Answer:
2/3
Step-by-step explanation:
[tex]AB \cong BC \implies AB=BC \\ \\ 3x+6=15x-2 \\ \\ 6=12x-2 \\ \\ 8=12x \\ \\ x=\frac{2}{3}[/tex]
help meeeeeeeeeeeeee
======================================================
Explanation:
To find the inverse, we swap x and y, then solve for y.
y = 2x-3
x = 2y-3
x+3 = 2y
2y = x+3
y = (x+3)/2
y = x/2 + 3/2
y = (1/2)x + 3/2
This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.
--------------
Another approach:
Since we're given a list of multiple choice answers, we can rule out the non-answers.
Plug x = 0 into the first equation of choice A. It leads to y = 2
That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.
This allows us to rule out choice A. Choices B and C are similar stories.
Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.
Answer:
Step-by-step explanation:
Algorithm for deriving the formula of the inverse function
Step 1. In the formula for the original function, replace the notation of the argument and the value:
Step 2. From the resulting formula, express y(x).
Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.
[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]
[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]
Determine whether the statement is always, sometimes, or never true if three points are collinear , then they are also coplanar
always
sometimes
never
The statement is sometimes true.
What is collinear points?Points that are located along a single or shared straight line are referred to as collinear points. If two or more points on a line are situated either close to or far from one another, they are said to be collinear in Euclidean geometry.
Three points are automatically coplanar if they are collinear.
What was just said is sometimes true.
This is because three points along a line are typically recognized to be collinear, however it is not always the case.
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if an expression is x+4=10 could x=6
Answer:
Yep,
Step-by-step explanation:
First the expression is in this way:
x+4=10
Now shift the 4 ro RHS, then it will become as follows:
x=10-4
Now 10-4 is 6
Therefore, x=6
PLEASE HELP ME!
How do the graphs of y = f (x) + k, y = f(x – h), and y = -f(x) compare to the graph of the parent function f?
f(x) + k will shift the graph up k units.
For example, the notation f(x) + 5 will shift the curve up by 5
If k is negative, then the curve shifts down that amount
-------------------------
f(x-h) shifts the graph to the right h units
Example: f(x-2) shifts to the right 2 units
Another example: f(x+7) shifts left 7 units. In this case, h = -7
--------------------------
y = -f(x) is a reflection over the x axis
This is because we're multiplying each y coordinate by -1
A point like (1,2) reflects to (1,-2)
MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges
$2.50 to rent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling
alley B?
Bowling alley A:__ or more games
Bowling alley B:__
or __
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)?Explain.
Using linear functions, we have that:
a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
b. For any number of games, the cost at alley B will be less.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The slope is the cost per game.The intercept is the cost of 2 shoes.Hence they are given as follows:
A(x) = 4x + 7.5.B(x) = 4.5x + 5.The cost for A will be less when:
A(x) < B(x).
Hence:
4x + 7.5 < 4.5x + 5
-0.5x < -2.5
0.5x > 2.5
x > 2.5/0.5
x > 5.
Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
For item b, with the increase of $0.5 per game, we have that:
A(x) = 4.5x + 7.5.
Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.
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The data set represents the number of pages in the last book read by each of 20 students over the summer. 163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431 Create a histogram to represent the distribution of the data.
The required histogram is attached as a picture.
Given the information on how many pages each of the 20 pupils read throughout the summer.
163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431
With frequency on the y axis and class on the x axis.
we observe the histogram and make out that:
class 160 - 220 has the highest frequency of 6 students whereas
400 - 460 has the least with 2 students.
The classes between them range as follows:
220 - 280 has 5 students
280 - 340 has 4 students
340 - 400 has 3 students.
Hence the required histogram is created .
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how many mg of vitamin c does tomato juice have per serving?
What is equivalent to —4 —9
[tex]- 4 - 9 = - 13[/tex]
I need help with this asap
The function rules for each of the given tables are;
11) f(x) = 4x
12) f(x) = x - 3
13) f(x) = x + 12
14) f(x) = x/10
15) This doesn't have a function rule.
16) Function rule here is non existent
How to state the required function rule?
