In the triangle ABC.
angle ABC is twice the size of angle BAC.
angle ACD is 31° more than angle ABC.
Work out the size of angle ACB.

The statement of the solution to the system is the system has one solution

From the question, we have the following parameters that can be used in our computation:

5x + 4y = -3

y = -3x + 5

Substitiute the second equation in the first equation

Using the above as a guide, we have the following:

5x + 4(-3x + 5) = -3

So, we have

5x - 12x + 20 = -3

Evaluate the like terms

-7x = -23

So, we have

x = 23/7

The above means that the equation has a solution

Hence, the number of solutions in the equation is 1

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There could be many other combinations of scores that would result in the same mean, median, and mode.

What is mean ?

Mean can be defined as ratio sum of given observations, total number of observations.

Since the median is 7 and the mode is 8, we can assume that the majority of her scores were in the range of 7-8 points. We can also assume that there were a few games in which she scored lower than 7 points and a few games in which she scored higher than 8 points.

Here's one possible set of scores that would result in a mean of 6, a median of 7, and a mode of 8:

Game 1: 3 points

Game 2: 5 points

Game 3: 6 points

Game 4: 7 points

Game 5: 7 points

Game 6: 8 points

Game 7: 8 points

Game 8: 8 points

Game 9: 9 points

Game 10: 10 points

Game 11: 11 points

Note that this is just one possible set of scores that would fit the given statistics.

Therefore, There could be many other combinations of scores that would result in the same mean, median, and mode.

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The slope of the line passing through the points (-5,5) and (5,8) is 0.3.

The slope of a line is the rate at which it rises or falls as it moves from left to right. It is defined as the change in the vertical distance divided by the change in the horizontal distance between any two points on the line.

The slope of a line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the slope formula:

slope = (y₂-y₁)/(x₂-x₁)

Using the coordinates (-5,5) and (5,8), we can plug in the values to get:

slope = [tex]\frac{(8-5)}{(5-(-5))}[/tex]

slope = [tex]\frac{3}{10}[/tex]

slope = 0.3

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The given relation that is a function is the fourth graph which shows a U- shaped curve.

The graph of a quadratic function is a U-shaped curve called a parabola, which can either face upwards or downwards depending on the value of "a". If "a" is positive, the parabola faces upwards, and if "a" is negative, the parabola faces downwards.

The coefficient "a" determines the width and direction of the parabola, while the constants "b" and "c" determine its position on the coordinate plane. This therefore shows that the fourth graph is a function.

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Using Algebraic expression we concluded, In practice, the angle of the pendulum may not be exactly equal to the calculated values due to factors such as air resistance, friction, and variations in the length of the pendulum.

What is Algebraic expression ?

A combination of variables and constants is an algebraic expression.

We can see that the pendulum's height drops with each swing if we make the assumption that each swing is measured from the same starting point.

Using a sequence is one technique to mathematically express this data. Assuming that n = 1, 2, 3, 4, let's define the sequence "a n" as the pendulum's height on the nth swing. Then, we could type:

a_1 = 80

a_2 = 76

a_3 = 72.2

a_4 = 68.59

Another way to represent this information is by using a formula that describes the height of the pendulum on each swing. One common formula for the height of a simple pendulum is:

[tex]h = L - L\times cos(\theta)[/tex]

where h is the height of the pendulum, L is the length of the pendulum, and θ is the angle that the pendulum swings from its resting position. Assuming that the length of the pendulum remains constant, we can use this formula to find the angle θ for each swing:

For the first swing, h = 80 cm, L = constant, so we can solve for θ:

[tex]80 = L - L\times cos(\theta)\\cos(\theta) = 1 - 80/L\\\theta = arccos(1 - 80/L)[/tex]

For the second swing, we have h = 76 cm, so we can use the same formula with h = 76 and solve for θ:

[tex]76 = L - L\times cos(\theta)\\cos(\theta) = 1 - 76/L\\\theta = arccos(1 - 76/L)[/tex]

Similarly, we can use the formula to find θ for the third and fourth swings:

For the third swing, h = 72.2 cm:

θ = arccos(1 - 72.2/L)

For the fourth swing, h = 68.59 cm:

θ = arccos(1 - 68.59/L)

Therefore, in practice, the angle of the pendulum may not be exactly equal to the calculated values due to factors such as air resistance, friction, and variations in the length of the pendulum.

