Answer:
r = 3t/t-1
Step-by-step explanation:
t = r/r-3
1. times both sides by r-3
t(r-3) = r
= tr - 3t = r
2. add 3t to both sides
tr = 3t + r
3. minus r
tr - r = 3t
4. factorise out r
r(t-1)=3t
5. divide by t-1
r = 3t/t-1
x^2-y=7 and y-5x=-11 The system of equations above has two solutions. The solution in Quadrant 1 is (A,B) and the solution in Quadrant 4 is (C,D) . Find the values of (A,B), (C,D)
By solving the system of equations, we can see that the solutions are:
(A, B) = (4, 9)
(C, D) = (1, -6).
How to solve the system of equations?Here we have the following system of equations:
x^2 - y = 7
y - 5x = -11
If we isolate the variable y in both equations, we get:
y = x^2 - 7
y = -11 + 5x
Now we can equate these two to get:
x^2 - 7 = -11 + 5x
now we have a quadratic equation, this can be rewritten as:
x^2 - 7 + 11 - 5x = 0
x^2 - 5x + 4 = 0
Using the quadratic formula, we will see that the solutions are:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}[/tex]
Solving that we get:
[tex]x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}[/tex]
So the two solutions for x are:
x = (5 + 3)/2 = 4
x = (5 - 3)/2 = 1
Evaluating the second equation in these x-values we get:
y = -11 + 5*4 = -11 + 20 = 9
y = -11 + 5*1 = -6
Then we have the coordinate pairs: (4, 9) (on the first quadrant) and (1, -6) on the fourth quadrant.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
4. tumbleweed, commonly found in the western united states, is the dried structure of certain plants that are blown by the wind. kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. scientists are concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. the us department of the interior claims that 20 percent of kochia plants are resistant to glyphosate. in 2017 another study by researchers at university of new mexico, 38.5 percent of 52 randomly selected kochia plants were resistant to glyphosate.
Using the z-distribution, as we are working with a proportion, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
What are the hypothesis tested?In null hypothesis, we test if there has been no increase, that is, the subtraction is of 0.
In this problem, we consider that:
p₁ is the proportion in 2014.
p₂ is the proportion is 2017.
H₀=p₂-p₁
By alternative hypothesis,
H₁=p₂-p₁≠0,
we test if there has been an increase
The proportions and standard errors are given by:
p₁=0.97, s₁=√0.97(0.803)/61=0.0509
p₂=0.385, s₁=√0.385(0.615)/52=0.0675
Hence, the distribution has mean and standard error given by:
p=p₂-p₁=0.0675-0.0509
s=√s₁²+s₂²=0.0845
Test static z=p bar-p/s
at p = 0 is the value tested at the null hypothesis,
z=0.0166/0.0845
z=0.2
By a right-tailed test, we are testing is the proportion is greater than a value, with a significance level of 0.05, the critical value is of
z=1.645
0.2<1.645 there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
More can be learned about the z-distribution at brainly.com/question/26454209
#SPJ1
Rectangle 1 has an area of 60.81 square centimeters. Rectangle 2 has an area of 61.44 square centimeters. Rectangle 3 has an area of 35.52 square centimeters. Rectangle 4 has an area of 47.88 square centimeters. Part A..Which two rectangles have the greatest difference in area? Part B Look at your answer to part A what is the difference between those two rectangles areas?
The two rectangles that is R3 and R4 have the greatest difference in the area.
How to calculate the area of the rectangle?
In mathematics, the rectangle is a closed polygon shape which has four vertex as well as four sides. And the opposite side are parallel to each other. To calculate the area, multiply the length and breadth. Similarly, for the perimeter means add all the sides.
According to the question, the given data in the form of the area of the rectangle is as follows:
Area of Rectangle1 = 60.81 square centimeters
Area of Rectangle2 = 61.44 square centimeters
Area of Rectangle3 = 35.52 square centimeters
Area of Rectangle4 = 47.88 square centimeters
Now, to calculate the greatest difference in the area of the rectangles:
Difference(Rect2 - Rect1) = 61.44 - 60.81 = 0.63
Difference(Rect1 - Rect3) = 60.81 - 35.52 = 25.29
Difference(Rect1 - Rect4) = 60.81 - 47.88 = 12.93
Therefore, the two rectangles that is R3 and R4 have the greatest difference in the area.
