Find the slope and write an equation of the line which passes through the points.
A
(5,6) and (3,4)

In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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Because we can't divide by zero, the correct option is x = 0.

For which value of x the quotient is not a rational number?

Here we have the quotient:

12/x

We want to find a value of x such that it is not a rational number, where a rational number is any number that can be written as the quotient of two integers.

Here is a trick, remember that we can't divide by 0, so if we choose x = 0, technically we can't take the quotient, so in that case we wouldn't have a rational number.

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Answer:

I think this is correct.

Step-by-step explanation:

Answer:

 x = 5.33333333333

Step-by-step explanation:

3x-5=11

   +5   +5

3x= 16

3      3      

u need to separate the 3x

so u use the opposite operation on - 5

add +5 on both sides

-5 plus 5 cancel each other

add 11 to 5 and that is 16

bring them down and divide both by 3

and ur 3 cancel each other,

now divide 16 by 3

and u get  x = 5.33333333333

Answer:

f(g(x) ) = x² + 2

Step-by-step explanation:

to find f(g(x) ) substitute x = g(x) into f(x)

f(g(x) )

= f(x²)

= x² + 2

Answer:

Step-by-step explanation:

The most appropriate choice for Linear Inequation and area will be given by-

value of h > 8.

What is Linear Inequation and area?

Linear Inequation involves comparision between two values with the help of <,   >,   [tex]\leq[/tex],  [tex]\geq[/tex].

Area of a 2D shape is the total space taken by that shape.

Here ,

Area of vegetable patch of Jake = [tex]h[/tex] [tex]m^{2}[/tex]

Area of vegetable patch of Aliya = ([tex]3h + 7[/tex]) [tex]m^{2}[/tex]

Area of vegetable patch of Lucy = [tex]5h[/tex] [tex]m^{2}[/tex]

Total area of vegetable patch of Jake, Aliya and Lucy

                                                                                       = [tex](h + 3h+7+5h)[/tex] [tex]m^{2}[/tex]

                                                                                       = [tex](9h+7)[/tex] [tex]m^{2}[/tex]

By the problem,

                          [tex]9h + 7 > 79\\9h > 79 - 7\\9h > 72\\h > \frac{72}{9}\\ h > 8[/tex]

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The numeric values for the given functions are as follows:

1. g(-4) = -21.

2. f(-1) = 3.

To find the numeric value of a function at input x = a, we replace each instance of the variable x in the function by the desired value of a.

For item 1, function g(x) is defined as follows:

g(x) = -x² - 5.

We want to find the numeric value at x = -4, hence the lone instance of x is replaced by -4 as is shown below:

g(-4) = -(-4)² - 5 = -16 - 5 = -21.

Hence g(-4) = -21 is the numeric value.

For item 2, the function f(x) is given as follows:

f(x) = -3(1 - x - 3x²).

To find the numeric value at x = -1, both instances of x have their values replaced by -1, hence the numeric value will be given as follows:

f(-1) = -3(1 - (-1) - 3(-1)²) = -3(1 + 1 - 3) = 3.

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Answer:

0.29761904761

Step-by-step explanation:

Brainlest, Please!

Answer:

25/84

Step-by-step explanation:

1. 2 1/10 is mixed number fraction so convert it into an improper fraction.

~ Multiply whole number and denominator and add the numerator of 1

~ Improper fraction: 21/10

2. So, new equation is (5/8) / (21/10)

3. Use the Keep, Change, Flip method:

~ Keep the 5/8

~ Change division to multiplication

~ Flip the improper fraction to 10/21

4. Solve the equation:

~ (5/8) x (10/21) = 50/ 168

5. Reduce fraction:

~ By 2

~ 25/84

In the picture, there is a square and a shaded region inside the square. The shaded portion has a 13.76 square meter area.

Given that,

In the picture, there is a square and a shaded region inside the square.

We have to find the shaded portion area.

The side of the square is 8cm.

Now,

First we see the unshaded region on the square is there are 4 unshaded regions.

In the figure u can see there is a unshaded region we named that has tile 1, tile2, tile 3, and tile 4.

If we restock them we can see that we got a circle with that 4 tiles.

Now, the side is 8 cm then the 1 tile will be of 4 cm.

So, the radius of the circle is 4 cm.

In the other picture we can see that the area of the shaded region is equal to area of square- area of circle.

