Answers
Answer:
B
Step-by-step explanation:
I cannot see option D but regardless, C is a function for the following reasons
A function y = f(x) is a relationship in x such that f(x) has only 1 value for a value of x.
In A, we see that for x = -1 we have y = 2 and y = 4 for a single value of x = -1
That alone is sufficient to dismiss this as a function. If that wasn't bad enough you see that y = -3 and -4 for x = 2
In C we see the same problem
For x = 5 there are two value of y = -3 and -2
So we can disregard C
In B we can see a definite pattern
Between x = -2 and x = 0 we see that y increases by 1 unit for every increase of 1 unit in x. This is a linear relationship with a slope of + 1
Between x = 0 and x = +2, for every increase of 1 unit in the x-value, the y-value decreases by 1 unit. This is also a linear relationship but with a slope of -1
In particular this is what is known as a piecewise function. Its function expression is different for different intervals of x value
It can be expressed as follows
f(x) = x + 2 for -2 ≤ x ≤ 0
= -x + 2 for 0 ≤ x ≤ 2
Related Questions
If a die is rolled three times, what is the probability of
getting a 2 on the first roll, an odd number on the second
roll, and a number less than 5 on the third roll?
Answers
Answer:
probability of getting 2 = 1/6
probability of getting an odd number=3/6=1/2
probability of getting number less than 5 = 4/6=2/3
multiply probabilities:
1/6x1/2x2/3
=2/36
=1/18
Exercice n'11: Calcule:
A = 19+ (8-25);
B=(-15+6)-(23-18)
C = (154-6) +3-(-9+7):
D=-13+ (5+8)-(-4+8)
E = (-5)-(17+ (-13))-((-8) - (+2)):
F = (12-(-3)) - (12-(-3))
G=15-(-3-((+12)-16)):
H=-12-(-15 +30) -(65-20) - 20
Answers
Answer:
Step-by-step explanation:
Here in all these questions we need to follow the rules of BODMAS which tells us the steps to solve and mathematical operation.
B-Bracket
O-Of
D- Division
M-Multiplication
A-Addition
S-Subtraction
now,
A. 19+(8-25)
we need to solve what's inside the bracket first
so, 8-25= -17
=19+(-17)
=2
B. (-15+6)-(23-18)
=(-9)-5
= -14
C. (154-6)+3-(-9+7)
= 148+3-(-2)
=148+3+2
= 153
D. -13+(5+8)- (-4+8)
= -13+13-4
= -4
E. (-5)-(17+(-13))-((-8) -(+2))
= -5 -(4)-(-10)
= -5-4+10
= 1
F. (12-(-3))-(12-(-3))
= 15-15
=0
G. 15 -(-3-((+12)-16))
= 15-(-3-(-4))
= 15- 1
= 14
That's how we do it try the last one by your self!
In which set(s) of numbers would you find the number-202/45Natural numberIntegerWhole numberReal numberIrrational number
Answers
Natural number: No, because when you divide -202/45 you do not get a integer.
Integer: No, for the reason given before.
Whole number: No, for the reason given before (it is not an integer)
Real number: Yes, because real numbers include negative fractions.
Irrational number: No, because you can write the number as a fraction of two integers.
You would find the number -202/45 in the set of the real numbers.
Which equation exemplifies the Associative Property of Multiplication?
O4×(2x5)= (2x5)×4
O4x(2x5)=4x(5x2)
O4x(2x5)= (4x2)x5
O4x2x5=5x2x4
Answers
19
Step-by-step explanation:
35*44
5555
75*69
*1235
the largest of the following integers which divides each of the numbers of the sequence $1^5 - 1,\, 2^5 - 2,\, 3^5 - 3,\, \cdots, n^5 - n, \cdots$ is:
Answers
The sequence's numbers are all multiples of 30. Every number can be divided by 30.
If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)
At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable
Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.
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The slope of line a is 5. The slope of line b is 15 . Which statement is true?
Answers
Step-by-step explanation:
I don't see any statements either.
anyway, the only thing that can be said about the 2 lines is that they are crossing each other at one point.
the lines are not parallel, they are not perpendicular (90° to each other), they are not identical.
nothing can be said about a specific point on the line of intercepts with the x- and y-axis.
they are also not parallel and not perpendicular to any of the x- or y-axis.
which choices is equivalent to the expression below?
