System of equations- does this have one solution, many solutions or no solution
y=4x-12
y=-12+4x

Answer:

Equilateral triangle means all sides have equal length.

Perimeter

As a sum: (x-4.5)+(x-4.5)+(x-4.5)

As a product: 3 * (x-4.5)

They are equivalent because 3 times a number is just the sum of three of the number.

Step-by-step explanation:

The velocity with which a ball reaches the ground when it is dropped

from a height of 64 m is 35.44m/sec

From the information given, we have that the equation representing the velocity of the ball is expressed as;

V = 4.43√h

Given that the parameters of the formula are;

Since the height of the ball from the ground is 64m, we have to substitute the value, we have;

V = 4.43√64

Find the square root of the value

V= 4.43(8)

Now, multiply both the values to determine the velocity, we get;

V = 35.44m/sec

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The probability that a 34 square foot metal sheet has at least 9 defects is 0.4308, rounded to four decimals.

Given that the sheet metal has an average of 7 defects per 20 square feet, we can find the rate parameter (λ) of the Poisson distribution as follows:

λ = (7 defects / 20 sq ft) = 0.35 defects per square foot

Let X be the number of defects in a 34 square foot metal sheet. Since X follows a Poisson distribution with rate parameter λ, we can find the probability that X is at least 9 defects using the cumulative distribution function (CDF) of the Poisson distribution:

P(X ≥ 9) = 1 - P(X < 9) = 1 - F(8)

where F(k) is the CDF of the Poisson distribution with rate parameter λ evaluated at k.

Using the Poisson distribution formula for F(k), we have:

F(k) = P(X ≤ k) = ∑(i=0 to k) [(λ^i * e^(-λ)) / i!]

Using a calculator or software, we can find that:

F(8) = P(X ≤ 8) = 0.5692

Therefore, we have:

P(X ≥ 9) = 1 - F(8) = 1 - 0.5692 = 0.4308

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Presumably you're talking about a geometrical interpretation of the identity,

(a + b + c)² = a ² + b ² + c ² + 2 (ab + ac + bc)

See the attached sketch for a visual "proof" of it.

A random sample of 16 statistics examinations from a large population was taken. The test statistic (t) for this hypothesis test is 1.8.

To determine whether the average grade of the population is significantly more than 75, we can perform a hypothesis test using the given sample data. We'll set up the null and alternative hypotheses as follows:

Null Hypothesis (H 0): The average grade of the population is not significantly more than 75.

Alternative Hypothesis (Ha): The average grade of the population is significantly more than 75.

To conduct the hypothesis test, we can use the t-test since the population variance is unknown. Here, we'll assume the sample is representative and the Central Limit Theorem applies.

To calculate the test statistic for this hypothesis test, we will use the t-distribution since the population standard deviation is unknown. The formula for the t-test statistic is as follows:

t = (sample mean - hypothesized mean) / (sample standard deviation / √(sample size))

Given the information:

Sample mean (x) = 78.6

Hypothesized mean (μ) = 75

Sample standard deviation (s) = √(variance) = √(64) = 8

Sample size (n) = 16

Let's calculate the test statistic using the formula:

t = (78.6 - 75) / (8 / √(16))

t = 3.6 / (8 / 4)

t = 3.6 / 2

t = 1.8

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Complete Question:

A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.

How do you get the test statistic?

Answer: Jas is 9, and Sandeep is 11.

Step-by-step explanation: 9 + 11 = 20

Answer:

To find increase/decrease, divide the starting number by the ending number.

40 to 20

20 ÷ 40 = 0.5

0.5 can be represented by 50%.

20 to 40

40 ÷ 20 = 2

2 can be represented by 200%. This is why decreasing 40 to 20 is a 200% increase. In the wording, it says it's a 100% increase. That would be 20 plus 20 times 1 (which is the same as 100%) which is 40.

Answer: It's A I hope this helps!

