The line l cuts the y-axis at (0, 5). l also passes through the point (2, 1). find the equation of the line which is parallel to l and which passes through the point (3, 0).

Answer:

Dilation of 3

Step-by-step explanation:

Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].

The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.

So, the scale factor is [tex]\frac{6}{2}=3[/tex].

The total number of years that must pass before only 25 grams of an original 100-gram sample of C-14 remains unchanged is approximately 5,730 years.

This is because C-14 has a half-life of approximately 5,730 years. Half-life is the amount of time it takes for half of a sample of a radioactive element to decay. Therefore, after 5,730 years, half of the original sample of 100 grams of C-14 will have decayed, leaving 50 grams remaining.

After another 5,730 years, half of the remaining sample (25 grams) will have decayed, leaving only 25 grams remaining. This means that it takes 5,730 years for half of the sample to decay and another 5,730 years for half of the remaining sample to decay, resulting in a total of 5,730 x 2 = 11,460 years for the entire sample to decay to 25 grams.

It is important to note that C-14 dating is a method of determining the age of organic materials, such as wood, bones, and teeth, by measuring the amount of C-14 remaining in the sample. This technique is widely used in archaeology, geology, and other fields to date materials that are thousands of years old.

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Answer:

a) To find the points of intersection, P and Q, of the tangents and the circle, we can use the fact that a tangent line is perpendicular to the radius at the point of tangency. Therefore, the slope of the tangent line is the negative reciprocal of the slope of the radius.

We know that the equation of the circle is (x-3)² + (y + 3)² = 52. To find the slope of the radius, we can differentiate the equation of the circle with respect to x and y.

dx/dt = 2(x-3) and dy/dt = 2(y+3)

We know that the slope of the tangents is a. So, the slope of the radius is -1/a

Now we can use the point slope form of a line to find the equation of the tangent line.

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We can substitute the point of tangency, which is on the circle, into the point slope form.

y + 3 = -1/a(x - 3)

We can now substitute the point (3, -3) and the slope -1/a into the point slope form to find the equation of the line

y + 3 = -1/a(x - 3)

y = -1/a

Step-by-step explanation:

Not sure if this helps, hope it does!

The 7 rules of exponents are:

It's worth noting that these rules are only valid for real numbers, with the exception of the zero exponent rule, which is valid for any number except for zero. Also, some rules may have restrictions such as the Negative exponent rule, where the base cannot be zero.

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The product of the given expression is option C. 6x^3 - 33x^2 + 45x - 6.

The product of two or more numbers implies the final value that would be derived when the numbers are multiplied with each other.

The given expression in the question involves the expansion of brackets.

Thus it can be solved as;

(3x - 6) (2x^2 - 7x + 1)

Considering the first bracket, the first term is 3x and second term is -6. To solve the question thus require to first expand the second bracket by 3x, then by -6 to have;

(3x - 6) (2x^2 - 7x + 1)  = 6x^3 - 21x^2 + 3x - 12x^2 + 42x - 6

                      = 6x^3 - 33x^2 + 45x - 6

Therefore, the product of given brackets is 6x^3 - 33x^2 + 45x - 6. Thus option C.

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The value of "w" in the algebraic equation

4w = 96 which makes it true is equal to 24.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

We shall evaluate for the value of w in the algebraic equation 4w = 96 as follows:

The coefficient of w is 4 and can be removed to allow w stand alone by dividing both sides of the equation by 4

4w/4 = 96/4

w = 96/4

96 = 24 × 4, so 4 can cancel out and we have;

w = 24

Therefore, 24 is the value of w in the algebraic equation 4w = 96 that makes it true.

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The distance from the base of the ladder to the bottom of the house is 6 feet and the distance between the top of the ladder and the ground is 8 feet.

Length of the ladder = 10 ft

Let the distance between the base of the ladder and the bottom of the house = x

Then the distance between the top of the ladder and the ground = (x+2)

x and x+2 distance are perpendicular to each other and making a right-angle triangle with the ladder of length 10-ft.

By applying pythagoras theorem,

(10)² = (x)² + (x+2)²

100 = x²+x²+4+4x

2x² + 4x - 96=0

x² + 2x - 48 = 0

x² + (8x-6x) - 48=0

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

(x-6)(x+8) = 0

x = 6, x = -8

Taking the positive value

x= 6 feet, and (x+2) = 8 feet

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The solution of the given expression is x>1/2 and x<5.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets with out specifying their real values. The fundamentals of algebra taught us the way to specific an unknown value the usage of letters together with x, y, z, and so forth. those letters are called right here as variables.

An algebraic expression can be a aggregate of both variables and constants. Any cost that is positioned earlier than and expanded with the aid of a variable is a coefficient.

Given

linear equality in one variable,

and the expression ,

1<2x<5

so,

1<2x

2x>1

x>1/2

and another one x<5.

