Given two points, (3, 2) and (7, 18), determine both the linear and quadratic equations crossing both points. Let f(x) and f(k) be the linear and quadratic equation respectively. Write both in standard form

Step-by-step explanation:

I think you have to change 20% to a fraction

The slope and the y-intercept of the given data table will be option A) Slope= -0.0018, y-intercept = 212

The y-intercept of any linear equation is the point at which the line or the curve intersects the vertical i.e the Y- axis.

To find this intercept, the value of x is taken to be 0 in the model, since on the Y-axis, the value of x is 0.

Here from the given table, we need to check the boiling point or the value of Y for which the value of the altitude or the x value is 0

Hence we get the y-intercept as 212° F.

Now, the formula for slope

= change in y/ change in x

here we will take any two data rows and divide the difference in boiling points by the difference in altitudes.

Taking the first 2 rows gives us

Slope = -0.9/500

= -0.0018

Hence we choose option A) Slope = -0.0018, y-intercept = 212

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Complete Question

The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y-intercept of the line that models this situation?

A. Slope= -0.0018, y-intercept = 212

B. Slope= 0.0018, y-intercept =-212

C. Slope =212, y- intercept= 0.0018

D. Slope=-212, y-intercept = 0.0018

Answer:

-4,-2,2

Step-by-step explanation:

look where line reaches zero

Answer:

31/24 or 1 7/24

Step-by-step explanation:

1 3/8 in an improper fraction is 11/8:

1 times the denominator (8)= 8, add the numerator (3), and get 11

then keep the original denominator

multiply 11/8 by 3 to get 33/24

multiply 1/12 by 2 to get 2/24

now you have the same denominator and can subtract

33/24-2/24= 31/24

In the circle below the  suppose m WXU=102° and mL XWV=68° then the following is m ZXUV = 88°.

Four-sided shapes with all four corners on the same circle are known as cyclic quadrilaterals. A cyclic quadrilateral's internal angles are always added up to 360 degrees.

(a) m / WXU = 102° (Given)

(b) To find m ZXUV, we can use the property that the angles in a cyclic quadrilateral add up to 360°. Since WXU, XWV, and XLV are all inscribed angles that intercept the same arc, they are congruent. Therefore, m WXU = m XWV = m XLV = 102°. Adding these angles together, we have:

102° + 102° + 68° + m ZXUV = 360°

Solving for m ZXUV, we get:

m ZXUV = 360° - (102° + 102° + 68°)

m ZXUV = 88°

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Answer:

The answer is 11

Step-by-step explanation:

The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11

Answer:

19.56

Step-by-step explanation:

PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]

RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]

Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] +  5[tex]\sqrt{2}[/tex] +  2[tex]\sqrt{17}[/tex] = 19.56

Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse.  Then you can use the Pythagorean theorem to find the length of each leg.  Add them all together to get the perimeter.

Answer:

You have to draw a graph.

Step-by-step explanation:

Multiply all of your sides together to figure out the area then plot the points.

As per the given points in the question, the slope in the simplest form will be equal to 0

Using two of the points on the line you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise and the horizontal change is called the run. The slope equals the rise divided by the run.

Here the given points are (−5,8) and (−11,8)

Hence the required slope of the line is

=   8     -       8

     11 -  [ - 5 ]

=      0      

 - 11 + 5

=        0    

        - 6

= 0

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If Imani was assigned to make 64 cookies for the bake sale. If Imani made 25% more than they were assigned. The number of cookies that were left after the bake sale is: 8.

Number of cookies  sold:

Number of cookies  sold = 0.90 × [(1+.25)×64]

Number of cookies  sold = 0.90 × [(1.25)×64]

Number of cookies  sold = 0.90 × 80

Number of cookies  sold = 72

Number of cookies left:

Number of cookies left = 80 - 72

Numbers of cookies left  = 8

Therefore the number of cookies left is 8 cookies.

