Which sentence illustrates the distributive property

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.

For more about the equation

brainly.com/question/2263981

#SPJ2

41.67 ounce of pure water should be added to 25 ounces of the 8% salt solution to dilute it to a 3% solution

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of pure water needed to dilute the solution. Hence:

8% * 25 = 3% * (x + 25)

2 = 0.03x + 0.75

x = 41.67 ounce

41.67 ounce of pure water should be added to 25 ounces of the 8% salt solution to dilute it to a 3% solution

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

It should be -1.16

Step-by-step explanation:

Hope this helps :)

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.

Learn more about fractions:https://brainly.com/question/10354322

#SPJ1

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.

If you want to learn more about ratios:

https://brainly.com/question/2328454

#SPJ1

Answer:

The number of children is 2500 and the number of adults that attended the game is also 2500.

Step-by-step explanation:

Let us consider that, number of children be x and number of adults be y that attend game.

Since, total 5000 people attend the game.

It costs $3 for children and $7 for adults and the total takings at the door was $25000

Substitute value of x from equation 1 into equation 2.

So that,

Thus, the number of children is 2500 and the number of adults that attended the game is also 2500.

Answer:

5 + 24x

Step-by-step explanation:

Given phrase - Five more than the product of 24 and a number.

In the given phrase, the word "more" means "addition". Therefore,

The word "product" defines multiplication between two numbers. In this case, the product of 24 and a number is 24(number).

The question stated to use the "n" to represent the unknown number. Let the unknown number be known as "n".

Therefore, the expression is 5 + 24n.

----------------------------------------------------------------------------------------------------------------

Learn more - https://brainly.com/question/13536824

Answer:

x = 6, -3

Step-by-step explanation:

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

Answer:

I think the answer is 33

Step-by-step explanation:

Extremely sorry if it's wrong

Answer:

7 1/5 cups of flour

Step-by-step explanation:

divide 3/5 which is 0.6 then multiply that by 12, which is 7.2

then convert that into a fraction which is 7 1/5

Answer:

180

Step-by-step explanation:

160= 1/3 * total
160*3 = total
480 = total

bridget = 1/4(total)
bridget = 1/4(480)
bridget took  120

Sasha took 1/2 of 360
Sasha took $180.

Answer:

x= 1.99

f(x) = 1.99x + 3

Step-by-step explanation:

Hope this helps! (;

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:

x=24

Step-by-step explanation:

x=√(26)²-(10)²

x=√676-100

x=√576

x=24

Answer:

$910

Step-by-step explanation:

there are 52 weeks in a year

52/2 = 26

if someone spends 35 every two weeks then

35x26=910

Answer:

840$

Step-by-step explanation:

2*2= 1 month (4weeks)

35*2= 70

70*12 (months of the year) = 840$

Answer:

put formula a square minus b square

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:

Step-by-step explanation:

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:

The answer is option C

Step-by-step explanation:

The solution is in the image

Answer:

Step-by-step explanation:

8x - 4y = 16

3x + 4y = 17

11x = 33

x = 3

12 - 2y = 8

-2y = -4

y = 2

(3, 2)

answer is C

The functions will be defined as y = x² if 0 ≤ x < 3, y = -x + 10 if 3 < x ≤ 6, and y = x + 2 if 6 ≤ x ≤ 10.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The graph is given below.

The function can be defined as

The parabolic equation will be

f(x) = x²

The equation of the absolute function will be

f(x) = |x - 6| + 4

Then we have

[tex]f(x) = \left\{\begin{matrix}y=x^2 & 0\leq x < 3 \\\\y=-x+10 & 3 < x\leq 6 \\\\y=x+2 & 6\leq x \leq 10 \\\end{matrix}\right.[/tex]

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ1

Checking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other. Therefore her plan will work.

A quadrilateral are shapes with 4 sides. A rectangle is a quadrilateral with 2 parallel sides.

According to Nala's plan to find out if the quadrilateral shown is a rectangle, she can do the following;

Checking if the two pairs of slopes are negative reciprocal will help he determine if the lines are perpendicular to each other.  

Learn more on quadrilateral here: https://brainly.com/question/21662845

#SPJ1

The exact height of the triangle is 20.8ft

The area of the right tringle in radical form is 72√3 ft²

The area of the triangle in decimal form is 124.7 ft²

The side XY or height of the triangle can be found as follows:

Using trigonometric ratios,

tan 60° = XY / 12

XY = 12 tan 60°

XY = 12 × 1.73205080757

XY = 20.7846096908

height = 20.8ft

The area of XYZ = 1 / 2 bh

where

Therefore,

The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145  = 124.7 ft²

The area in radical form = 1 / 2 × 12 × 12 tan 60°

The area in radical form =  1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²

learn more on triangles here: brainly.com/question/2773823

#SPJ1