Help! Equations of Lines!

In the triangles ABC and ADC the measure of ∠DAC = 25° and the length of AB is 12 cm.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

The triangle ABC and ADC follow the AAS theorem.

Here ∠C = ∠C, ∠A = ∠A and CD = CB

The line segment AC is the bisection of angle A, hence -

The missing angle is ∠A = ∠A.

Therefore, the missing angle measure is of 25°.

The missing side length is AB = AD.

Therefore, the missing side length is of 12 cm.

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So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

If Reena has completed one sixth of the 30 km run,

30 km / 6 = 5 km.

So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.

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Answer:

-4x + 5g

Step-by-step explanation:

4x + 7g - 2g - 8x

Combine the variable g with variable g and variable x with variable x

-4x + 5g

Answer:

the answer is 60990

Step-by-step explanation:

114×535

=60990

Answer:

-x + y = 2

Step-by-step explanation:

Graphing a shape means all the points in the shape will give you a true answer when you put the x and y back in the equation used to graph that shape.

Let's pick a point (0,2)

x = 1

0 = 1

This is not true, so the first option is wrong.

-x + y = 2

0 + 2 = 2

2 = 2

The second option is true.

x - y = 2

0 - 2 = 2

-2 = 2

This is not true, so the thrid option is wrong.

2x + y = 3

2(0) + 2 = 3

2 = 3

This is no true, so the fourth option is wrong.

The area of quadrilateral EFGH is closest to 29 square units.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

Based on the values or the sides, and the slopes given, the area will be:

= 1 + 4 + 8 + 8 + 2 + 4 + 2

= 29 units.

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Finally, to find the number of hours Geoff worked, we can divide both sides of the equation by 17.50:

h = 25

So Geoff worked 25 hours in his first week.

Let's call the number of hours Geoff worked in his first week "h". We can write an equation to find the value of h by using the information given.

Geoff's pay per hour is $17.50, so his pay for h hours would be 17.50h.

Including the $200 one-time hiring bonus, Geoff's total pay for the first week was $637.50, so we can write the equation:

17.50h + 200 = 637.50

To find the number of hours Geoff worked, we need to isolate the h term. To do this, we can subtract 200 from both sides:

17.50h = 437.50

Finally, to find the number of hours Geoff worked, we can divide both sides of the equation by 17.50:

h = 25

So Geoff worked 25 hours in his first week.

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The final solution to the given simultaneous equation is (0, -6)

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the set of equations below:

y = -x-6

x + 3y = -18

Using the substitution method;

Substitute equation 1 into 2 to have:

x + 3(-x - 6) = -18
x - 3x - 18  =-18
-2x = 0

x = 0

Since y = -x- 6

y = -0 - 6

y = -6

Hence the solution to the system of equation is (0, -6)

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C. When there is no outlier, the mean is the appropriate measure of center.

When there are no outliers in a dataset, the mean is a good measure of center because it takes into account the values of all the data points. The median is also a good measure of center, but it may not be the best choice if there are extreme values or outliers in the dataset, as it can be influenced by those values. However, when there are no outliers, both the mean and the median are appropriate measures of center.

Option A is not true because the mean is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and it can be affected by outliers, but not by the absence of outliers.

Option B is not true because the median is not skewed in one direction when there is no outlier. Skewness refers to the shape of the distribution, and the median is not affected by the shape of the distribution, but by the position of the values.

Option D is not true because the median can be used as the measure of center even when there is no outlier. It is a robust measure of center that is not influenced by extreme values.

Answer: 3x + 7

Step-by-step explanation: ??? I think you mean 3x + 7, yes? If I'm mistaken, please correct me :)))))

Answer:

Moore's Law states that the number of transistors on a microchip will double approximately every two years. So, if a microchip in a given year could hold 922,200 transistors, 19 years later, it could hold approximately 922,200 * 2^(19/2) = 922,200 * 2^9.5 = 922,200 * 15,564,224 = 14,225,067,008,000 transistors.

The expected value of the sum of the two dice is 72

It is calculated by finding the weighted average of all possible sums, where each possible sum is weighted by its probability of occurring.

