find the equation of the tangent line at the given point on the following curve.
x^2+y^2=8, (-2,-2)

If a || b || c, then a || c using Euclid's axiom.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation.

Here,

given,

a || b || c

Euclid's axiom states that “Things which are equal to the same thing are equal to one another.” Here, A and C are things which are equal to B, so A=C.

so using this,

a || c

If a || b || c, then using Euclid's axiom, a || c.

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Answer:

1250 in savings

Step-by-step explanation:

Answer:

1 microgram per day = 0.000000001/86400 kilograms per second

Value of expression 1: 176

Value of expression 2: 32

Are they equivalent? No

Equivalent expressions are expressions that work the same way even though they look different. They have the same value for all values of the variables. They can be transformed into each other using the rules of algebra, such as the commutative, associative, and distributive properties.

Since the value of y is 2

Expression 1: 4y (y + 20)

To evaluate 4y (y + 20), substitute y = 2 into 4y (y + 20). That is:

4*2 (2 + 20) = 8(2+20) = 8(22) = 176

Expression 2: 4y + 24

To evaluate 4y + 24, substitute y = 2 into 4y + 24. That is:

(4*2) + 24  = 8 +24 = 32

Since the value of expression 1 is not equal to the value of expression 2. Thus, they are not equivalent.

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if u can't do this then ur in the matrix and a failure to life

The unit rate of the number of pages penny reads per hour is; 56 pages per hour

A unit rate is also called unit ratio and it describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Now, we are told that;

Number of pages penny reads = 14 pages

Time he takes to read the 14 pages = 1/4 hours

Thus, applying the concept of unit rate gives;

Unit rate = 14/(1/4)

Unit rate = 14 * 4/1

Unit rate = 56 pages per hour

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Answer:

The percentage of increase in price is 175%. To calculate this, you can subtract the cost price (in this case, $1) from the selling price ($2.75) to find the profit ($1.75). Then divide that profit by the cost price and multiply by 100 to express it as a percentage.

$2.75 - $1 = $1.75

$1.75/$1 * 100 = 175%

If you want to calculate the percentage increase in price, use the formula:

Percentage Increase = (New Price - Original Price) / Original Price x 100

In this case, the original price is $1 (the price of buying the cards) and the new price is $2.75 (the price of selling the cards). So, plugging these values into the formula:

Percentage Increase = (2.75 - 1) / 1 x 100 = 175%

The percentage increase in price is 175%.

An ellipse's equation is (x - h)2/a2 + (y - k)2/b2 = 1.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called 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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

According to our question-

c is the distance between the center and the focus, and a and b are the distances from the center to the vertices, respectively, in the formula c2 = a2 - b2.

Therefore, we have 12 = 42 - b2.

As a result, 1 = 16 - b2, or b2 = 15.

The final equation is therefore written as x2/16 + y2/15 = 1.

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A. The given relation is a function, but is not one-to-one. A possible domain for the inverse is given as follows: x ≥ 4.

B. The inverse function is given as follows: [tex]f^{-1}(x) = \sqrt{0.5(x + 8)} + 4[/tex]

C. The composition of the function with it's inverse results in x, hence they are inverse.

The quadratic function for this problem is defined as follows:

y = 2(x - 4)² - 8.

The classifications regarding function and one-to-one are given as follows:

The inverse can only be obtained when the function is one-to-one, hence a possible domain is given as follows:

x ≥ 4.

(as the vertex is at x = 4).

To obtain the inverse, first we must exchange the variables x and y, hence:

x = 2(y - 4)² - 8.