And the differences are as follows:
Area(Rect1 - Rect3) = 60.81 - 35.52 = 25.29 square centimeters
Area(Rect1 - Rect4) = 60.81 - 47.88 = 12.93square centimeters
To learn more about the area of the rectangle from the given link:
https://brainly.com/question/17065463
#SPJ9
On a literature exam, there are 6 vocabulary questions for every 7 questions about
a book. If there are 12 vocabulary questions on the test, how many total questions
are on the test?
Answer:
26 total questions
Step-by-step explanation:
6 * 2 = 12
7 * 2 = 14
14 + 12 = 26
11. What is the value of the expression below?
1-10+6|-|3²-5|
The value of the expression |-10+6|-|3²-5| = 0
The expression given is |-10+6|-|3²-5|.
This contains absolute value which needs to be evaluated.
We will go through the definition of absolute value.
Absolute value for x = x, when x is a positive integer.
i.e., |x| = x, when x >0
Absolute value of (-x) = x, when -x is a negative integer.
So absolute value always gives the positive value of the number inside it.
Now |-10+6|-|3²-5| = |-4| - |9-5|
= 4 - |4| [Since |-4| = 4]
= 4 - 4 [Since |4| = 4]
= 0.
So the value of the expression |-10+6|-|3²-5| = 0
Learn more about absolute value at https://brainly.com/question/24368848
#SPJ1
Which relation represents a function?
In the given relations , the relation (B) represents a function, others are not function. To become a function each input should have only one output. Since others does not satisfy this criteria they are not functions.
How to check the relation is function or not ?Determine the input values. Determine the output values. If each input value results in only one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.To determine whether a graph represents a function, use the vertical line test. If a vertical line is moved across the graph and only touches the graph at one point at any time, the graph is a function. The graph is not a function, if the vertical line intersects it more than once.To learn more about relations refer to :
https://brainly.com/question/24779057
#SPJ13
Starting with the number 0, build a sequence of 5 numbers.
Answer:
How about:
0, 1, 2, 3, 4..............
lol jk here:
0, 66, 132, 198, 264
Step-by-step explanation:
Guess what it is! ;p
y=-5(-4)-17
please add an explanation
Answer:
y = 3
Step-by-step explanation:
y = -5(-4) - 17
multiply first
y = (-5*-4) - 17
y = +20 -17
y = 3
Fr fr stop fooling around I really need help if you explain this I’ll give you brainliest if you give me the answer straight up like this (1. “Answer” ) I’ll also give you brainliest if the other person doesn’t explain clearly just NO nonsense answer PLEASE
Answer:
1) 4, 1.25, 2
2) 12, 5, 3
3) 2, 18, 5
4)5, 8, 12
Step-by-step explanation:
1) You had to either multiply/divide by 4
2)You had to either multiply/divide by 3
3)You had to either multiply/divide by 6
4)You had to either multiply/divide by 5
Aryon has $20. He buys 2 cokes that each cost $1.50. He also buys a sandwich for $5.50. And a bag of chips that cost $2.25. After Aryon pays for his lunch, how much money does he have left.
Aryon is left with $9.25 of money after he has paid for his lunch.
According to the question,
We have the following details:
Total amount Aryon has = $20
The cost of 1 coke = $1.50
So, the cost of 2 cokes = $(2*1.50)
The cost of 2 cokes = $3
The cost of a sandwich = $5.50
The cost of a bag of chips = $2.25
So, the total cost of all the materials = the cost of 2 cokes + the cost of a sandwich + the cost of a bag of chips
The total cost of all materials = $(3+5.50+2.25)
The total cost of all materials = $10.75
Now, the money Aryon has = Total money he has - the total cost of all materials
The money Aryon is left with = $(20-10.75)
The money Aryon is left with = $9.25
Hence, the money Aryon is left with is $9.25.
To know more about money here
https://brainly.com/question/14253896
#SPJ1
Carlos is three times as old as Maria.
The sum of their ages is 56 years. How
old is each?
Maria's Age = 14 years old.
Carlos Age = 42 years old
Answer:
Carlos is 42, and Maria is 14.
