The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?

Answer: The numbers are 2 and 2.5

Explanation:

Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]

[tex]\rule{185}{2}[/tex]

Their product :

[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]    

[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]

Their sum :

[tex]\hookrightarrow \sf x + y = 4.5[/tex]

[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]

Solve them simultaneously:

[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]

cross multiply

[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]

distribute inside parenthesis

[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]

multiply by -1

[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]

factor them out

[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]

set to 0

[tex]\rightarrow \sf y = 2.5, \ 2[/tex]

Another number:

When one number is 2.5, then another: 4.5 - 2.5 = 2

When one number is 2, then another: 4.5 - 2 = 2.5

Check:

The numbers obtained by the given condition that the product of two numbers is 5 if their sum is 9/2 will be x =( 2 or 5/2) and y = ( 2 or 5/2).

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the first number is x and the second is y then

Product xy =  5

Sum x + y = 9/2

substitute y = 9/2 - x into first

x( 9/2 - x) = 5

2x² - 9x + 10 = 0

2x² -5x -4x + 10 = 0

x( 2x - 5 ) -2( 2x -5 ) = 0

(x -2)(2x -5) = 0

x =2 and x = 5/2

Corresponding to x y will be y = 2 and y = 5/2.

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By using the given ratio, we will conclude that she made 24 baskets.

We know that the ratio of the number of baskets she missed to the number of baskets she made is 3:8.

This means, for each 3 missed baskets, she made 8.

Here we know that she missed 9. If we divide that by 3, we get:

9/3 = 3.

This means that she missed 3 baskets 3 times. And for each one of these 3 times she makes 8 baskets (for the given ratio).

Then we conclude that she makes 8*3 = 24 baskets.

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Fraction refers to a part of a whole; e.g when cup is not completely filled, it covers only a part of the cup

The term fraction refers to a part of a whole. To design an instructional activity that  could help learners recognize that decimal fractions can be applied across environmental situations, we could look at certain things in the house.

For instance, when cup is not completely filled, it contains water that covers only an fraction of the cup. Also, we could boil a part and not a whole cup of rice. These are all examples of fractions.

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Answer:

17.3

Step-by-step explanation:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Find the difference between coordinates:

(x2 - x1) = (-9 - 8) = -17

(y2 - y1) = (-6 - -3) = -3

Square the results and sum them up:

(-17)^2 + (-3)^2 = 289 + 9 = 298

Now Find the square root and that's your result:

Exact solution: √298 = √298

Approximate solution: 17.2627

Answer:

  $19,201.09

Step-by-step explanation:

The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...

  A = P(1 +r)((1 +r)^n -1)/r

where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.

  A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09

The value will be $19,201.09.

Answer: 2+2= DA ROCK

Step-by-step explanation:

SCAM..... ITS ABOUT DRIVE ITS ABOUT POWER WE STAY HUNGRY WE DEVOURE PUT IN THE WORK PUT IN THE HOUR AND TAKE WHATS OURSSSSSSSSSSSSSSSSSSSSS


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Answer:

see the attachment photo!

Answer:

I think the answer is 33

Step-by-step explanation:

Extremely sorry if it's wrong

Answer:

The correct answer is x = 51.

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x.

We can see that both angles are supplementary (adding up to 180 degrees), so we can set an equation as:

x + 23 + 2x + 4 = 180

x + 2x + 4 + 23 = 180

3x + 27 = 180

3x + 27 - 27 + 180 - 27

3x = 153

3x/3 = 153/3

x = 51

Therefore, the value of x is 51.

Hope this helps:) Goodluck!

Answer:

Step-by-step explanation:

2x + 4 + x + 23 = 180

3x + 27 = 180

3x = 153

x = 51

Answer:

Step-by-step explanation:

Based on what we know a function to be today, Euler mean an analytic expression "an expression formed from operations such as addition, multiplication, powers, and roots"

According to Euler, a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

The function is. combination of expression which includes variables and constants using various operations such as roots, power and multiplication.

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Answer:

140

Step-by-step explanation:

Angles in a triangle add up 180 :

180 = 107 + 33 + y

y = 180 - (107+33)

y = 180 - 140

y = 40

Angles on a straight line add up to 180 so :

180 = x + y

180 = x + 40

x= 180 - 40

x = 140

Hope this helped and have a good day

Answer:

x = 140°

Step-by-step explanation:

Concepts

The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.

Application

In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.

Solution

Answer:

A

Step-by-step explanation:

the answer is A because I said its C :)

Step-by-step explanation:

let p be the point which is at a distance of 4 units from the x-axis and at a distance of 5 units from the y axis

(i) When P lies in the first quadrant then the coordinates of P are (5,4).

(ii) When of P lies in the second quadrant then the coordinates of P are (-5,4).

(iii) When P lies in the third quadrant then the coordinates of P are (-5,-4).