Now we must isolate the variable y, as follows:

2(y - 4)² = x + 8

(y - 4)² = 0.5(x + 8)

[tex]\sqrt{(y - 4)^2} = \sqrt{0.5(x + 8)}[/tex]

[tex]y - 4 = \sqrt{0.5(x + 8)}[/tex]

[tex]f^{-1}(x) = \sqrt{0.5(x + 8)} + 4[/tex]

The composition of the two functions is given as follows:

[tex](f \circ f^{-1}(x)) = 2(\sqrt{0.5(x + 8)} + 4 - 4)^2 - 8)[/tex]

[tex](f \circ f^{-1}(x)) = 2(\sqrt{0.5(x + 8)})^2 - 8[/tex]

[tex](f \circ f^{-1}(x)) = x + 8 - 8[/tex]

[tex](f \circ f^{-1}(x)) = x[/tex]

As the composition results in x, they are inverses.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \:f(x) = {x}^{2} + 2x + 9[/tex]

[ plug in the value of x in the expression ]

[tex]\qquad \sf  \dashrightarrow \: f(3) = (3) {}^{2} + 2(3) + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 9+6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 24[/tex]

Concluding that there is an effect when in reality no effect exists is known as a: Standard error.

The approximate standard deviation of a statistical sample population is known as the standard error (SE) of a statistic.

By utilizing standard deviation, the standard error is a statistical concept that assesses how accurately a sample distribution represents a population. In statistics, the difference between a sample mean and the population's actual mean is known as the standard error of the mean.

The difference between the population's computed mean and one that is widely regarded as correct is described by the standard error.

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Answer:

The expression G³-h² + 8, when g = 3 and h = 5, evaluates to:

3³ - 5² + 8 = 27 - 25 + 8 = 10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

3^3=27,

5^2=25,

27-25=2,

2+8=10

The price of an adult ticket is $14 and the price of a children's ticket is $8.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the price of an adult's ticket and y be the price of a children's ticket.

One family bought 1 adult ticket and 3 children's tickets for a total of $38.

x + 3y = 38

Another family bought 2 adult tickets and 4 children's tickets for a total of $60.

2x + 4y = 60

We have two linear equations in two variables here.

x + 3y = 38

2x + 4y = 60

Multiplying the first equation throughout by 2, we get,

2x + 6y = 76

Subtracting the second equation 2x + 4y = 60 from the multiplied first equation 2x + 6y = 76, we get,

2x + 6y - (2x + 4y) = 76 - 60

2y = 16

y = 8

x + 3y = 38 ⇒ x = 38 - 24 = 14

Hence the price of an adult's ticket and children's ticket is $14 and $8 respectively.

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Chanice's approximate displacement is 8.60 km as she rides her scooter 7 kilometers north. She has lunch and then travels 5 kilometers east.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides. The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse.

Here,

To find the length of one missing side in a triangle, you can use the Pythagorean Theorem:

a² + b² = c²

7² + 5² = c²

49 + 25 = c²

74 = c²

√74 = c

c ≈ 8.60 km

8.60 km is Chanice's approximate displacement as she drives her scooter 7 kilometres north. She stops for lunch and then drives 5 kilometres east.

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Based on the changes that occurred in Ariel's bank account, the missing values are -$223.75, -$1.40, and -$4.40.

The missing values from the given table of the changes that occurred in Ariel's bank account balance is determined as follows:

Week 4 change:

Change = -$41.40 - $182.35

Change =  -$223.75

Week 5 balance: this is obtained from the sum of the change and the balance of the previous week:

Balance = -$41.4 + $40

Balance = -$1.40

Week 6 change:

Change = -$5.80 - (-$1.4)

Change  = -$4.40

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Answer:

-1/4

Step-by-step explanation:

perpendicular slopes are negative reciprocals

the negative reciprocal of 4 is -1/4

Answer: X = 25

Step-by-step explanation: We can use the Law of Cosines to solve for the remaining side of the triangle, which we'll call "x".

The Law of Cosines states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this triangle, we are trying to find side "x" (c) so we can use the following equation:

x^2 = 20^2 + 17^2 - 2(20)(17)cos(H)

Now we can substitute the known values into the equation:

x^2 = 400 + 289 - 680cos(H)

Now we can solve for x by taking the square root of both sides:

x = sqrt(400 + 289 - 680cos(H))

= sqrt(689 - 680cos(H))

= sqrt(9 + 289cos(H))

Alternatively, we can use Law of Sines to solve for side x.

