By consideration of congruence and collinearity, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.
What is the value of the variable behind a geometric system formed by two collinear line segments?
Two line segments are congruent when the line segments have the same length, then the following condition has to be fulfilled:
AB = BC (1)
Where AB and BC are the lengths of the line segments AB and BC.
If we know that AB = 4 · x + 1 and BC = 20 · x - 5, then we solve the equation for x is:
4 · x + 1 = 20 · x - 5
6 = 16 · x
16 · x = 6
x = 6 / 16
x = 3 / 8
Then, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.
To learn more on collinear line segments: https://brainly.com/question/17719606
#SPJ1
Cookies cost $3 each, and candies cost $2 each. Tim has
$25. Which inequality represents the number of cookies, x,
and the number of candies, y, that Tim can buy?
Answer:
8x < 12y
Step-by-step explanation:
If you divide 25 by 3, you get 8.3333... (the threes go on forever), which you can round to 8, because little Timmy isn't going to buy .3 of a cookie. If you divide 25 by 2, you get 12.5, which you round down to 12. I know you normally don't round 5 down, but we are talking about food here.
Therefore, Tim can buy less cookies than candies. He can buy 8 cookies, and 12 candies.
Either way, Timmy's gonna be fat.
solve for the missing value
1/2:4=1/3:x
If the area of a rectangle is x^2+13x+36 and the length is x+9 what is the width
Answer:
width = (x+4)
Step-by-step explanation:
Answer:
Width is x+4 units
Step-by-step explanation:
Since the area of a rectangle is length*width, then width=area/length:
-9 | 1 13 36
____-9 -36_
1 4 | 0
Therefore, the width of the rectangle is x+4 units
A group of 72 children completed a survey on what kind of sport they like. The choices were: Chess, Swimming, and Football. Everyone liked at least one sport except 7 kids, which doesn't like any of these three kind of sports.
12 children liked Chess and Football but not Swimming,
16 children liked Chess and Swimming but not Football,
8 children liked Swimming and Football but not Chess,
10 children liked Chess only,
40 children liked Swimming,
32 student liked Football.
What is the probability that a randomly-chosen child from this group does not like active kinds of sport?
Answer:
\(\dfrac{17}{72}\)
Step-by-step explanation:
From the given information:
Total number of students, \(n(U)=72\)
The choices were: Chess(C), Swimming(S), and Football(F).
Everyone liked at least one sport except 7 kids, \(n( C \cup F \cup S)'=7\)
Chess is not an active sport; and
10 children liked Chess only, \(n( C \cap F' \cap S')=10\)
The probability that a randomly-chosen child from this group does not like active kinds of sport is the Probability that a student plays chess only or like no kind of sport at all.
\(P( C \cup F \cup S)'+P(C \cap F' \cap S')=\dfrac{n( C \cup F \cup S)'+n(C \cap F' \cap S')}{n(U)} \\=\dfrac{10+7}{72} \\=\dfrac{17}{72}\)
Factor the polynomial:4x^4y^2-16x^4y^2+8x^2y
Answer:
\(4x^2y(x^2y - 4x^2y+2)\)
Step-by-step explanation:
Given
\(4x^4y^2-16x^4y^2+8x^2y\)
Required
Factor
\(4x^4y^2-16x^4y^2+8x^2y\)
Factor out \(4x^2\)
\(4x^2(x^2y^2 - 4x^2y^2+2y)\)
Factour out y
\(4x^2y(x^2y - 4x^2y+2)\)
i need help!!!! does anyone know this..!!???
The period of oscillation is 3 seconds
What is period of oscillation?A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.
The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds
Oscillation can also be vibration or revolution or cycle.
Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.
This means that the period of the particle is 3 seconds.
learn more about period of oscillation from
https://brainly.com/question/22499336
#SPJ1
(3 pts)If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty. b) (3 pts)If 2 different study subjects are randomly selected (without replacement), find the probability that they both were sentenced to prison. c) (3 pts)Find the probability of being sentenced to prison, given that the subject entered a plea of guilty. d) (3 pts)Find the probability of being sentenced to prison, given that the subject entered a plea of not guilty.
Answer:
Follows are the solution to this question:
Step-by-step explanation:
The missing data and a solution file is define in attached file please find it.
