PQ and RS are two chords of a circle with centre O. The perpendiculars drawn from O to PQ and RS are OX and OY respectively. Show that PQ² - RS² = 4OY - 4OX.​

PQ And RS Are Two Chords Of A Circle With Centre O. The Perpendiculars Drawn From O To PQ And RS Are

Answers

Answer 1

Answer:

Step-by-step explanation:

Radii PO and RO will be called r

Pythagorean theorem

r² = PX² + OX²

r² = RY² + OY²

      PX² + OX² = RY² + OY²

       PX² - RY² = OY² - OX²

similar triangles based on diameters rather than radii

(2PX)² - (2RY)² = (2OY)² - (2OX)²

      PQ² - RS² = 4OY² - 4OX²

Going by the picture provided rather than your posted question which is missing a couple of squaring exponents on the right hand terms.


Related Questions

need help asap please please please please​

need help asap please please please please

Answers

Answer:

What is the question actually asking for?

Step-by-step explanation:

will mark brainleist pls help

will mark brainleist pls help

Answers

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

If the zeros of a quadratic functions are -2 and 4, which graph could represent the function? A. A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10). B. A parabola declines from (negative 5 point 8, 10), (negative 5, 7), (negative 4, 0), (negative 8, negative 2), (negative 1, negative 8 point 4) and rises through (2, 0), (3, negative 6) and (3 point 9, 10). C. A downward open parabola rises from (negative 6 point 2, negative 10), (negative 5 point 2, negative 6), (negative 4, 0), (negative 3, 1) and declines through (negative 1 point 4, negative 2), (1, negative 4), (0, negative 8), and (0 point 5, 10). D. A downward open parabola rises from (negative 0 point 5, negative 10), (0, negative 8), (1, negative 4), (2, 0), (3, 1), and declines through (5, negative 4), (6, negative 8), and (6 point 5, negative 10) on the x y coordinate plane.

Answers

Option A. The only graph that could represent the function with the zeros of -2 and 4 is the graph is : A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10).

How to determine the graph

The zeros of a quadratic function are the x-values where the function equals zero (where it crosses the x-axis). In this case, you mentioned that the zeros of the function are -2 and 4.

Looking at the provided options:

A. This graph crosses the x-axis at (-2, 0) and (4, 0), which are indeed the zeros of the function. Therefore, this could be a possible representation of the function.

B. This graph crosses the x-axis at (-4, 0) and (2, 0). These are not the zeros given for the function (-2 and 4), so this graph is not a possible representation of the function.

C. This graph crosses the x-axis at (-4, 0), but it never crosses at x=4. Instead, it crosses at x=2. Therefore, this is not a possible representation of the function.

D. This graph crosses the x-axis at (2, 0), but does not cross the x-axis at x=-2. Therefore, this is not a possible representation of the function.

So, the only graph that could represent the function with the zeros of -2 and 4 is the graph provided in Option A.

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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.

The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.

Answers

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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luck is preparing food for his dog he mixes 3 cup of dry food and some cup of wet food he put all the food into 4 bowls he puts 5/4 cups into each bowl

Answers

To find the amount of wet food Luck mixed with the dry food, we can use the fact that he put 5/4 cups into each of the 4 bowls. Therefore, he used a total of 5/4 x 4 = 5 cups of wet food.

Thus, Luck mixed 3 cups of dry food and 5 cups of wet food to prepare the dog's meal.

2.) 3(10x + 9) - 9(3x - 5)


SHOW WORK PLEASE

Answers

Answer:

3x+72

Step-by-step explanation:

Let's first simplify the equation 3(10x+9)−9(3x−5)

You want to distribute first

=(3)(10x)+(3)(9)+(−9)(3x)+(−9)(−5)

=30x+27+−27x+45

And then combine like terms:

=30x+27+−27x+45

=(30x+−27x)+(27+45)

=3x+72 (answer)

Answer:

Let's simplify step-by-step.

3(10x+9)−9(3x−5)

Distribute:

=(3)(10x)+(3)(9)+(−9)(3x)+(−9)(−5)

=30x+27+−27x+45

Combine Like Terms:

=30x+27+−27x+45

=(30x+−27x)+(27+45)

=3x+72


James T-shirt business uses the demand function P = -Q+31 and the supply function P = Q-17. According to these functions, what will the
equilibrium point (P.Q) be for James T-shirt business?

