Put the following equation of a line into slope-intercept form, simplifying all fractions.
4y−6x=24

The average rate of change for the given function is -72.

What Is the Average Rate of Change?

To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change. To determine the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.

The rate of the change for the interval [a,b] is given by

[tex]\frac{f(b)-f(a)}{b-a} \\[/tex]

For the given interval [3,11],

[tex]= \frac{f(11)-f(3)}{11-3} \\\\= \frac{-623+47}{8} \\\\= -72[/tex]

So, the required average rate of change is -72.

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Angelique needs 3 8/15 hours to completely build the fence.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Angelique builds a fence and she can build 5/8 of the fence in 2 5/6 = 17/6 hours.

We know a number multiplied to its reciprocal is 1.

Therefore, The amount of time Angelique needs to complete the fence is,

(5/8)×(8/5) the complete fence in (17/6)×(8/5) hours.

= 136/30 hours.

= 3 16/30 hours.

= 3 8/15 hours.

Q. Angelique builds a fence. After working for 2 5/6 hours, she has built 5/8 of the fence, how much time she needs to complete the fence?

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The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.

The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.

In interval notation, the domain of -2x is (-∞, ∞).

However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].

To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].

Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].

So, the domain of g(x) is [-16, 8] in interval notation.

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We can use the two points given to find the slope of the line (which represents the population growth) and then use the point-slope form of the equation of a line to write an equation.

The population at time t=4 is 1580, which means P(4) = 1580. The population at time t=7 is 2000, which means P(7) = 2000. We can use these two points to find the slope:

slope = (P(7) - P(4)) / (7 - 4) = (2000 - 1580) / 3 = 140

So the slope of the line representing population growth is 140. Now we can use the point-slope form of the equation of a line to write an equation:

P - 1580 = 140(t - 4)

Simplifying and rearranging, we get:

P = 140t - 380

So the correct equation that represents the situation is:

P(t) = 140t - 380.

Answer:

im pretty sure ia 31,61

Step-by-step explanation:

Answer: 10⁰

Step-by-step explanation:

We know that,

 the summation of 3 angles of a triangle is 180⁰.

now, (6x-5)⁰+(5x-5)⁰+8x⁰=180

 or, 19x-10=180⁰

 or, 19x=190⁰

 or, x= (190/19)⁰

 or, x= 10⁰

Answer:

First option: 4.9 in

Step-by-step explanation:

The area of a circle, given radius = r is computed using the formula
A = πr²

Here we are given the area and asked to find the radius r

A = 75.43 in² = πr²

So
πr² = 75.43
r² = 75.43/π
   = 24.01
   = 24 rounded to nearest integer

r = √24
  = 4.9

Answer:

956 centimeters is equal to 9.56 meters.

How many meters are in 956 centimeters?

Well, first, we must understand the conversion from meters to centimeters and centimeters to meters.

1m=100cm and 1cm=0.01m. So multiply by 100 if converting from m to cm and divide by 100 if converting from cm to m.

In this problem, we're looking at cm to m.

Take 956cm and divide that by 100. You'll get 9.56m. That's your answer.

Hope this helped!

Answer: To find the height of the roof, we need to find the point where the ball reaches the maximum height, i.e., the point where the velocity of the ball is equal to 0.

The velocity of the ball can be found by taking the derivative of the function s. The derivative of the function s = −t^2 + 3t + 4 is given by v = ds/dt = 3 − 2t, and the derivative of the function s = −2t^2 + t + 7 is given by v = ds/dt = 1 − 4t.

Setting v = 0, we get 3 − 2t = 0 and t = 3/2 seconds.

Plugging t = 3/2 seconds into the first equation, s = −t^2 + 3t + 4, we get s = −(3/2)^2 + 3(3/2) + 4 = 9/4 + 9/2 + 4 = 7 metres.

Therefore, the height of the roof from the ground is 7 metres.

Step-by-step explanation:

The factors of the quadratic function  x² - 2x - 4  is equal to

(x + 1 + √5)(x - 1 + √5)

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, The zeros of the quadratic function x² - 2x - 4  are,

(1 + √5) and (1 - √5). (As they occur in conjugate pairs).

Therefore, The factors of (x + (1 + √5))(x + (x - (1 - √5))

x² - 2x - 4 = (x + 1 + √5)(x - 1 + √5)

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Answer:

15.81 ft

Step-by-step explanation:

Basically it's giving your 2 sides of the right angle triangle & ask you for the long side length.

15²+5²=250

√250 =15.81

The probabilities of all the events related to drawing two marbles without replacement are discussed below.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

  Number of blue marbles B = 2

 Number of red marbles R = 3

Number of marbles drawn = 2

a) Sample points are different possible combinations.

  { R,R} , {R,B}, {B, R}, {B,B}

b) Probablitiy of  { R,R} = 3/5 * 2/4 = 6/20 = 3/10 = 0.3

    Probablitiy of {R,B} = 3/5 * 2/4 = 0.3

    Probablitiy of {B,R} = 2/5* 3/4 = 0.3

     Probablitiy of {B,B} = 2/5 * 1/4 = 0.1

c) A: { Two blue marbles are drawn. }

    Probability = 2/5 * 1/4 = 0.1

  B:{ A red and a blue marble are drawn. }

 Probability = 0.3 ( from above)

C:{ Two red marbles are drawn. }

 Probability = 0.3 (from above)

Therefore the different sample points are found and probabilities of different events are also found.

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Answer:

Step-by-step explanation:

Here are three ways to compare A and B, where A= 51,102 is the number of deaths due to a deadly disease in the United States in 2005 and B= 17,056 is the number of deaths due to the same disease in the United States in 2009:

Magnitude: A is approximately three times larger than B. This means that the number of deaths due to the disease was significantly higher in 2005 than in 2009.