Step-by-step explanation:

Answer:

y= 1/2x-5

Step-by-step explanation:

Slope intercept equation: y = mx + b

1) find the slope

A (16, 3)   B (12,1)

slope = 1/2

2) find b

- we know the slope is 1/2, so...

y = 1/2x+b

substitute the x and y values:

1=1/2(12) + b

1=6+b

b= -5

so, our slope intercept equation is

y = 1/2x - 5

The cosine of ZT is (√59)/√69.

To find the cosine of ZT, we need to know the values of the adjacent and hypotenuse sides of the right triangle containing angle ZT.

From the given terms, we can see that side TU is the hypotenuse, and side US is the adjacent side. We need to find the length of these sides to determine the cosine of angle ZT.

Using the Pythagorean theorem, we can find the length of side TU:
TU² = TS² + US²
TU² = (√10)² + (√59)²
TU² = 10 + 59
TU² = 69
TU = √69

Now, we can use the definition of cosine to find the value of cos(ZT):
cos(ZT) = adjacent/hypotenuse
cos(ZT) = US/TU
cos(ZT) = (√59)/√69

Therefore, the cosine of ZT is (√59)/√69.

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Answer:

(1, 2), (3, 4), (5, 2)

Step-by-step explanation:

To find the vertices of the triangle given the midpoints of its sides, we can use the midpoint formula:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)

Let the vertices of the triangle be:

Let the midpoints of the sides of the triangle be:

Since D is the midpoint of AB:

\(\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)=(2,3)\)

\(\implies \dfrac{x_B+x_A}{2}=2 \qquad\textsf{and}\qquad \dfrac{y_B+y_A}{2}\right)=3\)

\(\implies x_B+x_A=4\qquad\textsf{and}\qquad y_B+y_A=6\)

Since E is the midpoint of BC:

\(\left(\dfrac{x_C+x_B}{2},\dfrac{y_C+y_B}{2}\right)=(4,3)\)

\(\implies \dfrac{x_C+x_B}{2}=4 \qquad\textsf{and}\qquad \dfrac{y_C+y_B}{2}\right)=3\)

\(\implies x_C+x_B=8\qquad\textsf{and}\qquad y_C+y_B=6\)

Since F is the midpoint of AC:

\(\left(\dfrac{x_C+x_A}{2},\dfrac{y_C+y_A}{2}\right)=(3,2)\)

\(\implies \dfrac{x_C+x_A}{2}=3 \qquad\textsf{and}\qquad \dfrac{y_C+y_A}{2}\right)=2\)

\(\implies x_C+x_A=6\qquad\textsf{and}\qquad y_C+y_A=4\)

Add the x-value sums together:

\(x_B+x_A+x_C+x_B+x_C+x_A=4+8+6\)

\(2x_A+2x_B+2x_C=18\)

\(x_A+x_B+x_C=9\)

Substitute the x-coordinate sums found using the midpoint formula into the sum equation, and solve for the x-coordinates of the vertices:

\(\textsf{As \;$x_B+x_A=4$, then:}\)

\(x_C+4=9\implies x_C=5\)

\(\textsf{As \;$x_C+x_B=8$, then:}\)

\(x_A+8=9 \implies x_A=1\)

\(\textsf{As \;$x_C+x_A=6$, then:}\)

\(x_B+6=9\implies x_B=3\)

Add the y-value sums together:

\(y_B+y_A+y_C+y_B+y_C+y_A=6+6+4\)

\(2y_A+2y_B+2y_C=16\)

\(y_A+y_B+y_C=8\)

Substitute the y-coordinate sums found using the midpoint formula into the sum equation, and solve for the y-coordinates of the vertices:

\(\textsf{As \;$y_B+y_A=6$, then:}\)

\(y_C+6=8\implies y_C=2\)

\(\textsf{As \;$y_C+y_B=6$, then:}\)

\(y_A+6=8 \implies y_A=2\)

\(\textsf{As \;$y_C+y_A=4$, then:}\)

\(y_B+4=8\implies y_B=4\)

Therefore, the coordinates of the vertices A, B and C are:

Answer:

238m^3

Step-by-step explanation:

Volume = lwh (length times width times height)

so do 4 x 7 x 8 1/2

this gets you 238m^3 (because you have to cube your answer with units)

The value of y that optimizes the function is y = 3/2. The Lagrange Multiplier in this case is -105/8.