Area of the shaded region =s²-πr²

Area of the shaded region =8²-π(4)²

Area of the shaded region =64-π(16)

Area of the shaded region =64-16π

Area of the shaded region =64-16(3.14)

Area of the shaded region =64-50.24

Area of the shaded region =13.76

Therefore, The shaded portion has a 13.76 square metre area.

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The least common multiple of 32, 48, and 16 is 96

The first step is to get the prime factors of each number

The prime factors of 32 are 2, 2, 2, 2 and 2.

The prime factors of 48 are  2, 2, 2, 2 and 3

The prime factors of 16 are 2,2,2 and 2

The least common multiple of 32, 48 and 16 can be calculated as follows

2 × 2 × 2 × 2 × 2 × 3

= 32 × 3

= 96

Hence the least common multiple of 32, 48, and 16 is 96

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Answer:

3x + 4

.................

The factor 3x + 4 have common in both the given expressions.

A whole number that is a factor of two or more numbers is referred to as a common factor. The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).

The given expressions are,

[tex]9x^2 + 24x + 16, 9x^2 - 16[/tex]

The expression [tex]9x^2 + 24x + 16[/tex] is of the form [tex](a + b)^2[/tex]

where [tex]a = 3x , b = 4[/tex]

Therefore,   [tex]9x^2 + 24x + 16 = (3x + 4)^2.[/tex]

The expression [tex]9x^2 - 16[/tex]   is of the form [tex]a^2 - b^2[/tex].

It can be written as, [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

Here, [tex]a = 3x , b = 4[/tex]

Therefore,

[tex]9x^2 - 16 = (3x - 4)(3x + 4)[/tex]

So, in both the expressions the factor (3x + 4) is common.

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The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)

We are given the quadratic function;

f(x) = (x - 5)(x + 1)

1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.

2) The y-intercept is the point at which x = 0. Thus;

f(0) = (0 - 5)(0 + 1)

f(0) = -5

y-intercept is at; (0, -5)

Thus, Jacob is wrong.

3) The x-coordinate of the vertex is;

x = -b/2a

The equation is; x² - 4x - 5

Vertex = -(-4)/(2 * 1) = 2

y-coordinate is;

y = 2² - 4(2) - 5

y = -9

Thus, Jacob is correct

4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.

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[tex]\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\[/tex]

Multiply both parts of the equation by 7:

[tex]\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}[/tex]

The properties of the function are:

The absolute value equation of the function is given as

y = |x|

On the incomplete table of values, we do not have any x values

So, we can make use of any x value

To do this, we make use of the following x values

x = -3, -1, 0, 1 and 3

Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x|

So, we have:

y = |-3| = 3

y = |-1| = 1

y = |0| = 0

y = |1| = 1

y = |3| = 3

When represented on a table of values, we  have

x | y

-3 | 3

-1 | 1

0 | 0

1 | 1

3 | 3

Next, we plot the graph of the absolute value equation

See attachment for the graph of the absolute value equation

From the graph of the absolute value equation, we have the following properties:

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Answer:

y=8

Step-by-step explanation:

The statement that explains why one source is the most reliable is D. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.

Reliable sources are necessary for reliable information. A trustworthy source will offer a "complete, well-reasoned hypothesis, argument, etc. based on substantial evidence," according to UGA Libraries.

Scholarly, peer-reviewed articles and books are examples of widely regarded sources. trade publications, professional books, etc.

It should be noted that a reliable source should be based in facts and should not be biased.

Therefore, the correct option is D.

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Answer: top: x= 2   bottom: x= -5

Step-by-step explanation: First you need to get rid of everything on the x side, so for example on the top one you would do 9-9 to get 0 so that x is by itself and then you also have to 11-9 because whatever you do to one side you have to do to the other. And then 11-9=2 so you are left with x= 2.

Answer: 8:16

24(games)-16(wins)=8. 8=the losses

Step-by-step explanation:

Answer:

answer is D prettyy sure

Answer: a = 6 and 1/4

Step-by-step explanation:

you subtract the 1/4 to the other side and theres your answer

A statement which best describes the meaning of function f(150) is that: A. This is the average number of days the house stayed on the market before being sold for $150,000.

The average rate of change can be defined as a type of function that is used for describing the average rate at which a quantity either decreases or increases with respect to another quantity.

A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this scenario, the function f(150) can be evaluated as follows:

Function f(150) = 150 × p

Function f(150) = 150 × $1,000.