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complete question -

Answer: Add.

Step-by-step explanation: When you multiply two numbers, all you have to do is simply add the exponents!

Example: 3^4 × 3^2 = 3^(4 + 2) = 3^6

Hope this helps!!

The quadratic equation (c+5)²=36 will give c = 1,-11.

A quadratic equation is a type of equation in algebra that involves a variable (usually denoted as "x") raised to the power of 2, or squared. The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants, with a≠0. The goal is to solve for the variable x, which may have one or two possible solutions depending on the coefficients of the equation.

Now,

To solve the equation (c + 5)² = 36:

Taking the square root of both sides of the equation

√(c + 5)² = ±√36

Simplify the left-hand side using the rule that √a² = |a|:

|c + 5| = ±6

Solve for c in each case by subtracting 5 from both sides of the equation:

c + 5 = 6 or c + 5 = -6

Solve for c in each equation:

c = 1 or c = -11

Therefore, the solutions to the equation (c + 5)² = 36 are c = 1 and c = -11.

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The vertices of the image of the triangle BCD are B'(x, y) = (- 3, 13), C'(x, y) = (0, 19) and D'(x, y) = (18, 10). The representation of the resulting figure is in the image attached below.

Herein we find the representation of a triangle on Cartesian plane, whose image, that is, the result of a dilation, must be found. The formula to be used is introduced below:

P'(x, y) = P(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that B(x, y) = (- 3, 7), C(x, y) = (- 2, 9), D(x, y) = (4, 6), O(x, y) = (- 3, 4) and k = 2, then the coordinates of the vertices of the image are listed below:

B'(x, y) = (- 3, 7) + 2 · [(- 3, 7) - (- 3, 4)]

B'(x, y) = (- 3, 7) + 2 · (0, 3)

B'(x, y) = (- 3, 7) + (0, 6)

B'(x, y) = (- 3, 13)

C'(x, y) = (- 2, 9) + 2 · [(- 2, 9) - (- 3, 4)]

C'(x, y) = (- 2, 9) + 2 · (1, 5)

C'(x, y) = (- 2, 9) + (2, 10)

C'(x, y) = (0, 19)

D'(x, y) = (4, 6) + 2 · [(4, 6) - (- 3, 4)]

D'(x, y) = (4, 6) + 2 · (7, 2)

D'(x, y) = (4, 6) + (14, 4)

D'(x, y) = (18, 10)

Now we proceed to plot the image by means of a graphing tool.

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Answer: 16π

Step-by-step explanation:

The area of a full circle is πr^2. We only need a quarter so we'll use, A = 1/4(πr^2)

Area = 1/4(π(8)^2)

Area = 1/4(64π)

Area = 16π

Hope this helps

Answer:

I thing it 16 pi if u get it wrong I'm sry but since I just learned this pi stuff this is what I came up with

The cost Analysis for the two proposed plans for building a low ultra-light bicycle concluded on the recommendation that d that Bici Bicycle Company follow the first plan.

The first plan involves a cost of $125,000 to design and build a prototype bicycle. The combined materials and labor costs for each bike made under the first plan will be $225. This means that for every bike Bici Bicycle Company produces under the first plan, it will incur a total cost of $350 ($125,000 + $225).

On the other hand, the second plan involves a cost of $100,000 to design and build the prototype. The combined materials and labor costs for each bike made under the second plan will be $275. This means that for every bike Bici Bicycle Company produces under the second plan, it will incur a total cost of $375 ($100,000 + $275).

Therefore, while the second plan has a lower initial cost of prototype development, it will ultimately result in a higher cost per unit produced. The first plan, although it has a higher initial prototype development cost, will ultimately result in a lower cost per unit produced.

To determine the break-even point, we can set the total cost of producing a bike under each plan equal to each other and solve for the number of bikes produced.

For the first plan:

Total cost = $125,000 + ($225 x n)

For the second plan:

Total cost = $100,000 + ($275 x n)

Setting these equal to each other, we get:

$125,000 + ($225 x n) = $100,000 + ($275 x n)

$25,000 = $50 x n

n = 500

Therefore, Bici Bicycle Company would need to produce at least 500 bicycles for the cost per unit of the first plan to be less than that of the second plan.

In conclusion, based on my analysis, I would recommend that Bici Bicycle Company follow the first plan, as it will ultimately result in a lower cost per unit produced. However, if the company anticipates producing fewer than 500 bicycles, the second plan may be more cost-effective.