To optimize the function \(f(x, y) = -4x^2 + 4xy - 2y^2 + 6x + 8y\) subject to the constraint xy ≤ 15, we can use the method of Lagrange multipliers.

The Lagrangian function is defined as:

L(x, y, λ) = f(x, y) - λ(g(x, y) - 15)

where g(x, y) = xy is the constraint equation.

To find the optimal value of y, we need to solve the following system of equations:

∂L/∂x = -8x + 4y + 6 - λy = 0 (1)

∂L/∂y = 4x - 4y + 8 - λx = 0 (2)

g(x, y) - 15 = xy - 15 = 0 (3)

From equation (1), we can rearrange it as:

-8x + 4y - λy = -6 (4)

From equation (2), we can rearrange it as:

4x - 4y - λx = -8 (5)

To solve this system of equations, we can eliminate λ by multiplying equation (4) by x and equation (5) by y, and then subtracting the resulting equations:

\(-8x^2 + 4xy - λxy = -6x (6)\\4xy - 4y^2 - λxy = -8y (7)\)

Subtracting equation (7) from equation (6), we get:

\(-8x^2 + 4xy - 4y^2 = -6x + 8y\)

Simplifying this equation gives:

\(-8x^2 - 4y^2 + 4xy = -6x + 8y\)

Rearranging terms, we have:

\(-8x^2 + 4xy + 6x - 4y^2 - 8y = 0\)

Factoring, we get:

(2x - y)(-4x - 2y + 6) = 0

Setting each factor equal to zero gives:

2x - y = 0 (8)

-4x - 2y + 6 = 0 (9)

From equation (8), we can solve for y:

y = 2x (10)

Substituting equation (10) into equation (9), we get:

-4x - 4x + 6 = 0

Simplifying, we have:

-8x + 6 = 0

Solving for x, we find:

x = 3/4

Substituting this value of x into equation (10), we can find y:

y = 2 * (3/4) = 3/2

Therefore, the value of y that optimizes the function is y = 3/2.

To find the Lagrange Multiplier, we substitute the optimal values of x and y into the constraint equation (3):

xy - 15 = (3/4) * (3/2) - 15 = 9/8 - 15 = -105/8

Hence, the Lagrange Multiplier is -105/8.

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Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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Length of the golf club where Bruce plays = 7,040 yards

Solution:

1. Let's convert 7,040 yards to miles:

1 yard = 0.000568182 mile

Now, we can use Direct Rule of Three, as follows:

Yards Miles

1 0.000568182

7,040 x

2. Solve for x:

1 * x = 0.000568182 * 7,040

x = 4 miles

Step-by-step explanation:

We can also simply calculate the total number of possible outcomes of 3 coin flips, meaning the overall probability of exactly 2 coin flips out of 3 being tails is 37.5%.

The inequality that is represented by the given graph is; y ≤ (3/4)x - 2

From the given inequality graph, we see that;

Slope; m = 3/4

x-intercept = -2.5

y-intercept = -2

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, our graph is ordinarily;

y = (3/4)x + (-2)

y =  (3/4)x - 2

However, it is an inequality that is shaded at the bottom with a thick line and so the inequality becomes;