[tex]\sqrt{-20}[/tex]
Answers
The expression √-20 has an equivalent of 2√-5
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the equivalent expression?The expression is given as
√-20
Express 20 as the product of 4 and -5
So, we have the following equation
√-20 = √4 * -5
Expand the equation
So, we have the following equation
√-20 = √4 * √-5
Evaluate the exponent
√-20 = 2√-5
Hence, the equivalent expression of √-20 is 2√-5
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Joanna has a big paper due. yesterday, she started typing her hand-written draft. she typed 862 words of it and saved her work to continue later. if she types at a rate of 70 words per minute, and the paper is 1,562 words long, how much more time does she have to spend typing? a. 10 minutes b. 15 minutes c. 18 minutes
Answers
Answer:
10 minutes
Step-by-step explanation:
if 70 words = 1minute
862 words will be 862÷70=12.31 minutes
1,562 words will be 1562÷70=22.31 minutes
time needed to finish will be 22.31-12.31= 10 minutes
So the total time needed to finish will be 10 minutes
If * = 8 units, y= 13 units, and h= 11 units, then what is the area of the parallelogram shown above?
Answers
The figure below has an area equivalent to 88 square units.
The parallelogram's characteristicsIn Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.
The opposing or confronting sides and the opposing angles in a parallelogram are of equal length.
Area = length * breadth is the formula for computing the area of a parallelogram.
Substituting the given values
Area = x * h
Area of the parallelogram = 8 * 11
Area of the parallelogram = 88 square units.
Consequently, the parallelogram above has an area of 88 square units.
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After receiving her paycheck Karen lends her sister $21 buys groceries for $71 and pays her $85 gym membership if she is now left with $73 how much was her paycheck
Answers
After using Arithmetic we'll get - Total of her paycheck $250
What is Arithmetic ?
The study of the characteristics of the standard operations on numbers, including addition, subtraction, multiplication, division, exponentiation, and root extraction, constitutes the fundamental subject of arithmetic. Giuseppe Peano, an Italian mathematician, formalised arithmetic in the 19th century with the help of his Peano axioms, which are still crucial to the modern study of mathematical logic. There are only a few artefacts from the early history of mathematics that may have shown how addition and subtraction were first thought of. The best-known of them is the disputedly interpreted Ishango bone from central Africa, which dates from between 20,000 and 18,000 BC.
The Amount Karen spent:
She lends sister = $21
Buys Groceries = $71
Pays Gym membership = $85
After spending this much she left with $73
The paycheck she receive = 21 + 71 + 85 + 73
= $250
Hence , her paycheck was $250
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a stack of paper measures 0.9 centimeter thick. each piece of paper is 0.01 centimeter thick. how many pieces of paper are in the stack? could each of 25 students get 3 pieces of paper?
Answers
Please Help me, I will mark brainiest. What are the vertex and range of y = |x + 2| − 3?
(−2, −3); −∞ < y < ∞
(−2, −3); −3 ≤ y < ∞
(0, −1); −∞ < y < ∞
(0, −1); −3 ≤ y < ∞
Answers
The vertex and the range of the absolute value function are given as follows:
(−2, −3); −3 ≤ y < ∞.
How to find the vertex and the range of the absolute value function?The absolute value function in the context of this problem is defined according to the following rule:
y = |x + 2| − 3.
For the general equation, with vertex (h,k), the definition is given as follows:
y = |x - h| + k.
Hence, in the context of this problem, the coefficients of the vertex are given as follows:
h = -2, k = -3.
Hence the vertex is:
(-2,-3).
The range of a function is the set containing all the output values assumed by the function. For the absolute value function, it is given by the following interval:
k ≤ y < ∞
Hence, for the function defined in this problem, the interval is given by:
-3. ≤ y < ∞
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Let f(x) = x^2 + 2x and g(x) = 4x^2 − 3. Find the function. f + g
Answers
The function operation ( f + g )( x ) in the functions f( x ) = x² + 2x and g( x ) = 4x² - 3 is 5x² + 2x - 3.
What is the function operation ( f + g )( x ) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = x² + 2xg( x ) = 4x² - 3( f + g )( x ) = ?First, replace the function designators in f + g with actual functions.