(iv) When P lies in the fourth quadrant then the coordinates of P are (5,-4).

Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.

There are 720 different ways the campaign staff can arrange her travel route

The given parameter is:

Cities = 6

The candidate cannot be at all 6 cities at the same time.

This means that we make use of factorial.

So, we  have:

Ways = 6!

Evaluate the factorial expression

Ways = 720

Hence, there are 720 different ways the campaign staff can arrange her travel route

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Answer:

$14,903.85

Step-by-step explanation:

So, Ms. Lui earns $775,000 each year. To find the weekly salary, we have to divide the annual income by the amount of weeks in a year. There are about 52 weeks in one year. Let's find the weekly salary:

[tex]\frac{775000}{52} = 14,903.85[/tex]

Therefore, Ms. Lui earns $14,903.85 a week.

Hope this helps! If you have questions about my work, please leave them in the comments!

Answer:

The answer is c

Step-by-step explanation:

one add the numbers 108 & 96=204

then add the numbers from c which is 30+30=60 43+43=86 29+29=58

then add 60+86+58 which will be 204 so c is the answer your welcome

come

Answer:

  (a)  1024 ways

  (b)  243 ways

Step-by-step explanation:

When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.

__

The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.

The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.

__

There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...

  3^5 = 243

A student can answer all questions wrong in 243 different ways.

Answer:

32

Step-by-step explanation:

Answer:

  i) 52

  ii) 66

Step-by-step explanation:

This sort of problem is usually solved using some sort of table or Venn diagram. We have used a table in the attachment such that each of the cells in the grid represents one of the 8 possible combinations of coffee, tea, or chocolate.

The numbers in black are given directly by the problem statement. The numbers in blue are calculated from the numbers in black and one of the other given numbers in the problem statement. The numbers in red are calculated so the totals work out correctly.

The cells shaded blue-gray are "one and only one" of the drinks. The cell shaded purple-gray is "don't like any".

__

We assume that any form of "coffee" is "black coffee." The problem statement tells us 52 people like coffee.

__

The last number we calculated is the number who like none of the drinks: 66. This brings the total of non-coffee drinkers to 148.

_____

Additional comment

As noted above, the colors more or less indicate the order of the calculations. We started with 36 who like coffee only, and 46 who like coffee and not tea. That means 46-36=10 like coffee and chocolate, but not tea.

Since 16 like coffee and chocolate, that leaves 16-10=6 who like coffee and tea and chocolate (all three).

96 like chocolate, but 16 of those like chocolate and tea. The other 80 like chocolate, but not tea.

46+16=52, so there must be 0 who like coffee and tea, but not chocolate.

The number who like only one is 108. We already have 36 that are coffee only, 80-10 = 70 that are chocolate only, so there must be 108 -70 -36 = 2 who like tea only.

Now, we can finish filling the top row of the table and the totals in the bottom row.

The equation that is equivalent to S=pi r^2 h is h = S/pir^2

This is a way of representing a variable with another. Given the equation

S=pi r^2 h

We are to make 'h" the subject of the formula.

Divide both sides by pir^2

S/pir^2 =pi r^2 h/pir^2

h = S/pir^2

Hence the equation that is equivalent to S=pi r^2 h is h = S/pir^2

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#2

The shape can be cut into four rectangles and two squares.

Total surface area:

⇒ four rectangles + two squares

⇒ 4(Length × Width) + 2(side × side)

⇒ 4(6 × 1.5) + 2(1.5 × 1.5)

⇒ 36 + 4.5

⇒ 40.5 inch²

Therefore, the surface area of the rectangular prism is 40.5 inch²

#3

The polygons that would be used in this net surface area are:

✔ rectangle

✔ square

Answer:

40.5 in²

Step-by-step explanation:

Formula applied :

Surface Area (rectangular prism)

⇒ 2(Length × Width + Width × Height + Length × Height)

=============================================================

Given :

⇒ Length = 6 inches

⇒ Width = 1.5 inches

⇒ Height = 1.5 inches

============================================================

Solving :

⇒ Surface Area = 2(6 × 1.5 + 1.5 × 1.5 + 6 × 1.5)

⇒ Surface Area = 2(9 + 2.25 + 9)

⇒ Surface Area = 2 × 20.25

⇒ Surface Area = 40.5 in²

The correct interpretation of the probability P(X < 5) is; 0.8

We are given the probability of the spin values are;

Probability of Spin Value of 0 = 0.4

Probability of Spin Value of 1 = 0.2

Probability of Spin Value of 2 = 0.2

Probability of Spin Value of 5 = 0.1

Probability of Spin Value of 10 = 0.1

P(X < 5) simply means the probability of getting a spin value less than 5. Thus;

P(X < 5) = P(0) + P(1) + P(2)

P(X < 5) = 0.4 + 0.2 + 0.2

P(X < 5) = 0.8

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