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calculated margin of error = 0.376

It is a statistical term that implies the amount of permissible error within the survey data. This error indicates the difference between statistical result and actual result.

margin of error can be determined by multiplying the critical value to the standard deviation.

given, mean GPA of 75 sophomores = 3.26 = Xi

standard deviation = 0.62 = s

sample number = 75 = n

total sophomores = 500

z value of the sophomores = mean / standard deviation = 3.26 / 0.62

Z value = 5.26

margin of error = Z value × standard deviation / (√number of sample)

margin of error = 5.26 × 0.62/ √ (75)

                      = 0.376

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If triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the number be x

tripple of a number added to its half part

3x+x/2

Difference between four times the number and 12

4x-12

So tripple of a number added to its half part its equal to the difference between four times the number and 12

3x+x/2=4x-12

6x+x=2(4x-12)

Apply distributive property on RHS

7x=8x-24

Subtract 7x on both sides and add 24

24=x

Hence, if triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

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Answer:

Step-by-step explanation:

Ya

NO, A triangle has sides of lengths 8,10, and 15 is not a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

Properties of right angle:

The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.

The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.

consider c=15 a=10, b=8 substitute in above formula:

15²=10²+8²

⇒225=100+64

⇒225[tex]\neq[/tex]164

Therefore, and 8,10,15 is not right triangle.

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The degree of polynomial 7x³ + 4x² is 3 as the highest power is 3.

One of the fundamental ideas in mathematics is the degree of polynomials, which determines the maximum number of solutions a function can have and how frequently a function will cross the x-axis on a graph.

Polynomials are also useful in understanding how functions can be represented mathematically. It has the highest exponential power in the polynomial equation.

The greatest power of a variable in a polynomial equation is its degree. When calculating the degree of a polynomial function, only terms with variables are considered. The degree of the polynomial can be determined by looking at the variable term with the highest exponential power.

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Therefore, amu (atomic mass unit) and Avogadro's number are not the same things.

A unit of measurement for atomic and molecular weight is the atomic mass unit (amu).

Molecular weight, commonly known as molecular mass, is the mass of a substance's molecules, calculated using the atomic weight of carbon-12, which is 12.

No, amu and Avogadro's numbers are not the same things because An atomic mass unit (amu) is a unit of measurement for atomic and molecular weight. It is defined as one twelfth of the mass of a neutral atom of carbon-12. It is commonly used in chemistry to express the masses of atoms and molecules While Avogadro's number (N) is a fundamental constant of nature that relates the number of atoms or molecules in a sample to the mass of that sample. It is defined as the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms or molecules per mole.

So, amu is a unit of measurement for atomic and molecular weight, while Avogadro's number is a constant that relates the number of atoms or molecules in a sample to the mass of that sample.

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It means that the grocer has to pay $1.38 for each pound of strawberries. So the constant of proportionality for this scenario is $1.38

Proportionality is a mathematical relationship between two variables, where the ratio of one variable to the other is always the same, regardless of the values of the variables. The variables are said to be in proportion if there is a constant of proportionality "k" such that one variable is equal to "k" times the other variable. In other words, if y is proportional to x, the relationship is represented by an equation of the form y = kx, where "k" is the constant of proportionality.

A constant is a value that does not change. In mathematical terms, it refers to a value in an equation that remains the same and does not depend on the variables. For example, in the equation y = kx, "k" is a constant. It is a fixed numerical value that relates two variables in a proportionality relationship. Constants can be represented by a number, a letter or a symbol.

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On using the distribution method the value could be  [tex]e ^ {t^{2}[/tex]/ 2

What is the Gamma Distribution  ?

A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.

Given,

Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).

Using the distribution method, find the pdf of U = Z 2.

And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.

Suppose e Z ∼ N (0, 1),  then

mZ (t) = 1√2πetxe−x2/2dx

= et2/21/√2π

[tex]e ^ {-(x-t)^{2} /2[/tex] dx

= [tex]e ^ {t^{2}[/tex]/ 2

hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2

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(a) x² + 2xy - y² must be added to x² + xy + y² to get 2x² + 3xy. (b)  5a + b -6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.

a)

Here we are given the expression x² + xy + y²

Now we need to add something so that this expression becomes x² + 3xy

Let the expression to be added be p.

Hence we get

x² + xy + y² + p = 2x² + 3xy

or, p = 2x² + 3xy - (x² + xy + y²)

or, p = 2x² + 3xy - x² - xy - y²

or, p = x² + 2xy - y²

Hence, x² + 2xy - y² must be added.

b)

Here we are given the expression 2a + 8b + 10

We need to subtract another expression to get -3a + 7b + 16

Let the expression be t. Hence we get

2a + 8b + 10 - t = -3a + 7b + 16

or, t = 2a + 8b + 10 - (-3a + 7b + 16)

or, t = 2a + 8b + 10 + 3a - 7b - 16

or, t = 5a + b - 6

Hence 5a + b - 6 must be subtracted,

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Correct Question

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?

On solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

Given is the expression as follows -

√{(x + c)² + y²} = x (a/c) + a

√{(x + c)² + y²} = xa/c + a

√{(x + c)² + y²} = a{x/c + 1}

√{x² + c² + 2xc + y²} = a{x/c + 1}

{x² + c² + 2xc + y²} = ± (a{x/c + 1})²

Now, we can write -

{x² + c² + 2xc + y²} = (a{x/c + 1})²              ...... (1)

and

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                 ......... (2)

Solving (1) as -

{x² + c² + 2xc + y²} = (a{x/c + 1})²    

{x² + c² + 2xc + y²} = a²(x/c + 1)²

{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)

{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)

y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}

Solving (2) as -

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                

y² =  - (a{x/c + 1})² - (x² + c² + 2xc)

y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}

y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}

Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

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Answer: 7

Step-by-step explanation:

The number of hours after which the cars will be 350 miles apart is 34 hours.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Vehicle 1.

Speed = 55.5 mph

Distance(1) = 55.5 x Time

Vehicle 2.

Speed = 45(1/4) mph

Distance(2) = 45(1/4) x Time

The difference in the distance = 350 miles.

Distance(1) - Distance(2) = 350

55.5 x Time - 45(1/4) x Time = 350

55.5 x Time - (181/4) x Time = 350

(55.5 - 181/4) x Time = 350

Time = 350 / (55.5 - 45.25)

Time = 350 / 10.25

Time = 34 hours.

Thus,

The car will be 350 miles apart after 34 hours.

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Answer:

  18 tickets at $7

Step-by-step explanation:

You want a "Singapore Math" model solution to the number of $7 tickets Mrs. Hana bought if she got $14 change from $200, and she received a total of 30 tickets, some of which cost $5 each.

The attachment shows the model we decided upon. Starting from $200, we subtract $14 in change, then divide the remainder into tickets costing $7 each and tickets costing $5 each. The point where the total number of tickets is 30 is the point that identifies the solution.

Mrs. Hana bought 12 tickets at $5 each, and 18 tickets at $7 each.

__

Additional comment

Most illustrations of Singapore Math models are solving for a single variable. Here, we must choose values for two variables (the numbers of $5 and $7 tickets) so the intended model isn't clear.

The model we have used is adequate for the purpose, but tedious to construct. It requires us to identify the point at which the count of $7 tickets (top bar) and the count of $5 tickets (bottom bar) has a sum of 30.

The required inequality expression for the third side is 1 < m < 25. The correct option is (B).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The sides of the triangle are given as 12 and 13 units respectively.

As per the rule for sides of a triangle, the third side is always less than the sum and greater than the difference of two sides.

Then, the inequality can be written as,

13 - 12 < m < 13 + 12

⇒ 1 < m < 25

Hence, the measure of third side can be written in inequality as 1 < m < 25.

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Answer: 0.28 Km^2

Step-by-step explanation:

A= L x W

=0.4x0.7

=0.28

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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The slope of the line that passes through the graph is 3

From the graph, the points are given as

(0, 0)  and (1, 3)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0)  and (1, 3)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0)  and (1, 3)

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(1 - 0)

Evaluate

Slope = 3

Hence, the slope of the line is 3

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An equation that shows what the cost of renting a car will be: C=R+mc.

Let the rental cost = R

consider m to be the number of miles driven= m

let c be the cost per mile

And C is the total cost of renting;

Then C = R+mc

the given equation $40 + $0. 10 per mile

Now, in the above equation consider:

R =$40 ( the rental cost)

c = $0.10 ( the cost per mile)

The total cost is C = $40+$0.10m

Ex:

if m is known assume m=1000 miles

Then the total cost C = $40+($0.10/mile)(1000miles)

then  C = $40+$100=$140

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Answer:

$2581.60

Step-by-step explanation:

In order to find the amount owed after 4 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the amount owed after t years

P is the principal, or initial amount borrowed

r is the interest rate

n is the number of times the interest is compounded per year

t is the number of years

Plugging in the given values, we have:

A = $2000(1 + 0.07/2)^(2*4)

= $2000(1.035)^8

= $2000(1.2908)

= $2581.60

Therefore, the amount owed after 4 years would be $2581.60.

Answer:The student needs to score 20 points

Step-by-step explanation:

? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20