50 POINTS ASAP Use the image to determine the type of transformation shown.

image of polygon ABCD and a second polygon A prime B prime C prime D prime above it

180° clockwise rotation
Horizontal translation
Reflection across the x-axis
Vertical translation

The nature of the solution is a consistent and dependent system, and the solution point is (4, 0).Based on the given system of linear equations:

Equation 1: y = (4/3)x - 8

Equation 2: 4x - 3y = 24

The solution to the system of linear equations is (4, 0).

By substituting the value of y from Equation 1 into Equation 2, we get:

4x - 3((4/3)x - 8) = 24

4x - 4x + 24 = 24

0 = 0

This means that both equations are equivalent and represent the same line. The two equations are dependent, and the solution is not a unique point but rather a whole line. In this case, the solution is consistent and dependent.

The equation y = (4/3)x - 8 can be rewritten as

3y = 4x - 24, which is equivalent to

4x - 3y = 24. Therefore, any point that satisfies one equation will also satisfy the other equation. In this case, the point (4, 0) satisfies both equations and represents the solution to the system.

So, the nature of the solution is a consistent and dependent system, and the solution point is (4, 0).

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One possible function to model the firework scenario is h(t) = -4.9t² + 77.8t + 0.5, derived from a parabolic path due to gravity, with a maximum height of 760.5 meters and landing 78 meters away from launch.

One possible function to model this scenario could be:

h(t) = -4.9t² + 77.8t + 0.5

where h(t) is the height (in meters) of the firework above the ground at time t seconds after it was launched.

To derive this function, we first note that the path of the firework can be modeled by a parabolic function due to gravity. The vertex of this parabola corresponds to the maximum height of the firework, which occurs at t = 77.8 / (2 * 4.9) = 7.96 seconds.

At this time, the height of the firework is h(7.96) = 760.5 meters, which we can use to solve for the coefficient of the quadratic term (-4.9) in the function h(t). We also know that the firework lands 78 meters away from where it was launched, which means that it spends a total of 15.92 seconds in the air (assuming no air resistance). We can use this fact to solve for the linear term (77.8) in the function h(t).

Finally, we add a constant term of 0.5 to adjust for the initial height of the firework above the ground at t = 0.

Note that this function assumes idealized conditions and does not take into account air resistance or other factors that may affect the flight of the firework.

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Complete question:

The fire department is setting off fireworks. They notice that the casing of the firework hits the ground 78 meters from where the firework was launched. The firework exploded at a maximum height of 760. 5 meters. Write a function to model this scenario.

The point of intersection for the function is  (2, 2)

Considering to the line passing through the points (0,6) and (3,0)  to be f(x).Therefore the slope intercept of the function is

m = 0-6/3-0 = -2

So, the functions F(x) in the slope-intercept form f(x)= -2x+6  ......1

interchanging the variable x to y and y to  x

=> x =-2y + 6

=> 2y = -x + 6

=> y= -0.5x + 3

let  f⁻¹(x)= y

f⁻¹(x) =-0.5x+3   ......2

Solving the equation  1 and 2, we get

=> -0.5x + 3 = -2x + 6

=> 2x - 0.5x = 6 - 3

=> 1.5x = 3

=> x = 2

Substituting the values of x in the function  we get,

f( x) = -2(2) + 6 = 2

Thus, the outcome is (2,2)

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Answer:

mean = 5+9+9+6+6+11+8+4/7 = 8.29

median = 6

mode = 6

range = 11 - 4 = 7

Answer:

Step-by-step explanation:

5 , 9 , 6 , 6 , 11 , 8 , 4

Mean = sum of all data ÷ number of data

         \(= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7\)

Median: To find median, arrange in ascending order and medianis the middle term

4 , 5 , 6 , 6 , 8 , 9 , 11

Middle term = 4th term

Median = 6

Mode: a number that appears most often is mode

6 appears 2 times

Mode = 6

Range:

Range = maximum value - minimum value

          = 11 - 4

          = 7

A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;

c + f = 13

200c + 650f = 4400

where; c is the number of cans of soup and f is the number of frozen dinners.

