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
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.
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
Q:Resolve this into partial fraction.
9/(X-1)(X+2)^2
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]
At 12 noon, the
temperature was
3°F. Then the
temperature fell
steadily and reached
-1°F at 2:00 PM.
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.
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
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
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?
Answer:
No, Its not.
Step-by-step explanation:
Kindo forgot Why and How.. Sorry!!
Three is added to a number, and the sum is multipled by 4. What is the equation and answer? Explain too please.
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 ;]
if the sides of a triangle are produced in order prove that the sum ofexterior angles so formed is equal to four right angles
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.
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?
Answer:
1:4
Step-by-step explanation:
No of girls :3
No. Of boys:12
Hence 3:12
1:4
Find the measure of the indicated angle
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
Which expression is equivalent to x ^2 – 8x + 16?
(x – 4) ^2
(x - 8)(x + 2)
(x + 4) ^2
(x – 4)(x + 4)
Answer:
Step-by-step explanation:
x^2 - 8x + 16 = (x - 4)^2
the first one
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.
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!
1. 2(4x - 3) - 8 = 4 + 2x
Can sb help slove this using PEMDAS ?
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
(-8, 4), (10, -9)
Find the midpoint
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]
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.
Answer:
y+8 inches
Step-by-step explanation:
since it's eight inches taller we have to add 8 inches to niki's height
Eight times the sum of a number and 6 is 4
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
Answer: Your answer is 7x-13.
how do u solve this pleaase
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
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
The sum of two odd numbers is even
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.
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.
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 is the greatest common factor (GCF) of 51 and 68?
A. 12
B. 3
C. 17
D. 2
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!
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?
Answer:
30 cmStep-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
Multiply the binomials (5x + 3) and (2x + 4).
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
Garrett answered 90% of 40 test problems correctly.How many problems did Garrett get wrong
Answer:
he got 4problems wrong
can you please give me brainliest
I need help!! Variables
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
0.11 in expanded form
Answer:
1.1
Step-by-step explanation:
As we move left, we multiply by 10 to obtain the new place value.
i need help please please :((
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!
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.
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
What quantity measures the amount of space and object occupies
Answer:
its volume
Step-by-step explanation:
Answer:
Volume is the unit that measures space of an object
5/6w+21=-1/3(2w-9)
please help