Please guys i really need your help for this question

The solutions for the given system of equations are:

(x, y) = (2√3, 1/(2√3)) and (x, y) = (-2√3, -1/(2√3)).

(a) The given system of equations is:

\(2y + x^2 = 1\)...(1)

\(y^2 = 6ac\)...(2)

To find the solutions for this system, we need to solve equations (1) and (2) simultaneously.

From equation (2), we can see that \(y^2 = 6ac\)., which implies y = ±√(6ac).

Substituting this value of y into equation (1), we get:

2(±√(6ac)) + \(x^2\) = 1

Solving for x, we get two possible solutions:

Case 1: y = √(6ac)

2√(6ac) + \(x^2\)     = 1

\(x^2\) = 1 - 2√(6ac)

x = ±√(1 - 2√(6ac))

So one solution is (x, y) = (√(1 - 2√(6ac)), √(6ac)).

Case 2: y = -√(6ac)

2(-√(6ac)) + \(x^2\)  = 1

\(x^2\) = 1 + 2√(6ac)

x = ±√(1 + 2√(6ac))

So another solution is (x, y) = (√(1 + 2√(6ac)), -√(6ac)).

Therefore, the solutions for the given system of equations are:

(x, y) = (√(1 - 2√(6ac)), √(6ac)) and (x, y) = (√(1 + 2√(6ac)), -√(6ac)).

(b) The given system of equations is:

1 = 2λα

2 = 2xy

3 = 2λx^2 + \(y^2 + x^2\)= 14

To find the solutions for this system, we need to solve equations (1), (2), and (3) simultaneously.

From equation (1), we can see that 2λα = 1, which implies λα = 1/2.

Substituting this value of λα into equation (3), we get:

2(1/2) +  \(y^2 + x^2\) = 14

\(y^2 + x^2\)= 13

Now, from equation (2), we have 2 = 2xy, which implies xy = 1.

We can substitute xy = 1 into the equation  \(y^2 + x^2\)= 13 to get:

1 +  \(y^2 + x^2\) = 13

x^2  = 12

x = ±√12

x = ±2√3

Substituting these values of x back into xy = 1, we get the corresponding values of y:

For x = 2√3, y = 1/(2√3)

For x = -2√3, y = -1/(2√3)

So the solutions for the given system of equations are:

(x, y) = (2√3, 1/(2√3)) and (x, y) = (-2√3, -1/(2√3)).

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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\(Hiya!\)

The answer is....

Hopefully, this helps you!!

\(Sokka\)

Answer:

I hope it helps you :)

Step-by-step explanation:

y isn't directly proportional with x because the graph doesn't cross O the origin, it starts from a y-intercept wich is not a property for proportional portions

Answer:

X Intercept is 3,0 and y intercept is 0, 5/2

Step-by-step explanation:

the 5/2 Is a Fraction

1. 288 tons of oats can be stored in the silo.

2. 432 tons of barley can be stored in the silo.

3. 540 tons of wheat can be stored in the silo.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A storage silo for grain can house 18,000 bushels of grain.

1. One bushel of oats weighs 32 pounds which is equal to 32/2000 tons.

= 0.016 tons.

Therefore, The number of tons of oats that can be stored is,

= 0.016×18000.

= 288 tons.

2. One bushel of barley weighs 48 pounds or 48/2000 = 0.024 tons.

Therefore, The number of tons of barley that can be stored is,

= 0.024×18000.

= 432 tons.

3. One bushel of wheat weighs 60 pounds or 60/2000 tons = 0.03 tons.

Therefore, The number of tons of wheat that can be stored is,

= 0.03×18000.

= 540 tons.