Let us denote c as the number of cans of soup and f is the number of frozen dinners.

The total number of items is 13 and so, we can write;

c + f = 13

The total amount of sodium is 4400 mg.  Each can of soup has 200 mg, and each frozen dinner has 650 mg.

200c + 650f = 4400

We can use substitution or elimination to solve the equation for c and f but we are not asked to find it. Thus, we will conclude that;

A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;

c + f = 13

200c + 650f = 4400

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Answer:

Step-by-step explanation:

11970658976

Answer:

5 hundred millions, 4 millions, 6 thousands, 2 tens = 504,006,020

Step-by-step explanation:

504,060,020 > 5 hundred millions, 4 millions, 6 thousands, 2 tens

                                                                                      (504,006,020)

Answer:

(x + 12)(x - 3)

Step-by-step explanation:

\( {x}^{2} + 9x = 36 \\ {x}^{2} + 9x - 36 = 0 \\ {x}^{2} + 12x - 3x - 36 = 0 \\ x(x + 12) - 3(x + 12) = 0 \\ (x + 12)(x - 3) = 0\)

Answer:

0.5 g/cm^2

Step-by-step explanation:

Volume of the cube: Base * height

7 * 2 = 14 * 3 = 42 cm^2

Density of the cube: grams / cm^2

21 grams / 42 cm^2 = 0.5 g/cm^2

The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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Compute the speed of the car:

\(\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}\)

So after 1 hour, Sal will have driven about 56 mi.

Answer:

.83 cents

Step-by-step explanation:

Answer: Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?

$\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$

Solution

Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram.

[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("$A$",A,N); dot("$O$",O,NW); dot("$B$",B,W); dot("$C$",C,E); dot("$H$",H,S); label("$2$",O--(-.7,-.385),N); label("$1$",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]

We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.

See Also

Answer:yes

Step-by-step explanation:

but if the y intercept is 0 then it’ll show like: y= 3x which is equal to y=3x plus or minus 0

No, a piecewise function does not always have an x and y intercept.

A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain interval of the main function's domain.

An x-intercept is the point where the function crosses the x-axis, and a y-intercept is the point where the function crosses the y-axis.

It is possible for a piecewise function to not have an x or y intercept if none of the sub-functions cross the x or y axis. For example, the piecewise function f(x) = {2x + 1 for x < 0, -2x + 1 for x > 0} does not have an x or y intercept because neither of the sub-functions cross the x or y axis.

In conclusion, a piecewise function does not always have an x and y intercept. It depends on the sub-functions that make up the piecewise function.

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The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Step-by-step explanation:

\( { \cot^{2}x}(1 + \tan^{2}x) \\ = \frac{1}{ \tan^{2}x} (1 + \tan^{2}x)\)

\( = \frac{1}{ \tan^{2}x } + 1\)

\( = \frac{ \cos^{2} x }{ \sin^{2}x } + 1 = \frac{ \cos^{2}x + \sin^{2}x}{ \sin^{2} x } \)

\( = \frac{1}{ \sin^{2}x } = \csc^{2} x\)

To find the formula for the position function r(t), we need to integrate the given velocity function v(t) with respect to t.

Given:

v(t) = ⟨3cos(t), 3sin(t), -1⟩

Integrating each component of v(t) separately, we get:

∫3cos(t) dt = 3sin(t) + C₁

∫3sin(t) dt = -3cos(t) + C₂

∫-1 dt = -t + C₃

Now, we have the following components for the position function r(t):

x(t) = 3sin(t) + C₁

y(t) = -3cos(t) + C₂

z(t) = -t + C₃

To find the constants C₁, C₂, and C₃, we use the initial condition r(0) = ⟨3, 1, 1⟩:

x(0) = 3sin(0) + C₁ = 3 + C₁ = 3

y(0) = -3cos(0) + C₂ = -3 + C₂ = 1

z(0) = -0 + C₃ = C₃ = 1

From the initial condition, we have:

C₁ = 0

C₂ = 4

C₃ = 1

Substituting these values back into the components of r(t), we get:

x(t) = 3sin(t)

y(t) = -3cos(t) + 4

z(t) = -t + 1

Therefore, the formula for the position function r(t) is:

r(t) = ⟨3sin(t), -3cos(t) + 4, -t + 1⟩

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Answer:

Yes.

