11. Find the equation for the circle with center ​(−2​,4​) and passing through ​(5​,−3​).

By finding the magnitude and bearing, we conclude that the correct option is:

"about 29 miles at 25° south of west"

For a vector (x, y), the polar coordinates are the magnitude R and the bearing θ.

Such that:

[tex]R = \sqrt{x^2 + y^2} \\\\\theta = Atan(y/x)[/tex]

In this case, the original vector is (-26, -12), replacing that we get:

[tex]R = \sqrt{(-26)^2 + (-12)^2} = 28.6 \\\\\theta = Atan(-12/-26) = 24.7\°[/tex]

Where the angle is measured from the negative x-axis counterclockwise, so it is South of West.

Then we can describe this vector as:

"About 29 miles at 25° south of west".

The first option is the correct one.

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Inequalities help us to compare two unequal expressions. The correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The situation that can be represented by the inequality 150 ≤ 15x + 55 is Thomas has 55 baseball cards in his collection. He will buy 15 new ones every month. Thomas collects baseball cards for x months. For what values of x will Thomas have at most 150 baseball cards?

Hence, the correct option is C.

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[tex]~~~~~~\text{Arc length} = r \theta \\\\\implies 4\pi = r\left( 45 \times \dfrac{\pi}{180} \right)~~~~~~~~;[\theta ~ \text{is in radians.}]\\\\\implies 4 = \dfrac{45r}{180}\\\\\implies 45r = 180 \times 4 = 720\\\\\implies r = \dfrac{720}{45}\\\\\implies r = 16~ \text{units.}\\\\\text{Now,}\\\\\text{Area} = \pi r^2\\\\~~~~~~~=\pi \cdot 16^2\\\\~~~~~~~=256\pi~ \text{units}^2[/tex]

The interquartile range for the given data is 1 quesadilla.

The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.

To get the interquartile range, we must know the first and third quartiles. To find those, we need to know the median of the data.

There are 11 data points, so we can cross out 5 numbers on the left and cross out 5 numbers on the right. That leaves a median of 1.

Since we know the median is 1, we can find the first quartile by finding the median of the following numbers:

0, 0, 1/4, 1/2, 1/2  (any number less than 1).

There are five numbers, so cross out two numbers from the left and cross out two numbers from the right. We are left with the first quartile of 1/4.

Now that we have the first quartile, we need to find the third quartile. Since the median was actually the first "1" in the data set, the third quartile will be the median of the numbers to the right of that "

1: 1, 1, 5/4, 2, 2.

Cross out the leftmost two numbers, and cross out the rightmost two numbers. We are left with the third quartile of 5/4.

Now that we have both the third and first quartiles, we can find the interquartile range! The IQR is calculated by finding the third quartile minus the first quartile.

5/4 - 1/4 = 4/4 = 1.

Therefore, the interquartile range is 1 quesadilla.

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Answer:

11

Step-by-step explanation:

volume of a prism = area of base × height

plug in what we are given

275 = 25 × height

==> divide both sides by 25

11 = height

Answer:

The water in a lake is not safe for drinking, high turbidity levels in the lake​ Coliform bacteria occur innately in soil and in the intestines of humans and other organism.

CORRECT ANSWER: high turbidity levels in the lake​.

Step-by-step explanation:

The value of the given expression will be equal to ( x + y )² = a + 8.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The expression will be calculated as:-

( x + y )² = x² + y² + 2 xy

( x + y )²  =  a  +  2 x ( 4 )

( x + y )²  =  a  +  8

Therefore the value of the given expression will be equal to ( x + y )² = a + 8.

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Answer:

24 trillion miles. The nearest-known exoplanet is a small, probably rocky planet orbiting Proxima Centauri – the next star over from Earth. A little more than four light-years away, or 24 trillion miles.

The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.

Conversion means to convert the same thing into different units.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The nearest-known exoplanet from the earth is 4.25 light-years away.

We know that 1 lightyear = 5.879 × 10¹² miles.

Then the number of miles in 4.25 light-years will be

⇒ 4.25 light-years

⇒ 4.25 × 5.879 × 10¹² miles

⇒ 24.986 × 10¹² miles

The number of miles in 4.25 light-years will be 24.986 × 10¹² miles.

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Answer:

vertex = (0, 1 )

Step-by-step explanation:

f(x) = 9x² + 1 ← has it's vertex on the y- axis

let x = 0 in f(x)

f(0) = 9(0)² + 1 = 0 + 1 = 1

vertex = (0, 1 )

Answer:

C neither

the coordinates shows that only the x intercepts are moving not y the line of the graph will be horizontal and straight . it is not a function

The values of the numbers m and n that makes the given expression true are 3 and 12 respectively

From the question, we are to determine the values of the numbers m and n that will make the given expression true

The given expression is

(2x + m)² = 4x² + nx + 9

Opening the bracket on the left hand side,

(2x + m)²

(2x + m)(2x + m)

4x² + 2mx + 2mx + m²

4x² + 4mx + m²

∴ 4x² + 4mx + m² = 4x² + nx + 9

By comparing,

4mx = nx;

Then, 4m = n

and

m² = 9

∴ m = ±√9

m = ±3

Since we are given that both m and n are positive numbers,

∴ m = 3

Substitute the value of m into the equation, 4m = n

4×3 = n

∴ n = 12

Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively

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Answer:

∠A≅∠X          AB≅XZ

∠B≅∠Z          AC≅XY

∠C≅∠Y          BC≅ZY

ΔABC≅ΔZYX

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Step-by-step explanation:

no, no, you use the equation to identify a, b and c.

then you use the formula with these values to get the solutions to the equation (the values of x for which the equation delivers 0).

always remember, a quadratic equation always has 2 solutions. sometimes at least one of them are not a real number, sometimes the 2 springs are equal, ...