Let's call the 8-sided die "A" and the 9-sided die "B". Then, the possible sums are:

2 (A: 1, B: 1), 3 (A: 1, B: 2), 4 (A: 1, B: 3), ..., 16 (A: 8, B: 8)

The probability of each sum is the product of the probabilities of the individual dice outcomes:

P(2) = (1/8) * (1/9)

P(3) = (1/8) * (2/9)

...P(16) = (8/8) * (8/9)

The formula gives the expected value of the sum:

E = ∑P(x) * x

where x is each possible sum and P(x) is its probability.

Plugging in the values, we get:

E = (1/8) * (1/9) * 2 + (1/8) * (2/9) * 3 + ... + (8/8) * (8/9) * 16

E = (1/72) * (2 + 3 + ... + 16) + ... + (8/72) * (16)

E = (1/72) * [2 + 3 + ... + 16] * 8 + ... + (8/72) * 8 * 8

E = (1/9) * [2 + 3 + ... + 16]

We can now use the formula for the sum of an arithmetic series:

S = n/2 * (a + b)

where n is the number of terms, a is the first term, and b is the last term.

Applying this formula to the series [2, 3, ..., 16], we get:

S = 8/2 * (2 + 16) = 8 * (9) = 72

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The definition of the f, h, and g functions, indicates the possible damains, range and composite functions are as follows;

(a) The domain of f is the set of real numbers except x = 5

The range is the set of all real numbers except f(x) = 0

(b) (f○g)(x) = 1/(3·x + 1)

(f○h)(x) = 1/(cos(x + 1) - 5)

(g○f)(x) = (6·x - 27)/(x - 5)

(c) g⁻¹(x) = (x - 6)/3

(d) The domain is; x ∈ R, and x ≠ 5

The domain of a function is the set of the possible input values of the function.

The specified functions are;

f(x) = 1/(x - 5), g(x) = 3·x + 6, h(x) = cos(x + 1)

(a) The domain of f is the set of numbers such that the rational polynomial, 1/(x - 5) is defined

The polynomial, f(x) = 1/(x - 5) is defined when x - 5 ≠ 0, therefore;

x - 5 + 5 ≠ 0 + 5 = 5

x - 0 ≠ 5

x ≠ 5

The polynomial, f(x) = 1/(x - 5) is difined where x ≠ 5

The domain is the set of all real numbers, such that x ≠ 5

The range of the function, is the set of the possible output values, such that as (x - 5) ≠ 0, f(x) ≠ 0

The range is therefore; -∞ < f(x) < ∞, f(x) ≠ 0

(b) The composite functions (f○g)(x) = f(g(x))

Therefore; (f○g)(x) = f(g(x)) = f(3·x + 6)

Plugging in x = (3·x + 6) in the function, f(x) = 1/(x - 5), we get;

f(g(x) = 1/((3·x + 6) - 5) = 1/(3·x + 1)

f(g(x) = 1/(3·x + 1)

(f○h)(x) = f(h(x))

h(x) = cos(x + 1), therefore; (f○h)(x) = f(cos(x + 1))

Plugging in x = cos(x + 1) in f(x) = 1/(x - 5), we get;

(f○h)(x) = f(cos(x + 1)) = 1/((cos(x + 1)) - 5)

(g○f)(x) = g(f(x))

g(f(x)) = g(1/(x - 5)) = 3/(x - 5) + 6 = (6·x - 27)/(x - 5)

(c) g⁻¹(x)

g⁻¹(x) is the inverse of the function, g(x), which can be foiund as follows;

Plugging in; y = g(x) = 3·x + 6

y = 3·x + 6

y - 6  = 3·x

x = (y - 6)/3

Therefore;

(d) (f + g)(x) = f(x) + g(x)

f(x) + g(x) = 1/(x - 5) + 3·x + 6

The use of a graphing calculator indicates that we get;

1/(x - 5) + 3·x + 6 = (3·x² - 9·x - 29)/(x - 5)

Therefore; (f + g)(x) = (3·x² - 9·x - 29)/(x - 5)

The domain is therefore, the possible values of x at which the denominator is not zero, that is x ≠ 5

The domain is the set real numbers except x = 5, which is; x ∈ R, x ≠ 5

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Based on the information provided, it can be concluded the sum is $11,000.