Hence, The solution of the given expression is x>1/2 and x<5.

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100,60,20 are the values in the triangle.

What is known as a triangle?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees in total.

                    The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to a total of 180 degrees.

5x+ 3x + x = 180°

 9x = 180

   x = 180/9

    x = 20

5x = 5 * 20 = 100

3x = 3 * 20 = 60

x = 20

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Using Trigonometric Identities, The value of y equals 20.36.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

These identities are in use when trigonometric function-based expressions need to be made simpler. The integration of non-trigonometric functions is a crucial application; a typical method is employing the substitution rule with a trigonometric function first, and then simplifying the resulting integral with a trigonometric identity.

Using Trigonometric ratios,

Sin θ = perpendicular / hypotenuse

Sin 69 = 19 / y

0.933 = 19 / y

y = 19 / 0.933

y = 20.36

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Given statement is True.

A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.

The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.

In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.

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Answer:

Step-by-step explanation:

Therefore , as a result after answering the question, we may state that the numbers in the tables of ten are 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

A set of numbers who represents the result of a calculation with several inputs is the concept of a mathematical table. data that is organized into rows and columns and contains numbers and descriptions. It is simple to recollect the table and ten pattern. The numbers are in the following order: 10, 20, 30, 40, 50, 60, 70, 80, 90, etc. Value tables are used to visualize connections between data elements. The values table can be used in your science lesson. To store data and look for patterns in that data, scientists and researchers utilize tables of values. Forecasting then makes use of this pattern.

Here,

table of ten are as follows:

10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

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The additive inverse of 9/-11 is 11/-9, and this can be calculated using the formula of multiplying the number by -1.

The additive inverse of any number is the opposite number of that number. The formula for finding the additive inverse is to multiply the number by -1. To find the additive inverse of 9/-11, we can use the formula and multiply -11 by -1. This gives us 11/-9. This means that the additive inverse of 9/-11 is 11/-9.

To explain the calculation in more detail, an additive inverse is the opposite of any number. This means that two numbers that are opposite of each other add up to zero. For example, the additive inverse of 3 is -3, and when 3 and -3 are added together, the result is 0.

The formula for finding the additive inverse is to multiply the number by -1. This means that the additive inverse of any number is the same number multiplied by -1. Applying this formula to 9/-11, we can multiply -11 by -1 to get the additive inverse. This gives us the result of 11/-9, meaning that the additive inverse of 9/-11 is 11/-9.

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There is no single answer to this question as there are many different types of inequalities and each one can have a different number of solutions.

Inequalities are mathematical statements that compare two values or expressions using an inequality sign. These signs can be:

Depending on the type of inequality and the values involved, the number of solutions can vary.

For example, a linear inequality with two variables will have an infinite number of solutions as the two variables can take on any real number value.

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As the word himself says, "midpoint" means "the point in the middle or center". Finding a midpoint is not too hard and has applications in many areas of statistics, from confidence intervals to sketching distributions, to means.

To Find the Midpoint Between Two Numbers.

If the numbers are given, then the midpoint is become the average of the two numbers. To calculate or answer the midpoint, we first add them up and then divide the result by 2. The formula is as follows:

Let x and y be two numbers. So, the midpoint is:

M = x + y/2

A midpoint is a point that lying between two points and is in the center of the line joining the two points.

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According to the given angle of elevation, she now ascend to get back to sea level at 111.6 feet.

The term in angle of elevation in math is defined as an angle that is formed between the horizontal line and the line of sight.

Here we have given that  a scientist uses a submarine to study ocean life.

Here we also know that She begins at sea level, which is an elevation of o feet.

As we all know that she descends 28.7 feet and then She ascends 9.9 feet.

Finally she descends a second time, 92.8 feet.

Now, she is at the level of,

In first stage, she is at the level of

=> 28.7 - 9.9

=> 18.8

Then she descends at the level of

=> 18.8 + 92.8

=> 111.6

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Answer:

13/20 or 0.65

Step-by-step explanation:

6/10=0.6

1/5=0.2

1/4=0.25

0.25+0.2+0.6=0.65

The perimeter of the rectangle ABCD in the coordinate plane is 8 units

An equation is an expression that shows the relationship between variables and numbers.

The distance between two points in the coordinate plane is given by:

[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The vertices of the rectangle is A(-6, -4), B(-4, -4), C(-4, -2) and D(-6, -2). Hence:

[tex]AB=\sqrt{(-4-(-4))^2+(-4-(-6))^2}=2\ units \\\\BC=\sqrt{(-2-(-4))^2+(-4-(-4))^2}=2\ units[/tex]

Perimeter of ABCD = 2(AB + BC) = 2(2 + 2) = 8 units

The perimeter is 8 units

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The equation of the perpendicular bisector of the segment with endpoints (3,7) and (-1,-5) is y = -1/3x + 4/3.

