Jill, Ally, and Maria ran the 50-yard dash. Jill ran the race in 6.87 seconds. Ally ran the race in 6.82 seconds. Maria ran the race in 6.93. Who ran the race the fastest? Explain how you can use a place-value chart to find the answer.

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

Answer:

the mean is the average of a set of numbers

Step-by-step explanation:

for example, if a set of numbers were 1,2, and 3, the mean would be 2 because the average is 2.

This can be calculated by adding 1, 2, and 3, and dividing them among all three numbers

1+2+3 = 6

6/3 =2

there are three numbers in the data set that we were trying to get the mean from

give brainliest, please! hope this helps :)

Answer:

  generally, the sum divided by the number of summands

Step-by-step explanation:

In math the term "mean" can have different meanings, depending on the context. It will generally refer to the arithmetic mean, if no additional qualifiers are given. The arithmetic mean is also called the average.

__

The arithmetic mean of a set of numbers is their sum, divided by the number of numbers. It is sometimes represented by the Greek letter μ or a variable with an overbar.

  [tex]\overline{x}=\dfrac{x_1+x_2+\dots +x_n}{n}[/tex]

The geometric mean will be the n-th root of the product of n numbers.

  [tex]\text{geometric mean}=\sqrt[n]{x_1\cdot x_2\dots\cdot x_n}[/tex]

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.

  [tex]\text{harmonic mean}=\dfrac{n}{\dfrac{1}{x_1}+\dfrac{1}{x_2}+\dots+\dfrac{1}{x_n}}[/tex]

In a proportion written as ...

  a/b = c/d

The two values closest to the middle of the expression (b and c) are called the "means". Those farthest away (a and d) are called the "extremes". It is said that ...

  the product of the means is equal to the product of the extremes

Answer:

x = 6, -3

Step-by-step explanation:

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

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:

Step-by-step explanation:

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:

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

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!

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

Answer:

y=48

Step-by-step explanation:

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:

x=24

Step-by-step explanation:

x=√(26)²-(10)²

x=√676-100

x=√576

x=24

Answer:

put formula a square minus b square

Child labor is a service rendered by children in any field during their childhood. This is done due to lack of resources for subsistence, irresponsibility of the parents or lack of resources by the owner to increase their returns on low investment.

This does not matter with the cause of child labor as all the reasons force children to live life without childhood. Childhood is the greatest and happiest period of everyone’s life, during which one learns about the basic strategy of life from parents, loved ones and nature. Child labor interferes with the proper growth and development of children in all aspects, mentally, physically, socially and intellectually.

☆...hope this helps...☆

_♡_mashi_♡_

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 :)

Answer:

same rin tayo ganyan rin akin ang hirap

Step-by-step explanation:

good evening po

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

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$

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

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.

The polynomial for the given operation A, B, and C will be (-x²-x-1),(-x²-x-1), and (-x²-x-1).

A polynomial is an algebraic statement made up of variables and coefficients.

Variables are sometimes known as unknowns. We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.

a)Given polynomials;

⇒(3x − 2x² + 4) + (x² - 4x - 5)

⇒− 2x²+x²+3x-4x+4-5

⇒-x²-x-1

b)The opposite of the given polynomial is found by changing the sign in the polynomial as;

⇒3x² - x + 1

⇒(-3x²) -(- x) + (-1)

⇒-3x²+x-1

c)The subtraction operation in the polynomial is found as;

(x² + 3x-4) - (4x-2x²-3)

(x²-2x²)+(+3x-4x)+(-4+3)

-x²-x-1

Hence,the polynomial for the given operation A, B, and C will be (-x²-x-1),(-x²-x-1), and (-x²-x-1).

To learn more about polynomials, refer to:

https://brainly.com/question/17822016

#SPJ1

Answer:

B

Step-by-step explanation:

First, we have to find the rate of change for this problem. To do this, we subtract any two numbers of days and the coordinating two total questions. Let's just use the first two rows. 8-4=4, and 40-20=20. For every 4 days, he answers 20 questions. We can further simplify this by dividing both sides by 4. 4/4=1, and 20/4=5. For every 1 day, he answers 5 questions. Now, to find 16 days, we just multiply both sides by 16. 16*1=16 and 16*5=80. For every 16 days, he answers 80 questions. 80 is our answer.

Hope this helps!

Answer:

x= 1.99

f(x) = 1.99x + 3

Step-by-step explanation:

Hope this helps! (;

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:

12x7 4 times add it up u got the anwser