y ≤ (3/4)x - 2

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To begin with, let's recall the definition of a one-to-one function. A function f: A → B is one-to-one if every element in A is mapped to a unique element in B. In other words, no two distinct elements in A are mapped to the same element in B.
Now, let's assume that f is one-to-one and even. This means that f(-x) = f(x) for all x in R. To prove that f cannot be both one-to-one and even, we will use a proof by contradiction. Suppose f is both one-to-one and even. Then, for any x and y in R, if f(x) = f(y), we must have x = y. Now, let's consider the case when x and y are negative numbers such that x ≠ y. Since f is even, we have f(-x) = f(x) and f(-y) = f(y). However, since f is one-to-one, we cannot have f(-x) = f(-y) because x and y are distinct.Therefore, f cannot be both one-to-one and even. Alternatively, we could use the contrapositive of the statement. The contrapositive of "f one-to-one => f not even" is "f even => f not one-to-one". This means that if f is even, then it cannot be one-to-one. This is true because, as we showed earlier, if f is even, there exist distinct negative numbers that are mapped to the same value, which violates the one-to-one property. In conclusion, we have shown that if a function f is one-to-one, then it cannot be even, using either a proof by contradiction or the contrapositive of the statement.

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(a) Using a first-order method, we can approximate f"(1) as:

f"(1) ≈ [f(x-2h) - 2f(x) + f(x+3h)] / (5\(h^2\))

(b) The exact value of f"(1) is -1, so the approximation error for each of the above calculations is:

Error = |1.6 - (-1)| ≈ 2.6

(a) Using a first-order method, we can approximate f"(1) as:

f"(1) ≈ [f(x-2h) - 2f(x) + f(x+3h)] / (5\(h^2\))

(b) Using the three-point centered difference formula for the second derivative, we have:

f"(x) ≈ [f(x-h) - 2f(x) + f(x+h)] / \(h^2\)

For f(x) = 1-5 and x = 1, we have:

f(0.9) = 1-4.97 = -3.97

f(1) = 1-5 = -4

f(1.1) = 1-5.03 = -4.03

For h = 0.1, we have:

f"(1) ≈ [-3.97 - 2(-4) + (-4.03)] / (\(0.1^2\)) ≈ 1.6

For h = 0.01, we have:

f"(1) ≈ [-3.997 - 2(-4) + (-4.003)] / (\(0.01^2\)) ≈ 1.6

For h = 0.001, we have:

f"(1) ≈ [-3.9997 - 2(-4) + (-4.0003)] / (0.00\(1^2\)) ≈ 1.6

The exact value of f"(1) is -1, so the approximation error for each of the above calculations is:

Error = |1.6 - (-1)| ≈ 2.6

Therefore, the first-order method and three-point centered difference formula provide an approximation to f"(1), but the approximation error is relatively large.

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we are asked to develop a first-order method for approximating the second derivative of a function f(1), using data points f(x-2h), f(x), and f(x+3h). A first-order method uses only one term in the approximation formula, which in this case is the point-centred difference formula.

This formula uses three data points and approximates the derivative using the difference between the central point and its neighboring points. For part (b) of the question, we are asked to use the three-point centred difference formula to approximate the second derivative of a function f(x)=1-5, for different values of h. The approximation error is the difference between the true value of the derivative and its approximation, and it gives us an idea of how accurate our approximation is. (a) To develop a first-order method for approximating f''(1) using the data f(x-2h), f(x), and f(x+3h), we can use finite differences. The formula can be derived as follows: f''(1) ≈ (f(1-2h) - 2f(1) + f(1+3h))/(h^2) (b) For f(x) = 1-5x, the second derivative f''(x) is a constant -10. Using the three-point centered difference formula for the second derivative: f''(x) ≈ (f(x-h) - 2f(x) + f(x+h))/(h^2) For h = 0.1, 0.01, and 0.001, calculate f''(1) using the formula above, and then determine the approximation error by comparing with the exact value of -10. Note that the approximation error is expected to decrease as h decreases, and the final answers for derivative values should be reported to 6 decimal digits.

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Answer:

8x units

Step-by-step explanation:

A rectangle has an area of 56x²y units². If the height of the rectangle is 7xy. What is the length of the rectangle.

