56% and 64%.
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if the highest number in a range is 40 and lowest is 22, an estimate of the standard deviation is 3.
Answers
By using standard deviation, it can be concluded that
The given estimate of standard deviation = 3 is not true
What is Standard Deviation?
At first, it is important to know about variance.
Variance is the sum of the square of deviation from mean divided by the total number of observations. Standard Deviation is the square root of variance.
Highest number = 40 and lowest number = 22
Range = 40 - 22 =18
Standard deviation = \(18 \div 4\)
Standard deviation = 4.5
So the above statement is false
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SOMEONE PLEASE HELP ME I WILL GIVE YOU A GOOD RATE AND MAKE YOU THE BRAINIEST I WILL ALSO GIVE YOU A GREAT REVIEW. PLEASE I AM PRAYING I NEED HELP!!!!!!!!!
Answers
Answer:
-9
Step-by-step explanation:
-18 divided by 3 is -6
(-15)-(-6) is -9
D - Add, Subtract, Multiply, and Divide Integer A submarine Is at a depth of 350 feet below sea level. It makes the following moves. • First, it goes down 150 feet. • Next, it goes up 132 feet. • Then, it goes down 179 feet. • Finally, it goes down 145 feet. Which statement describes its current depth? A It is 692 feet below sea level, because -350 + (-150) + 132 + (-179) + (-145) = -692. B It is 8 feet below sea level, because 350 + (-150) + 132 + (-179) + (-145) = 8. c It is 256 feet below sea level, because 350 + (-150) +..(-132) + (-179) + (-145) = -256. D It is 342 feet below sea level, because 150 132 179 145 = 342. AI B ci D
Answers
We have the next information
A submarine Is at a depth of 350 feet below sea level means -350
First, it goes down 150 feet. means -150
Next, it goes up 132 feet. means +132
Then, it goes down 179 feet. means -179
Finally, it goes down 145 feet means -145
then we have the next operations
-350+(-150)+132+(-179)+(-145)=-692
The sing minus means that It is below the sea level
therefore the correct choice is
A It is 692 feet below sea level, because -350 + (-150) + 132 + (-179) + (-145) = -692.
The wrestling team wants to sell pies for a
fundraiser, The cafeteria helped out by
donating 2 pies. Each pie will be cut into 4
pieces. If the team wants to sell at least 32
pieces, how many pies must the wrestling
team bake ?
Answers
Answer:
6
Step-by-step explanation:
2x4=8
32-8=24
24/4=6
=6
explanation: they already have 2 pies which was 8 slices. 32-8= 24. 24 divided by 4 slices each equals 6.
can someone help me please.
Answers
Answer:
A. 11.18
Step-by-step explanation:
(1, -2) will be x1 and y1.
(-9, 3) will be x2 and y2
The formula is
Distance = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Substitute in all the variables.
\(\sqrt{(-9-1)^2+(3-(-2))^2}\)
Solve.
\(\sqrt{(-10)^2+5^2}\)
\(\sqrt{100+25}\)
\(5\sqrt{5}\)
11.18033988.....
I hope this helps!
pls ❤ and mark brainliest pls!
11.18 units
Step-by-step explanation:
d = distance
d = √((x2 - x1)² + (y2 - y1)²)
Where the first point = (x1, y1)
Where the second point = (x2, y2)
Points: (1, -2) & (-9, 3)
d = √((-9 - 1)² + (3 - -2)²)
d = √((-10)² + (5)²)
d = √((100) + (25))
d = √125
d = 11.18
The distance is 11.18 units
-9d-4p-6-10d+8
pls i need help !!