Step-by-step explanation:
14 x 3 = 42,
14 + 42 = 56,
So, the answer is Carlos = 42, Maria = 14.
Hope this helps!
Btw, Brainliest please, thanks!
Rebecca Sweet was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 806 points. The number of two-point field goals that Rebecca made was 52 less than double the number of three-point field goals she made. The number of free throws (each worth one point) she made was 28 less than the number of two-point field goals she made. Find how many free throws, two-point field goals, and three-point field goals Rebecca Sweet made during the 2006 regular season.
In the year 2006, the number of free throws is 100, number of 2 point field goals 128 and the number of 3 point field goals 90.
Let x = number of free throws
y = number of 2 point field goals
z = number of 3 point field goals
However given that Rebecca has a total of 806 points,
Thus x + 2y + 3z = 806 ---------- equation 1
Number of 2 point field goals that Rebecca made was 52 less than double the number of three-point field goals she made ;
thus y = 2z - 52 ---------------- equation 2
Number of 3 point field goals that Rebecca made was 28 less than the number of two-point field goals she made ;
thus x = y - 28 ------------------ equation 3
Thus on solving these three above mentioned equations :
we get x = 2z - 52 -28 [ substituting values in eq 3 from eq 2]
x = 2z - 80 ------------- equation 5
So equation 1 becomes ; 2z - 80 + 2y + 3z = 806
5z + 2y = 886 -------------- equation 4
Thus on solving equation 4 and 2 we get
2 X equation 2 = 4z - 2y = 104
5z + 2y = 886
= 11 z = 990
thus z = 90 and so y = 4 × 90 - 104 = 2y
y= 360 - 104 / 2
= 256/2 = 128
thus y = 128 .
And x= 2z -80 from equation 5 ; x = 180 - 80 = 100 .
To know more about linear equation visit:
https://brainly.com/question/19549073
#SPJ9
Which of the following is not a correct name for the line above? A. ij B. Kn C. kj D. ki
Can someone pls help me i will mark for whoever helps me
The answers to all the subparts are:
(A) 0.21 : Rational number(B) 3/12 : Rational number(C) 4.125 : Rational number(D) 8⅒ : Rational number(E) π/3.14/(22/7) : Rational numberWhat are rational numbers?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.So, the reason for rational or irrational numbers:
(A) 0.21
It is a rational number as it can be represented in fractions.
(B) 3/12
It is a rational number as it is in fractions.
(C) 4.125
It is a rational number as it can be represented in fractions.
(D) 8⅒
It is a rational number as it can be represented in fractions.
(E) π/3.14/(22/7)
It is a rational number as it can be represented in fractions.
Therefore, the answers to all the subparts are:
(A) 0.21 : Rational number(B) 3/12 : Rational number(C) 4.125 : Rational number(D) 8⅒ : Rational number(E) π/3.14/(22/7) : Rational numberKnow more about rational numbers here:
https://brainly.com/question/28622954
#SPJ13
Which equation is equivalent to −(5−x)=5−x? Responses
Answer:
x = 5
Step-by-step explanation:
The perimeter of the flag is 2260 ft Determine the flag's width and length if the length is 350 ft greater than the width.
The length is 780 feet and the width is 430 feet.
Distance is measured in length.
The dimension of distance is a property of length in the International System of Quantities.
The majority of measurement systems have a base unit for length from which all other units are derived. The meter is the primary unit of length in the International System of Units (SI) system.The term "length" is usually considered to refer to an object's longest dimension.Nevertheless, depending on the position of the object, this isn't always the case.There are several terms used to describe the length of a fixed object, including height, which is also known as vertical length or vertical extension, and width, breadth, or depth.Let the length be x
Width = x - 350
Perimeter = 2260 feet
Now : 2(x + x +350) = 2260
or, 2 x + 700 = 2260
or, 2x = 1560
or, x = 780 feet
So length is 780 feet
Width = 780 -350 = 430 feet
Therefore the length is 780 feet and the width is 430 feet.
To learn more about length visit:
brainly.com/question/15601403
#SPJ1
12 > w + 3 solve the inequality for w and simplify your answer as much as possible
The solution to given inequality 12 > w + 3 is w < 9
In this question, we have been given an inequality 12 > w + 3
We need to solve the inequality for w.
