Lawrence High prevailed in Saturday's track
meet with the help of 20 individual event
placers earning a combined 68 points. A
first place finish earns 5 points, a second-
place finish earns 3 points, and a third-place
finish earns 1 point. Lawrence had a strong
second-place showing, with as many second
place finishers as first and third-place
finishers combined.

Answers

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Let x represent a first place finish, y represent a second place finish and z represent a third place finish.

Since there is a total of 20 individual events, hence:

x + y + z = 20          (1)

A first place finish is 5 point, a second place finish is 3 point and third place finish is 1 point. Therefore:

5x + 3y + z = 68      (2)

The second  place finishers is as much as first and third-place  finishers combined. Hence:

y = x + z                   (3)

Solving equation 1, 2 and 3 simultaneously gives:

x = 7,  y = 10 and z = 3

This means the number of first place finishes was 7, second place finishes was 10 and third place finishes was 3


Related Questions

Today, Nate has 100 bananas. He will eat 2 of them every day.
Is the number of bananas Nate has left proportional to the number of days that pass?

Answers

Answer:

No, Its not.

Step-by-step explanation:

Kindo forgot Why and How.. Sorry!!

Q:Resolve this into partial fraction.
9/(X-1)(X+2)^2

Answers

Answer:

[tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]

Step-by-step explanation:

Expressing as a partial fraction

[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{A}{(x-1)}[/tex] + [tex]\frac{B}{(x+2)}[/tex] + [tex]\frac{C}{(x+2)^2}[/tex] ( A, B, C are numerical values to be found )

Multiply both sides by (x - 1)(x + 2)²

9 = A(x + 2)² + B(x - 1)(x + 2) + C(x - 1)

Choose value for x that are zeros of the factors and substitute into right side

x = - 2 : 9 = - 3C ⇒ C = - 3

x = 1 : 9 = 9A ⇒ A = 1

x = 0 : 9 = 4A - 2B - C , that is

9 = 4 - 2B + 3 = - 2B + 7 ( subtract 7 from both sides )

2 = - 2B ⇒ B = - 1, then

A = 1, B = - 1, C = - 3

Thus

[tex]\frac{9}{(x-1)(x+2)^2}[/tex] = [tex]\frac{1}{x-1}[/tex] - [tex]\frac{1}{x+2}[/tex] - [tex]\frac{3}{(x+2)^2}[/tex]

Beth is solving this equation: 1/x + 3 =3/x
she says "I can multiply both sides by X and get the linear equation 1 + 3x = 3 whose solution is x = 2/3 ."
which of the following statements makes this a correct argument, or shows that it is in correct? Select all that apply.

a. you cannot multiply both sides by x because you do not know what x is.

b. you can assume x = 0 because both sides are undefined if x = 0

c. after multiplying both sides by X you need to subtract 1 from both sides.

d. the equation is not linear, so you cannot use the methods normally used for solving linear equations.

Answers

Answer:

a. you cannot multiply both sides by x because you do not know what x is.

Step-by-step explanation:

Given:

[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]

Required

Select which of the option that applies

Considering (a):

A is incorrect:

Because: Multiplying both sides by x has nothing to do with whether the value of x is known or not

Considering (b):

B is incorrect:

Substitute 0 for x in the given expression

[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]

[tex]Und efi ned[/tex]

Both sides of the equation are undefined

However, you cannot assume x to be 0

Considering (c):

C is correct:

Start by multiplying both sides by x

[tex]x (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]

[tex]1 + 3x = 3[/tex]

Then, subtract 1 from both sides

[tex]1 - 1 + 3x = 3 - 1[/tex]

[tex]3x = 2[/tex]

Divide through by 3

[tex]x = \frac{2}{3}[/tex]

Considering (d):

D is incorrect;

Because, the equation is linear

Garrett answered 90% of 40 test problems correctly.How many problems did Garrett get wrong

Answers

Answer:

he got 4problems wrong

can you please give me brainliest

Pete’s Painting Company will charge a one-time fee of $60 for labor and $20 for each room painted. Carla’s Creative Colors will charge $40 a room but only $20 to hire workers. Write a function rule for Pete’s Painting Company in function notation. Write a function rule for Carla’s Creative Colors in function notation.

