The graph of the piecewise function f(x) is shown.
What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
Answers
Answer:
Domain is {x| 1<=x <5}
Step-by-step explanation:
The graph of the piecewise function f(x) is shown.
In the given graph of piecewise function
Domain is the set of x values for which the function is defined
first graph is from x= 1 to 3, 3 is excluded
second graph is from x= 3 to 5, 5 is excluded
So the graph of x values is from x=1 to 5 ( 5 excluded because we have open circle at 5)
Domain is {x| 1<=x <5}
Related Questions
What is the prime factorization of 19??
Answers
The prime factorization of 19 is 19, as it is a prime number and can only be divided by 1 and itself.
To determine the prime factorization of a number, we identify all the prime numbers that multiply together to give the original number. In the case of 19, we need to check if it can be divided by any primes (like 2, 3, 5, 7, 11, 13, 17).
After testing, we find that 19 is only divisible by 1 and itself, making it a prime number. Therefore, the prime factorization of 19 is simply 19.
54,625 written in expanded form
Answers
hope this helps you
convert 5/8 to percent notation
Answers
5/8 = 0.625
0.625 x 100 = 62.5%
4x+5y=6 and 6x-7y=-20
Answers
If you are asking for how to make it into y=mx+b form:
4x + 5y = 6
5y / 5 = -4x+6/ 5
Answer: y= -4/5x + 6/5
6x - 7y = -20
-7y/-7 = -6x - 20/ -7
Answer: y= 6/7x +20/7
Hope this helps!!
let f=cos^2x and g=sin^2x which of the following lie in the space spanned by f and g
a)cos2x
b)3+x^2
c)1
d)sinx
e)0 ...?
Answers
solve for x enter your answer in interval notation using grouping symbols x²+2x<8
Answers
The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?
Answers
Answer:
Option 3rd is correct
4: 3
Step-by-step explanation:
Perimeter(P) of rectangle is given by:
[tex]P =2(l+w)[/tex]
where, l is the length and w is the width of the rectangle respectively.
Given that:
The dimensions of a smaller rectangle are 3 ft. by 9 ft.
Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.
It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.
Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.
We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]
Substitute the given values we have;'
[tex]\frac{32}{24}=\frac{4}{3}[/tex]
Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3
betty has a cow.the cow produces 5 liters of milk in a day. if the cows diet is improved the cow will produce 200% more milk.how much milk would the cow make in a day.
Answers
Write a function rule for the area A of a triangle whose base, b, is 2 cm less than seven times the height, h. What is the area of the triangle when the height hits 16 cm.
A. 4h^2-5h;944cm^2
B. 4h-5/2; 29.5***********
C. 4h^3-5h/2; 427
D. 4h-5; 59cm
I think it is B
Answers
Proof that x^y + y^x > 1 for all x,y > 0 ...?
Answers
Case 1: x >= 1, y >= 1
It is obvious that
x^y >= 1, y^x >= 1
x^y + y^x >= 2 > 1
x^y + y^x > 1
Case 2: x >= 1, 0 < y < 1
Considering the following sub-cases:
- x = 1, x^y = 1
- x > 1,
Let x = 1 + n, where n > 0
x^y = (1 + n)^y = f_n(y)
By Taylor Expansion of f_e(y) around y = 0,
x^y = f_n(0) + f_n'(0)/1!*y + f_n''(0)/2!*y^2 + ...
= 1 + ln(1 + n)/1!*y + ln(1 + n)^2/2!*y^2 + ...
Since ln(1 + n) > 0,
x^y > 1
Thus, we can say that x^y >= 1, and since y^x > 0.
x^y + y^x > 1
By symmetry, 0 < x < 1, y >= 1, also yields the same.
Case 3: 0 < x, y < 1
We can prove this case by fixing one variable at a time and by invoking symmetry to prove the relation.
Fixing the variable y, we can set the expression as a function,
f(x) = x^y + y^x
f'(x) = y*x^(y-1) + y^x*ln y
For all x > 0 and y > 0, it is obvious that
f'(x) > 0.
Hence, the function f(x) is increasing and hence the function f(x) would be at its minimum when x -> 0+ (this means close to zero but always greater than zero).
lim x->0+ f(x) = 0^y + y^0 = 0 + 1 = 1
Thus, this tells us that
f(x) > 1.
Fixing variable y, by symmetry also yields the same result: f(x) > 1.
Hence, when x and y are varying, f(x) > 1 must also hold true.
Thus, x^y + y^x > 1.
We have exhausted all the possible cases and shown that the relation holds true for all cases. Therefore,
x^y + y^x > 1
----------------------------------------------------
I have to give credit to my colleague, Mikhael Glen Lataza for the wonderful solution.
I hope it has come to your help.
Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses Gerber daisies is 94%. Given the probability that she has both roses and orchids is 0.87 and the probability that she has both Gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or Gerber daisies?