Function f(150) = $150,000

Therefore, the function f(150) simply means the average number of days this house stayed on the market before it was then sold for $150,000.

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The Venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon

We have given that

The Distance of moon from the earth(in miles)= a=  [tex]2.4 * 10^5[/tex] miles

The Distance of venus from the earth(in miles)= b =   [tex]1.59 * 10^8[/tex] miles

The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects.

Now,

Let the distance from which venus is further away from the earth than the moon be x

So, x = b - a

x = [tex]1.59 * 10^8-2.4 * 10^5[/tex]

x = [tex]1590 * 10^5 - 2.4*10^5[/tex]

x = [tex](1590 - 2.4)*10^5[/tex]

x = [tex]1587.6*10^5[/tex]

x = [tex]1.5876 * 10^8[/tex]

Therefore, venus is at a distance of  [tex]1.5876 * 10^8[/tex] further away from the earth than the moon.

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Possible outcomes are Head, Middle, and Tail.

Since all outcomes are equally likely, the probability of each event is same, therefore

P(Head) = P(Middle) = P(Tail)

= 1/3

P(B|A) is 1/3

P(C|A) is 2/3

A and B are independent

A and C are not independent

Part a

Finding the sample space, S

S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }

Part b

Finding  P(B|A) and P(C|A):

n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(B|A) = 1/3

n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(C|A) = 2/3

Part c

Finding if A and B are independent, or if A and C are independent

Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,

P(A) = P(first toss is Middle) = 3/9 =1/3

P(B) = P(second toss is Tail) = 3/9 = 1/3

P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9

P(A)*P(B) = (1/3)*(1/3)

= 1/9 = P(A and B)

Hence, we can say that events A and B are independent.

For A and C, we have,

P(A) = P(first toss is Middle) = 3/9

P(C) = P(total no. of Heads is 0) = 4/9

P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9

P(A)*P(C) = (3/9)*(4/9)

= 4/27 P(A and C)

Hence, events A and C are not independent.

The question was incomplete, the complete question is:

(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times

a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.

Let;

A = event the first toss is Middle,

B = event the second toss is Tail, and

C = event the total number of Heads is 0.

b) Find

P(B|A)

P(C|A)

c) Are A and B independent? YES, NO, Why?

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Step-by-step explanation:

what do you need to do ?

the only thing we can do here without any further information is simplification if the expression:

-23x² + x² - 6x + 10 + 2x²

now we group ask the terms of the same variable exponents :

-23x² + x² + 2x² - 6x + 10

-20x² -6x + 10

we could do

2×(-10x² - 3x + 5)

but I personally don't find this more simplified that the previous form.

Si definimos N como el nuevo número de esferas en la urna, entonces la expresión algebraica será:

N = x - 3.

Sabemos que tenemos una urna con x esferas, donde x representa un numero entero.

Sabemos que 3 esferas se extraen de la urna, es decir, el número total de esferas en la urna decrese en 3 unidades.

Entonces podemos escribir la expresión algebraica como:

N = x - 3

Donde definimos N como el nuevo número de esferas en la urna.

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Answer:

7.071068 ≈ 7.07

Step-by-step explanation:

The distance, d,  between 2 points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

The two points as determined from the graph are (1, 5) and (2, -2)

[tex]d = \sqrt {(2 - 1)^2 + (-2 - 5)^2}[/tex]

[tex]d = \sqrt {(1)^2 + (-7)^2}[/tex]

[tex]d = \sqrt {{1} + {49}}[/tex]

[tex]d = \sqrt {50}[/tex]

[tex]d = 7.071068[/tex]

Using permutation, there are a total of 24 different orders possible.

If there are a total of 4 floats in a parade then the number of possible orders = 4!

If we further calculate it we will get,

               4 x 3 x 2 x 1 = 24

So there are a total of 24 possible orders in which the floats should appear.

The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.

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The total cost of painting per cm will be 45.2% i.e. option(d).

Total cost of painting = Rate × Surface area of sphere

We know the radius is increases by 10%.

Thus, the Surface area will change by 21%

using formula a + b + (a × b)/ 100

The total change in cost of painting will be

= 20+21 +(20x21)/100

= 45.2%.

What is surface area?

The total area of all faces (or surfaces) on a 3D form is the surface area. For example:

There are six rectangular faces of a cuboid.

Add the areas of each of the cuboid's six faces to determine its surface area.

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