In point A:
Formula for sentenced to prison:
\(=\frac{\text{total of sentenced to prison}}{ \text{guilty}}\)
\(= \frac{880}{1324} \\\\= 0.66\)
In point B:
Formula for both prison: Sentenced to Prison/Guilty
\(=\frac{\text{Sentenced to Prison}}{ \text{guilty}}\)
\(=\frac{370}{1185}\\\\=0.31\)
In point C:
Formula for: Sentenced to Prison and not Guilty
\(= \frac{\text{Sentenced to Prison and not Guilty}}{ \text{not guilty}} \\\\=\frac{74}{139}\\\\= 0.53\)
F(x)= 1/x-2 g(x)= 4/x find (fog)(x)
We have the functions f and g:
f(x) = 1/x - 2
g(x) = 4/x
To obtain the composite function (f o g)(x):
(f o g)(x) = f(g(x)) = 1/g(x) - 2
Then:
(f o g)(x) = 1/(4/x) - 2
(f o g)(x) = x/4 - 2
Now, to calculate the composite function (g o f)(x):
(g o f)(x) = g(f(x)) = 4/f(x)
(g o f)(x) = 4/(1/x - 2) = 4/((1 - 2x)/x)
(g o f)(x) = 4x/(1 - 2x)
the answer to the question and also please give the domain interval notation and also the range interval notation. whether If -1 is constant
Given:
The function os given as
\(f(x)=-1\)Required:
We want to find the domain, interval and also graph the given function,
also identify that the given function is constant or not
Explanation:
The graph of the given function is as below
The given function is constant
Domain of function is
\(\left(-\infty \:,\:\infty \:\right)\)range of function is
\(-1\)Final answer:
\(\begin{gathered} \left(-\infty \:,\:\infty \:\right) \\ -1 \end{gathered}\)
A CD usually sells for $15.00. If the CD is 20% off, and sales tax is 6%, what is the total price of the CD, including tax?
A.
$12.84
B.
$11.93
C.
$12.90
D.
$12.72
Answer:
$14.28. Step-by-step explanation: If the CD is $17 and is have a 20% off then you multiply .20 and 17 to get the amount that is off.
Step-by-step explanation:
plz mark brainliest
Solve for y 2/5x + y = 3
Answer:
y=-2/5x +3
Step-by-step explanation:
You get the y to be alone on it's side of the equal sign.
So you subtract 2/5 x from that side and what you do to one side you have to do to the other.
You get: y=-2/5x +3
Two expressions with equal sign is Equation. y= 3-2/5x is the solution for y if equation is 2/5x + y = 3.
What is Equation?Two expressions with equal sign is called as Equations.
Given Equation is 2/5x + y = 3, we need to solve for y.
You get the y to be alone on it's side of the equal sign.
So you subtract 2/5 x from that side and what you do to one side you have to do to the other.
2/5x + y = 3
y = 3-2/5x
Therefore y=3-2/5x is the solution for 2/5x + y = 3 equation.
To learn more on equations click:https://brainly.com/question/6204440
#SPJ2
Please answer I need help
I need help please help me with this
Answer:
120
Step-by-step explanation:
MNT is equal to RQT.
That means R equal to M, T equal to T, equal to N.
Q also equals 180-(T+R)
Q=180-(35+25)
Q=180-60
Q=120
(2x + 3) + 90 = 180 solve for x
your question:
(2x + 3) + 90 = 180 solve for x
answer:
(2x + 3) + 90 = 180 ~ remove the already reduced parenthesis
2x + 3 + 90 = 180 ~ add numbers together
2x + 93 = 180 ~ subtract 93 from both sides
2x = 87 ~ divide by two on both sides to find x
x = 43.5
x = 43.5 or x= 43 ½ (fraction form)
Hope this helps, have a great day! :)
Write an equation that represents each mixed number as a sum of whole numbers and unit fractions. 4 1/4 and 1 5/6
The solution is, (X*b+a)/b = X a/b, is an equation that represents each mixed number as a sum of whole numbers and unit fractions.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
let,
X= whole numbers
a/b= unit fractions
X a/b-- >mixed number
equation=(X*b+a)/b
so,
1 ⅚=(1*6+5)/6
=11/6
4 1/4 = (4*4+1)/4
=17/4
Hence, the answer is (X*b+a)/b.
To learn more on number click:
brainly.com/question/17429689
#SPJ1
An entrepreneur invests in a new play. The cost includes an overhead of $33,750 plus production costs of $1700 per performance. A sold-out performance brings in $2325 . Assume every performance is sold out, and let x represent the number of sold-out performances.
The entrepreneur's revenue is $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is $625x - $33,750
The entrepreneur's revenue from x sold-out performances is given by the formula:
Revenue = (Price per Performance) x (Number of Performances)
Revenue = $2325 x x
Revenue = $2325x
The entrepreneur's cost from x sold-out performances is given by the formula:
Cost = Overhead + (Production Cost per Performance) x (Number of Performances)
Cost = $33,750 + $1700x
The entrepreneur's profit from x sold-out performances is the revenue minus the cost:
Profit = Revenue - Cost
Profit = $2325x - ($33,750 + $1700x)
Profit = $625x - $33,750
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Can someone help me?