Answers
the answer would be b.) .84
if the tank is half full, approximately how many miles has troy driven since last filling up his tank
BTW troy truck has a 30 gallon gas tank and gets an average of 21 miles per gallon
ASAP plz I really need help
Answers
30 Gallon Tank on Half: 30 / 2 = 15.
21 miles per gallon: 21 x 15 = 315 Miles.
I hope this helps!
Answer:
Toy truck will drive 315 miles since last the tank was filled.
Step-by-step explanation:
BTW troy truck has tank of capacity = 30 gallons
Since the toy truck is half filled so gas in the tank = [tex]\frac{30}{2}[/tex]
= 15 gallons of gas
Average of the toy truck is given as = 21 miles per gallon
That means in 1 gallon truck travels = 21 miles
Therefore in 15 gallons of gas truck will travel = 21 × 15
= 315 miles
Toy truck will drive 315 miles since last the tank was filled.
∠A∠A and ∠B∠B are vertical angles with m∠A=xm∠A=x and m∠B=5x−80m∠B=5x−80 . What is m∠Am∠A ?
Answers
The Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent .Given <A and <B are vertical angles so they are equal.
<A=<B.
Measure of <A=x and <B=5x-80
Or 5x-80=x
Adding 80 both sides
5x-80+80=x+80
5x=x+80
Subtracting x both sides
5x-x=x-x+80
4x=80
Dividing both sides by 4
x=20
Measure of <A= x= 20 degrees.
Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.
Answers
L = 2*r*pi
He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi
To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds
v = L'/t = [tex] \frac{3*r*pi}{2*105} [/tex]
v = r* pi/70
If we take that r = 1 answer is [tex] \pi /70[/tex]
One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with the mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?
Answers
The chronological age of a person with a mental age of 40 and an IQ of 80 is calculated to be 50 years by using the direct and inverse proportionality of the IQ, Mental Age, and Chronological Age.
Explanation:The subject of your question is related to a mathematical concept known as Direct and Inverse Proportion. In this scenario, the IQ is directly proportional to the Mental Age and inversely proportional to the Chronological Age. Therefore, the formula is given as: IQ = (Mental Age / Chronological Age) * 100.
From the first example that indicates a person with the mental age of 25 and a chronological age of 20 has an IQ of 125, we can determine the proportionality constant as follows: 125 = (25 / 20 ) * 100.
Now, to find out the chronological age of a person with a mental age of 40 and an IQ of 80, we use the same proportionality and solve the equation for chronological age: 80 = (40 / Chronological Age) * 100. Solving the equation, the Chronological Age equates to 50 years.
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To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. The specific chronological age depends on the value of the constant of variation, k.
Explanation:To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. Let's denote the chronological age as x. We can set up the equation as follows:
IQ = (k * mental age) / chronological age
where k is the constant of variation.
Given that the mental age is 40 and the IQ is 80, we can plug in these values into the equation:
80 = (k * 40) / x
To solve for x, we can cross-multiply and then divide both sides by 80:
80x = k * 40
x = (k * 40) / 80
Since we don't have the value of k, we can't determine the specific value of x. However, we can determine the relationship between x and the mental age:
x = 40 / k
Therefore, the chronological age of a person with a mental age of 40 and an IQ of 80 depends on the value of the constant of variation, k.
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Convert 0.84 into a simplified fraction
Answers
Or
84 upon 100
Maybe the answer is correct
In triangle abc, sin a = 2425. which other expression has a value of 2425?
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Expand and simplify 2 (x+7)+3(x+1)
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What value(s) of x make the equation x2 - 18x + 81 = 0 true?
Answers
Answer:
9
Step-by-step explanation:
Explain the correlation between the graph of a line, direction of the line and the positive or negative slope of the line.
Answers
how many times does 28 go into 126
Answers
It would be:126/28 = 4.5
So, your final answer is 4.5
Hope this helps!
A school soccer team has just purchased new uniforms. The team now has 2 different colors of shorts (white and red) and 3 different colors of shirts (white, red, and gold).
How many different uniform combinations are there? ...?
Answers
number of shorts * number of shirts = 2 * 3
so the answer will be 6.
Whut is 2 pus 2 i dount no
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Lamar bought 20 pounds of dog food for $4.99 for his dog, Buster. The next day, the shop down the street offered 50 pounds of the same brand of dog food for $12.50. Did Lamar get a better deal? ...?
Answers
First shop:
4.99/20 = 0.2495$/pound
Second shop:
12.50/50 = 0.25$/pound
This means that first shop had slightly better deal since at that place pound was a bit less expensive.
Find the equations of all lines tangent to y = 9–x^2 that pass through the point (1, 12). ...?
Answers
The equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.
Explanation:To find the equations of all lines tangent to y = 9 - x^2 that pass through the point (1, 12), we need to find the slope of the tangent line at the point (1, 12) and use it to form the equation of the line.