( f + g )( x ) = ( f )(x) + ( g )( x )
( f + g )( x ) = ( x² + 2x ) + ( 4x² - 3 )
Remove the parenthesis
( f + g )( x ) = x² + 2x + 4x² - 3
Collect and add like terms
( f + g )( x ) = x² + 4x² + 2x - 3
( f + g )( x ) = 5x² + 2x - 3
Therefore, the function operation ( f + g )( x ) is 5x² + 2x - 3.
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5. Which function does NOT have a range of all real numbers?
a. f(x) = 3x
b. f(x) = -0.5x + 2
c. f(x) = 8 - 4x 8
d. f(x) = 3
Answers
Helppp
[tex]7 \sqrt{?} = 55[/tex]
Plsss
[tex] \frac{5}{10} = what[/tex]
Answers
Answer:
The first questions unknown equals
[tex] \frac{3025}{49} [/tex]
The second question is unclear. I assume it is to simplify if that is the case the answer will be.
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
First Question I made ?=x for simplicity.
[tex]7 \sqrt{x} = 55[/tex]
then I divide both sides by 7
[tex] \sqrt{x} = \frac{55}{7} [/tex]
then I square both sides
[tex]x = \frac{3025}{49} [/tex]
Question 2
I simplified by dividing both the denominator and the numerator by their HCF (highest common factor) which is 5
[tex] \frac{5 \div 5}{10 \div 5} [/tex]
which equals
[tex] \frac{1}{2} [/tex]
Answer:
[tex]\textsf{1.} \quad 7\sqrt{\dfrac{3025}{49}}=55[/tex]
[tex]\textsf{2.} \quad \dfrac{5}{10}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Question 1Let x be the unknown number:
[tex]\implies 7\sqrt{x}=55[/tex]
Divide both sides of the equation by 7:
[tex]\implies \dfrac{7 \sqrt{x}}{7}=\dfrac{55}{7}[/tex]
[tex]\implies \sqrt{x}=\dfrac{55}{7}[/tex]
Square both sides of the equation:
[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{55}{7}\right)^2[/tex]
[tex]\implies x=\dfrac{55^2}{7^2}[/tex]
[tex]\implies x=\dfrac{3025}{49}[/tex]
Question 2Divide the numerator and the denominator by the highest common factor:
[tex]\implies \dfrac{5 \div 5}{10 \div 5}=\dfrac{1}{2}[/tex]
The two triangles above are similar. a. Find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work. b. Find x using the ratio of the sides 6 cm and 8 cm. Show your work. c. Explain why the answer to (a) and (b) should be the same.
Answers
a)
If the triangles are similar, the corresponding sides vary on the same proportion, so the ratios between the corresponding sides are equal.
For
[tex]\frac{x}{20}=\frac{12}{16}[/tex]To solve for x you have to multiply both sides of the expression by 20
[tex]\begin{gathered} \frac{20x}{20}=(\frac{12}{16})\cdot20 \\ x=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}[/tex]b)
Following the same logic, the ratio between x and 20 is the same as the ratio between 6 and 8
[tex]\frac{x}{20}=\frac{6}{8}[/tex]6/8 can be simplifies as 3/4. Then multiply both sides by 20 to determine the value of x.
[tex]\begin{gathered} \frac{x}{20}=\frac{6}{8} \\ 20\cdot\frac{x}{20}=(\frac{3}{4})\cdot20 \\ x=15 \end{gathered}[/tex]As mentioned above, when two triangles are similar, the corresponding sides are always in the same ratio, that is why the results in a and b are the same.
On a piece of paper, Graph y = 2x-3. Then determine which answer matches the graph you drew.
Answers
A graph of the linear function (y = 2x - 3) which matches the answer is shown in the image attached below.
What is a graph?A graph refers a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis decreases or increases, the values on the y-axis decreases or increases simultaneously as shown in the image attached below.
In conclusion, a graph representing the given linear function shows a proportional relationship between the value of x and y.
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5. Rachel typed 48 words in 3/4 minute. What is her typing speed in words per minute?