11) In this table, we can observe that the output values are all four times the input value. Thus, the function rule here is;
f(x) = 4x
12) In this table, we can observe that the output values are all 3 units less than the input value. Thus, the function rule here is;
f(x) = x - 3
13) In this table, we can observe that the output values are all 12 units more than the input value. Thus, the function rule here is;
f(x) = x + 12
14) In this table, we can observe that the output values are equal to the input value divided by 10. Thus, the function rule here is;
f(x) = x/10
15) This doesn't have a function rule as the values don't match a pattern
16) Function rule here is non existent
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What is the area of the base of this right circular cone in terms of л?
r = 4 m
h = 6 m
___ л m^2
Answer:
16π m²
Step-by-step explanation:
area of circle = πr²
area = π × (4 m)²
area = 16π m²
he zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x + 4)
B.
f(x) = (x + 6)(x − 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
The answer is option C
Step-by-step explanation:
The roots of the quadratic equations are x= 6 or x= -4
X-6=0 or x+ 4=0
⇒(x-6)(x+4)
F(x)=(x-6)(x+4)
31. What is the formula for the perimeter of a square with the side s
and a perimeter p?
Answer: p = 4s
Step-by-step explanation:
The perimeter is the measurement around a shape's sides. In other words, if a square has four sides, we will add up all the sides to find the perimeter.
Since a square's sides are all congruent, we can multiply the length of one side (s) by 4 to find the total perimeter (p). This becomes:
p = 4s
HELP PLS TEACHER GONNA FAIL ME
Answer:
B and D
Step-by-step explanation:
50 PoInts for math homework Waxton
What is the quotient of three and two thirds divided by 3 fifths?
quotient = the answer to a division problem
ex. 6/3 = 2The quotient of 6 and 3 is 2.To divide by a fraction, multiply by the reciprocal of the fraction
reciprocal of a fraction = the numerator and denominator are reversed
Solving the QuestionFirst, convert "three and two thirds" into an improper fraction:
[tex]3\dfrac{2}{3}[/tex]
⇒ Multiply the whole number by the denominator and add the numerator:
[tex]\dfrac{11}{3}[/tex]
Now, we want to divide this number by three fifths:
[tex]\dfrac{11}{3}\div\dfrac{3}{5}[/tex]
⇒ Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]= \dfrac{11}{3}\times\dfrac{5}{3}\\\\=\dfrac{55}{9}[/tex]
Answer[tex]\dfrac{55}{9}[/tex]
theannswer wold be 100 .33 .87
The Yankees won 95 games in 2010 and 97 games in 2011. What is the percent change in the number of wins from 2010 to 2011?
Please answer
The percentage change is 2.1%
How to calculate the percentage change ?The Yankees won 95 games in 2010
They also won 97 games in 2011
Therefore the percentage change can be calculated as follows
= 97 - 95/97 × 100
= 2/97 × 100
= 0.021 × 100
= 2.1
Hence the percentage change is 2.1%
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the amount of water in the cooler w dropped by 37 cups during the day at work site, ending at 15 cup. Write an equation to represent this situation. then solve the equation for w to determine the amount of water in the cooler at the beginning of the day
An American dollar is worth about €0.89 in Euro currency. Which is approximately equal to €550 Euros?
(A) $635 U.S. dollars
B $621 U.S. dollars
D
$337 U.S. dollars
$331 U.S. dollars
Question 4
Which operation would produce the correct answer for
Answer:
Step-by-step explanation: Well €550 Euros is equal to $547.42 US dollars in currency. But since this is approximately, (D) should be correct.
algebra, im so confused
By analyzing and understanding the graph of the absolute value function, we find that the function evaluated at the x-value equal to 1 is equal to the y-value equal to 3.
What is the y-value associated to a given x-value of an absolute value function?
In this problem we find the representation of an absolute value function, where the horizontal axis corresponds to the values of the domain, whereas the vertical axis is for the values of the range. In that picture we must look up for the y-value associated with a given x-value.
Then, we proceed to evaluate the absolute value function at x = 1. In accordance with the graph, the y-value , that is, from the vertical axis, associated with the x-value, that is, from the horizontal axis, equal to 1 is equal to a value of 3.
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Dice have 6 sides, with values 1, 2, 3, 4, 5, and 6. which expression randomly rolls one dice, directly yielding one of those values?
(rand() % 6) + 1 is the expression randomly rolls one dice, directly yielding one of those values.