Answers

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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Write an equation that represents each side of the figure. Write your equations in slope-intercept form.

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The equation for the left side of the figure is y = -3x + 4. This equation is in slope-intercept form and describes a line with slope -3 and y-intercept 4.

The equation for the right side of the figure is y = x + 2. This equation is also in slope-intercept form and describes a line with slope 1 and y-intercept 2.

Help please I need to finish this IXL

Help please I need to finish this IXL

Answers

If the equation for a line "u" be represented as [y = (-2x + 10)], then the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)].

As per the question statement, the equation for a line "u" can be represented as [y = (-2x + 10)],

And we are required to determine the equation of another line "v", which is  parallel to line "u" and passes through the point (-1, 2).

To solve this question, first we need to know about a property of parallel lines, which is, "Any straight line parallel to a line of known slope will also have the same slope"

Now, the formula to determine the equation of a straight line having a known slope, say "m" and a y-intercept of "c" goes as, [y = (mx + c)], also known as the slope-intercept form of line. Comparing the equation of line "u" with this slope-intercept form, we get, [m = (-2)] and [c = 10].

That is, the slope of line "u" is (-2), and hence, the slope of line "v" must also be (-2) since they are parallel to each other.

Also, the formula to determine the equation of a straight line having a known slope, say "m", and passing through a known point, say (x₁, y₁), goes as, [(y - y₁) = {m(x - x₁)],  and using [m = (-2)] and [(x₁, y₁) = ((-1, 2)] in this formula, we get,

[(y - 2) = (-2){x - (-1)}]

Or, [(y - 2) = (-2)(x + 1)]
Or, [(y - 2) = (-2x - 2)]

Or, [y = (-2x - 2 + 2)]

Or, [y = (-2x)]

That is,  the equation of line "v", being parallel to line "u" and passing through the point (-1, 2) will be [y = (-2x)]

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-) Find the equation of the line that passes through (1,0) and (3,6).

Answers

The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

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

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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solve y''+y=t using laplace inverse with y(0)=1 and y'(0)=-2

Answers

The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

What is equation?

Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.

We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:

L[y''+y]=L[t]

Using the properties of Laplace transform, we can write this as:

s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)

Substituting the initial conditions and rearranging terms, we have:

Y(s)= (1/s) + (2/s2) + (1/s2)

We can then invert the Laplace transform to get the solution of the original equation:

y(t)= 1-2t+te-t

Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

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A certain antihistamine is often prescribed for allergies. A typical dose for a 100​-pound person is 22 mg every six hours. Complete parts​ (a) and​ (b) below. a. Following this​ dosage, how many 12.3 mg chewable tablets would be taken in a​ week? b. This antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6mL. Following the prescribed​ dosage, how much liquid antihistamine should a 100​-pound person take in a​ week?

Answers

On solving the provided question, we can say that equation is 532/13.5 = 39.4 doses

What is equation?

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

equation is

week * 7( days/week) * 24(hours/day) * 19/6(MILIGRAMS/HOURS)

532 milligrams for a week

532/13.5 = 39.4 doses

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Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.



Which statements about the function are true? Select three options.

The vertex of the function is at (–4,–15).
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.
The graph is negative on the interval x < –4.

Answers

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

9876x 96- 703

WILL MARK BRAINLEST

Answers

Answer:

947393

Step-by-step explanation:

you have the option of buying 20 tickets at the fair for 15$ or 45 for 27$ which is te best deal

Answers

45 tickets for 27$is definitely the best deal because if you go with the first option and buy it twice you will pay 25$for only 40 I can’t Explain properly but definitely 45 for 26$

Select the graph of y=cot x.

Answers

Answer:Suppose y= cot x is our parent function then remember general rules of transformation.1) y= -f(x), reflects the graph of f(x) across x-axis.2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.Now, apply these rules to y= -4 cot(x)the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.



Select the graph of y=cot x.
Select the graph of y=cot x.

