distribute -3(9x^2+10x)

{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

For more questions on ordered pairs as function

https://brainly.com/question/11267211

#SPJ4

The function satisfies the following properties:

(a) satisfies (u,v) = (v,u)

(c) satisfies (u, v+w) = (u,v) + (u,w)

(e) satisfies c(u,v) = (cu,v)

(g) satisfies (v,v) >= 0 and (v,v) = 0 if and only if v = 0

(a) The function satisfies (u,v) = (v,u) because the order of the elements in the inner product does not affect the result.

(c) The function satisfies (u, v+w) = (u,v) + (u,w) because it follows the distributive property of addition.

(e) The function satisfies c(u,v) = (cu,v) because it follows the property of scalar multiplication.

(g) The function satisfies (v,v) >= 0 and (v,v) = 0 if and only if v = 0 because it fulfills the requirements for a non-negative value for the inner product and the condition for the inner product to be zero only when the vector is the zero vector.

To know more about function refer here:

https://brainly.com/question/31062578

#SPJ11

Answer:

50% decrease

Step-by-step explanation:

it would be a 50% decrease because half of 8 is 4 and 1/2 is 50 %.

The number of people with blood type B in a random sample of 46 people is a discrete variable. In statistics, a discrete variable is one that can only take on specific, distinct values.

In this case, the variable represents the count of people with blood type B in a sample of 46 individuals. The number of people with blood type B can only be a whole number and cannot take on fractional or continuous values. It is determined by counting the individuals in the sample who have blood type B, resulting in a specific, finite number. Therefore, the number of people with blood type B in a random sample of 46 people is considered a discrete variable.

Learn more about discrete and continuous here : brainly.com/question/24315217

#SPJ11

Answer:

The answer is A.

As seen in my graph the purple line is exactly like the line in the picture and it uses the first equation or A.)

Step-by-step explanation:

Hope this helped.

A brainliest is always appreciated.

Answer:

-y+(x-12)=-1

Step-by-step explanation:

Answer:

If x = 3 then y = 10

If x = -3 then y = -2

If x = 4 then y = 12

If x = -2 then y = 0

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

For more questions on Isosceles .

https://brainly.com/question/29793403

#SPJ8

The longest portion is 18 inches longer than the shortest portion.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

We know that the ratio of the portions is 1:2:4, so we can use this ratio to find the length of each portion by dividing 42 inches by the sum of the ratio, 1+2+4 = 7.

So each portion is 42 inches / 7 = 6 inches.

The longest portion is 4 times the length of the shortest portion, which is 6 inches. So the longest portion is 4 * 6 inches = 24 inches.

24 - 6 = 18 inches ,

Therefore, the longest portion is 18 inches longer than the shortest portion.

To learn more about algebraic equation visit : brainly.com/question/953809

#SPJ4

Increasing the sample size by a factor of 4 b) decreases the standard error of the sample mean by a factor of 2

The standard error of the sample mean is calculated as the standard deviation of the population divided by the square root of the sample size. When the sample size is increased by a factor of 4, the denominator of the equation (i.e., the square root of the sample size) becomes twice as large.

This causes the standard error to decrease by a factor of 2 (i.e., the standard error is halved). Therefore, option b is the correct answer. The mean of the sample mean is not affected by the sample size and remains the same.

Option c and d are incorrect. Option a is also incorrect as increasing the sample size actually decreases the standard error, not increases it.

For more questions like Sample mean click the link below:

https://brainly.com/question/31101410

#SPJ11

Answer:

x=17

Step-by-step explanation:

(5x-58)=(2x-7)  ->(because of cosine-rule)

3x=51

x=17

Answer:

D

Step-by-step explanation:

Answer:

\(d)\ y=\frac{1}{3}x +2\)

Step-by-step explanation:

Slope (m) form: \(\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-2}{3-0} \\\\m=\frac{1}{3} \\\\m=\frac{1}{3}\)

\(y=mx+b\\y=\frac{1}{3}x +b\)

(3, 3)

\(y=\frac{1}{3}x +b\\3=\frac{1}{3}(3) +b\\3=1+b\\-1-1\\2 =b\)

\(y=\frac{1}{3}x +2\)

Check your answer:

\(y=\frac{1}{3}x+2 \\3=\frac{1}{3}(3)+2\\3=1+2\\3=3\)

This statement is true

Hope this helps!

Answer:

5 hours

Step-by-step explanation:

This is a classic pre-algebra question.