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Answer:

The arc length of a sector:

\(A = \frac{9}{10} \pi\)

Step-by-step explanation:

-The equation for finding the Arc length, would be:

\(Arc length = \frac{a}{360\textdegree} 2\pi r\)

-Use the given radius and the central angle for the equation:

\(A = \frac{18\textdegree}{360\textdegree} 2\pi (9)\)

-Then, solve the equation:

\(A = \frac{18\textdegree}{360\textdegree} \times 2\pi \times 9\)

\(A = \frac{1}{20} \times 2\pi \times 9\)

\(A = \frac{2}{20}\pi \times 9\)

\(A = \frac{1}{10}\pi \times 9\)

\(A = \frac{9}{10}\pi\)

So, the arc length of a sector is \(\frac{9}{10} \pi\) .

Answer:

The Answer is A

Step-by-step explanation:

Answer:

x = 1°

Step-by-step explanation:

Bisection means splitting the angle in to 2

So that means 4x-1 = 2x+1

4x-1 = 2x +1

4x = 2x + 2

2x = 2

x = 1°

If my answer is incorrect, pls correct me!

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-Chetan K

The measures of position that divide a set of data into four equal parts are called quartiles.

Quartiles are statistical measures that divide a dataset into four equal parts, each containing approximately 25% of the data. These quartiles are denoted as Q1, Q2, and Q3.

Q1, also known as the first quartile or the 25th percentile, represents the value below which 25% of the data falls. It splits the lowest 25% of the dataset from the rest.

Q2, also known as the second quartile or the 50th percentile, is the median of the dataset. It represents the value below which 50% of the data falls, dividing the dataset into two equal parts.

Q3, also known as the third quartile or the 75th percentile, represents the value below which 75% of the data falls. It separates the highest 25% of the dataset from the rest.

These quartiles are useful in analyzing the distribution and dispersion of data, providing insights into the spread and central tendency.

They are commonly used in box plots, where the box represents the interquartile range (IQR), which is the range between Q1 and Q3, while the line inside the box represents the median (Q2).

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In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.

We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.

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The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.

Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.

The PMF of x is given by the binomial probability formula:

P(x) = (n C x) * p^x * (1 - p)^(n - x)

where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).

In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).

Let's calculate the PMF for x:

P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004

P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588

P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432

P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192

The PMF for x is:

P(x = 0) = 0.0004

P(x = 1) = 0.0588

P(x = 2) = 0.3432

P(x = 3) = 0.941192

To calculate the CMF, we sum up the probabilities up to x:

F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)

Using the calculated probabilities, the CMF for x is:

F(x = 0) = 0.0004

F(x = 1) = 0.0592

F(x = 2) = 0.4024

F(x = 3) = 1.0

Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

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Answer:

The range is -7 ≤ y ≤ 8

Step-by-step explanation:

The range is the full measurement of a graph on the y-axis.

I know this can be confusing at times as I had struggles with this in the past

Hopefully, this helps!

Answer:6 feet

Step-by-step explanation:area = PI x r^2

28.26 = 3.14 x r^2

r^2 = 28.26 / 3.14

r^2 = 9

r = sqrt(9)

r = 3

diameter = 2r = 2(3) = 6 feet

Answer:

Answer down below!

Step-by-step explanation:

Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)

The point that we will use is (2,2)

So, starting from there we use rise/run to get our answer

We go up 1 and over -2

So, our slope will be (since we cannot simply it...)

-1/2

Hello!

To find the slope:

 ==> need to pick two points on the line

   (x₁, y₁): (0,3)

   (x₂,y₂): (4,1)

   \(Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}\)    <== Answer

Hope that helps!

Answer:

26 minutes

Step-by-step explanation:

620-230=390

390/15=26

hope this helped, have a nice day!!

Answer:

240

Step-by-step explanation:

Answer:

p = 0.70z

Step-by-step explanation:

p is the food the penguins eat

z is the food the zebras eat

We are told that:  p < z

Then we are told that:  p = 70% of z

This can be written as p = 0.70z

An alternative way this can be written is:  p/z = 0.70  [The ratio of p to z is 0.7]

Answer:

Some of the statement is false.

Step-by-step explanation:

84 driveways / 7 days = 12 driveways per day.