Answers

Answer:

Pete's: [tex]f(x) = 20x + 60[/tex]

Carla's: [tex]f(x) = 40x + 20[/tex]

Step-by-step explanation:

Let's assume that [tex]x[/tex] is the amount of rooms painted, and [tex]f(x)[/tex]

For Pete's Painting Company, they charge a flat fee of $60, so we will have a constant of 60.

They also charge 20$ per room, meaning that we will multiply 20 by [tex]x[/tex], the amount of rooms painted.

This gets us the function [tex]f(x) = 20x + 60[/tex]

For Carla's Creative Colors, they charge 20$ to hire the workers, meaning this will be our constant.

They also charge $40 a room, meaning we will multiply 40 by [tex]x[/tex], the amount of rooms painted.

So the function is  [tex]f(x) = 40x + 20[/tex].

Hope this helped!

The sum of two odd numbers is even

Answers

Answer:

Yes.

Step-by-step explanation:

The sum of two odd numbers is always even. The product of two or more odd numbers is always odd. The sum of an even number of odd numbers is even, while the sum of an odd number of odd numbers is odd.

yes, the sum of two odd numbers is always even but the product of two or more odd numbers is always odd

Desmond is 8 inches taller than Niki. If we let y represent Niki's height in inches, write an algebraic expression for Desmond's height.

Answers

Answer:

y+8 inches

Step-by-step explanation:

since it's eight inches taller we have to add 8 inches to niki's height

5/6w+21=-1/3(2w-9)

please help

Answers

Proceidure
Hope this helps

There are 15 players on a soccer team, 3 girls and 12 boys. What is the ratio
of girls to boys on the soccer team?

Answers

Answer:

1:4

Step-by-step explanation:

No of girls :3

No. Of boys:12

Hence 3:12

1:4


Multiply the binomials (5x + 3) and (2x + 4).

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{10 {x}^{2} + 26x + 12}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(5x + 3)(2x + 4)}[/tex]

Use distribute property to multiply each term of the first binomial by each term of the second binomial.

[tex] \dashrightarrow{ \sf{5x(2x + 4) + 3(2x + 4)}}[/tex]

[tex] \dashrightarrow{ \sf{10 {x}^{2} + 20x + 6x + 12}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{10 {x}^{2} + 26x + 12}}[/tex]

Hope I helped !

Best regards! :D

Megan bought 3 pounds of apples that cost x dollars per pound. She gave the cashier a 20-dollar bill.
Which equation could Megan use to find the amount of change, y, she should receive?
A. y = 20-3
O B. y = 20 - 3
) C. y = 20 x
D. y = 20 - 3x
Ey = 3x - 20

Answers

Answer:

3x-20

Step-by-step explanation:

I had this test yesterday and this was the correct answer

The equation  D. y = 20 - 3x Megan use to find the amount of change.

What is an equation ?

An equation is is a tool that expresses two equality of two given expressions.

According to the given question Megan bought 3 pounds of apples that cost x dollars per pound. She gave the cashier a 20-dollar bill.

Let y denotes the change she received.

If 1 pound of apple cost x dollars then 3 pounds of apples will cos 3×x = 3x dollars.

∴ y = 20 - 3x.

learn more about equations here :

https://brainly.com/question/13795677

#SPJ2

1. 2(4x - 3) - 8 = 4 + 2x
Can sb help slove this using PEMDAS ?

Answers

Answer:

x=3

Step-by-step explanation:

1) get rid of the parenthesis by distributing the 2. You will get 8x-6-8=4+2x

2) Now combine like term on each side of the equal sign. You will get 8x-14=4+2x

3) Move the 14 to the right side of the equation making it +14 and move your 2x to the left side of the equation making it -2x. You will get 8x-2x=4=+14

4) calculate each side. You will get 6x=18

5) Divide both sides. You will get x=3

if the sides of a triangle are produced in order prove that the sum ofexterior angles so formed is equal to four right angles

Answers

Step-by-step explanation:

Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.