\(5h+5=8h-10\\5=3h-10\\15=3h\\h=5\)

Answer:

B, C, A, B

Step-by-step explanation:

i. 60+ 10 +110 = 180 ( so it can be scalene)

ii. 60 +120 =180 ( they have to, to make a triangle)

iii. Obtuse is 90 degrees or more

iv. 90 +60+30=180 (so it can be)

Okay, here we have this:

Considering the provided information, we obtain the following:

I read a math book. (p)

I start to fall asleep (q)

I drink soda (r)

I must eat a candy bar. (s)

Therefore:

I start to fall asleep if I read a math book. This can be rewritten as: "if I read a math book then I start to fall asleep". And this is p⇒q.

I drink soda whenever I start to fall asleep. This can be rewritten as:"if I start to fall asleep then I drink soda" . And this is q⇒r.

If I drink a soda, then I must eat a candy bar. And this is r⇒s

Now, we need to check: "If I read a math book, then I eat a candy bar.". That is p⇒s.

So, according with the table this argument satisfy the Transitive Reasoning, so this means that the argument is valid.

Given function f is differentiable n times in the region around a point c. The Taylor series for f centered at c is given by the following formula:

T(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + ... + f^(n)(c)(x-c)^n/n!

Taylor series is a power series representation of a function about a point. It is used to approximate a function with a polynomial by taking into account the derivatives of the function at the point of expansion. The Taylor series for f centered at 9 can be found using the formula:

T(x) = f(9) + f'(9)(x-9) + f''(9)(x-9)^2/2! + ... + f^(n)(9)(x-9)^n/n!

where f^(n)(9) = (-1)^n * n! * 8^n * (n + 4) is given.

Substituting this into the formula, we can obtain the Taylor series as:

T(x) = f(9) - 8(x-9) - 224/3(x-9)^2 - 160/3(x-9)^3 - 1024/15(x-9)^4

where the first few terms of the series have been evaluated.

The Taylor series can be used to approximate the value of the function f(x) near the point of expansion x = 9. The accuracy of the approximation depends on how many terms of the series are used. As more terms are added, the approximation becomes more accurate. However, in practice, only a finite number of terms are used to approximate the function. This is because computing an infinite number of terms is not feasible in most cases.

The Taylor series for f centered at 9 can be found using the formula T(x) = f(9) + f'(9)(x-9) + f''(9)(x-9)^2/2! + ... + f^(n)(9)(x-9)^n/n!, where f^(n)(9) = (-1)^n * n! * 8^n * (n + 4) is given. By substituting the given values in the formula, we can obtain the Taylor series. The Taylor series can be used to approximate the value of the function f(x) near the point of expansion x = 9. However, only a finite number of terms are used in practice to compute the approximation as computing an infinite number of terms is not feasible.

To know more about Taylor series visit:

brainly.com/question/32235538

#SPJ11

Answer:

Step-by-step explanation:

Negative numbers don't have real square roots since a square is either positive or 0. so it doesn't exist

Answer:

i

Step-by-step explanation:

the square root of  negative one is not real.

It is classed as an imaginary number denoted by  i , that is

\(\sqrt{-1}\) = i

All the condition for to show whether cost is proportional to area in the situation represented are shown below.

Since, we know that;

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y = kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin.

Now, We can Verify each case;

case 1) Sod that is quoted at a set price per square yard plus a labor fee

The Cost is NOT proportional to Area, because the line don't pass though the origin (the equation has an y-intercept equal to the labor fee)

case 2) Pavers that cost a set amount per square foot

The Cost is Proportional to Area

In this problem the constant of proportionality k is equal to the set amount per square feet

case 3) Hardwood flooring that cost $16 for every 2 square feet

The Cost is Proportional to Area

The constant of proportionality k is equal to

k = y/x

k = 16 / 2

k = 8

The linear equation is,

⇒ y = 8x

case 4) The given graph

Is a line that passes though the origin

So, The Cost is Proportional to Area

case 5) The given table

Find the constant of proportionality k for each ordered pair

If all values of k are the same, then the cost is proportional to area

For x=2, y=3,000

k = 3000/2

k = 1500

For x=4, y=4,000

k = 4000/4

k = 1000

For x=6, y=6,000

k = 6000 / 6

k = 1000

Thus, the values of k are different

Therefore, The Cost is NOT proportional to Area.

case 6) A concrete patio quoted at a bulk cost for 50 square feet

Not enough information.

Learn more about the proportion visit:

https://brainly.com/question/1496357

#SPJ1

Answer:

x= 5

Step-by-step explanation:

factorised the equation is (x-5) (x+3)

x=5 x=-3

Answer:

a=(0,0)

Step-by-step explanation:

i actually dont know but thnks for the points BTW

The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

Learn more about density

https://brainly.com/question/29775886

#SPJ11

Answer:

32n = 100 - 20

n = 2.5

he purchased 2 sweaters

Step-by-step explanation:

32n = 100 - 20

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n which means that he was able to but 2 sweaters and got $16 back. Therefore the formula would be 32n = 100 - 20

The formula for the number of sweaters will be 32n = 100 – 20.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Favian received a $100 gift card to a clothing store.