12 driveways x 12 days = 144 driveways

Answer:

Step-by-step explanation:

use ratio and proportion:

5 miles  =    x miles

8 km            22.3 km

8(x) = 22.3 (5)

x = 111.5 / 8

x = 13.94 miles

Answer:

-30

Step-by-step explanation:

-5/2 × 12

= -5/2 x 12/1

= (-5 × 12)/(2 × 1)

= -60/2

= -30

Answer:

-30 if this equation is multiplication!

Step-by-step explanation:

-5/2 times 12 (OG equation)

-5/2 times 12/1 (Convert)

-5 times 12/ 2.1 (Fraction Rule)

-5 times 12/2 (Multiply)

-5 times 6 (divide 12 by 2)

-30 (Simplify)

Have a great day! :D

The answer is 067.

It takes an even number of steps for the object to reach (2,2), so the number of steps the object may have taken is either 4 or 6 .

If the object took 4 steps, then it must have gone two steps \($\mathrm{N}$\) and two steps E, in some permutation. There are \($\frac{4 !}{2 ! 2 !}=6$\) ways for these four steps of occuring, and the probability is \($\frac{6}{4^{4}}$\).

If the object took 6 steps, then it must have gone two steps N and two steps E, and an additional pair of moves that would cancel out, either N / S or W/E. The sequences N, N, N, E, E, S can be permuted in \($\frac{6 !}{3 ! 2 ! 1 !}=60$\) ways. However, if the first four steps of the sequence are N, N, E, E in some permutation, it would have already reached the point (2,2) in four moves. There are \($\frac{4 !}{2 ! 2 !}$\) ways to order those four steps and \($2 !$\) ways to determine the order of the remaining two steps, for a total of 12 sequences that we have to exclude. This gives \($60-12=48$\) sequences of steps. There are the same number of sequences for the steps N, N, E, E, E, W, so the probability here is \($\frac{2 \times 48}{4^{6}}$\).

The total probability is \($\frac{6}{4^{4}}+\frac{96}{4^{6}}=\frac{3}{64}$\), and \($m+n=067$\).

What is probability?

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The solution to the given integral is: frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

Given integral: int_0^1 (1-t^2)g(x) dt

To solve the given integral, we will make use of Beta function.

The Beta function is defined as follows:

B(p,q) = int_0^1 t^{p-1}(1-t)^{q-1} dt

Using substitution, t = sin theta, we get:

int_0^1 (1-t^2)g(x) dt = int_0^{frac{pi}{2}} (1-sin^2 theta)g(x) cos theta dtheta

= int_0^{frac{\pi}{2}} cos^2 theta g(x) d\theta

= frac{1}{2}\int_0^{\frac{\pi}{2}} (1+\cos 2\theta) g(x) d\theta

= frac{1}{2} \left(\int_0^{\frac{\pi}{2}} g(x) dtheta + int_0^{frac{pi}{2}} g(x) cos 2theta dtheta right)

Using B(p,q)$ for the second integral, we get:

int_0^1 (1-t^2)g(x) dt = frac{1}{2}left(frac{pi}{2}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x) right)

= frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

Hence, the value of the given integral int_0^1 (1-t^2)g(x) dt is frac{pi}{4}g(x) + frac{1}{2}cdot frac{Gamma(frac{3}{2})Gamma(frac{1}{2})}{Gamma(2)} cdot g(x).

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Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides, converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

We know,

Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Converse of Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle

Hence, Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides, converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

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Answer:

Step-by-step explanation:

Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides, converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangleA biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.We know, Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.Converse of Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangleHence, Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides, converse of the Pythagorean theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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Answer:

160

Step-by-step explanation:

If 1/4 of the number is 40, then the number will be 160

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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The statement that is not true concerning PivotTables in Excel is b. PivotTables summarize data for two variables. PivotTables can summarize data for multiple variables, not just two.

PivotTables allow you to analyze and summarize data from various perspectives, including multiple variables, by grouping, filtering, and calculating values based on different criteria. They provide flexibility in summarizing and organizing data in a tabular format, making it easier to extract insights and perform data analysis efficiently.

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