Answers
thats your answer
combine like terms
Answer:
-19d-4p+2
Step-by-step explanation:
This is very simple, we can rearrange this expression to make it easier to do the properties:
-9d-10d-4p-6+8
Next, we can subtract:
-19d-4p+2
This is the final expression, hope this helped :)
the area A enclosed by a recrangle, in square inches, is a function if the length of its sides x and 5 less than x, when measured in inches. this relation is expressed by the formula:A(x)= x^2-5x for x>0find A(6) and solve A(x)=36
Answers
we have
A(x)= x^2-5x for x>0
find A(6) and solve A(x)=36
Part 1
Find A(6)
that means
The value of A(x) when the value of x=6
For x=6
substitute
A(6)= 6^2-5(6)
A(6)=36-30
A(6)=6 in^2
Part 2
A(x)=36
Solve for x
substitute
A(x)= x^2-5x
36= x^2-5x
x^2-5x-36=0
Solve using the quadratic formula
we have
a=1
b=-5
c=-36
substitute
\(x=\frac{5\pm\sqrt[]{-5^2-4(1)(-36)}}{2}\)\(\begin{gathered} x=\frac{5\pm\sqrt[]{169}}{2} \\ \\ x=\frac{5\pm13}{2} \end{gathered}\)therefore
the solutions for x are
x=9 and x=-4
the solution is x=9 in (because the value of x can not be negative)
1. Describe the characteristics of the normal curve. (2 points) a. SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100. We can treat these values as population values, u = 500 and o = 100. Use these values to solve the following problems: o b. For a student with a math SAT-Math score of 590, convert their SAT score to a z score. (2 points) C. What percentage of students would have a SAT-Math score greater than 590? (2 points) d. What percent of students would be expected to have a SAT-Math score between 450 and 550? (2 points) e. What is the probability of having a SAT-Math score less than 540? (2 points)
Answers
Normal CurveThe normal curve is a bell-shaped curve that is symmetrical, and the curve's mean, median, and mode all are equal and located at the center. It is also called the Gaussian curve after the mathematician Carl Friedrich Gauss. Normal distribution is a common statistical analysis technique used to model various phenomena in probability theory, physics, finance, and social science. It can be characterized by its mean and standard deviation.MeanMean is the arithmetic average of the numbers in a dataset. To find the mean, sum all the numbers in the dataset and then divide by the total number of values in the dataset. For the given problem, the mean is 500.Standard DeviationThe standard deviation is a measure of the spread of data from its mean. It measures how far the data values are from their mean. For the given problem, the standard deviation is 100.(b)Convert SAT-Math score of a student with 590 to z-score.z-score = (score - mean) / standard deviationz-score = (590 - 500) / 100 = 0.9(C)What percentage of students would have a SAT-Math score greater than 590?The formula for calculating the percentage of students with a SAT-Math score greater than 590 is:P(Z > 0.9) = 1 - P(Z ≤ 0.9)From the normal distribution table, the area to the left of 0.9 is 0.8159, and the area to the right of 0.9 is 1 - 0.8159 = 0.1841. Therefore, the percentage of students with a SAT-Math score greater than 590 is 18.41%.(d)What percent of students would be expected to have a SAT-Math score between 450 and 550?We can calculate the z-scores for each of the scores using the formula,z-score = (score - mean) / standard deviationz-score for 450 = (450 - 500) / 100 = -0.5z-score for 550 = (550 - 500) / 100 = 0.5From the normal distribution table, the area to the left of -0.5 is 0.3085, and the area to the left of 0.5 is 0.6915. The area between these two values is 0.6915 - 0.3085 = 0.3830, which is 38.3%.(e)What is the probability of having a SAT-Math score less than 540?The formula for calculating the probability of having a SAT-Math score less than 540 is:P(Z < (540 - 500) / 100)From the normal distribution table, the area to the left of 0.4 is 0.6554. Therefore, the probability of having a SAT-Math score less than 540 is 0.6554 or 65.54%.
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1. Characteristics of normal curve: The normal curve is a type of probability distribution.
Some of the characteristics of the normal curve are:
It is a bell-shaped curve, symmetrical and unimodal with a single peak in the center of the curve.It is characterized by a mean, median, and mode that are all equal.It is asymptotic, meaning that the tails of the curve extend to infinity without ever touching the x-axis.
