Solve the following linear system by Gauss elimination. If the system is inconsisitent, type "NA" in the solution box. a = 48 b = -25 C = -7 || -2b + 6c = 4 4a + 12b - 16c = -4 4a + 6b+3c = 13

The statement that is true is:

Statements 1 and 3

Let's examine each statement individually:

If n is a multiple of 8, then n is a multiple of 4. This statement is true because every number that is divisible by 8 is also divisible by 4. Since 8 is a multiple of 4, any multiple of 8 will have factors of both 8 and 4. If n is a multiple of 18, then n is a multiple of 2.

This statement is also true. Any number that is divisible by 18 is also divisible by 2 because 18 contains a factor of 2. Every multiple of 18 will have at least one factor of 2.

Statement 2 is not true. If n is a multiple of 18, then n is a multiple of 9.

This statement is false because there are numbers that are multiples of 18 but not multiples of 9. For example, 18 itself is a multiple of 18 but not a multiple of 9, as 18 divided by 9 is equal to 2.

Therefore, the correct answer is c) Statements 1 and 3.

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Answer:

the perimeter is 10.99 units.

Step-by-step explanation:

We have a triangle with points in:

   X    //   Y

N    2    //   0

P    -1    //  -2

M    4    //   0

We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.

M - N = NM = 4 - 2 = 2 units of X

M - N = NM = 0 - 0 = 0 units of Y

This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.

Next side:

N - P = 2 -(-1) = 3 units of x

N - P = 0 - (-2) = 2 units of Y

We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:

\(\sqrt{3^2+2^2} =NP\\\sqrt{9 + 4} = \sqrt{13}\)

Now, we do the same with MP:

M - P = 4 - (-1) = 5 units of X

M - P = 0 - (-2) = 2 units of Y

we solve for MP

\(\sqrt{5^2+2^2} = \sqrt{25 + 4} = \sqrt{29}\)

We now add up:

\(NM + NP + MP\\2 +\sqrt{13} + \sqrt{29} =\\10.99071608\)

ANSWER:

500.5 m²

STEP-BY-STEP EXPLANATION:

To know how much artificial grass should be purchased to cover the athletic field, we must calculate the area corresponding to the figure.

The area of a trapezoid has the following formula:

Where b is the small base, B is the large base and h is the height, we substitute and calculate the area, like this:

It is necessary to purchase the amount of 500.5 m² to be able to cover the athletic field

Using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

The length of the wood needed to trim the window is the perimeter of the triangular shape shown in the image.

To find the perimeter, use the trigonometry ratio, to find the other two legs of the right triangle.

Thus:

Reference angle = 30°

Hypotenuse = 6 ft

Opposite = ?

Apply SOH:

sin 30 = opp/hyp

sin 30 = opp/6

Opp. = sin 30 × 6

Opp. = 3 ft

Find the other leg:

Reference angle = 30°

Hypotenuse = 6 ft

Adjacent = ?

Apply CAH:

cos 30 = adj/hyp

cos 30 = adj/6

Adj. = cos 30 × 6

Adj. = 5.2 ft

Perimeter of the triangle = 5.2 + 3 + 6 = 14.2 ft.

therefore, using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

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Answer:

Step-by-step explanation:

Using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

Trigonometry Ratios

The length of the wood needed to trim the window is the perimeter of the triangular shape shown in the image.

To find the perimeter, use the trigonometry ratio, to find the other two legs of the right triangle.

Thus:

Reference angle = 30°

Hypotenuse = 6 ft

Opposite = ?

Apply SOH:

sin 30 = opp/hyp

sin 30 = opp/6

Opp. = sin 30 × 6

Opp. = 3 ft

Find the other leg:

Reference angle = 30°

Hypotenuse = 6 ft

Adjacent = ?