Answer:
Translation: (x+3, y-7)
Step-by-step explanation:
The triangle went 3 units right(horizontally), and 7 units down(vertically).
Determine the average rate of change of this function over the interval -2≤x≤4
The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.
please help I need help
Answer:
Step-by-step explanation:
well if he road 12miles in 55 mines all u have to do is divide is 55 to 12.
Victor jumped 6 feet high and then 2 more yards. How many yards did he jump in all?
As per the given variables, Victor jumped a total of 4 yards.
Total yards jumped = 6 feet high
Additional yards = 2
A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.
Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.
There are 3 feet in a yard, therefore -
6 feet = 6/3
= 2
Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.
Calculating, the total distance Victor jumped in yards -
= 2 + 2
= 4
Read more about yards on:
https://brainly.com/question/30459658
#SPJ1
In each diagram, one square unit represents 10 square centimeters. Find the area of each figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
HELP PLEASE!! ASAP!!
Answer:
f(x) = -3x+1
Step-by-step explanation:
every straight graph has an equation f(x) = m * x + b
when the graph goes up when you look at it from left to right, m is a positive number. when it goes down, then m is negative.
the value of m you can read when you go 1 to the right and then count how many you need to go up/down to meet the graph. in this picture, you need to go down 3.
So m = -3
b is how many you habe to go up (+) or down (-) from the center point 0
so in this case you see on the picture that the graph is hitting the y line on 1
so your equation is -3x + 1
e-Test Active
2
3
=+
4
Of(x) = -3x+4
Of(x) = -x +
Of(v)=-3y+4
5
6
7
8
10
TIME REI
Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be
written using function notation?
42-
The function notation of 9x + 3y = 12 is given as follows:
f(x) = 4 - 3x.
How to write the function notation?The function in the context of this problem is given as follows:
9x + 3y = 12.
The format for the function notation is given as follows:
Hence we must isolate the variable y, as follows:
3y = 12 - 9x
y = 4 - 3x (each term of the expression is divided by 3).
f(x) = 4 - 3x.
More can be learned about functions at https://brainly.com/question/10687170
#SPJ1
Evaluate the formula for the given values of the variables.
d = rt; r = 54 miles per hour, t = 3 hours
O d = 324 miles
O d = 18 miles
O d = 162 miles
O d = 57 miles
Answer:
d=162 miles
Step-by-step explanation:
The formula is d=rt, so the distance is the rate multiplied by the time. Thus, it is 54 times 3 or 162.
Which of the following points satisfies y < 3x - 6?
(2, -4)
(1,0)
The point (2,-4) satisfies y < 3x - 6
Examine the linear equation. 8x -y = -6 Choose the slope-intercept form of the equivalent equation:
y= -8x-6
y= -8x + 6
y= 8x-6
y = 8x + 6
Answer:
The correct answer is D.
Step-by-step explanation:
Answer:
y=8x+6 or d
Step-by-step explanation:
Write the fraction or mixed number as a decimal 8 11/100
Answer:
Step-by-step explanation:
8 is the whole number
11/100 = 0.11
ANSWER: 8.11
In Exercises 9 to 14, find the limit of each function at the given point, or explain why it does not exist. 10. f(z) = Arg z at Zo--1 11. f(z) = (1-Im z)-1 at z,-8 and then at zo-8 +1 12.f(z) = (z _ 2) log(z-21 at zo = 2 13, f(z) =-, z#0 at zo = 0 14. f(z) = 2+21,
Previous question
The limit of each function at the given point i n the question 10 to 14, is explained below.
Limit Of A function:A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.
When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a
10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.
11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.
However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.
12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.
13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.
14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.
Learn more about limit of function, visit:
https://brainly.com/question/7446469
#SPJ1
The figure below shows a right triangle:What is r÷ q equal to?
Given the figure of a right-angle triangle.
The hypotenuse of the triangle = q units
One of the legs of the triangle = r units
The side (r) is the opposite side to the angle (y) and the adjacent side to the angle (x)
So,
\(\frac{r}{q}=cosx=siny\)Now, check the options to select the correct answer
So, the answer will be option 3) sin y°
prove that, given a nonnegative integer , there is a unique nonnegative integer such that m^2 < sqrt n < (m 1)^2
It is proved that m = √n.
To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:
m^2 ≤ n < (m + 1)^2.
So, after taking the square root, it will be:
m ≤ √n < m + 1
From that we can see m = √n is the unique m.
What is a nonnegative integer?A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.
Learn more about nonnegative integer at: https://brainly.com/question/13684481
#SPJ4
Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.