What is dice?Small objects (polyhedrons) used as playing pieces for dice games and other gambling-related activities. The cube, the most popular type of die, has one to six tiny dots on each side (spots). The spots are positioned in the following traditional patterns: 1 and 6, 2 and 5, 3 and 4, so that spots on opposite sides always sum up to 7. The poker and crown and anchor dice, as well as many other types of dice with 4, 5, 7, 8, 10, 12, 16, and 20 sides, are examples of dice with different configurations of spots or other face designs. The majority of the time, dice are employed to generate a random outcome (usually a number or a mixture of numbers), and the mathematical probabilities depend on the physical characteristics and quantity of dice thrown.
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what is the conclusion of the following conditional? A number divisible by two is the number is even
The conditional operator creates a compound statement that sets up a condition for something to be true. Therefore, if the condition is met, the statement is true. The parts of the conditional statements are two, the first simple statement in a conditional is called the antecedent and the second simple statement is called the consequent. So, for two statements A (antecedent) and B (consequent) we will have that:
A → B that means: If A then B
In this problem:
A: A number is even.
B: The number is divisible by 2.
Thus:
A → B: If a number is even, then the number is divisible by 2.
So, the conclusion of this conditional statement is the consequent, that is, the number is divisible by 2.
Accordingly, the right answer is D. The number is divisible by 2.
the complete question is
What is the conclusion of the following conditional? A number is divisible by 2 if even.
A. The sum of the digits of the number is divisible by 2.
B. If a number is even, then the number is divisible by 2.
C. The number is even.
D. The number is divisible by 2.
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Sam has worn a green shirt on 10 of the last 20 days. Considering this data, how many times would you expect Sam to wear a green shirt in the next 12 days?
Answer:
6 trust me
Step-by-step explanation:
I need some help please
Step-by-step explanation:
[tex] = \frac{ {2}^{4} }{ {2}^{7} } [/tex]
[tex] = {2}^{4 - 7} [/tex]
[tex] = {2}^{ - 3} [/tex]
[tex] = \frac{1}{ {2}^{3} } [/tex]
[tex] = \frac{1}{2 \times 2 \times 2} [/tex]
[tex] = \frac{1}{8} [/tex]
The answer is not 8, but 1/8.
I don’t know what that symbol is used for
Answer:
Perpendicular lines.
Solve the equation −14 + x = −19 for x.
Answer:
x = -5
Step-by-step explanation:
add 14 to both sides:
x = -19 + 14
x = -5
What is the value of x in the equation 4x + 8y = 40, when y=0.8
Answer:
when you =0.8=4/5
4x + 8(4/5)=40
4x=40-32/5
4×=(200-32)/5
x=168/20
Step-by-step explanation:
4x+8y=40, when y=0.8
4x+8(0.8)=40
4x+6.4=40
4x=40-6.4
4x=33.6
x=33.6/4
x=8.4
a = 17.6 cm, b = 9.5 cm and c = 13.6 cm for the triangle shown below.
Answer: Click on this: a=13.6cm,b=9.5cm and c=2.6cm for the triangle show it has a step by step way
Step-by-step explanation:
A is between c and t. if ct = 25 and at = 18, what is the length of segment ca?
The length of the segment CA is 7.
Length of the segment
Basically, length of the line segment is fixed, which is the distance between two fixed points.
The length here can be measured by metric units such as centimeters (cm), millimeters (mm) or by conventional units like feet or inches.
Given,
A is lies between C and T.
Then the values of CT = 25 and AT = 18.
Now we have to find the length of the segment CA.
Consider the point C, A and T are in straight line.
Then A lies between C and T.
So, it is the center point between C and T.
Here we have the length of total line that is
=> CT = 25.
And the length of AT, that is
=> AT = 18.
Then we need to find the length of the segment CA,
By subtracting the length of AT from the total length CT,
That is,
=> CA = CT - AT
Apply the values,
=> CA = 25 - 18
=> CA = 7.
Therefore, the length of the segment CA is 7.
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Adding -6 is the same as:
Answer:
It is the same as subtracting 6.
Step-by-step explanation:
1 + (-6) = 5
1 - 6 = 5
2. Which of the following shows 3 less than an unknown value?
a. n-3
b. n + 3
C. 3- n
d. 3 + n
Answer:
a
Step-by-step explanation:
the unknown value is n then 3 less than this value is
n - 3
Answer:
answer is C
because other equations normally n>3 but C equation normally is n<3
so answer is C