Apply CAH:

cos 30 = adj/hyp

cos 30 = adj/6

Adj. = cos 30 × 6

Adj. = 5.2 ft

Perimeter of the triangle = 5.2 + 3 + 6 = 14.2 ft.

therefore, using the trigonometry ratio to find the remaining missing legs of the triangle, the approximate length of the wood needed is: A. 14.2 ft.

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Answer:

linear

Step-by-step explanation:

equal slope throughout

Answer:

the number of protons identifies what element it is, since it has 35 protons it is Bromine

number of protons=atomic number

The element is Bromine which as atomic number of 35.

The number of protons in an atom is equal to atomic number.

It is given that, an atom of a certain element has 35 protons and has 7 valence electrons.

So that, atomic number of atom \(=35\)

From periodic table, It is observed that Bromine has atomic number of 35.

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Answer:

Profit means your business is making more money than it spends to stay in business so yes.

To maximize the area,

The radius of the semicircle, r = 124.6in

Height of the rectangle, h = 124.6in

Given,

Perimeter of the window, P = 890in

P = 2L + 2r + πr

From this Length of window,  \(L=\frac{P-2r-\pi r}{2}\)

Length is equal to the Height of window.

So, \(H=\frac{P-2r-\pi r}{2}\)

Radius of the semicircle,

\(r=\frac{P}{4+\pi }\)

\(r=\frac{890}{4+\frac{22}{7} }\)

\(r=124.6\)

Then,

\(H=\frac{P-2r-\pi r}{2}\)

\(H=\frac{890-2(124.6)-\frac{22}{7}(124.6) }{2}\)

\(H=\frac{890-249.2-391.6}{2}\)

\(H=\frac{249.2}{2}\)

\(H=124.6\)

Area  of the window,

\(A=Pr-2r^{2} -(\frac{1}{2})\pi r^{2}\)

\(A=890(124.6)-2(124.6)^{2} -(\frac{1}{2} )(\frac{22}{7})(124.6)^{2}\)

A = 110894 - 31050.32 - 24396.68

A = 55447

From the above calculations we have to conclude that:

To maximize the area,

The radius of the semicircle, r = 124.6in

Height of the rectangle, h = 124.6in

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Answer:

7 m

Step-by-step explanation:

We are told that;

100 cm = 1 m

Thus; 2.54 cm = 2.54 × 1/100 = 0.0254 m

This means that;

1 inch = 0.0254 m

Thus; 275 inches will give; 275 × 0.0254/1 = 6.985 m

Approximating to the nearest metre gives 7 m

Answer:

2714.3 or 864 pi

Step-by-step explanation:

There were 89 points in the original data set.

To solve this problem, we can use the formula for the mean of a set of numbers:

Mean = (sum of all values) / (number of values)

Let's denote the number of points in the original data set as n.

The sum of the original data set is n  10 since the mean is 10.

When a point with a value of 100 is added, the new sum becomes n × 10 + 100.

The new mean is given as 11.

Using the formula for the mean, we can write the equation:

11 = (n × 10 + 100) / (n + 1)

To solve for n, we can multiply both sides of the equation by (n + 1):

11(n + 1) = n × 10 + 100

11n + 11 = 10n + 100

11n - 10n = 100 - 11

n = 89

Therefore, there were 89 points in the original data set.

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The kind of sample that is described in the scenario is a lottery sample.

The lottery sample is the kind of sample that is described in the scenario in which 500 people attend a charity event, and each of them buys a raffle ticket.

The ticket stubs are placed in a drum and mixed thoroughly, and out of them, a few are drawn.

People whose tickets are drawn are declared winners of a prize. It is a type of probability sampling that depends on the element of chance.

In this type of sample, the probability of selecting an element is unknown and cannot be measured. I

t is a random process in which the probability of winning or being selected for the sample is entirely based on chance.

Hence, the lottery sampling technique is the appropriate one in the scenario.