x² - 4x - 2 = 0

a, b, c are the factors of the terms in x and the constant term.

so,

a = 1

b = -4

c = -2

x = (-b ± sqrt(b² - 4ac))/(2a)

x = (4 ± sqrt((-4)² - 4×1×-2))/(2×1) =

= (4 ± sqrt(16 + 8))/2 = (4 ± sqrt(24))/2 =

= (4 ± sqrt(4×6))/2 = (4 ± 2×sqrt(6)) / 2 =

= 2 ± sqrt(6)

x1 = 2 + sqrt(6)

x2 = 2 - sqrt(6)

Answer:

x = 4.45 and x=-0.45

Step-by-step explanation:

A = 1

B= -4

C = -2

= [tex]\frac{-(-4) \sqrt{ (-4)^{2} -4 (1)(-2) } }{2(1)}[/tex]

= [tex]\frac{4\sqrt{16+8} }{2}[/tex]

=  [tex]\frac{4\sqrt{24} }{2}[/tex]

X = 4 + [tex]\sqrt{24}[/tex] / 2

x = 4.45

For x2

x= 4 - [tex]\sqrt{24}[/tex] / 2

x=-0.45

The inverse of the given function is expressed as y =  ±√x + 38

Given the equation below expressed as:

y = x²  - 36

Replace y with x

x = y² - 38

Add 38 to both sides of the equation

x + 38 = y² - 38 + 38
y² = x + 38

Take the square root of both sides

√y² = ±√x + 38

y =  ±√x + 38

Hence the inverse of the given function is expressed as y =  ±√x + 38

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Answer:

B on edge 2022

Step-by-step explanation:

took the quiz

The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

Instantaneous velocity  is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16[tex]t^{2}[/tex] + 600

a) Height at t = 0 = 600 feet

    Height at t = 3 seconds = f(3) = -16[tex](3)^{2}[/tex] + 600 = 456 feet

Distance travelled  = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken  = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = [tex]\frac{df(t)}{dt}[/tex] = [tex]\frac{d(-16t^{2} + 600) }{dt}[/tex] = -32t

  when instantaneous velocity equal average velocity

     -32t = -48

      t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

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Answer:

13.9

Step-by-step explanation:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Find the difference between coordinates:

(x2 - x1) = (-5 - 0) = -5

(y2 - y1) = (-3 - 10) = -13

Square the results and sum them up:

(-5)^2 + (-13)^2 = 25 + 169 = 194

Now Find the square root and that's your result:

Exact solution: √194

Approximate solution: 13.9284

The quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

The table of values is given as:

x: 0     1       2    3     4     5   6

y: 4.1 -0.9 -3.9 -5.1 -4.1 -4.1 -1.1

To determine the quadratic regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following calculation summary:

a = 0.7, b = -5.04 and c = 3.76

A quadratic regression equation is represented as:

y = ax² + bx + c

Hence, the quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

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Answer:

a) 38.40 yd  (2 dp)

b) 211.18 yd²  (2 dp)

Step-by-step explanation:

Formula

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]

[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]

Calculation

Given:

[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}[/tex]

[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}[/tex]

Please note:  As you have not specified if π should be approximated, I have not used an approximation for π.

Based on the points given about the locations these trees are planted, the trees that will be planted exactly on the x-axis are (a) Amla and Mango.

When plotting a line on a graph, the points that will be found on the x-axis are those that will have a y coordinate of 0.

From the table given, both Mango and Amla have y coordinates of 0 which means that they will be planted exactly on the x-axis.

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Answer:

  155 miles

Step-by-step explanation:

The sum of n terms of an arithmetic series is given by the formula ...

  Sn = (2·a1 +d(n -1))(n/2)

__

The number of miles Ryan ran in July is described by the arithmetic series ...

  0.5 +0.8 +1.1 +... (a total of 31 terms)

The first term is a1=0.5, and the common difference is d=0.3.

The total number of miles Ryan ran in July is ...

  S31 = (2(0.5) +0.3(31 -1))(31/2) = (1 +9)(31/2) = 155

Ryan ran 155 miles in July.

The volume that the similar aquarium will hold is 400 cubic feet

Similar figures are figures that have similar angles and sides.

Given the following parameters

Volume of similar aquarium

Substitute into the formula

V/H = v/h

4000/10 = v/1

400 = v

v = 400 cubic feet

Hence the volume that the similar aquarium will hold is 400 cubic feet

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Answer:  Let's just say that each of the units are 1 inch in sides, and since it's an irregular shape you have to separate each shape. So, the rectangle I separated is 14 inches.

The semicircle is 12.56.

Adding those two answers together comes out to 26.56.

Based on the triangle inequality theorem, the possible length of the third side of the triangle is: 9 < x < 51

The triangle inequality theorem states if a and b are two sides of a triangle, the possible length of the third side would be: a + b < x < a - b.

Two given sides of the triangle are 30 ft and 21 ft. The possible length of the third side of the triangle would be:

30 - 21 < x < 30 + 21

9 < x < 51

Possible length of the third side would range between: 9 < x < 51

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The length of the rope remaining after Nick cut off a piece of the rope is 1 29/36 yards

Length remaining = 5/9 of original length

5/9 of 3 1/4

= 5/9 × 13/4

= 65/36

= 1 29/36 yards

Therefore, the length of the rope remaining after Nick ncur off a piece of the rope is 1 29/36 yards

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Answer:

(-2.5,-2.5)

Step-by-step explanation:

(-4+-1)÷2=-2.5

(-3+-2)÷2=-2.5

Answer:

(-7, -4)

Step-by-step explanation:

Equating A and B to the Midpoint (M) :

Equations formed :

    2. -2 + y / 2 = -3

Coordinates of B :