find an equation for the circle that goes through the points (0, 0), (0, 8), and (6, 12). find an equation for the line that is tangent to this circle at (6, 12).

Answer:

The correct equations are 2x +3y=100 and x+y=48. These equations can be used to find the number of multiple-choice and free response questions on the test. The first equation, 2x +3y=100, shows that the total number of points for the multiple-choice questions (2x) plus the total number of points for the free response questions (3y) equals 100. The second equation, x+y=48, shows that the total number of multiple-choice and free response questions on the test is equal to 48. These equations can be solved simultaneously to find the values of x and y.

Answer:

5

Step-by-step explanation:

(20/12)(3)=5

The parallel line has an equation of y = 1/3x + 2

The equation is given as

3y-x=-12

Make y the subject in the equation

So, we have

y = x/3 - 4

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 1/3

The slopes of parallel lines are equal

This means that the slope of the other line is 1/3

i.e. m = 1/3

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m = 1/3

Also, we have

(x, y) = (6, 4)

So, we have

4 = 1/3 * 6 + c

This gives

c = 4 - 2

Evaluate

c = 2

So, we have

y = 1/3x + 2

Hence, the equation of the parallel line is y = 1/3x + 2

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The required volume of the right circular cone is 135.83409in³.

A right circular cone is one whose axis is the line between the vertex and the circular base's midway.

In other words, a right angle is formed when the center point of the circular base and the cone's peak are united.

So, the right circular cone volume formula:

V=1/3hπr²

Diameter = 8.8 in

Radius = 8.8/2 = 4.4 in
Now, calculate the volume as follows:

V = 1/3hπr²

V = 1/3(6.7)π(4.4)²

V = 135.83409 in³

Therefore, the required volume of the right circular cone is 135.83409in³.

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Original shape will contract when scale factor is less than 1 , expand when scale factor is greater than 1 and it doesn't change when scale factor is 1

A scale factor is a number that can be used to change the size of any geometrical figure or shape in relation to its original size. It is the ratio of the sizes of the original and dilated figures.

It is denoted by "k"

The magnitude of the scale factor is taken into account, and it cannot be zero. The scale factor has the ability to either increase or decrease the size of an object.

The basic formula for calculating the scale factor of a dilated figure is as follows:

Scale = dimension of preimage / dimension of image

According to the question,

(a) If scale factor is less than 1 , k < 1 then the original shape will contract means It's size will decrease

(b) If scale factor is greater than 1 , then image will enlarge and it would expand

(c) If scale factor is equal to 1 , then No change in shape nor in size

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Answer:   -25x + 15

Step-by-step explanation:

Because you asked

Answer:

To simplify the expression, we can use the rules of order of operations, which dictate that we should perform operations in the following order:

Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost.

Perform any exponents or radicals.

Perform all multiplications and divisions, working from left to right.

Perform all additions and subtractions, working from left to right.

Applying these rules to the expression -5(-3 + 5x), we get:

Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost:

$-5(-3 + 5x)$

$-5(-3) + -5(5x)$

$15 + -5(5x)$

Perform any exponents or radicals:

$15 + -5(5x)$

Perform all multiplications and divisions, working from left to right:

$15 + -5(5x)$

$15 + -25x$

Perform all additions and subtractions, working from left to right:

$15 + -25x$

Therefore, the simplified expression is 15 + -25x.

Step-by-step explanation:

Answer: i-Ready and c

Step-by-step explanation: I hope this helps

Answer:

y=14x−3 .

Step-by-step explanation:

We know that the equation of a line is y=mx+b with m being the slope and b being the y-intercept. We can plug in your slope ( 14 ) and your y-intercept ( −3 ). This simplifies to y=14x−3 .

Answer:$ 16.50

Step-by-step explanation:If you are adding, you do

$8.50+

8.00

------------

16.50

0 plus 0 is nothing.

5 plus 0 is 5.

8 plus 8 is 16.

Your answer is now "16.50" .

The value of C to the nearest tenth, is 70.5.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

We have the triangle ABC.

Where c = 22ft, a = 18ft and b = 20ft

Law of Cosines:

c² = a² + b² - 2ab cosC

Substituting the value of a, b and c to the above equation.