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The true statements are:

A sort of transformation comprehended a translation involves moving each point in a figure the same distance in the same direction.

Reworking text from one language into another while preserving the original message and communication is called translation. But, there are various approaches to translation, and they range in both form and purpose, just like anything else.

An operation is a transformation if it moves, flips, or otherwise alters a figure to produce a new figure. Rigid transformations sometimes referred to as isometry or congruence transformations, do not alter the size or shape of a figure.

therefore, the true statements are:

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Answer:

1 mile is equal to 1,760 yards. Therefore, 3 miles is equal to 3 x 1,760 = 5,280 yards.

Comparing 5,280 yards to 1,000 yards, we can see that 5,280 yards is greater than 1,000 yards.

To determine how much greater, we can subtract 1,000 from 5,280:

5,280 - 1,000 = 4,280

Therefore, 3 miles is 4,280 yards greater than 1,000 yards.

The sin of the angle is 0.6 and the cos of the angle is 0.8.

In a right triangle, the sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse. The cosine (cos) of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

In this case, the side opposite to the angle is 6 and the side adjacent to the angle is 8. To find the hypotenuse, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

Plugging in the given values:

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

c = 10

So the hypotenuse of the right triangle is 10.

Now we can find the sin and cos of the angle:

sin = opposite/hypotenuse = 6/10 = 0.6

cos = adjacent/hypotenuse = 8/10 = 0.8

Therefore, the sin of the angle is 0.6 and the cos of the angle is 0.8.

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Answer:

Step-by-step explanation:

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, to find the interval of hours that represents the lifespan of the middle 68% of light bulbs, we need to find the interval that is one standard deviation away from the mean in either direction.

Since the mean is 1400 hours and the standard deviation is 50 hours, we can use the following formula to find the interval:

(mean - standard deviation, mean + standard deviation)

Plugging in the values, we get:

(1400 - 50, 1400 + 50)

Simplifying, we get:

(1350, 1450)

Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is from 1350 hours to 1450 hours.

Answer:

(1350,1450)

Step-by-step explanation:

The Empirical Rule states that 68% of data points fall within one standard deviation of the mean. So, subtract 50 from the mean and add 50 to the mean to find the lifespan of the middle 68% of bulbs.

Rotate point A 180 counterclockwise about the origin to get point A'. -2,-3 coordinate is A'

What is counterclockwise rotation?

Rotations that are counterclockwise (CCW) travel in the opposite direction from how a clock's hands move. Positive numerals are used to indicate these rotations.

Rotation in either a clockwise or anticlockwise direction refers to a change in the electrical activity flowing through the heart in a horizontal plane. Consider the observer as being at the bedside of the sufferer. It is known as anticlockwise rotation if the patient's heart's electrical activity has shifted more to their right side. It is known as clockwise rotation if the patient's heart's electrical activity has shifted more to the left.

Our point A(x,y) rotates 180 degrees anticlockwise around the origin to become A' (-x,-y). Making both x and y negative is all we do as a result.

Here we can see in the graph ‘A’ is present on (2,3)

So the -2,-3 coordinate is A’.

Hence the correct answer is c, -2,-3

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Answer:

3/4 x 2/5 => NO

2/5 x 5/6 => NO

1/10 x 1/5 => NO

1/2 x 3/5 => YES

Step-by-step explanation:

3/4 x 2/5 = 6/20 => NO

2/5 x 5/6 = 10/30 => NO

1/10 x 1/5 = 1/50 => NO

1/2 x 3/5 = 3/10 -> YES

By answering the above question, we may state that We must thus locate function the value of h that makes the equation true in order to estimate the height of the tower platform.

Mathematicians study numbers, as well as their variations, equations, related forms, and conceivable arrangements of these. Function refers to the relationship between a set of inputs, each of which has an associated output. A function is an association of inputs and outputs, where each input leads to a single, identifiable output. Each function is given a domain, codomain, or scope. The letter f is frequently used to represent functions (x). A cross is typed. The four primary types of accessible functions are on functions, one-to-one capabilities, so numerous capabilities, in capabilities, and on functions.

The projectile's starting height above the earth must be determined. Setting the time to zero (t = 0) and finding h will allow us to do this.