By interior angle sum postulate of a triangle:

a + b + c = 180°... (1)

Therefore, by remote interior angle theorem:

x = b + c.... (2)

y = a + c..... (3)

z = a + b.... (4)

Adding equations (2), (3) & (4)

x + y + z = b + c + a + c + a + b

x + y + z = 2a + 2b + 2c

x + y + z = 2(a + b + c)... (5)

From equations (1) & (5)

[tex]x + y + z = 2 \times 180 \degree \\ x + y + z = 360 \degree \\ x + y + z = 4 \times 90\degree \\ x + y + z = 4 \: right \: angles[/tex]

Thus, the sum of exterior angles so formed is equal to four right angles.

Proved.

a carpenter has a wooden dowel that is 96 cm long. she wants to cut it into two pieces so that one piece is 5 times as long as the other. what is the length of the longer piece? ​

Answers

Answer:

30 cm

Step-by-step explanation:

In this problem (word problem), we are examined on how to express equations from words.

let us initialize some variables

let the length of the first piece (the short piece) be x

and that of the second(the longer piece) be 5x

given that the total length is 96 cm

Also from the problem statement, the total length can be expressed as

5x+x= 96

6x= 96

divide both sides by 6 to solve for x

x= 96/6

x= 16

now the longer side = 5x

        the longer side= 5*6

       the longer side = 30 cm

(-8, 4), (10, -9)
Find the midpoint

Answers

Answer:

The midpoint between 2 points is (1,2.5) .

Step-by-step explanation:

We have to apply midpoint formula :

[tex]midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

[tex]let \: (x1,y1) \: be \: ( - 8,4)[/tex]

[tex]let \: (x2,y2) \: be \:(10 , - 9)[/tex]

[tex]midpoint = ( \frac{ - 8 + 10}{2} , \frac{4 + ( - 9)}{2} )[/tex]

[tex]midpoint = ( \frac{2}{2} , \frac{ - 5}{2} )[/tex]

[tex]midpoint = (1,2.5)[/tex]

What is the greatest common factor (GCF) of 51 and 68?
A. 12
B. 3
C. 17
D. 2

Answers

Factors of 51: 1, 3, 17, 51

Factors of 68: 1, 2, 4, 17, 34, 68

As you can see the greatest common factor of both numbers is 17.

Therefore, the answer is C.

Best of Luck!

the answer is C, 17. The factors of 51 are 1,3, and 17. The factors of 68 are 1,2,4,17, and 34. 17 is the GREATEST common factor

Which expression is equivalent to x ^2 – 8x + 16?
(x – 4) ^2
(x - 8)(x + 2)
(x + 4) ^2
(x – 4)(x + 4)

Answers

Answer:

Step-by-step explanation:

x^2 - 8x + 16 = (x - 4)^2

the first one

Find the measure of the indicated angle

Answers

Answer:

[tex]m\angle A = 98[/tex]

Step-by-step explanation:

Since it's a triangle all it's interior angles sum up to 180°

The triangle is isosceles which means two of it's angles are equal

From the question

[tex]m\angle B = m\angle C = 41 \degree[/tex]

So to find [tex]m \angle A[/tex] add up all the angles and equate it to 180° and solve for A

That's

[tex]m\angle A + m\angle B + m\angle \: C = 180 \\ m\angle A = 180 -m\angle B - m\angle \: C \\ m\angle A = 180 - 41 - 41 \\ = 180 - 82[/tex]

We have the final answer as

[tex]m\angle A = 98[/tex]

Hope this helps you

Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z? Write your answer as a fraction or percent rounded to the nearest tenth.

Answers

Answer:

25/26 or 96.2%

Step-by-step explanation:

In the alphabets, we have 26 letters

If we remove Z, we have A -Y which is 25 alphabets

The question requires us to find the theoretical probability of choosing any other letter that is not Z

Probability= ratio of other alphabets that are not z to the number of letters in the alphabets.