22² = 18² + 20² - 2(18)(20) x cosC

484 = 724 - 720 x cosC

Rearranging

-240 = -720 x cosC

Divide both sides by

-7200.3333333333 = cosC

To find the value of C:

C = Arc cos 0.3333333333

Now the value of arc cos from the trigonometric table,

C = 70.52877936753502

Therefore, the C = 70.5 rounded to the nearest tenth.

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Answer:

To use coordinates on a coordinate grid, you first need to determine the scale of the grid, which is represented by the proportion M=24R. This means that for every 24 units on the grid, the corresponding real-world distance is equal to R units.

Once you have determined the scale of the grid, you can use the coordinates to locate points on the grid. To do this, you will need to know the coordinates of at least one point on the grid, which is known as the origin. The origin is typically represented by the coordinates (0,0).

To find the coordinates of a point on the grid, you can use the following steps:

For example, if you wanted to find the coordinates of a point that is 5 units to the right of the origin and 3 units above the y-axis, the coordinates of the point would be (5, 3).

The theorem that proves that the triangles are congruent is the Side-Side-Side (SSS) Congruence Theorem.

The Side-Side-Side (SSS) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This theorem is useful for proving that two triangles are congruent without having to use angles. The SSS Congruence Theorem is a useful tool for solving geometry problems involving triangles. It can be used to find the unknown side length of a triangle given the lengths of the other two sides, or in more complicated proofs involving multiple triangles. This theorem is also helpful in determining the area of a triangle, as the area is proportional to the product of the lengths of the sides.

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The solution is A = 7

The value of the equation A = 9 - ( 8/S ) when S = 4 is 7

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

The equation A = 9 - ( 8/S )

Now , when S = 4

Substitute the value of S = 4 in the equation , we get

The value of A = 9 - ( 8/S )

The value of A = 9 - ( 8 / 4 )

The value of A = 9 - ( 2 )

The value of A = 7

Therefore , the value of A is 7 when S = 4

Hence , The value of the equation A = 9 - ( 8/S ) when S = 4 is 7

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Approximately 1700 Americans died of AIDS in 1983. In 2006, 14,260,633,600 individuals would have perished from AIDS if the trend had remained unchecked.

When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

When people in a population reproduce at a certain pace, exponential growth results. After a time of exponential expansion, a population's growth slows or pauses, which is known as logistic growth.

Exponential growth model Growth factor = 2

model y = a(2)^t

a = initial

y = final

Let 1983 as t=0

y = 1700 × (2)^t

In 2006

t = 2006 - 1983

= 23

y = 1700 × (2)^23

= 1700 × (8388608)

= 14,260,633,600 people would have died

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Yes, you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Here Rin says that you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

The statement is right because for the calculation of the y-intercept we need one point to pass through the line and the slope of the line.

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Answer:

7

Step-by-step explanation:

4x+7=4x+7

-4x-7=-4x-7

The value of the function h(f(x)) for x = 3 is h(f(3)) = 348.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is

  [tex]f(x)=x^3+8x\\\\g(x)=\sqrt{2x}\\\\h(x)=7x-9[/tex]

Now we have to find the value of the function h(f(x)),

            [tex]h(f(x))=7(f(x)) - 9\\\\h(f(x))=7(x^3+8x)-9\\\\h(f(x))=7x^3+56x-9\\\\$at x = 3, $\\\\h(f(3))=7(3)^3+56(3)-9\\\\h(f(3))=7*27+168-9\\\\h(f(3)) = 348[/tex]

Hence, the value of the function h(f(x)) for x = 3 is h(f(3)) = 348.

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Answer:

Step-by-step explanation:

We first rewrite the terms of 48x² +38x + 5 to 48x² + 8x + 30x + 5

We then regroup terms into two proportional parts: (48x² +8x) + (30x + 5)

Factor the expression: 8x(6x + 1) + 5(6x + 1)

We then factor 8x(6x + 1) + 5(6x + 1) to (6x + 1)(8x + 5)

Now that we know (ax + b) and (cx + 1) is (6x + 1)(8x + 5) we just need to apply the numbers to their corresponding letters:

A=8

B=5

C=6

Yes. The matrix A-2I is invertible because 2 is an eigenvalue for matrix A.

When the matrix (transformation) is applied to some vectors (eigenvectors), the eigenvalues of the matrix are scalars. In other words, if A is a square matrix of order n x n and v is a non-zero column vector of order n x 1, and Av = v (the product of A and v is just a scalar multiple of v), then the scalar (real number) is called an eigenvalue of the matrix A that corresponds to the eigenvector v.