A triangle's perpendicular bisectors are lines that pass through the midpoint of each side and are perpendicular to the given side.

Here,

Given :

The perpendicular bisector is the line that passes through the midpoint and has an opposite-reciprocal slope.

The GH slope is:

m = (-5-7)/(-1-3)=-12/-4-3

The slope of a perpendicular line is: -1/m = -1/3

The GH midpoint is:

x=(3-1)/2=2/2=1

y= (7-5)/2=2/2=1

The slope of the line that passes through point (1, 1) is:

In point-slope form, 9-1-1/3(x-1) And

In slope-intercept form, y = -1/3 + 4/3.

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3x-y=2 i hope my answer helped

Jerrod can score 97 on the next test to have an average of at least 85

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.

We need to find the score on the next test to have an average of at least 85

Let x be the score of the next text.

75+82+94+77+x/5≥85

328+x/5≥85

328+x ≥ 85×5

328+x ≥425

Subtract 328 from both sides

x≥425-328

x≥97

Hence,  Jerrod can score 97 on the next test to have an average of at least 85

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After calculating , when k = 2 the matching area could be 48 for k=5 ,the matching area could be 300 and for k=1.2 ,the matching area could be 17.28 and for k=1 ,the matching area could be 12,for k=1/4 ,the matching area could be 3/4 .

What is area of rectangle ?

area of rectangle is defined as the product of length and breadth is called as the area of rectangle.

Given,

A rectangle with area 12 square units is dilated by a scale factor of k.

When linear dimensions of similar figures are related by a factor of k, their areas are related by a factor of k².

For an original figure of area 12, each image figure dilated by a factor of k will have an area of 12k².

For k=2, the area is =

 12(2)² = 12*4 = 48 square units

For k=5, the area is =

 12(5)² = 300  square units

For k=1, the area is =

 12(1)² = 12*1 = 12 . square units

For k=1/4, the area is =

 12(1/4)² = 12/16 = 3/4 . square units

For k=1.2, the area is =

 12(1.2)² = 12*1.44= 17.28 square units

Hence, After calculating , when k = 2 the matching area could be 48

for k=5 ,the matching area could be 300 and for k=1.2 ,the matching area could be 17.28 and for k=1 ,the matching area could be 12,for k=1/4 ,the matching area could be 3/4

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Answer:

$43.20

20% off 50 Is 40 and 8% of 40 is 3.2 so 43.20

A value which must be added 2x² - 7xy + 5y² to obtain x² + 4xy - 3y² include the following: -x² - 8y² + 11xy.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the standard form of a quadratic function is given by;

ax² + bx + c = 0

Let the variable k represent the value which must be added to the given quadratic function. Therefore, a mathematical expression which models and represent the situation is given by;

2x² - 7xy + 5y² + k = x² + 4xy - 3y²

k = x² + 4xy - 3y² - (2x² - 7xy + 5y²)

k = x² + 4xy - 3y² - 2x² + 7xy - 5y²

By collecting like terms, we have the following:

k = (x² - 2x²) + (-3y² - 5y²) + (4xy + 7xy)

k = -x² - 8y² + 11xy.

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Complete Question:

What must be added to 2x² - 7xy + 5y² to obtain x² + 4xy - 3y²?

Missing values: 2 cups, 4 cups, 9 cups,Equivalent ratios: 34:13, 23:3, 1:6, 2:4, 13:9

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Answer: if The parabola is passing right through (0, 0) and (9, 0). Then the correct option is C. The correct graph is C. I did this assessment before

Step-by-step explanation:

c² = a² + b² then the triangle is a right-angle triangle.

If c² > a²+ b² then it is an obtuse triangle.

If, C²< a²+ b². Then the triangle is an acute triangle

An acute angle is an angle whose measure is less than 90°. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are acute.

A right angle is an angle whose measure is equal to 90°. That is the measure of the angles of perpendicular lines.

An obtuse angle is an angle whose measure is greater than 90°. That is, in a pair of intersecting non-perpendicular lines, the larger of the angles are obtuse.

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The mistake that Yuri has made is that : he divided the equation by n instaed of dividing the equation by n-1

While finding the standard deviation of a group of scores, the formula has the denominator as n - 1

where n is the total number of values in the data set.

the data set is 12, 14, 9 and 21. Hence n = 4

N - 1 = 3

Going ahead to work with n = 4 would give a wrong result.

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the correct question is

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. he finds the mean is 14. his steps for finding the standard deviation are below. what is the first error he made in computing the standard deviation

The image is attached as well to the question

On solving the provided question we can say that the domain and Range of algebraic linear equation is all real number.

Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in measurements of continuously altering quantities such as size and time.

f(x) = 5 - x - 3

Domain is all real number.

and Range is also all real number.

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