The Area of a Rectangle is calculated with the formula

Length × Width ( Height)

Area = 56x²y square units

Height = 7xy units

Length =Area of the rectangle/Height of the rectangle

= 56x²y square units/7xy units

= 8x units

The inequalities which the number lines represent are as follows;

x > 3

x <= 2.

A mathematical comparison and expression of the relationship between two expressions is known as an inequality.

It can be seen as a generalization of an equation and is denoted by a symbol like ">", "", "", or "".

In contrast to an equation, which only has one solution, an inequality may have several answers or none at all.

The values that give rise to an inequity are its remedies.

The range of potential values for a variable is one example of how inequality models limits or limitations in the real world.

They can also be used to describe how two variables relate to one another, such as when one is more than or less than the other.

According to our question-

the inequality is; x <= 2

the inequality is; x > 3

x > 3

x <= 2

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Answer:

B. (10, 2000)

Step-by-step explanation:

5000 - 300t = 1400ft - 1200f

=> t = 10

10 => (5000 - 300t) = 2000

So the answer is B. (10, 2000)

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

20

Step-by-step explanation:

lol

Answer:

20

Step-by-step explanation:

B = 47°

a = 10.9

b = 11.7

How are the angles and sides of the right triangle calculated?

a) Finding B

We know that ,the sum of every angles of a triangle = 180°

So, B + 90° +43° = 180°

     B+ 133° = 180°

     B = 180° - 133°

        =47°

b) Finding a

We know,

\(sin\theta =\frac{opposite}{hypotenuse} \\\\sin 43^{\circ} =\frac{a}{16} \\\\a= 16(sin 43^{\circ})\\\\a = 16 (0.681)\\\\a=10.9\)

c) Finding b

We know,

\(cos\theta = \frac{adjacent}{hypotenuse} \\\\cos 43^{\circ} =\frac{b}{16} \\\\b = (cos 43^{\circ})16\\\\b= (0.731) 16\\\\b= 11.7\)

What is a right triangle?

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Algorithm 2 is the better proposal for this problem.

The reason for this is because of the specific nature of the problem statement.

The prompt calls for a count of the numbers that are multiples of either 5 or 10. However, Algorithm 1 only counts the numbers that are multiples of both 5 and 10.

This means that Algorithm 1 will not capture all the relevant numbers in the list, thus leading to incorrect results.

On the other hand, Algorithm 2 correctly counts all the numbers that are multiples of either 5 or 10. This is because it checks for multiples of 5 first and increments count if it finds a multiple.

Then, it checks for multiples of 10 and increments count again if it finds a multiple. By doing this, Algorithm 2 correctly captures all the relevant numbers in the list, thus leading to correct results.

Overall, Algorithm 2 is the better proposal for this problem.

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Answer:

a is a linear equation

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

cut tghe shape into one rectangle and a two cimi circles

area of a rect. is b x h --> 7x14 = 98ft^2

now make the two cimi circles a whoal and find the area of a circle

pie r^2 --> 3.14x3.5^2 = 38.48

add both getting about 136.48

Answer:

136.48 ft^2 (B)

Step-by-step explanation:

First, we need to find the area of a rectangle.

A(rectangle) = l * w

  = 14 ft * 7 ft

  = 98 ft^2

Next we need to find the area of the two semicircles.

A(semicircle) * 2 = πr^2/2 * 2

                           = π(3.5 ft)^2

                           = 12.25π ft^2

                           = 38.48 ft^2

Finally, you add the two areas:

98 ft^2 + 38.48 ft^2 = 136.48 ft^2

Hope this helps!

According to the similarity-attraction hypothesis, when two individuals from different cultures perceive a greater similarity between themselves, it is likely that they will experience increased attraction towards each other.

This means that the perception of shared characteristics, values, and beliefs between individuals can lead to a stronger sense of connection and positive feelings. It is important to note that this hypothesis suggests perceived similarity and attraction, but it does not guarantee the formation of relationships or friendships.

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