Using only the gift card, he was able to purchase n sweaters that cost $32 each and 1 belt for $20.

If there was no tax on the sweaters and belt,

Then the equation will be

32n + 1 x 20 = 100

    32n + 20 = 100

             32n = 80

                 n = 2.5 ≈ 2

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n, which means that he was able to but 2 sweaters and got $16 back.

Therefore, the formula would be 32n = 100 – 20.

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

Answer:

The equation of the parabola

( y +2 )² = 16 (x-2)

Step-by-step explanation:

Step(i):-

Given the focus of the Parabola ( 6, -2 )

we know that the Focus of the Parabola

                ( h + a , k ) = ( 6 , -2 )

Comparing

              h + a = 6 ...(i)

          and  k = -2

Given directrix of the parabola

           x = -2

The  directrix of the parabola  x = h - a = -2

        h - a = -2 ...(ii)

Adding (i) and (ii) equations , we get

    h + a + h-a = 6 -2

                2 h = 4

           ⇒    h  = 2

Substitute 'h' = 2 in equation (i) , we get

          h + a = 6

          2 + a = 6

                a = 6 -2 =4

Step(ii):-

The equation of the parabola having Vertex ( h,k) = (2 , -2) and a = 4

\((y-k)^{2} = 4a ( x-h)\)

( y - (-2))² = 4 (4) ( x -2)

Final answer:-

The equation of the parabola

\((y-(-2))^{2} = 4(4) ( x-2)\)

( y +2 )² = 16 (x-2)

We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.

Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).

Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².

By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:

First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²

These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.


Learn more about rational expressions here : brainly.com/question/30488168

#SPJ11

The sum u + v is given as 7.4<cos227, sin227.

Vector addition is the process of combining two or more vectors into a single vector.

To add vectors, you can follow these steps:

Make sure the vectors are in the same dimension, i.e., they have the same number of components.

Add the corresponding components of the vectors.

Write the resulting vector in the same format as the original vectors.

Therefore,

Given that:

u + v (they are vectors)

6<cos 215, sin 215> + 2<cos 265, sin 265)

= <-5.08922, -5.43384

= 7.4 < cos 227, sin227>

Read more about vectors here:

https://brainly.com/question/25811261

#SPJ1

Answer:

1.0612

I tried using the alogarithm of ratios but am confused please help me

Answer:

-2 Answer

Step-by-step explanation:

SEE IMAGE for Solution

Answer:

1

Step-by-step explanation:

1/4x=1/4

x=(1/4)/(1/4)

x=(1/4)(4/1)

x=4/4

x=1

Answer: 1

Step-by-step explanation:

                 1

Simplify   —

                 4

  1         1

 (— • x) -  —  = 0

  4         4

9514 1404 393

Answer:

Step-by-step explanation:

1. The value can be read from the graph. At 3 units to the right of the vertical axis, the line is 3 units above the horizontal axis. The independent variable has a value of 3 at that point.

__

2. The dependent variable has a value of -5 at the next grid line just below the bottom of the graph shown. The value of the independent variable is -1 at that point.

The equation of the line in point slope form is y - 105 = 4 (x - 10) and the equation of the line in slope intercept form is y = 4x + 65.

Slope is defined as the change in the y coordinates of the point divided by the change in x coordinates of the point.

Slope of a line through any two points (x₁, y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

We have the points (10, 105), (15, 125), (20, 145), (25, 165) and (30, 185).

Considering the points (10, 105) and (15, 125),

m = (125 - 105) / (15 - 10) = 20/5 = 4

Equation of a line in point slope form is,

y -  y₁ = m (x - x₁)

Substituting m = 4 and a point (10, 105),

y - 105 = 4 (x - 10)

Equation of a line in slope intercept form is,

y = mx + c, where c is the y intercept which is the point where the line intersects the Y axis. The x coordinate at that point will be zero.

Substituting x = 0 in the point slope form,

y - 105 = 4 (0 - 10)

y - 105 = 4 × -10

y = -40 + 105

y = 65, which is the y intercept.

The equation of the line in slope intercept form is,

y = 4x + 65.

Hence the equation of the line in point slope form and slope intercept form are y - 105 = 4 (x - 10) and y = 4x + 65 respectively.