Consider given inequality,
12 > w + 3 ............(Given)
12 - 3 > w + 3 - 3 ...........(Subtract 3 from each side)
9 > w
This means, w is less than 9.
Therefore, the solution to given inequality 12 > w + 3 is w < 9
Learn more about an inequality here:
brainly.com/question/19003099
#SPJ1
Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine x x, the number of gigabytes Mayerlin can use while staying within her budget.
The number of gigabytes that Mayerlin can use while staying within her budget is 5.
How many gigabytes can she use?The first step is to determine the appropriate inequality sign to use. Here are the inequality signs:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is <
The form of the inequality is:
flat cost + (cost per gigabyte x number of gigabytes) < total budget
$55 + $5x < $70
5x < $70 - $55
5x < 25
x < 25 / 5
x = 5
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
A skydiver is planning her jump out of an airplane. Typically, she will jump at a height of 13,500 feet, and she will pull the cord when she is 5000 feet above the ground. If the equation for the distance traveled during freefall is given as d(t)=16t2 , how long should she wait before pulling the cord?
Skydiver should wait 23.04 sec before pulling the cord, after freefall.
what is freefall?
An item that is falling only due to gravity is said to be in free fall. Any item that is merely subject to the effects of gravity is referred to as being in free fall.Air resistance does not exist for falling objects in free fall.On Earth, all falling objects experience a downward acceleration of 9.8 m/s/s (commonly represented as 10 m/s/s in quick calculations).Height of jump = 13500ft
Height from which cord will be pulled = 5000ft
Freefall, d=13500-5000 =8500ft
Distance traveled during freefall, d=16t²
substituting values, we get,
8500=16t²
t=23.04 sec
Skydiver should wait 23.04 sec before pulling the cord, after freefall.
Learn more about freefall here:
https://brainly.com/question/12167131
#SPJ1
i need help with this problem i’m struggling with
what is 5.3 x 10^2 in standard form?
Answer:
530 x
Step-by-step explanation:
The sum of 2 and b is less than or equal to -16 translate the scentence into an inequaltiy
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{G\textsf{uide:}}[/tex]
[tex]\bullet\large\textsf{ Greater than or equal to}\rightarrow\mathsf{\geq}\\\bullet\large\textsf{ Greater than}\rightarrow\mathsf{ > }\\\bullet\large\textsf{ Less than or equal to}\rightarrow\mathsf{\leq}\\\bullet\large\textsf{ Less than}\rightarrow\mathsf{ < }[/tex]
[tex]\star\large\textsf{ The word \boxed{\rm{difference}} means subtract/subtraction}\\\star\large\textsf{The word \boxed{\rm{product}} means multiply/multiplication}\\\star\textsf{The word \boxed{\rm{quotient}} means divide/division}\\\star\large\textsf{The word \boxed{\rm{sum}} means add/addition}[/tex]
[tex]\large\text{Now, let us answer your given question}[/tex]
“[tex]\large\textsf{The \underline{SUM} of 2 and b is \underline{LESS THAN or EQUAL to} }\mathsf{-}\large\textsf{16}[/tex]”
[tex]\large\text{Your equal should possibly look like this:}\large\textsf{ 2 + b }\mathsf{\leq\ -}\large\textsf{16}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{2 + b \leq -16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
2.d = f + fx; for
x. How to solve
Answer:
x = [tex]\frac{d - f}{f}[/tex]
Step-by-step explanation:
d = f + fx
Subtract f from both sides
d - f = fx
Divide both sides by f
[tex]\frac{d - f}{f}[/tex] = x
7th grade math please help a girl out
You are holding a kite string in your hand. The angle of elevation from your hand to the kite is 66 degree and the distance to the kite is 303 feet. Your hand is 4 feet above the ground. How high is the kite? Round your answer to the nearest tenth of a foot.
For given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.
As given,
Shown in diagram attached,
Angle of elevation ∠AEB=66°
Distance to the kite AE=303 feet
Hand above the ground DE=4feet
DE=BC
BC=4feet
Let 'h' be height of AB
Height of the kite=(h +4)feet
In ΔABE,
sin66°=h/303
⇒h=sin66° ×303
=0.9135 ×303
=276.7905
≈276.8 feet
Height of kite=(h +4) feet
=276.8 +4
=280.8 feet
Therefore, for given angle of elevation equals to 66 degree and distance to kite is 303feet and hand is 4 feet above the ground then kite is 280.8feet high.