The formula for the projectile's height at time t is:

[tex]vt + h + -16t2 = h(t)[/tex]

where h represents the projectile's initial height and v its initial velocity.

t = 0 results in:

[tex]h(0) = -16(0)^2 + v(0) + h h(0) = h[/tex]

Hence, h, the height of the tower platform, is the projectile's beginning height.

We must thus locate the value of h that makes the equation true in order to estimate the height of the tower platform.

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Hypothesis: The P-value for this test is 0.026251 which is less than the significance level of 0.05.

Hypothesis is a statement or explanation proposed to explain a phenomenon. It is a logical conjecture, based on observations or experiments, made in order to draw out and test its consequences. In scientific research, a hypothesis is used as a starting point for further investigation and is tested through the scientific method. A hypothesis must be testable and falsifiable, meaning it can be tested and disproved using scientific evidence.

Therefore, we can reject the null hypothesis that there is no difference in the proportions of almonds in the new and old recipes. This means that the proportion of almonds in the new recipe is greater than in the previous recipe.

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Work Shown:

[tex]45\text{ km}/\text{hr} = \frac{45\text{ km}}{1\text{ hr}}\\\\=\frac{45\text{ km}}{1\text{ hr}}*\frac{1000\text{ m}}{1\text{ km}}*\frac{1\text{ hr}}{60\text{ min}}*\frac{1\text{ min}}{60\text{ sec}}\\\\=\frac{45*1000*1\text{ m}}{1*1*60*60\text{ sec}}\\\\=\frac{45000\text{ m}}{3600\text{ sec}}\\\\=12.5 \text{ m}/\text{s}\\\\[/tex]

Pay close attention to how the conversion fractions are set up on the second line. This placement is done specifically to have the units of "km", "hr", and "min" cancel out. The goal is to be left with "meters" up top and "seconds" down below.

Answer:

Step-by-step explanation:

[tex]f(9)[/tex] means we need to find the value of [tex]f(x)[/tex] when [tex]x=9[/tex], so

[tex]f(9)=2[/tex]×[tex]9=18[/tex]

Step-by-step \frac{1}{2} x^{5} - 15x

Market Price: The point where supply and demand are equal.

Market price is the current price of a good or service that is determined by the interactions of buyers and sellers in a competitive market. It is the result of the forces of supply and demand and is determined by the number of buyers and sellers in the market and their respective levels of demand and supply. Market prices are affected by both external and internal market forces such as government policies, taxation, economic conditions, and availability of resources.

Demand: The quantity of a good or service that consumers are willing and able to buy

Supply: The quantity of a good or service that businesses are willing and able to provide

Producers: Individuals and organizations that determine what products and services will be available for sale

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The given system of equations is:

3x + 2y + 4z - w = 13

-2x + y + 5z = 5

We can write this system in the form of an augmented matrix as:

| 3 2 4 -1 | 13 |

| -2 1 5 0 | 5 |

To transform this matrix to echelon form, we perform the following elementary row operations:

Add 2 times the first row to the second row:

| 3 2 4 -1 | 13 |

| 0 5 13 -2 | 31 |

Divide the second row by 5 to obtain a leading 1:

| 3 2 4 -1 | 13 |

| 0 1 13/5 -2/5 | 31/5 |

Subtract 4 times the second row from the first row:

| 3 0 -6/5 3/5 | 9/5 |

| 0 1 13/5 -2/5 | 31/5 |

Multiply the second row by 6/5 and add it to the first row:

| 3 0 0 16/5 | 57/5 |

| 0 1 13/5 -2/5 | 31/5 |

The matrix is now in echelon form. Using back substitution, we can solve for the variables:

From the second row, we have:

y + (13/5)z - (2/5)w = 31/5

y = (2/5)w - (13/5)z + 31/5

Substituting y in the first row, we have:

3x + 2[(2/5)w - (13/5)z + 31/5] + 4z - w = 57/5

3x + (4/5)w - (26/5)z = 2/5

Solving for x, we have:

x = (2/15)w + (26/15)z - 2/15

So the solution is:

x = (2/15)w + (26/15)z - 2/15

y = (2/5)w - (13/5)z + 31/5

z = z

w = w

This is a parametric solution, as we have one free variable (z) and can express the other variables in terms of it. Therefore, the system has infinitely many solutions.

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Best describes the translation of the figure moves Left and down.

A translation is a transformation that moves every point of a figure or object by the same distance and in the same direction without changing its shape, size, or orientation. It is a type of rigid transformation that preserves the distance between points and angles between lines.