The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C)

Knowing all the angles in the triangle we can use the following equation

x/sin(K) = 20/sin(P) = 17/sin(H)

Now we can substitute the known values into the equation

x = (20*17)/sin(H)

In both case we get x = 25.

On solving the provided question, we can say that perimeter of the quadrilateral  the value of x =0.8333333333.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

Here quadrilateral sides are 3x+2, x, 2x+5, 6x-17

To find the perimeter of a quadrilateral,

we need to add all the lengths of four sides,

i.e., the perimeter of ABCD Quadrilateral = sum of lengths of all sides

                         = AB +BC + CD + DA.

                         = 3x+2+x+ 2x+5+6x-17

                         = 12x+(7-17)

                        = 12x-10

      Simplifying

 12x + -10 = 0

Reorder the terms:

-10 + 12x = 0

Solving

-10 + 12x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.

-10 + 10 + 12x = 0 + 10

Combine like terms: -10 + 10 = 0

0 + 12x = 0 + 10

12x = 0 + 10

Combine like terms: 0 + 10 = 1

12x = 10

Divide each side by '12'.

x = 0.8333333333

Simplifying

x = 0.8333333333

so the value of x =0.8333333333

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The answer is 75.96 degree.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The perpendicular = 2 and base=8

 Thus tan ∅ = 2/8

           tan ∅=1/4

                 ∅=tan⁻¹(1/4)

                   = 14.03

Therefore the required angle is 180-(90+14.03)=  75.96°

Hence, The answer is 75.96 degree.

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0.3221469052

I hope its right

Answer:

[tex]\dfrac{223}{64}=3.484375[/tex]

Step-by-step explanation:

The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.

The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.  

As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.

The number of partitions is the number of rectangles used.  

Partitions can be of equal length or not of equal length.

Given:

The given partition divides the interval [0, 1] into 3 subintervals:

To calculate the areas of the rectangles, multiply the width of each rectangle by its height.

The width is the difference between the x-values of each subinterval.

The height is the minimum value of the function across the subinterval. For the given function, this is the value of the function for the right side of the subinterval.

First rectangle [0, 1/2]:

[tex]\begin{aligned}\implies \left(\dfrac{1}{2}-0\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{2} \cdot \left(4-\left(\dfrac{1}{2}\right)^2\right)\\\\&=\dfrac{1}{2} \cdot \dfrac{15}{4}\\\\&=\dfrac{15}{8}\end{aligned}[/tex]

Second rectangle [1/2, 3/4]:

[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(4-\left(\dfrac{3}{4}\right)^2\right)\\\\&=\dfrac{1}{4} \cdot \dfrac{55}{16}\\\\&=\dfrac{55}{64}\end{aligned}[/tex]

Third rectangle [3/4, 1]:

[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(1\right)&=\dfrac{1}{4} \cdot \left(4-\left(1\right)^2\right)\\\\&=\dfrac{1}{4} \cdot 3\\\\&=\dfrac{3}{4}\end{aligned}[/tex]

Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:

[tex]\implies \dfrac{15}{8}+\dfrac{55}{64}+\dfrac{3}{4}=\dfrac{223}{64}=3.484375[/tex]

Answer: To find the solution of a system of equations, we can either use substitution or elimination method.

For this system of equations, we can use the substitution method:

First, we solve one equation for one of the variables. For example, we can solve the first equation for y: y = -2x - 4

Then, we substitute this expression of y into the second equation and solve for x: 1/2x + 6 = -2x - 4

We can simplify this equation by adding 2x to both sides: 1/2x + 2x + 6 = -4

And then by adding 6 to both sides: 1/2x + 2x + 12 = 2

And then by multiplying both sides by 2: x + 4x + 24 = 4

And then by simplifying: 5x = -20

Finally, we find x = -4

Now that we have found x, we can substitute it back into one of the equations to find y:

y = -2(-4) - 4 = 8 - 4 = 4

So the solution of the system of equations is x = -4 and y = 4

We can check that this solution satisfies both equations.

