Solve the simultaneous equations

X-Y=-1
2X-Y=0

Answer:

Step-by-step explanation:

[tex]\frac{275}{8}=34,375[/tex]

The quadratic function's equation, when given the numbers in the table, can be found to be f(x) = x^2 - 5x + 6.

We are given a table of values and need to find the quadratic function in standard form: f(x) = ax^2 + bx + c. Let's use the points (-6, 72), (-4, 42), and (-3, 30).

For point (-6, 72):

72 = a(-6)^2 + b(-6) + c

For point (-4, 42):

42 = a(-4)^2 + b(-4) + c

For point (-3, 30):

30 = a(-3)^2 + b(-3) + c

Let's use the elimination method.

1 - 3) 42 = 27a - 3b

2 - 3) 12 = 7a - b

b = 7a - 12

Substitute this expression for b into the first equation:

42 = 27a - 3(7a - 12)

42 = 27a - 21a + 36

6 = 6a

a = 1

Now that we know a = 1, let's find b:

b = 7(1) - 12

b = -5

Finally, let's find c by substituting a and b into any of the original equations. We'll use the first one:

72 = 36(1) - 6(-5) + c

72 = 36 + 30 + c

6 = c

So, the quadratic function in standard form is:

f(x) = x^2 - 5x + 6

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Answer:

To find the estimated standard error for the sample mean, we need to use the formula:

SE = s/√n

where s is the sample standard deviation and n is the sample size.

However, we are not given the sample standard deviation, but we are given the sum of squares (SS). We can use this to find the sample variance (s^2) and then take the square root to find the sample standard deviation.

For a sample size of n = 9, the degrees of freedom (df) are:

df = n - 1 = 9 - 1 = 8

Using the formula for the sample variance:

s^2 = SS/df = 1152/8 = 144

Taking the square root, we find the sample standard deviation:

s = √144 = 12

Now we can find the estimated standard error:

SE = s/√n = 12/√9 = 4

Therefore, the estimated standard error for the sample mean is 4.

Answer:

To find the estimated standard error for the sample mean, we need to divide the sample standard deviation by the square root of the sample size. However, we are given the sum of squares (SS), not the sample standard deviation, so we first need to calculate the sample variance. The formula for the sample variance is: s^2 = SS / (n - 1) where s^2 is the sample variance, SS is the sum of squares, and n is the sample size. Using the given values, we have: s^2 = 1152 / (9 - 1) = 144 Now we can find the estimated standard error: SE = s / sqrt(n) where SE is the estimated standard error, s is the sample standard deviation, and n is the sample size. Since s = sqrt(s^2), we have: SE = sqrt(s^2

Answer:

it was c

Step-by-step explanation:

because on my fraction test I got the same answer and it was right

Answer:

C

Step-by-step explanation:

because it

We have shown that P(F) is the direct sum of W1 and W2.

What is a polynomial?

a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

To prove that P(F) is the direct sum of W1 and W2, we need to show two things: first, that every polynomial in P(F) can be written as a sum of a polynomial in W1 and a polynomial in W2, and second, that this decomposition is unique.

Let's begin by showing that P(F) can be written as the direct sum of W1 and W2. Consider an arbitrary polynomial f(x) in P(F). We can write it as a sum of even and odd terms as follows:

f(x) = [f(x) + f(-x)]/2 + [f(x) - f(-x)]/2

The first term on the right-hand side is even, while the second term is odd. Let's define g(x) = [f(x) - f(-x)]/2 and h(x) = [f(x) + f(-x)]/2. Note that g(x) is odd and h(x) is even. Thus, we have expressed f(x) as a sum of an even polynomial h(x) and an odd polynomial g(x).

To show that this decomposition is unique, suppose that f(x) can be written in two ways as a sum of an even polynomial and an odd polynomial:

f(x) = h1(x) + g1(x) = h2(x) + g2(x)

where h1(x) and h2(x) are even polynomials, and g1(x) and g2(x) are odd polynomials. Then we have:

[h1(x) - h2(x)] = [g2(x) - g1(x)]

Since h1(x) - h2(x) is even, and g2(x) - g1(x) is odd, we have:

[h1(x) - h2(x)] = 0 and [g2(x) - g1(x)] = 0

This implies that h1(x) = h2(x) and g1(x) = g2(x), so the decomposition is unique.

Therefore, we have shown that P(F) is the direct sum of W1 and W2.

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From given quadratic function we get that the rocket will hit the ground after 4.75 seconds and the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.