2. Conversion of SAT score to z-score:
Formula to find z-score is: z = (x - μ) / σ
where z = z-score, x = raw score, μ = mean and σ = standard deviation
So, for a student with a math SAT-Math score of 590, the z-score would be:
z = (590 - 500) / 100z = 0.9
Therefore, the z-score for a student with a math SAT-Math score of 590 is 0.9.3.
Percentage of students with SAT-Math score greater than 590:
To find the percentage of students who would have a SAT-Math score greater than 590, we need to find the area under the normal curve to the right of the z-score corresponding to 590.
Using a standard normal table, we find that the area to the right of a z-score of 0.9 is 0.1841 or 18.41%.
Therefore, approximately 18.41% of students would have a SAT-Math score greater than 590.
4. Percentage of students with SAT-Math score between 450 and 550:
To find the percentage of students who would be expected to have a SAT-Math score between 450 and 550, we need to find the area under the normal curve between the z-scores corresponding to 450 and 550.
Using a standard normal table, we find that the area to the left of a z-score of -0.5 is 0.3085, and the area to the left of a z-score of 0.5 is 0.6915.
Therefore, the area between -0.5 and 0.5 is:
0.6915 - 0.3085 = 0.3830 or 38.30%
Therefore, approximately 38.30% of students would be expected to have a SAT-Math score between 450 and 550.5.
Probability of having a SAT-Math score less than 540:
To find the probability of having a SAT-Math score less than 540, we need to find the area under the normal curve to the left of the z-score corresponding to 540.
Using a standard normal table, we find that the area to the left of a z-score of 0.4 is 0.6554.Therefore, the probability of having a SAT-Math score less than 540 is approximately 65.54%.
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help me pleaseeee
it’s algebra 2
Answers
(Solving for the missing variable)
Answer: yes
b.
c.
Solve the formula for b.
Use the new formula to find the
base of the triangle.
A = 36 mm²
h = 6 mm
b=1/2 by
Answers
Answer:
b = 12mm
Step-by-step explanation:
Area of Triangle: (base x height)/2
A = 36
h = 6mm
A = (bh)/2
2A = bh
b = 2A/h
b = (2 x 36)/6
b = 12
a large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. a sample of 10 employees was selected and the following data were collected. If required, enter negative values as negative numbers. a. Select a scatterlingram for these data
Answers
A study conducted by a large city hospital aimed to examine the connection between the distance employees travel to work and the number of unauthorized days they are absent. Data was collected from a sample of 10 employees.
To analyze the relationship between the distance traveled to work and the number of unauthorized absences, a scattergram can be used. A scattergram, also known as a scatter plot, is a graphical representation that displays the relationship between two variables. In this case, the distance (in miles) traveled to work would be plotted on the x-axis, while the number of unauthorized absences per year would be plotted on the y-axis. Each data point representing an employee's distance and corresponding number of unauthorized absences would be plotted on the scattergram. By examining the resulting scattergram, it would be possible to observe any patterns or trends in the data, such as whether there is a positive or negative correlation between the distance traveled and the number of unauthorized absences.
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Given the following uniform continuous probability distribution, solve for the height, h. Uniform Continuous Probability Distribution f(x) ht PluSxsw) = V =4 w = 7 Range of Outcomes O (a) 1 O (b) 1/3 O (c) 1/6 O (d) 1/9
Answers
The value of height h is 1/3. Therefore, option (b) is correct.
To solve for the height, h, we need to use the formula for a uniform continuous probability distribution:
f(x) = 1/w for a ≤ x ≤ b
where a is the lower limit of the range of outcomes, b is the upper limit of the range of outcomes, and w is the width of the range of outcomes (b - a).
From the given information, we have:
a = 4
b = 7
w = 3
Substituting these values into the formula, we get:
f(x) = 1/3 for 4 ≤ x ≤ 7.
To find the height, h, we need to find the maximum value of f(x), which occurs at the midpoint of the range of outcomes:
midpoint = (a + b)/2 = (4 + 7)/2 = 5.5
So, we need to evaluate f(5.5):
f(5.5) = 1/3
Therefore, the height, h, is equal to 1/3 which corresponds to option (b).