Step-by-step explanation:

The range for the given domain is {4, -5, -1, 44}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Here set A is the domain and the images of the elements of set A is range.

Given the function,

f(x) = x² - 5

Domain is {-3, 0, 2, 7}

Domain is the values of x and range is the value of f(x).

If x = -3, f(x) = (-3)² - 5 = 4

If x = 0, f(x) = 0² - 5 = -5

If x = 2, f(x) = 2² - 5 = -1

If x = 7, f(x) = 7² - 5 = 44

So the range is {4, -5, -1, 44}

Hence the set {4, -5, -1, 44} is the range of the function given.

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Answer: -3

Step-by-step explanation:

ubuve 2.2 it stay the same -2.4 is -3

The  slope of the line with the points (-2/3,-3) and (-1.5,-5/7) is 2.743.

The concept that will be used is the slope. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The slope of  the line passing through the points9 x1 y1) and (x2, y2 ) can be written as :

m= (y2 - y1)/(x2 -x1)

x1 = -2/3 , y1 = -3

x2 = -1.5 , y2 = -5/7

Then substitute the values,

Then the slope = [ (-5/7+3) / (-1.5+2/3 )]

= (16/7)/(-5/6)

=2.743

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Answer:

[tex]\huge\boxed{\sf Option\ C.}[/tex]

Step-by-step explanation:

3x² = -12

x² = -12/3

x² = -4

√x² = √-4

x = √-1 × √4

We know that [tex]\sqrt{-1} =i[/tex]

i(iota) is an imaginary number. So, we can say that the equation has no real solutions.

[tex]\rule[225]{225}{2}[/tex]

Answer:

66 units

Step-by-step explanation:

Diagonals in a rectangle are congruent (equal)

14x + 10 = 11x + 22

Subtract 11x from the right side and subtract -10 from the left to isolate the x's with a constant

You would get: 3x = 12

Divide both sides by 3 to isolate the x by itself;

You would get: x = 4

Next, plug in the value of 4 for whichever equation you want.

11(4) + 22 is what I chose and I got 66.

Hope this helps.

Answer: -4

Step-by-step explanation: u have to do -14x+11x=-3 then u do 22-10=12 now u  have to do 12 divide by -3 and u will get -4 as ur answer

The probability that the teenager picked at random is male and their favorite hobby is playing video games is given as follows:

1/16.

The definition of a probability is that it is calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired and the total outcomes for this problem are given as follows:

Of the 14 males, 2 have playing videogames as their favorite hobby, hence the number of desired outcomes is given as follows:

2.

Then the probability is calculated as follows:

p = 2/32

p = 1/16.

The probability was simplified as the quotient of 32 and 2 has a result of 16.

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Answer:

( Where is says “ Use the answers to the problems above to help solve some of those below “ I cannot see the left side. Therefore, I cannot help you there )

3/4 of 32=24

74x32=2368

1/4 of 33=8.25

74x33=2442

0.75x32=24

76x32=2432

0.75x33=24.75

76x33=2508

75x32=2400

0.76x32=24.32

75x33=2475

0.76x33=25.08

24x96=2304

75x37=2775

0.74x32=23.68

76x112=8512

Step-by-step explanation:

Answer:

[tex]C = \dfrac{1}{3} L[/tex]

Step-by-step explanation:

Number of cups of flour/number of loaves = constant, k

We can see this ratio is constant throughout the table

6/2 =9/3 = 15/5 = 3

Therefore the equation can be written as

C/L = 3

or

C = (1/3)L

where C is the number of cups needed to make L loaves