Trend: There was a significant decrease in the number of deaths due to the disease between 2005 and 2009. The number of deaths decreased by approximately 67%, from 51,102 in 2005 to 17,056 in 2009.

Impact: Despite the significant decrease in the number of deaths, the disease still caused a significant number of deaths in both 2005 and 2009. This highlights the ongoing importance of disease prevention and treatment efforts to reduce the impact of the disease on public health.

Solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.

What is a quadratic equation?

Any equation in algebra that can be written in standard form:

          ax² + bx + c =0

where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

The given equation of height h = -16t² + 156t +5

a) The time when the height is 269 feet can be found by substituting this value for h in the above equation.

            h = -16t² + 156t +5

         169 = -16t² + 156t +5

         16t² - 156t + 164 = 0

     Solving we get t = 8.55 s, 1.99s

b) The time when the object reaches the ground.

For this, we can take h = 0

   -16t² + 156t +5 = 0

  t = -0.03, 9.78

The negative value can be ignored.

Therefore solving the quadratic equation, we found that the object is at a height of 269 feet when t is 1.99s and 8.55s and the object reaches the ground when t = 9.78s.

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Answer:

pop'n = 358000*(1-0.25%)^t

Step-by-step explanation:

pop'n = 358000

decreasing rate = 0.25%

after t years

pop'n = 358000*(1-0.25%)^t

The midpoint is given by the coordinates M ( 6 , 7.5 )

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Measure the distance between the two end points, and divide by 2.

Let A ( x₁ , y₁ ) be the first point

Let B ( x₂ , y₂ ) be the second point

The midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Given data ,

Let the midpoint of gazebo and the ice cream shop in town be M ( a , b )

Now , the equation will be

The coordinates of the point Gazebo = G ( 10 , 12 )

The coordinates of the point Ice Cream = C ( 2 , 3 )

Now , midpoint between A and B is M ( a , b ) where

a = ( x₁ + x₂ )/2

b = ( y₁ + y₂ ) / 2

Substituting the values in the equation , we get

a = ( 10 + 2 ) / 2

a = 12 / 2

a = 6

b = ( 12 + 3 ) / 2

b = 15 / 2

b = 7.5

So , the coordinates of the midpoint is M ( 6 , 7.5 )

Hence , the midpoint is M ( 6 , 7.5 )

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Answer: The annual percentage yield for Rahela's account can be calculated by finding the effective annual interest rate, which takes into account the frequency of compounding. The effective annual interest rate is calculated as follows:

Effective annual interest rate = (1 + (6.5/2))^2 - 1 = 6.6725%

So, the annual percentage yield for Rahela's account is 6.6725%.

Step-by-step explanation:

The center of dilation is (1, -4).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

From the given graph,

Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).

Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).

Here, the center of dilation is (1, -4).

The transformation is enlargement by scale factor 1.5

Therefore, the center of dilation is (1, -4).

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Answer:

2

Step-by-step explanation:

10-5=5.....the ones she ate

5-2=3 .... the 2 she gave to Mary

3-1 =2.....the one she threw away

2 mangoes!

10 - 5 = 5

5 - 2 = 3

3 - 1 = 2

Answer:

60%

Step-by-step explanation:

12/20 = 3/5 = 0.6 = 60%

Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.

Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.

The length of the triangle is given by the equation L = 15.9 yards

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the length of the triangle be represented as L

Now , the equation will be

Let the base of the triangle be represented as W

Now , the value of W = 8 yards

The area of the triangle = 63.6 yards²

Now , Area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of the triangle A = ( 1/2 ) x 8 x L

4L = 63.6

Divide by 4 on both sides of the equation , we get

L = 15.9 yards

Hence , the length of the triangle is 15.9 yards

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Answer:

3C ÷ 21 = 63 C = 21

great question BTW

The equations that represent the balance A after m months are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, we have that each month, the balance increases by 100, hence the slope m is given as follows:

m = 100.

Hence:

y = 100x + b.

When x = 5, y = 1200, hence the intercept b is given as follows:

1200 = 500 + b

b = 700.

Hence these following two equations are correct:

Taking the fifth month as the initial month, we consider an intercept of 1200, hence the final equation is given as follows:

A = 1200 + 100(m - 5).

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The area needed to be iced is 263.76 inches².

The circular cake is 12 inches in diameter and 4 inches high. The side and top of the cake are to be covered with icing. The area of the cake that will be iced can be found as follows;

The area to to be iced is the top and the lateral area.

Therefore,

area to be iced = πr² + 2πrh

area to be iced = πr(r + 2h)

Therefore,

r = 12 / 2 = 6 inches

h = 4 inches

Hence,

area to be iced = 6π(6 + 2(4))

area to be iced = 6π(14)

area to be iced = 84π

area to be iced = 263.76 inches²

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The value of proportionality is not same.So the it is not proportional.

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Let

y ∝ x

y = kx , k is constant

Take x = 2, y = 3

3 = k(2)

k = 3/2 = 1.5

At x= 4, y = 7

7 = k(4)

k = 7/4 = 1.75

The value of proportionality is not same.So the it is not proportional.

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Answer:

7.4

Step-by-step explanation:

Use Pythagorean Theorem: [tex]a^2+b^2+c^2[/tex]

In this case we have a and c. So let's plug those into the equation:

[tex](6.7)^2+b^2=10^2[/tex]

[tex]44.9+b^2=100[/tex]

[tex]b=\sqrt{55.1}[/tex]

[tex]b=7.4[/tex]

Answer:

$60

50×3=150

182-150=32

so Sally made 3 $50 so 20+20+20=60

A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

An even degree  must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.

Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.

Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.

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