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On a coordinate plane, triangle R S T has points (negative 5, 6), (3, 4), and (negative 2, 2). Which expression can be used to find the area of triangle RST? (8 â™ 4) - One-half (10 12 16) (8 â™ 4) - (10 12 16) (8 â™ 4) - One-half (5 6 8) (8 â™ 4) - (5 - 6 - 8).
Answers
The area of a triangle is the amount of space on the triangle
The expression that represents the area of the triangle is \(A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|\)
The coordinates of the triangle are given as:
\(R = (-5,6)\)
\(S = (3,4)\)
\(T = (-2,2)\)
The area (A) of a triangle from its coordinates or vertices are:
\(A = \frac 12|x_1(y_3 -y_2) +x_2(y_3 -y_1) + x_3(y_2 -y_1)|\)
Substitute values for x's and y's
\(A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|\)
Hence, the expression that represents the area of the triangle is \(A = \frac 12|-5(2 -4) +3(2 -6) -2(4 -6)|\)
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2 Points
What is the vertex of the graph of this equation y=-4x2 - 16x - 12?
O A. (-2,-4)
O B. (2, 4)
O C. (2, -4)
D. (-2,4)
Help need this solved fast
Answers
Answer:
D
Step-by-step explanation:
Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
\(x_{vertex}\) = - \(\frac{b}{2a}\)
y = - 4x² - 16x - 12 ← is in standard form
with a = - 4 and b = - 16 , thus
\(x_{vertex}\) = - \(\frac{-16}{-8}\) = - 2
Substitute x = - 2 into y for corresponding y- coordinate
y = - 4(- 2)² - 16(- 2) - 12 = - 16 + 32 - 12 = 4
vertex = (- 2, 4 ) → D
I NEED HELP FAST!!
What is the best estimate for this sum?
1/8+1/6
A. The sum will be close to 1/4.
B. The sum will be close to 1/2.
C. The sum will be close to 1.
Answers
Explanation keep 1 the same and half 8 1/4 sorry if I’m wrong
Explain why 2 is NOT a solution of x 7 5
Answers
Based on the information provided, 2 is not a solution of x>5 because a possible solution requires a number greater than 5.
How to solve inequality?Inequalities include symbols such as >, ≤, ≥, among others that should be interpreted correctly to solve the inequality. In this case, the symbol in the inequality is >, which means greater than. Based on this, the value of x should be greater than 5, for example, 7, 19, 2948, etc.
Therefore, 2 is not a solution to the inequality x>5 because a number greater than 5 rather than less than 5 is required to solve this expression.
Note: This question is incorrect and incomplete; here is the complete question:
Explain why 2 is NOT a solution of x>5
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Now look at this information
\(2y + 3 \leqslant 11\)
What is the largest value that y could be?
Answers
Answer:
4
Step-by-step explanation:
Given
2y + 3 ≤ 11 ( subtract 3 from both sides )
2y ≤ 8 ( divide both sides by 2 )
y ≤ 4
Since y has to be less than or equal to 4
Then the largest value y could be is 4
Franklin high school wanted to see if more boys than girls participate in school sports. A random survey of high school students was conducted, and the results are shown below. Number of students. if a student is chosen at random from those who participated in the survey, what is the probability that the student is a female or does not participate in school sports.answer choices:0.390.640.781.00
Answers
Answer:
1.00
Explanation:
We have the following information:
Number of females = 100 + 110 = 210
Number of students that do not participate = 180 + 110 = 290
Total number of students = 500
The probability that the student is a female or does not participate in school sports:
\(\begin{gathered} P=\frac{P_{female}}{Total}+\frac{P_{no\text{ participate}}}{Total} \\ P=\frac{210}{500}+\frac{290}{500} \\ P=\frac{290+210}{500} \\ P=\frac{500}{500} \\ P=1.00 \\ \\ \therefore P=1.00 \end{gathered}\)Therefore, the answer is 1.00