What is quadratic function?

A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are constants and x is the independent variable. This function is a second-degree polynomial, which means it has a degree of two.

Now,

To find out when the rocket will hit the ground, we need to find the value of t when h(t) = 0:

-16t² + 76t = 0

Factor out -16t:

-16t(t - 4.75) = 0

So either t = 0 or t = 4.75 seconds. However, we can discard t = 0 because it represents the initial launch and not the impact with the ground. Therefore, the rocket will hit the ground after 4.75 seconds.

To find out when the rocket will be 70 feet above the ground, we need to solve the following equation:

-16t² + 76t = 70

-16t² + 76t - 70 = 0

Dividing both side

8t² - 38t + 35 = 0

Factor the equation:

(4t - 5)(2t - 7) = 0

So either t = 5/4 or t = 7/2. However, we can discard t = 5/4 because it represents a time before the rocket reaches 70 feet. Therefore, the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.

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1. H × (3/7) and 2. H - (4/7)H are two different numerical expressions to model the height of the British telecom tower.

What are the expressions?

Let H be the height of the Empire State Building. Then, the height of the British Telecom Tower can be modeled using the following expressions:

1. H × (3/7)

This expression finds 3/7 of the height of the Empire State Building, which represents the height of the British Telecom Tower.

2. H - (4/7)H

This expression finds the remaining height after taking away 3/7 of the height of the Empire State Building.

Simplifying, we get (3/7)H, so subtracting this from H gives (4/7)H, which represents the height of the Empire State Building above the height of the British Telecom Tower.

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Answer: To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation and simplify.

For example, if you want to find f(2), you would substitute x=2 into the equation:

f(x) = 6 + 3x

f(2) = 6 + 3(2)

f(2) = 6 + 6

f(2) = 12

Therefore, f(2) = 12.

Step-by-step explanation:

The value of f(x) is 18 given that the value of x is substituted as 4. The expression is usually solved with substitution method.

To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation for f(x) and solve for f(x).

For example, if you want to find the value of f(x) when x = 4, you would substitute x = 4 into the equation for f(x) as follows:

f(4) = 6 + 3(4)

Simplifying the expression on the right-hand side:

f(4) = 6 + 12

f(4) = 18

Therefore, the value of f(x) when x = 4 is 18.

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The circumference of the circle is 340 units.

What is circle ?

In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.

Let's use the formula relating the length of an arc to the circumference of a circle:

Length of arc = (central angle / 360) x circumference

Plugging in the given values, we get:

17 = (18/360) x circumference

Simplifying and solving for the circumference, we get:

circumference = 17 x (360/18) = 17 x 20 = 340

Therefore, the circumference of the circle is 340 units.

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The correct order will be:

Length of the blue segment.   - 12 units

Length of the green segment (circumference of the base) - 18 units

Length of the orange segment. - 24 units

Area of one base.                - 452.4 unit²

Area of the rectangle.        -  2,261.9 unit².

A cylinder is a three-dimensional shape that consists of two parallel circular bases that are connected by a curved surface. The bases are usually identical in size and shape and are located on opposite ends of the cylinder. The curved surface that connects the bases is in the form of a rectangle that has been wrapped around the cylinder, creating a tube-like shape.

Area of one base =   r² = 3.142 × 12 × 12 = 452.448 = 452.4 unit².

Area of the rectangle = 2πr (h + r) = 2 × 3.142 × 12 (18 + 12) = 2,261.9 unit².

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The solutions to the equation are x = a and x = a/2.

We can simplify the left-hand side of the equation using the common denominator of x^3:

(x-a)x/x^3 + (x-a)(-1)/(3a^2 x^3) + (x-a)(-2)/(3a x^3) + (x-a)(1)/(x^3)

= [(x-a)x^2 - (x-a)/(3a^2) - 2(x-a)/(3a) + (x-a)x]/x^3

= [(x^3 - a^3)/x^2 - (1/(3a^2))(x-a) - (2/(3a))(x-a)]/x

= [(x^2 + ax + a^2)(x-a)/(x^2 a^2) - (x-a)/(3a^2) - (2/3)(x-a)/a]/x

= (x^2 + ax + a^2)/(x^2 a^2) - 1/(3a^2) - 2/(3a)/x

= (3x^2 + 3ax + 3a^2 - x^2 a - ax^2 - a^3)/(3a^2 x^2)/x

= (2x^2 + 3ax + 3a^2 - ax^2 - a^3)/(3a^2 x^2)/x

= (x^2 + 3ax + 3a^2 - a^3)/(3a^2 x^2)/x

Now, we can see that the expression on the right-hand side is:

(x-a)/(x^3)

Multiplying both sides by x^3, we get:

(x-a)x = (x^2 + 3ax + 3a^2 - a^3)/3a^2

Multiplying both sides by 3a^2, we get:

(x-a)3a^2x = x^2 + 3ax + 3a^2 - a^3

Expanding (x-a)(3a^2)x, we get:

3a^2x^2 - 3a^3x = x^2 + 3ax + 3a^2 - a^3

Moving all terms to one side, we get:

2x^2 - 3ax + 2a^2 = 0

This is a quadratic equation, and we can solve for x using the quadratic formula:

x = [3a ± sqrt((9a^2 - 8a^2)/4)]/4

x = [3a ± a]/4

x = a or x = 2a/4 = a/2

Therefore, the solutions to the equation are x = a and x = a/2.

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Answer: 2x^2-1/2

Step-by-step explanation:

mulityply this by the given lenght

Answer: 44.64ft^2

Step-by-step explanation:

Triangle 1:
A = 1/2 x 5.3 x 7.2
A = 19.08

Triangle 2:
A = 1/2 x 7.1 x 7.2
A = 25.56

25.56 + 19.08 = 44.64
Total area of triangles = 44.64ft^2

After answering the presented question, we can conclude that As a result, the average monthly rate of change in price during the housing bubble was $2,000.

The term "average rate" can have different meanings depending on the context in which it is used. In general, it refers to the amount of change that occurs over a certain period of time, divided by the length of that time period. Here are a few examples of how the term might be used in different fields.

The average monthly rate of change in price can be estimated by dividing the total price change by the number of months:

(final price - beginning price) / number of months = average rate of change

The beginning price was $240,000, the final price was $276,000, and the time duration was 18 months in this example. Hence, using these data, we can calculate the average rate of change as:

(276000 - 240000) / 18 = 36000 / 18 = 2000 Average rate of change

As a result, the average monthly rate of change in price during the housing bubble was $2,000.

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The equation of the circle with center (0, 5) and a point on the circle (2, 4) is x² + (y - 5)² = 5

In geometry, a circle is a closed two-dimensional shape that is formed by a set of points that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

The equation of a circle with center (h, k) and radius r is given by:

 r²=(x - h)² + (y - k)²  

In this case, the center of the circle is (0, 5) and a point on the circle is (2, 4). The radius of a circle, which is the separation between its centre and any point on the surface, may be calculated using the following formula:

r = √((2 - 0)² + (4 - 5)²) = √(5)

Now we can substitute the values of the center and the radius into the equation of the circle:

(x - 0)² + (y - 5)² = (√(5))²

Simplifying, we get:

x²+ (y - 5)² = 5

As a result, the circle's equation with its centre (0, 5) and a point on it (2, 4) is:

x² + (y - 5)² = 5

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1. The picture depicts the circle theorem

2. I wonder how the circle theorem fully apply to the image

3. The informed is that the angle between a radius and a tangent at the point of contact is a right angle.

The angle between a radius and a tangent at the point of contact is a right angle.

Suppose FGC

Then FC is the hypothenuse of triangle FGC

So, FC greater than FG

FC greater than FB+BG

FC greater than FC+BG (impossible)

This is the case on either side of C along the tangent

So, the shortest distance between F and the tangent is FC

When the distance between a point and a line is minimum, the angle between them is right angled.

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Answer: 4y^2y-80+y^2/4y

Step-by-step explanation:

En resumen, al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², obtenemos un cociente de 2x³-x² y un residuo de -2x²+7.

Para encontrar los cocientes y el residuo al dividir Sea=4x⁵-x³+7 entre b(x)=2x⁵+x², debemos realizar la división larga de polinomios. El procedimiento es similar a la división larga de números enteros:

        2x³    -x²    +0x   +0
   ---------------------------------
2x⁵ |  4x⁵   +0x⁴  -x³   +0x²  +0x  +7
        4x⁵   +0x⁴
       -------------
            0x⁴  -x³
            0x⁴  +0x³
           -------------
                   -x³   +0x²
                   -x³   +0x²
                   -------------
                            0x²  +0x
                            0x²  +0x
                            ------------
                                      7
                                      2x⁵  +x²
                                      --------
                                         -2x²  +7

Por lo tanto, el cociente de la división es 2x³-x², y el residuo es -2x²+7. Es importante notar que el grado del residuo (grado 2) es menor que el grado del divisor b(x) (grado 5), como se requiere en la definición de la división de polinomios.