A translation can be described using the horizontal and vertical shift or displacement of the object. If a point (x, y) is translated by a distance of 'a' units to the right and 'b' units upwards, the new location of the point would be (x + a, y + b).

Question says that a figure is translated using the mapping (x, y) → (x + a, y + b).

If the value of 'a' is negative and the value of 'b' is negative in the mapping (x, y) → (x + a, y + b), it means that the figure is being translated to the left and downwards.

The x-coordinates are being decreased by the absolute value of 'a', which means that the figure is moving left. Similarly, the y-coordinates are being decreased by the absolute value of 'b', which means that the figure is moving downwards.

Therefore, the best description of the translation is "the figure moves left and down"

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The degree and terms of the polynomial are explained and an example is also discussed.

What are polynomials?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. It is a mathematical expression made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division (No division operation by a variable).

The expression's components that are divided up by the operators "+" or "-" are referred to as polynomial terms. In polynomials, like terms are ones that share the same variable and power. Unlike terms are those that have dissimilar variables and/or dissimilar powers.

The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. A polynomial equation's maximum number of solutions can be calculated using the degree.

The different types of polynomials based on terms are:

The different types of polynomials based on the degree are:

Example,

Consider a polynomial 3x² + 5x + 4

Number of terms = 3 (Trinomial)

Degree = 2 (Quadratic polynomial)

Therefore the degree and terms of the polynomial are explained and an example is also discussed.

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The answer is:

Work/explanation:

Here's how we classify polynomials based on the number of terms:

monomial - has only one term

binomial - has two terms

trinomial - has three terms

polynomial - has four terms or more

As for degrees, those are the highest exponents the polynomial.

Example: Classify [tex]\bf{2p^2+p}[/tex].

It has 2 terms so it's a binomial.

Its highest exponent is 2 so it's a second degree binomial.

Answer: There are 10 candidates for each position, and since a candidate can only hold one leadership position, the number of ways to fill the president position is 10. After the president position is filled, there are 9 candidates remaining for the vice president position. Finally, there are 8 candidates remaining for the secretary position.

The total number of ways to fill the three positions is the product of the number of ways to fill each position. Therefore, the number of ways to fill the three positions is:

10 x 9 x 8 = 720

So there are 720 different ways to fill the three leadership positions using the 10 possible candidates.

Step-by-step explanation:

The vertex of a parabola (1.75, -0.25). The vertical intercept of a parabola is (0, 11). The two intercepts of the parabola ((7 + √5)/4, 0) and ((7 - √5)/4, 0).

A) The vertex of a parabola is given by the formula (h, k), where h = -b/2a and k = f(h). In this case, a = 4, b = -14, and c = 11. So, h = -(-14)/2(4) = 14/8 = 1.75. Plugging this value back into the equation, we get k = f(1.75) = 4(1.75)^2 - 14(1.75) + 11 = -0.25. Therefore, the vertex of the parabola is (1.75, -0.25).

B) The vertical intercept is the point where the parabola crosses the y-axis, which occurs when x = 0. Plugging this value into the equation, we get f(0) = 4(0)^2 - 14(0) + 11 = 11. Therefore, the vertical intercept is the point (0, 11).

C) The two intercepts of the parabola are the points where it crosses the x-axis, which occur when f(x) = 0. We can use the quadratic formula to find these values:

x = (-b ± √(b^2 - 4ac))/2a

x = (-(-14) ± √((-14)^2 - 4(4)(11)))/2(4)

x = (14 ± √(196 - 176))/8

x = (14 ± √20)/8

x = (14 ± 2√5)/8

x = (7 ± √5)/4

Therefore, the two intercepts are the points ((7 + √5)/4, 0) and ((7 - √5)/4, 0).

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The three points that are not collinear are J, K and L

In geometry, points that are not collinear are points that do not lie on the same straight line. i.e. points that are not collinear are points that are not on the same line

Using the above as a guide, the non-collinear points are points J, K and L

Opposite rays are two rays that have the same endpoint and extend indefinitely in opposite directions.

Using the above definition, we have

Opposite rays = HG and HI

The line JH can be named based on its endpoints

So, another name for JH is HJ

Three points are required to form a plane

This means that the planes that contain HL can be named as GHL and JHL

There are other planes that contained HL too

See attachment for the sketch

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