Probability = 25/26 (as a fraction)

Probability = 0.9615 x 100 = 96.2% (as a percentage and to the nearest tenth)

What quantity measures the amount of space and object occupies

Answers

Answer:

its volume

Step-by-step explanation:

Answer:

Volume is the unit that measures space of an object

Three is added to a number, and the sum is multipled by 4. What is the equation and answer? Explain too please.

Answers

Answer:

3+X=[3+X]4

Step-by-step explanation:

Let the number be X

we add x by three = 3+x

the sum of 3+x is 3+x

so we multiply the whole sum by 4 which is [3+x]4

so the ans is 3+x=[3+x]4

GOODLUCK ;]

 

BRAILYEST The area of a square poster is 37 in.2. Find the length of one side of the poster to the nearest tenth of an inch. The length of one side of the poster is nothing in.

Answers

Answer:

Length of the square poster = 6.1 in

Step-by-step explanation:

Area of a square poster = 37 in^2

Area of a square = length^2

37 = lenght ^2

Find the square root of both sides

√37 = √ length ^2

Length = 6.0828 in

Approximately

Length of the square poster = 6.1 in

At 12 noon, the
temperature was
3°F. Then the
temperature fell
steadily and reached
-1°F at 2:00 PM.

Answers

Noon to 2:00 pm is 2 hours

3 degrees to -1 degree is a total of 4 degrees.

The temperature changed 4 degrees in 2 hours.

4/2 = 2

The temperature dropped 2 degrees per hour.

i need help please please :((

Answers

Answer: 9^-16

Step-by-step explanation:

If an exponents have the same base and are  being multiplied together, all you do is just add the exponents and make the base stay the same

9[tex]9^{-53} * 9^{37} = 9^{-16}[/tex]

Negative exponents can be rewritten as positive exponents if you put them in the denominator.

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Using this rule, we can rewrite the equation.

[tex]9^{-53}*9^{37}=\frac{1}{9^{53}}*9^{37}[/tex]

[tex]\frac{9^{37}}{9^{53}}[/tex]

Then, we can use exponent division rules.

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\frac{9^{37}}{9^{53}}=9^{37-53}[/tex]

[tex]9^{-16}[/tex] or [tex]\frac{1}{9^{16}}[/tex]

Hope this helps.

頑張って!

I need help!! Variables

Answers

Answer:

the correct answer is 20 .

Step-by-step explanation:

x^2 - ( x + 4 ) - y = ?

6^2 - ( 6 + 4 ) - 6 = ?

36 - ( 10 ) - 6 = ?

26 - 6 = 20

20 is the correct answer

0.11 in expanded form

Answers

Answer:

1.1

Step-by-step explanation:

As we move left, we multiply by 10 to obtain the new place value.

Eight times the sum of a number and 6 is 4

Answers

Answer:

80

Step-by-step explanation:

6+4=10

10x8=80

Hope this helped!!! Have a nice day and please mark me brainliest!!!

UwU

Step-by-step explanation:

8(n + 6) = 4

8n + 48 = 4

8n = 4 - 48

8n = -44

n = - 5.5

4x - 2 (x -2) -9 +5x-8

Answers

Idk if X is what you news but here it goes

Answer: Your answer is 7x-13.

how do u solve this pleaase

Answers

Answer:

[tex] \huge \frac{4}{9 {x}^{4} {y}^{6} }[/tex]

Step-by-step explanation:

[tex] \huge \bigg( \frac{2 {x}^{ - 2} }{3 {y}^{3} } \bigg)^{2} \\ \\ \huge = \frac{ {2}^{2} ( {x}^{ - 2})^{2} }{ {3}^{2} ( {y}^{3} ) ^{2} } \\ \\ \huge = \frac{4 {x}^{ - 4} }{9 {y}^{6} } \\ \\ \huge = \frac{4}{9 {x}^{4} {y}^{6} } \\ [/tex]

9x - 6xy + 9 + 9xy - 6y

HELPP

Answers

Answer:

9x-6y+3xy+9

Step-by-step explanation:

firstly rearrange

9x-6y-6xy+9xy+9

then simplify those that can

-6xy + 9xy = +3xy

hence

9x-6y+3xy+9

9x+3xy+9-6y
3(3x+xy + 3 -2y)
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