First, find the derivative of y = 9 - x^2 to get dy/dx = -2x.Substitute x=1 into dy/dx = -2x to find the slope of the tangent line at (1,12). In this case, the slope is -2.Next, use the point-slope form of a line and the given point (1, 12) to write the equation of the tangent line:y - y1 = m(x - x1)
y - 12 = -2(x - 1)
Rewrite the equation in slope-intercept form:
y = -2x + 14
Therefore, the equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.
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80 POINTS!!!
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Answers
Answer:
1). Slope = (-2)
2). Midpoint = (2, -2)
3). Slope of the perpendicular bisector = (1/2)
4). Equation of perpendicular bisector will be x - 2y = 6
Step-by-step explanation:
A line segment has the endpoints at (4, -6) and (0, 2).
1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)
2). Mid point of the line segment is given by [tex](\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})[/tex]
Therefore midpoints of the line segment will be [tex]\frac{4+0}{2},\frac{-6+2}{2}[/tex] = (2, -2)
3). Slope of the perpendicular bisector is represented by [tex]m_{1}.m_{2}=(-1)[/tex]
⇒ (-2)×m2 = (-1)
⇒ [tex]m_{2}=\frac{1}{2}[/tex]
4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).
Since standard equation of the line will be given as y = mx + c
[tex]y=\frac{1}{2}x+c[/tex] passes through (2, -2).
[tex](-2) = \frac{1}{2}(2) + c[/tex]
c = (-1) - 2 = -3
Finally the equation of perpendicular bisector will be
[tex]y=\frac{1}{2}x+(-3)[/tex]
⇒ 2y = x - 6
⇒ 2y - x = -6
⇒ x - 2y = 6
Answer: the answers are in the explanation, they are also in order
Step-by-step explanation:
-2
(2,-2)
1/2
y=(1/2)x - 3
**URGENT HELP???!!!*
Suppose that b(x) varies directly with x and b(x) = 4325 when x= 25.
What is b(x) when x =19?
A.) 4325
B.) 3287
C.) 173
D.) 9.1
I can't remember how problems like these are suppose to go and how to write them out, could you tell me how you got the answer once you get it. Thanks ;)
Answers
hope that helps
..................................
4325/25 = 173
173 * 19 = 3287
Answer:
B.3287
Step-by-step explanation:
We are given that
b(x) varies directly with x.
b(x)=4325 when x=25
We have to find the value of b(x) when x=19
According to question
[tex]b(x)\propto x[/tex]
[tex]b(x)=kx[/tex]
Where k=Proportionality constant
Substitute the values then we get
[tex]4325=k(25)[/tex]
[tex]k=\frac{4325}{25}=173[/tex]
[tex]k=173[/tex]
Now, substitute the value of k then, we get
[tex]b(x)=173 x[/tex]
Substitute the value of x=19
Then, we get
[tex]b(x)=173 \times 19=3287[/tex]
Hence, option B is true.
Choose two axioms that allow 6 + (x + 5) to be written x + 11.
A) commutative - addition
B) distributive
C) associative - multiplication
D) symmetric
E) commutative - multiplication
F) associative - addition
G) identity - addition
Answers
associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true
Basic number properties:
The Distributive Property: [tex]a\cdot (b+c)=a\cdot b+a\cdot c;[/tex]The Associative Property for addition: [tex]a+(b+c)=(a+b)+c;[/tex]The Associative Property for multiplication: [tex]a\cdot (b\cdot c)=(a\cdot b)\cdot c;[/tex]The Commutative Property for addition: [tex]a+b=b+a;[/tex]The Commutative Property for multiplication: [tex]a\cdot b=b\cdot a;[/tex]Identity Property : Any number add to the zero the answer is the number itself;The symmetric property states that if one number is equal to a second number, then the second number is equal to the first number.For the expression 6 + (x + 5):
use The Commutative Property for addition - 6+(x+5)=(x+5)+6;use The Associative Property for addition - (x+5)+6=x+(5+6)=x+11. When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is two times the value of f'(4).
Answers
How many solutions does this linear system have?
y = x+ 2
6x – 4y = –10
one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions
Answers
6x-4 (x+2)= -10x
6x-4x-8= -10
2x= 2
x= 1
y=1+2=3
The solution of a linear system of an equations is (-1, 1).
The given linear system of equations are y = x+ 2 and 6x – 4y = –10.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The system of linear equations can be solved as follows
x-y=-2 --------(1)
6x – 4y = –10 --------(2)
Multiply equation (1) by 4
That is, 4x - 4y= -8 --------(3)
Subtract equation (3) from the equation (2)
So, 6x-4y-(4x-4y)=-10-(-8)
2x=-2
⇒ x=-1
Put x=-1 in x-y=-2
Now, y=1
So, solution is (-1, 1)
Therefore, the solution of a linear system of an equations is (-1, 1).
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