Answers
Find the exact value and the approximate value of the perimeter of the triangle
Answers
the perimeter of triangle is equal to the sum of all the side of the triangle,
The perimeter of given triangle is x+y+9+3
Solve for x and y,
Apply pythagoras theorem in triangle ADC,
[tex]\begin{gathered} AC^2=DC^2+AD^2 \\ y^2=81+AD^2^{} \\ AD^2=y^2-81 \end{gathered}[/tex]Now, in triangle ADB
Apply pythagoras,
[tex]\begin{gathered} AB^2^{}=BD^2+AD^2 \\ x^2=9+AD^2 \\ AD^2=x^2-9 \end{gathered}[/tex]Compare the value of AD from both the equation,
[tex]\begin{gathered} x^2-9=y^2-81 \\ x^2-y^2=-72 \end{gathered}[/tex]Now, in triangle ABC
[tex]\begin{gathered} BC^2=AB^2+AC^2 \\ 12^2=x^2+y^2 \\ x^2+y^2=144 \end{gathered}[/tex]Add the equation
[tex]\begin{gathered} x^2+x^2-y^2+y^2=-72+144 \\ 2x^2=72 \\ x^2=36 \\ x=6 \end{gathered}[/tex]Substitute x=6 in the above equation,
[tex]\begin{gathered} x^2_{}+y^2=144 \\ 36+y^2=144 \\ y^2=144-36 \\ y^2=108 \\ y=10.39 \end{gathered}[/tex]So, the value of the other side of triangle are 6, 10.39
Perimeter of triangle =sum of all sides of triangle
[tex]\begin{gathered} \text{Perimeter}=AB+BC+AC \\ \text{Perimeter}=AB+BD+CD+AC \\ \text{Perimeter}=6+3+9+10.39_{} \\ \text{Perimeter}=28.39 \end{gathered}[/tex]ANSWER : Perimeter is 28.39
Cynthia was offered two different jobs for the summer. Working as a camp counselor, she will earn $20 per hour plus an additional $25 bonus. Her earnings after x hours can be represented by the function f(x) = 20x + 25. Working as a lifeguard, Cynthia will earn $15 per hour and an additional $50 bonus. Her earnings after x hours can be represented by the function g(x) = 15x + 50. The arithmetic operation (f − g)x can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours. What is the function (f − g)x?
Answers
The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours (f − g)x = 5x - 25.
What is a function?A function can be defined as the set of inputs that results in output.
Given, Cynthia earns 20 dollars per hour working as a camp counselor plus an additional 25 dollars as a bonus which is f(x) = 20x + 25, and as a lifeguard 15dollars per hour and an additional 50 dollars bonus which is g(x) = 15x = 50.
We know (f - g)x = f(x) - g(x).
∴ The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours is f(x) - g(x).
= (20x + 25) - (15x + 50).
= 20x - 15x + 25 - 50.
= 5x - 25.
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jesse earns $6 an hour babysitting for his younger brother. his mom gave him $20 for an allowance. how many hours would jesse have to babysit to earn enoug money to buy a $80 football ticket?
Answers
Answer:
Step-by-step explanation:
10 hours. 80-20 is 60, which means he needs 60 more dollars. he makes 6 an hour, and 6x10 equals 60(what he needs) and that is your answer.
Solve for x: 3x/6 + 1 = 7
Answers
3x/6=7-1
Then get multiple 6 to each side
3x=36
Then divide by three
X=12
Answer is x=12
Answer:
X = 12
Explanation:
3x/6 + 1= 7
/2 + 1 = 7
x/2 + 1 = 7
x/2 + 2/2 = 7
X+2/2 = 7
X = 12
hope this helps you :)
Please help! Please and thank you
Answers
Answer:
4
Step-by-step explanation:
Length time width times high , 8x8=16 square rooted equals 4
simplify a5/a2. i don’t even know what this is
Answers
Answer:
a3 is your simplified answer.
Step-by-step explanation:
a5 divided by a2 is a3/1 which is a3.
Answer:
Step-by-step explanation:
a^3
How to find the size of angle x in a triangle
Answers
Answer:
it depends on the question
Usually if it a triangle with 2 angles and an x
you will add the 2 angles and rearrange to give the answer
Step-by-step explanation:
Hope this helps!!!
Answer:
A right triangle has one angle measuring 90 degrees. The side opposite this angle is known as the hypotenuse (another name for the longest side). The length of the hypotenuse can be discovered using Pythagoras's theorem, but to discover the other two sides, sine and cosine must be used. These are trigonometric functions of an angle.