The eigenvalues can be determined by formula,

[tex]|A-\lambda I|=0[/tex]

Where, [tex]\lambda[/tex] = eigenvalues.A square matrix with an inverse is known as an invertible matrix. A square matrix is said to be invertible if and only if the determinant is not equal to zero. In other words, a 2 x 2 matrix is only invertible if its determinant is not zero.

Given,

A is a 4x4 matrix whose eigen values are λ=1,2,3,4

we need to determine that A-2I is invertible or not.

We know that 2 is an eigen value of matrix A, so, if we substitute 2 to find determinant of A-2I, then we will get zero as answer.

So, when determinant of A-2I is zero then the matrix is invertible.

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The speed of 150 kilometres in five hours is 30 kilometres per hour.

The speed is calculated by the formula -

Speed = total distance covered ÷ total time taken

The distance covered is 150 kilometres and time taken is five hours.

Keep the values in formula to find the speed -

Speed = 150/5

Performing division on Right Hand Side of the equation to find the speed

Speed = 30 kilometres per hour

Hence, the speed of mentioned data covering the distance 150 kilometres in time duration of five hours is 30 kilometres per hour.

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The temperature on a cold winter day in Minnesota was - 6ﾟ F. the temperature decreased by 4ﾟ from a high of 2ﾟ earlier in the day situations could explain how the temperature became - 6ﾟF.

A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, temperature is measured. Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin (SI).The temperature was -6ﾟ F. This means that the temperature must have decreased from a higher temperature to reach - 6ﾟF. This can be explained by option C, the temperature decreased by 4ﾟ from a high of 2ﾟ earlier in the day.

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The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.

What is an Exterior Angle?

An Exterior Angle is the angle formed by a polygon's side and an extended neighbouring side; an angle generated by a transversal as it cuts one of two lines and located on the line's outside.

Solution:

Using the Alternate Exterior Angle Property we can say

Adjecent Angle of Angle 2 and Angle 3 are equal

Also, Angle 2 + Adjecent Angle of Angle 2 = 180

So, we can write Angle 2 + Angle 3 = 180

The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.

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Based on the CPCTC, the statement that is not true is: A. ∠BCA ≅ ∠BCT.

CPCTC stands for "corresponding parts of congruent triangles are congruent". This simply means that if two triangles are congruent to each other, every of its corresponding angles and corresponding sides are equal or congruent to each other.

In the image given, we are told that ∆BAT ≅ ∆CAT. Thus, this implies that all the corresponding angles are congruent to each other, so also are all their corresponding sides.

Therefore:

Therefore, the statement that is not true is:

A. ∠BCA ≅ ∠BCT

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Answer: 10(4z+5)

Step-by-step explanation:

Find the Greatest common factor, which is 10

10(4z+5)

The value of the slope is 1 and the value of the y-intercept is 6.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = (10 - 6 ) / ( 4-0)

Slope = 4 / 4 = 1

The y-intercept will be calculated as,

y = mx + c

6 = 0 + c

C = 6

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The value of the given elements are: 0.829.

Given:

The given numbers are: 8,9,33,44,57,60,62,64,73,74,77,86

Here, the largest Number is 86 = Xₐ

and the smallest number is 8 = Xₙ

Now,

Range = Xₐ -Xₙ

           = 86 - 8

           = 78

Therefore,

Coefficient  of Range = Xₐ - Xₙ / Xₐ +Xₙ

                                    = 86 - 8 / 86 +8

                                    = 78 / 94

                                    = 0.829

Therefore, the value is 0.829.

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y = 3x – 2 is the equation of the line which passes through 1/3 and 2 5 with slope.

We can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We know one point on the line, which is (1/3, 2.5). We can calculate the slope by calculating the rise (change in y) divided by the run (change in x), which is (2.5 - 0) / (1/3 - 0) = 2.5 / 0.33 = 7.5. Therefore, the equation of the line is y = 7.5x + b. To solve for b, we can substitute in our point, (1/3, 2.5) into the equation. We get 2.5 = 7.5(1/3) + b, or 2.5 = 2.5 + b. Therefore, b = 0, and the equation of the line is y = 7.5x + 0, or y = 7.5x.

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Answer:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Step-by-step explanation:

umm....I really hope this helps u