Step-by-step explanation:

Yes. They are normal

Answer:

Average

Step-by-step explanation:

If a and b are the lengths of the bases, then a+b/2 is the length of the midsegment of the trapezoid.

Answer:

If the initial angle is given in the form or radians, add or subtract 2π instead of 360°. radians. Adding 2π to the original angle yields the positive coterminal angle. By subtracting 2π from the original angle, the negative coterminal angle has been found.

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

so if Lily has $60 and takes out (subtracts) 12 a week then it would look like this

    TOTAL STARTED WITH       EACH WEEK

          $60                  -12              48

         $48               -     -12           36

         $36                      -12          24

           $24                  -12          12

          $12                   -12           0

SO Lily will have enough money to deposit for 5 weeks

The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

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If Lola uses only ³/₄ gallons of fruit juice, proportionately, she will need the following quantities of the other ingredients:

Proportion is the ratio or relative relationship of one value against another.

Proportion is used to show the quantity of a number contained in another.

Proportions are depicted using fractions, decimals, or percentages.

Available Ingredients for a Punch Recipe:

Bottles of ginger ale = 2 liters

Gallons of fruit juice = 1 gallon

Gallons of sherbet = ¹/₂ gallons

The proportion of fruit juice used = ³/₄ gallons

The proportion of ginger ale to be used = 1¹/₂ liters (2 x ³/₄)

The proportion of sherbet to be used = ³/₈ gallons (¹/₂ x ³/₄)

Thus, in proportion, Lola will use 1¹/₂ liters of ginger ale and ³/₈ gallons of sherbet if she cuts the recipe by using ³/₄ gallons of fruit juice.

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A poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. The dimensions that maximize the printed area are 500 cm x 23.52 cm.

The problem can be solved using the following concept:

Suppose we have a function f(x), then at the maximum/minimum point, it holds:

          f '(x) = 0

In the given problem, let:

q = length of the poster

p = width of the poster

Then,

p x q = 11760

or q = 11760/p

Let f(p,q) be the function of printed area, then:

f(p,q) = (p - 20)(q - 12)

f(p) = (p - 20) (11760/p - 12)

f(p) = -p² + 1000p - 980 x 20

At the maximum point:

f '(p) = 0

-2p + 1000 = 0

p = 500

Substitute p = 500 to get q:

q = 11760/p = 11760/500 = 23.52

Hence, the maximum printed area obtained if the dimensions are 500 cm x 23.52 cm

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer: -10,-5,3,15

A,C,D,E

The next one is a= -5, b=1, c=-5, d=-12

The last one is 3 & 4

The rational root theorem is used to determine the potential roots of a function.

The potential roots are: \(\mathbf{-10, -5, 3, 15}\)

The function is given as:

\(\mathbf{P(x) = x^3 + 6x^2 - 7x - 60}\)

For a polynomial function:

\(\mathbf{P(x) = px^n +.............+ q}\)

The potential roots are:

\(\mathbf{Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}}\)

The factors of 60 are:

\(\mathbf{60 = \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30, \pm 60}\)

The factor of 1 is:

\(\mathbf{1 = \pm 1}\)

So, we have:

\(\mathbf{Factors= \frac{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30, \pm 60}{\pm 1}}\)

\(\mathbf{Factors= \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 10, \pm 12, \pm 15, \pm 20, \pm 30, \pm 60}\)

The potential roots in the option are:

\(\mathbf{Factors= -10, -5, 3, 15}\)

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Answer:

see explanation

Step-by-step explanation:

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³