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Answer:

$4.45

Step-by-step explanation:

First, we try to find the slope of the table. We can do this by doing the following-  \(\frac{Change \ in \ y }{Change \ in \ x}\)

When we do this, we find that the slope (or the change in y / change in x) is equal to 5.27

Now we subtract this from the slope of the price of steak at Store B which is 9.72

\(9.72-5.27 = 4.45\)

You get 4.45 which is $4.45 or 4 dollars and 45 cents.

Let's denote the radius of the circle by r. The radius of the circle is 5 meters.

The central angle of 2 radians means that it cuts off an arc whose length is equal to 2 times the radius, or 2r. The formula for the area of a sector is:

A = (1/2) r^2 θ

where A is the area of the sector, r is the radius, and θ is the central angle in radians. We can use this formula to find the radius of the circle:

25 = (1/2) r^2 (2)

25 = r^2

r = ±√25

Since the radius of a circle can't be negative, we take the positive square root:

r = 5 m

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Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

The amount of fluid in container B is 9.5 ounces.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To determine the amount of fluid in container B, we can divide the amount of fluid in container A by the given ratio of 8. Since container A contains 76 ounces, we divide 76 by 8 to find that each unit of the ratio represents 9.5 ounces. Therefore, container B would contain 9.5 ounces of fluid.

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The solution as an ordered pair to represent the point on the graph where the equations intersect is: (2, 1)

Equivalence methods are non-graphical methods of finding intersections or solutions to systems of equations.

Start with two equations of the form y = -2x + 5. y = -2x + 5 and y = x - 1. Takes two expressions equal to y and equates them. Now solve this new equation for x. See the example shown. -2x + 5 = x - 1

x = 2

Once you know the x-coordinate of the intersection point, plug the solution for x into one of the original equations to find y. In this example the first expression is used.

y = -2x + 5

y = -2(2) + 5

y = 1

A good way to check the solution is to substitute the solution for x into both equations and make sure you get equal y values.

y = x - 1

y = 2 - 1

y = 1  

The solution as an ordered pair to represent the point on the graph where the equations intersect.

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Answer:

(0,-5)

Step-by-step explanation:

This is the y intercept I graphed it

Answer:

(0,-5)

Step-by-step explanation:

3y-5x=-15

Add 5x on both sides

3y=5x-15

Divide each side by 3

y=5/3x-5

y=mx+b

b is the y-intercept

b=-5

Therefore (0,-5) is the answer

Answer:

Answer: There are 918 pupils now.

• Rise in percentage:

\( \dashrightarrow \: { \tt{(100 \% + 8\%) = 108\% }}\)

• let current number of pupils be n

\({ \tt{n}}\dashrightarrow \: { \tt{108\% \times 850}} \\ \\ { \tt{n = \frac{108}{100} \times 850}} \\ \\ { \tt{n = 918 \: pupils}}\)

Given: A right triangle with dimensions as shown in the figure

To Determine: The ratio for sin A and cos A

Solution

Given a right triangle ABC with a reference angle A, the trigonometry ratio is

From the given right triangle with reference angle A, the hypothenuse is the side facing the right angle. The side facing angle A is the opposite, and the other side is adjacent. This is as shown below

Hence

OPTION A is the correct option

a=2

Explanation

Step 1

subtract 10 in both sides

Step 2

divide each side by 4

The number of miles ran by Mick is 29 miles and the number of miles ran by Keith is 47 miles.

Given that, last month, Keith ran 18 more miles than Mick.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of miles ran by Mick be x.

Then, the number of miles ran by Keith will be x+18.

Here, total distance ran by both of them is 76 miles

So, equation is x+x+18=76

⇒ 2x+18=76

⇒ 2x=76-18

⇒ 2x=58

⇒ x=29 miles

So, x+18=47 miles

Therefore, the number of miles ran by Mick is 29 miles and the number of miles ran by Keith is 47 miles.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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The value of Erica's investment after 6 years is approximately $4,939.05.

