Find the slope!!!
Quickly please

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!

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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3x-y=2 i hope my answer helped

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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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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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

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:

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 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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The solution of the pair of linear equations 37x+41y=70, 41x+37y=86

x=5 andy=-3

An equation that has the highest degree of 1(one) is known as a linear equation.

The standard form of linear equations in two variables is expressed as

        Ax + By = C;

where A, B, and C are any real numbers,

x and y are the variables.

consider

37x+41y=70 ----------(1)

41x+37y=86 -----------(2)

By, Adding both the equations

78x+78y=156

taking 78 common

78(x+y)=156

x+y=2 --- (3)

sub. both the eq. so the sign will be changed

37x+41y=70

41x+37y=86

(-) (-) (-) {changing da signs}

-4x+4y= -16

taking -4 common

-4(x-y)=-16

x-y=8 --- (4)

now from (3) and(4)

x+y=2

x-y=8

Again adding (3) and (4)

2x=10

x=5

substitute x value in (3)

5+y=2

y=-3

so, values of x=5 nd y= -3

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Answer:

Step-by-step explanation:

a.v = 10 * 5 * 7 = 350cm^3

b.because 1m^3=1000dm^3=1000000cm^3

so 1cm^3=0.000001m3

350cm^3=0.00035m^3

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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The exact value of the sine of the angle is 21/29

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

(x, y) = (-20, 21)

We start by calculating the value of r using

r = √(x² + y²)

So, we have

r = √(-20² + 21²)

Evaluate

r = 29

Also, we have the following equation on a Cartesian plane

sin(θ) = y/r

So, we have

sin(θ) = 21/29

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Answer:

Step-by-step explanation:

The 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you could write the ratio as follows: 1: 3 if there is 1 male and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

So, we have the ratio:

18:21

3 more equivalent ratios will be:

18/21 = 6/7

18/21 * 2/2 = 36/42

18/21 * 5/5 = 90/105

Therefore, the 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.

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

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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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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 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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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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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?

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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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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Answer:

Step-by-step explanation:

Answer:

122.5

Step-by-step explanation:

First, multiply 86 by 122.

Then subtract 10492 from 10535.

Add a decimal point then add 0.

Multiply 86 by 5 and you get your answer.

The number of ways the players can be selected is given by combination and the value of C = 364 ways

The number of ways of selecting r objects from n unlike objects is given by combination :

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of selecting players be C

Let the total number of players n = 14 players

The number of players to be chosen x = 3 players

So , the combination is

ⁿCₓ = n! / ( ( n - x )! x! )

Substituting the values in the equation , we get

¹⁴C₃ = ( 14 )! / ( 14 - 3 )! 3!

On simplifying the equation , we get

¹⁴C₃ = ( 14 )! / ( 11 )! 3!

¹⁴C₃ = ( 14 x 13 x 12 ) / ( 3 x 2 x 1 )

¹⁴C₃ = 14 x 13 x 2

¹⁴C₃ = 364 ways

Hence , the combination of ways is 364 ways

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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].

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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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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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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