List the subsets of the set { dog,cat,rabbit}

Answers

Answer: so dog goes to cat, dog goes to rabbit and cat goes to rabbit I think

Step-by-step explanation:

The possible Subset is

Sub sets :  {dog}, {cat}, {fish}, {dog, cat}, {dog, fish}, {cat, fish}, {dog, cat, fish}.

What is a subset ?

If each constituent of a set A is a member of a different set B, then the sets A and B are subsets of one another.

To put it another way, A⊂B A and B stand for the subset connection.

Set A is referred to as a subset of Set B if all of the elements in Set A are also found in Set B. In other words, Set A is a part of Set B. A is the subset of B, for instance, if set A contains the elements X, Y, and set B contains the elements X, Y, and Z.

We have set,

Set :  {dog, cat, fish}

Then, the subset contain the elements of set A as

Sub sets :  {dog}, {cat}, {fish}, {dog, cat}, {dog, fish}, {cat, fish}, {dog, cat, fish}.

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solve the system by graphing {3x+y=-19
-3x+3y=3}

Answers

The solution to the system of equations is 3x + y = -19 and -3x + 3y = 3 is (-5, -4)

Finding the solution to the system of equations

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

3x + y = -19

-3x + 3y = 3

Next, we plot the graph of the system (see attachment)

Using the graphing function on a calculator, we have the solution to be

(-5, -4)

This is so because the equations 3x + y = -19 and -3x + 3y = 3 intersect at the point (-5, -4) and they are not equivalent equations

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solve the system by graphing {3x+y=-19 -3x+3y=3}

Q/r = f/a i need to find a

Answers

Answer:

This is easy.

Step-by-step explanation:

Q/r = f/a

imagine Q/r is a whole number

so, a= f/(Q/r)

a=f* r/Q

a=fr/Q

that's it pretty ez

An architect creates a blueprint using a scale of 1 inch = 3.5 ft. If the actual
length of a patio is 21 feet, how long will the patio's length appear in the
blueprint?
O 6 inches
O 7 inches
O 17.5 inches
O 73.5 inches

Answers

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

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Mean, Median, Mode, Appropriate Measures, Standard
Deviation
Use this data set to answer all questions on this page.
513, 490, 496, 380, 490, 513, 503, 513, 500, 492
Question 1 Which of the following would be APPROPRIATE measure(s) of center. (1)Mean (2)Median (3) Mode. Question 2 Find the standard deviation. Round your answer to the tenths place(one decimal place)

Answers

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

given that l has been defined to refer to a list, write an expression whose value is a set containing all the elements of l.

Answers

For given that L has been defined to refer to a list , the expression whose value is a set containing all the elements of L is

set = { 1,2,3,4}

Writing List in Python :

Lists are used to store multiple items in one variable. Lists are one of Python's four built-in data types used to store collections of data, the other three being tuples, sets and dictionaries, all of different qualities and uses.

A list is a container which holds comma-separated values (items or elements) between square brackets where items or elements need not all have the same type.

#Programme representation

Input:

#Python code

#A list L is initialised

L = [ 3,4,2,1 ]

#set L containing all elements of list L

print(str(set(L)))

Output:

{ 1, 2, 3, 4 }

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given that l has been defined to refer to a list, write an expression whose value is a set containing

Which expression is equivalent to (3x-1) (-5x+6)?

Answers

Answer:

−15x2+23x−6

Step-by-step explanation:

(3x−1)(−5x+6)

=(3x+−1)(−5x+6)

=(3x)(−5x)+(3x)(6)+(−1)(−5x)+(−1)(6)

=−15x2+18x+5x−6

=−15x2+23x−6

(Diversifying Portfolios MC)
Two investment portfolios are shown with the amount of money placed in each investment and the ROR.
Investment
Tech Company Stock $2,800
Government Bond $3,200
Junk Bond
$950
Common Stock
$1,500
Portfolio 1 Portfolio 2
$1,275
$2,200
$865
$1,700
O Portfolio 2 earns $38.17 more.
Which portfolio earns the most, and by how much?
O Portfolio 1 earns $38.17 more.
O Portfolio 1 earns $76.20 more.
ROR
-3.75%
2.95%
4.56%
O Portfolio 2 earns $76.20 more..
7.18%

Answers

Answer:  Portfolio 1:

Tech Company Stock: $2,800 * 2.95% = $82.60

Government Bond: $3,200 * 4.56% = $145.92

Total return for Portfolio 1 = $82.60 + $145.92 = $228.52

Portfolio 2:

Junk Bond: $950 * (-3.75%) = -$35.63

Common Stock: $1,500 * 7.18% = $107.70

Total return for Portfolio 2 = -$35.63 + $107.70 = $72.07

From the calculations, we can see that Portfolio 1 earns $228.52 in returns, while Portfolio 2 earns $72.07. Therefore, Portfolio 1 earns $228.52 - $72.07 = $156.45 more than Portfolio 2.

 

Step-by-step explanation:

Find the length of side AB. Round to the nearest hundredth inch.

Find the length of side AB. Round to the nearest hundredth inch.

Answers

The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

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Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.

Answers

Answer:

27/35

Step-by-step explanation:

We use combination to solve for this

C(n, r), =nCr = n!/r!(n - r)!

From the question, we are told that:

Four couples are at a party. Four of the eight people are randomly selected to win a prize.

Four couples = 8 people.

= 8C4 = 8!/4! (8 - 4)!

= 70

No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)

This can happen in 4 ways

[4C1 × 3C2 ] × 4=

[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways

= 4 × 3 × 4 ways

= 48

The probability that both of the members of at least one couple win prizes

48 + 4C2/ 8C4

4C2 = 4!/2!(4 - 2) !

= 6

8C4 = 8C4 = 8!/4! (8 - 4)!

= 70

48 + 6/ 70

= 54/70

= 27/35

Therefore, the probability that both of the members of at least one couple win prizes is 27/35.

The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.

Given :

Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize.

The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:

Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.

Step 2 - According to the given data, the total number of people is 8.

Step 3 - So, the probability that both of the members of at least one couple win prizes is:

\(\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}\)

Step 4 - Simplify the above expression.

\(\rm P =\dfrac{48+ 6}{70}\)

\(\rm P = \dfrac{27}{35}\)

So, the probability that both of the members of at least one couple win prizes is 27/35.

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X3-x-9=0 bisection method

Answers

Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

A bank deposit of $300 earned $9 interest. The interest was what fraction of the deposit?

Answers

The deposit is $300

earned $9 interest

If we divided the deposit between the interest we obtain the fraction

\(\frac{300}{9}=\frac{100}{3}\)

The perimeter of the quadrilateral is 14 meters. What is the length of the unlabeled side? 2 m 6 m 7 m 9 m 5 m 4 m NEXT QUESTION 3 m ASK FOR HELP​

Answers

The length of the unlabeled side is 5.5 meters

Calculating the length of the unlabeled side

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

The quadrilateral (see attachment)


Represent the unlabeled side with x

The perimeter of the quadrilateral is the sum of the side lengths

So, we have

Perimeter = 3 + 2 + 3.5 + x

Evaluate

Perimeter = 8.5 + x

This also means that

8.5 + x = 14

So, we have

x = 5.5

Hence, the length of the unlabeled side is 5.5 meters

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The perimeter of the quadrilateral is 14 meters. What is the length of the unlabeled side? 2 m 6 m 7

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Which best describes the transformation?

The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.

Answers

Answer:

Correct answer is:

The transformation was a 180° rotation about the origin.

Step-by-step explanation:

Given the triangle RST formed by points:

\(R (1, 1),\\S (3, 1)\ and\\T (1, 6)\)

is transformed using (x, y) → (–x, –y) such that coordinates of triangle R'S'T' :

\(R' (-1, -1),\\S' (-3, -1)\ and\\T' (-1, -6)\)

Please refer to the attached image for the given dimensions and coordinates.

It is clearly visible that:

The given triangle RST has coordinates in first quadrant.

and the resulting coordinates R'S'T' are in third quadrant.

The rotation of angle from 1st quadrant to 2nd quadrant is \(90^\circ\) and

The rotation of angle from 2nd quadrant to 3rd quadrant is \(90^\circ\).

\(\therefore\) total rotation is \(180^\circ\).

Triangle RST was transformed using the rule (x, y) (x, y). The vertices of the triangles are shown.R

Answer:

b

Step-by-step explanation:

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