Learn more about angle of elevation here
brainly.com/question/9817377
#SPJ1
A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
Inequality is 32.50x + $10.50 ≤ $160 and 4 people can go to the amusement park.
What is an inequality?inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Given that,
$160 = Amount of money they have
$10.50 = Parking Cost
$32.50 = Cost of tickets per person
Because they only have $160, they can't spend more than that amount.
Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:
32.50x + $10.50 ≤ $160
Solve the equation
$160 - $10.50 = $149.50 (149.50 is how much is left for tickets after subtracting the parking cost)
$32.50 x 4 = $130 (4 tickets can be bought for the price of $32.50)
$149.50 - $130 = $19.50 (19.50 isn't enough for another person)
So, the solution to the inequality is 4 people can go to the amusement park.
To learn more about the inequality from the given link:
https://brainly.com/question/24968315
#SPJ9
A survey was taken that asked a total of 400 participants whether or not they were happy withtheir jobs. An overall score was given. 100 of the participants were unhappy while 300 of theparticipants were happy with their job.What percent were happy with their job?
To find the percent of happy people, we just have to divide the number of happy participants by the total number of them.
[tex]\frac{300}{400}=0.75[/tex]Then, we multiply it by 10 to express it as a percentage.
[tex]0.75\cdot10=75[/tex]Hence, 75% of the participants were happy with their job.I’m failing geometry pls help. Why did my teacher mark me wrong on this problem and what are the correct answers?
Step-by-step explanation:
it is a bit difficult to read the handwriting (and even the printed original texts) in this diffuse picture.
let's go through the 3 problems as I could decipher them.
1)
from what I can see you made a calculation mistake for y.
but you were right with your approaches.
12x - 8 = 15x - 23
15 = 3x
x = 5
therefore,
12x - 8 = 12×5 - 8 = 60 - 8 = 52°
and the large angle up there is
52 + 70 = 122°
and now
6y + 96 = (12x - 8) + 70 = 122
6y = 26
y = 26/6 = 13/3
by the way, x and y are not angles (and degrees). they are just factors in the expressions to calculate some angles.
12, 15 and 6 are not ° either. all are calculation factors or terms, that then together define the ° of angles.
2)
you made a mistake with the identification of what angles the linear pair is.
3x = 5x - 20
20 = 2x
x = 10 (again, not °, just a number)
3x = 3×10 = 30° (this is then an angle)
= 5x - 20
for y we could then use 2 different approaches
a) your linear pair approach.
4y is one angle, true, but the other is (2y + 3x) !
so,
4y + 2y + 30 = 180
6y = 150
y = 25 (again, not °, just a number)
2y = 50°
4y = 100°
3)
I hope you are right with (11x + 19) and (12y - 24). I would have read this in the picture as (11x + 18). and it could be (12y + 24).
assuming you are right :
11x + 19 = 7x + 47
4x = 28
x = 7 (again, not °, just a number)
11x + 19 = 7x + 47 = 96°
7z + 17 = 87
7z = 70
z = 10 (again, not °, just a number)
and yes, for y we are using the linear pair again. the two combining angles are (12y - 24) and (11x + 19).
(12y - 24) + (11x + 19) = 12y - 24 + 96 = 180
12y + 72 = 180
12y = 108
y = 9 (again, not °, just a number)
12y - 24 = 12×9 - 24 = 108 - 24 = 84°
jared bought a table and 12 chairs for $2,400. each chair cost $ 165. find the cost of the table?
Answer:
Answer down below!
Step-by-step explanation:
Since we do have the value of the chairs, we can do 12 * 165 to get a total of 1,980
Now, with this, to find the price of the table, you do 2,400 - 1,980
That will give you your answer of 420.
In a pasture of grass and other plants, the biomass of insects makes up 5000 kilograms. This is 5% of the total biomass of the pasture. What is the total biomass of the pasture? Set up the problem and solve below.
5000kg------->5%
x------------------>100%
Using Cross-multiplication:
5000/x=5/100
Solving for x:
x=(100*5000)/5 =100000kg
You can verify the answer:
100000kg *5% =100000*0.05= 5000kg