To learn more about Slope, click :

https://brainly.com/question/3605446

#SPJ1

Probabilities are used to determine how likely it is for an event to happen.

(1) A roll of two dice

Let the dice be A and B. The sample space of each is:

\(A = \{1,2,3,4,5,6\}\\B = \{1,2,3,4,5,6\}\)

To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:

\(S = \{(1+1),(1+2),(1+3),(1+4),(1+5),(1+6),.............,(6+1),(6+2),(6+3),(6+4),(6+5),(6+6)\}\)

This gives

\(S = \{2,3,4,5,6,7,.............,7,8,9,10,11,12\}\)

The complete sample space is:

\(S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12\}\)

\(n(S) = 36\) --- the total outcomes

The probability of rolling a sum of 7 is:

\(P(7) = \frac{n(7)}{n(S)}\)

Where

\(n(7) = 6\) ---- number of 7's in the sample space

So, we have:

\(P(7) = \frac 6{36}\)

\(P(7) = 0.167\)

The probability of rolling a sum of 7 is 0.167

(2) Restaurant

We have:

\(Soup = \{A,B,C,D\}\)

\(Salads = \{1,2,3\}\)

To get the sample space (S), we simply pick the individual elements of the above data. So, we have:

\(S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}\)

(3) Disjoint events

Events are said to be disjointed if they cannot happen at the same time. 3 examples are:

(4) Bob and Sarah

Let

\(A \to\) Bob gets to work on time

\(B \to\) Sarah gets to work on time

\(P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%\)

The probability that Bob OR Sarah is late for work is represented as:

\(P(A'\ or\ B')\)

This is calculated using:

\(P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')\)

Where:

\(P(A') = 1 - P(A) = 1 - 80\% = 20\%\)

\(P(B') = 1 -P(B) = 1 - 90\% =10\%\)

\(P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%\)

So, we have:

\(P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')\)

\(P(A'\ or\ B') = 20\% + 10\% - 2\%\)

\(P(A'\ or\ B') = 28\%\)

\(P(A'\ or\ B') = 0.28\)

The probability that Bob OR Sarah is late for work is 0.28

(5) Jake's Pizza

Let

\(A \to\) The proportion of time they deliver on time

\(B \to\) You get your pizza for free

So:

\(P(A) = 92\%\)

You get your pizza for free if they didn't deliver within 30 minutes.

This means that:

\(P(B) = 1 - P(A)\) --- Complement rule

So, we have:

\(P(B) = 1 - 92\%\)

\(P(B) = 0.08\)

The probability that you get your pizza for free is 0.08.

(6) Students and Soccer

Let:

\(A \to\) Probability that a student likes soccer

So:

\(P(A) = 54\%\)

If all 3 selected students like soccer, the probability is calculated as:

\(Pr = P(A) \times P(A) \times P(A)\)

\(Pr = P(A)^3\)

\(Pr = 54\%^3\)

\(Pr = 0.157\)

The probability that all 3 selected students like soccer is 0.157

(7) Students and Soccer

Let:

\(A \to\) Probability that a student likes soccer

\(B \to\) Probability that a student does not like soccer

So:

\(P(A) = 54\%\)

\(P(B)= 1 - P(A)= 1 - 54\% = 46\%\) ---- Complement rule

If all 4 selected students do not like soccer, the probability is calculated as:

\(Pr = P(B) \times P(B) \times P(B) \times P(B)\)

\(Pr = P(B)^4\)

\(Pr = 46\%^4\)

\(Pr = 0.045\)

The probability that all 4 selected students do not like soccer is 0.045

(8) Marbles

\(Blue = 6 \\ Green = 4 \\ Red = 5\)

When the green marble is selected, we are left with

\(Blue = 6 \\ Green = 3 \\ Red = 5\)

The probability of selecting a red marble at this point is:

\(P(Red) = \frac{Red}{Blue + Green + Red}\)

\(P(Red) = \frac{5}{6+3+5}\)

\(P(Red) = \frac{5}{14}\)

\(P(Red) = 0.357\)

The probability that the next marble you draw is red is 0.357

(9) Studying for test

Let

\(A \to\) Students got an A

\(B \to\) Students studied for test

So:

\(P(A\ n\ B) = 60\% \\ P(B) = 75\%\)

The probability that a student got an A given that they studied for the test is  represented as:

\(P(A | B)\)

So, we have:

\(P(A | B) = \frac{P(A\ n\ B)}{P(B)}\)

\(P(A | B) = \frac{60\%}{75\%}\)

\(P(A | B) = 0.80\)

The probability that a student got an A given that they studied for the test is  0.80

Read more about probabilities at:

https://brainly.com/question/16693319