To know what is the sum, let's calculate the difference in the interest rate:

13% - 12% = 1%

This means the difference between the two interest rates presented is 1%. Based on this, let's calculate the 1% of the sums given:

Based on the above, the correct sum is $11,000 because only in this one 1%  is equivalent to $110.

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Answer:

The solution is B. (6x+8y)(6x-8y)

Step-by-step explanation:

(6x+8y)(6x-8y)

= 36x²-48xy+48xy-64y²

= 36x²-64y²

Or, we can use the formula (a-b)(a+b) = a²-b²

(6x+8y)(6x-8y)

= (6x)²-(8y)²

= 36x²-64y²

So, the answer is B

The solution of the expression 36x² - 64y² will be (6x - 8y)(6x + 8y).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 36x² - 64y². The expression will be solved as below,

E = 36x² - 64y²

E = (6x)² - (8y)²

E = ( 6x + 8y )( 6x - 8y)

The solution of the expression is E = ( 6x + 8y )( 6x - 8y).

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Los intervalos numéricos en la recta numérica para x=2, en donde x ∈R y x>2 y x<7, son: (2, 7).

En la recta numérica, los intervalos se definen utilizando dos números, uno inferior y uno superior. Por ejemplo, el intervalo (2, 7) representa todos los números entre 2 y 7, incluyéndolos. Esto significa que el intervalo (2, 7) incluiría 2, 3, 4, 5, 6 y 7. Además, los intervalos numéricos pueden incluir o excluir los números de los extremos. Por ejemplo, el intervalo (2, 7) representa todos los números entre 2 y 7, incluyéndolos, mientras que el intervalo (2, 7] sólo incluiría 3, 4, 5, 6 y 7.

The number intervals on the number line for x=2, where x ∈R and x>2 and x<7, are: (2, 7).

On the number line, intervals are defined using two numbers, one lower and one upper. For example, the interval (2, 7) represents all numbers between 2 and 7, including them. This means that the interval (2, 7) would include 2, 3, 4, 5, 6 and 7. In addition, numerical intervals can include or exclude the numbers at the ends. For example, the interval (2, 7) represents all numbers between 2 and 7, including them, while the interval (2, 7] would only include 3, 4, 5, 5, 6 and 7.

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Given that x, y, z are different and satisfy the equations:

x^3 + x^2 - x = 0

y^3 + y^2 - y = 0

z^3 + z^2 - z = 0

We can multiply the first equation by y, the second by z, and the third by x to obtain:

x^3y + x^2y - xy = 0

y^3z + y^2z - yz = 0

z^3x + z^2x - zx = 0

Adding these three equations together, we get:

x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0

Expanding and simplifying, we find that:

x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0

Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:

x^2 - x + y^2 - y + z^2 - z = 0

We can also write this as:

(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0

This expression can be factorized as:

(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0

Since x, y, and z are all different, we have that:

(x - 1)(x + 1) ≠ 0

(y - 1)(y + 1) ≠ 0

(z - 1)(z + 1) ≠ 0

Therefore, we have:

(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0

So, we can conclude that:

xyz = -1

And,

1 + xyz = 0

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Answer:

x > 50

Step-by-step explanation:

[tex]\frac{x}{10}[/tex] > 5 ( multiply both sides by 10 to clear the fraction )

x > 50

Answer:

Option D. 30 units

Step-by-step explanation:

The two sides of the right triangle will be 5 and 12 units as we can see from the diagram

Now to find the hypotenuse, we will use the Pythagoras Theorem

5² + 12² = Hypotenuse²

25 + 144 = Hypotenuse²

169 = Hypotenuse²

So,

Hypotenuse = root169 = 13

Perimeter of Right triangle = sum of all sides

Perimeter of Right triangle = 5 + 12 + 13

Perimeter Of Right triangle = 5 + 12 + 13 = 30

Option D. 30 units is the correct answer

Answer:

30

Step-by-step explanation:

See the attached worksheet.  The perimeter of the triangle is the sum of its three sides, labelled a, b, and c.

a and b can be calculated from the graph, as shown on the worksheet.