In the diagram below, one of the angles is represented by the Greek letter θ. (pronounced "the - ta"). Side a is known as the "opposite" side and side b is called the "adjacent" side because of their positions relative to the angle θ.
The vertical lines "||" around the words below mean "length of."
So sine, cosine and tangent are defined as follows:
Step-by-step explanation:
So sine, cosine and tangent are defined as follows:
sine θ = |opposite side| / |hypotenuse|
cosine θ = |adjacent side| / |hypotenuse|
Algebra 2
Functions
Skills Summative
Answers
Answer: See explanation
Step-by-step explanation:
For questions 1 - 4, it's asking you to plug in numbers into the original functions.
1. f(-2): You would plug -2 into f(x) = 2x^2 - 3x, getting
2(-2)^2 - 3(-2)
2(4) - (-6)
8 + 6 = 14
f(-2) = 14
2. f(x) - g(x): You're basically just subtracting the two functions
(2x^2 - 3x) - (2 - 5x)
2x^2 - 3x - 2 + 5x
Combine like terms
2x^2 + 2x - 2
3. You're multiplying them so (2x^2 - 3x)(2 - 5x)
4. f(g(x)): It's like f(-2), but instead of -2, you plug in the function of g(x)
So in 2x^2 - 3x, x would equal 2 - 5x:
2(2 - 5x)^2 - 3(2 - 5x)
And then simplify that.
For questions 5 - 6, it's asking for shifting from the parent function. Parent function is always f(x) or g(x) or whatever variable it is.
5. f(x - 8) + 9: The 9 is the y value shift, meaning the parent function is shifted up 9 units. For -8, think of what x needs to be for (x - 8) to be 0. If that number is positive, function shifts right; if negative, shift left. In this case, x needs to be 8 in order for (x - 8) to be 0. Therefore, f(x) is shifted right 8 units.
6. -3f(x) - 2: From the previous question, we now know that -2 means f(x) is shifted down 2 units. When you have 3f(x), you're multiplying the entire function by 3, so it's called a vertical stretch of 3. The negative means it's reflected over the x-axis since the y value is the opposite of what it used to be.
Tavon has a gift card for $150 that loses $3.50 for each 30-day period it is not used. He has another gift card for $130 that loses 3 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value?
Answers
Part a
[tex]150-3.50x=130-3x\\\\20=0.50x\\\\x=40[/tex]
After fourty 30-day periods, the balances on the cards will be equal.Part b
[tex]150-3.50(40)=10[/tex]
$10Jett is 6 feet 2 inches tall.
How tall is he in inches?
Answers
Answer:
74 inches
Step-by-step explanation:
6 feet= 72 inches plus 2 inches equals this amazing height
EXPLANATION:
One foot is equal to 12 inches
6 • 12 = 72
72 + 2 = 74
how to do this problem and find the measurements??????
Answers
The measure of x is found as 22 for the given vertically opposite angles.
What is meant as vertically opposite angles?When two lines intersect at a point, vertical angles are formed. They are always on equal footing. In other words, four angles are formed so when two lines traverse or intersect. We can see that two opposite angles are equal, and these are referred to as vertical angles. They are also acknowledged as'vertically opposite angles' due to their being perpendicular to each other.For the given question;
5x + 4 = 114 (As both lines intersecting and vertical angles are formed).
Solving the equation;
5x = 114 - 4
5x = 110
x = 22
Thus, the measure of x is found as 22.
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Deirdre is a member of a very small but high-class organization called Algebra Lovers Anonymous. She paid $10 in dues for each of her first 3 years as a member and $2 in dues each year after that. If Deirdre has paid a total of $38 in dues, for how many years has she paid $2 in dues?
Answers
For 4 years, Deirdre paid $2 in dues.
Deirdre paid each year for three years = 3 × 10 = 30.
Let's consider x as the number of years,
As Deirdre paid $2 for x years the value she paid will be 2x,
Deirdre paid = $2x (in x years)
Deirdre has paid $10 for three years each, a total of $38 in dues. So the final equation will be,
38 = 30 + 2x
38 - 30 = 2x
8 = 2x
x = 4
Thus, Deirdre has paid $2 in dues for 4 years.
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