La respuesta a la pregunta "cuál es la conciente de que (x)" no es clara, ya que no está claro lo que se está pidiendo. Podría ser una pregunta incompleta o una cuestión mal redactada.

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Answer: First one (top left)

Step-by-step explanation:

Answer:

One in the top left corner

Hope this helps!

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2+2 = 4

The answer is 2+2 = 4.

the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

what is right-angled triangle  ?

A right-angled triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). This angle is formed by the intersection of two sides of the triangle, which are called the legs or catheti, and it is opposite to the longest side of the triangle, which is called the hypotenuse. The hypotenuse is always opposite the right angle.

In the given question,

The area of a right-angled triangle is given by the formula:

Area = 1/2 x base x height

where the base and height are the two perpendicular sides of the triangle.

In this case, the adjacent side and opposite side of the right-angled triangle are both 2 units.

Let's call the hypotenuse of the triangle 'c'. Then, by the Pythagorean theorem, we have:

c² = 2² + 2²

c² = 8

c = √(8) = 2.8284 (rounded to 4 decimal places)

Now, we can use the trigonometric ratios to find the base and height of the triangle. In this case, we can use the tangent ratio:

tan(theta) = opposite/adjacent

tan(theta) = 2/2

tan(theta) = 1

theta = tan⁻¹(1) = 45 degrees

Therefore, the base and height of the triangle are:

base = adjacent x tan(theta) = 2 x tan(45) = 2 x 1 = 2

height = opposite x tan(theta) = 2 x tan(45) = 2 x 1 = 2

Now we can use the area formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 2 x 2

Area = 2 square units

Therefore, the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

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Answer:

( x - 5 )

Hope this helps!

Step-by-step explanation:

[tex]2x^{2} -7x-15[/tex] can factor into ( 2x + 3 ) ( x - 5 ).

( 2x + 3 ) ( x - 5 ) = ( cross multiply ) : [tex]2x^{2} -10x + 3x - 15[/tex] = [tex]2x^{2} -7x-15[/tex].

Answer: (D) 12 to 4

Step-by-step explanation:

        First, we will find the number of people waiting in line for each activity.

➜ Bumper cars is 12

➜ Slingshot is 4

        Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.

➜ 12 to 4

Step-by-step explanation:

using Pythagoras theorem

Answer:

4² + r² = (2+ r)²

16 + r² = 4 + 4r + r²

12 = 4r

r = 3

The probability that the next person will purchase more than one costume as a percent to the nearest whole number is 3%

.Out of the total 80 + 32 + 3 = 115 visitors, 80 did not purchase any costumes and 32 purchased exactly one costume. This means that the remaining 3 visitors purchased more than one costume.

Therefore, the probability that the next person will purchase more than one costume is 3/115, which is approximately 0.0261.

To express this as a percentage to the nearest whole number, we need to multiply by 100 and round to the nearest integer. Thus, the answer is:

0.0261 × 100 ≈ 3%

Therefore, the probability that the next person will purchase more than one costume is approximately 3%.

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The probabilities for the given events will be a) 1/13 b) 3/13 c) 10/13.

What exactly is probability?

Probability is a measure of the possibility of an event to be occurred. In mathematics, it is defined as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Now,

(a) The probability of drawing a 7 from a standard 52-card deck is 4/52 or 1/13. This is because there are 4 7s in the deck (one in each suit) and a total of 52 cards.

(b) The probability of drawing a face card from a standard 52-card deck is 12/52 or 3/13. This is because there are 12 face cards in the deck (4 jacks, 4 queens, and 4 kings) and a total of 52 cards.

(c) The probability of drawing a non-face card from a standard 52-card deck is 40/52 or 10/13. This is because there are 40 non-face cards in the deck (the 2s through 10s and the aces) and a total of 52 cards.

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The actual selling price of the camera after the 25% discount is $345.

The amount received by the buyer is the selling price of a product or service. Although the seller sets the price, a number of variables affect how the seller arrives at that particular figure. Depending on the seller's discretion, different customers may pay different prices for the same good or service.

If the normal price of the camera is $460, a 25% reduction in price would be:

25% of $460 = 0.25 x $460 = $115

This means the reduction in price when buying the camera duty-free is $115.

So the actual selling price of the camera after the discount is:

$460 - $115 = $345

Therefore, the actual selling price of the camera after the 25% discount is $345.

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