Once a and b are know, use the ZPythagorean Theorem to find c, which is 13.

Finially, add the sides a, b, and c:  5 + 12 + 13 = 30, the perimeter.

The ratio of cleaning product to water for the condition is 1/5

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

Given it is recommended that 4 ounces of the product are diluted using 20 ounces of water.

to find the ratio of cleaning products to water

ratio = cleaning product/water

cleaning product = 4 ounce

water = 20 ounces

ratio = 4/20

4/20 is equivalent to 1/5

ratio = 1/5

Hence option A is correct.

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The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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Answer:

201 eighth graders and 201 + 54 = 255 seventh graders at the middle school.

Step-by-step explanation:

The system of equations representing the situation is:

x + 54 = 456 - x

2x + 54 = 456

2x = 402

x = 201

where x represents the number of eighth graders. So, there are 201 eighth graders and 201 + 54 = 255 seventh graders at the middle school.

The base of the ladder must be placed 3 ft from the base of the building. The total length of the ladder is 15 ft.

1. The ladder must reach 12 ft up the wall, so we need to calculate the distance from the base of the building to 12 ft.

2. The total length of the ladder is 15 ft.

3. Subtract the length of the ladder (15 ft) fromthe desired height (12 ft) to get the distance from the base of the building.

4. 12 ft - 15 ft = -3 ft

5. Since the distance cannot be negative, the base of the ladder must be placed 3 ft away from the base of the building.

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The trigonometric ratio for sin Z is 3/5 in the given right triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The right triangle is given in the question, as shown.

As we know the cosine ratio, is as follows:

cos Z = base/hypotenuse

cos Z = YZ/XZ

cos Z = 32/40

cos Z = 4/5

Now, as we know the sine ratio, is as follows:

sin Z = √(1 - cos² Z)

sin Z = √(1 - (4/5)²)

sin Z = √(1 - 16/25)

sin Z = √(9/25)

sin Z = 3/5

Thus, the trigonometric ratio for sin Z is 3/5.

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Numbers that summarize a sample of data are called "sample statistics," and numbers that summarize populations are called "population parameters."

A sample statistic is a single value that describes a characteristic of a sample, such as the mean, median, or standard deviation. Sample statistics are used to make inferences about the population from which the sample was drawn.

A population parameter, on the other hand, is a single value that describes a characteristic of an entire population, such as the population mean, population standard deviation, or population proportion. Population parameters are usually not known and must be estimated from a sample.

For example, if you have a sample of 100 students' heights, the mean height of the sample (a sample statistic) can be calculated and used to make inferences about the mean height of the population of all students.

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The evaluation of the expression is 1198.4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Expression;  52 × (7.2 + 16) − 8

Now,

=52*23.2-8

=1206.4-8

=1198.4

Therefore, the algebra will give 1198.4.

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By AA similarity Triangle ABC and DEF are similar.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

First in Triangle ABC

using Angle Sum Property

<C= 180 - <A - <B

<C = 180 - 77 - 48

<C = 55 degree

and, In Triangle DEF

using Angle Sum Property

ND= 180- <E- <F

<D = 180- 55 - 48

<D = 77

As, In both Triangle ABC and DEF all angles triangles are Equal.

<A = <D= 77

<B = <E = 48

<C = <F= 55

So, by AA similarity Triangle  ABC and DEF are similar.

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The slope of the line is given as the change in y divided by the change in x.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. In contrast to the net change in the x coordinate, the net change in the y coordinate is y.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

Hence, the slope of the line is given as the change in y divided by the change in x.

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The value of the equation is  A = 81

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 4 ^ ( log₂ ( 9 ) )   be equation (1)

On simplifying the equation , we get

log₂ ( 9 ) = 2 log₂ ( 3 )

So , on further simplification , we get

A = 2² ^ ( 2 log₂ ( 3 ) )

A = ( 2⁴ )^log₂ ( 3 )

From the logarithmic rule , a^logₐ ( b ) = b

Substituting the values in the equation , we get

A = 2 ^ ( log₂(3) )4

A = 3⁴

A = 81

Hence , the equation is A = 81

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