To find the value of Erica's investment after 6 years, we can use the compound interest formula. The formula for compound interest is given as:

A = P\((1 + r/n)^(nt)\)

Where:

A is the final amount or value of the investment.

P is the initial principal or investment amount.

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Erica's initial investment is $4000, the annual interest rate is 4% (or 0.04 as a decimal), and the investment is growing annually. Therefore, we have:

P = $4000

r = 0.04

n = 1 (since the interest is compounded annually)

t = 6 years

Plugging these values into the compound interest formula, we can calculate the final value of the investment:

A = $4000(1 + \(0.04/1)^(1*6)\)

A = $4000(1 + 0.04)^6

A = $4000(1.04)^6

Evaluating this expression, we find:

A ≈ $4,939.05

Therefore, the value of Erica's investment after 6 years is approximately $4,939.05.

This calculation assumes that no additional investments or withdrawals were made during the 6-year period and that the interest rate remains constant at 4% per year.

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Answer:

a= 0.6

Step-by-step explanation:

This is the answer...........

Answer:

It is reciprocal.

A = 0.6

Step-by-step explanation:

Reciprocal” means “equality,”

To find the A. Use APE or Additive Property of Equality

-2. 7 = a - 3.3

-2.7 + 3.3 =  a

0. 6 = a

The equation for the number of 30 days periods until the value of both cards will be equal is 130 - 3x = 110 - 2.5x

let

Number of 30 days period = x

Gift card 1:

130 - 3x

Gift card 2:

110 - 2.5x

130 - 3x = 110 - 2.5x

130 - 110 = -2.5x + 3x

20 = 0.5x

x = 20/0.5

x = 40

So,

Gift card 1:

130 - 3x

= 130 - 3(40)

= 130 - 120

= $10

Gift card 2:

110 - 2.5x

= 110 - 2.5(40)

= 110 - 100

= $10

Therefore, the value of each card when they have equal value is $10

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The point (2, 3, 3), we have:

∂z/∂x = 1/8

∂z/∂y = -1/6

To use the equations given in the problem, we first need to check if Fz is not equal to zero at the point (2, 3, 3) in the equation 3z^3 − 3xy − 5yz + y^3 −9 = 0.

We can find Fz by taking the partial derivative of F with respect to z:

Fz = 9z^2 - 5y

At (2, 3, 3), we have:

Fz(2, 3, 3) = 9(3)^2 - 5(3) = 72

Since Fz is not equal to zero at the point (2, 3, 3), we can use the equations given in the problem to find ∂z/∂x and ∂z/∂y.

∂z/∂x = −Fx/Fz

To find Fx, we take the partial derivative of F with respect to x:

Fx = -3y

Therefore,

∂z/∂x = −Fx/Fz = -(-3y)/72 = 3y/72 = y/24

At the point (2, 3, 3), we have:

∂z/∂x (2, 3, 3) = 3/24 = 1/8

∂z/∂y = −Fy/Fz

To find Fy, we take the partial derivative of F with respect to y:

Fy = -5z + 3y^2

Therefore,

∂z/∂y = −Fy/Fz = -(-5z + 3y^2)/72 = (5z - 3y^2)/72

At the point (2, 3, 3), we have:

∂z/∂y (2, 3, 3) = (5(3) - 3(3)^2)/72 = -4/24 = -1/6

Therefore, at the point (2, 3, 3), we have:

∂z/∂x = 1/8

∂z/∂y = -1/6

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The value of x as an int variable is 0

An int(integer) variable is a variable containing only whole numbers.

Given the expression;

x = - 3 + 4 % 6/ 5

Let's make into proper fraction, we have

x = - 3 + {}4/ 100 × 6/ 5

Multiply through

x = -3 + 6/ 5/ 4/ 100

x = -3 + {6/ 5 ÷ 0. 4}

x = -3 + {3}

expand the bracket

x = -3 + 3

Add like terms

x = 0

Thus, the value of x as an int variable is 0

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Complete question;

Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;