Answers
Related Questions
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}
kelly has 4 times as many songs on her music player as Lou. Tiffany has 6 times as many songs on her music player as Lou. Altogether, they have 682 songs on their music players. How many songs does kelly have?
Answers
tiffany = t
Lou = l
k = 4l
t = 6l
4l + 6l + l = 682
11l = 682
l = 62
k = 4l
k = 4 * 62
k = 248
Kelly has 248 songs on her music player.
Area of a kite
Solve for d2: A=1/2d1d2
Answers
Answer:
The value of the equation for [tex]d_2[/tex] is [tex]d_2=\frac{2A}{d_1}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]A=\frac{1}{2}d_1d_2[/tex]
We need to solve the equation for [tex]d_2[/tex].
Multiply both the sides by 2.
[tex]2A=2\times \frac{1}{2}d_1d_2[/tex]
[tex]2A=d_1d_2[/tex]
Divide both sides by [tex]d_1[/tex].
[tex]\frac{2A}{d_1}=\frac{d_1d_2}{d_1}[/tex]
[tex]d_2=\frac{2A}{d_1}[/tex]
Hence, the value of the equation for [tex]d_2[/tex]is [tex]d_2=\frac{2A}{d_1}[/tex].
What are the variable terms in the expression?
6x^2 + 3xy + 4z
Answers
Answer:
[tex]6x^2,3xy,4z[/tex]
Step-by-step explanation:
We are given that an expression
[tex]6x^2+3xy+4z[/tex]
We have to find the variable terms in the given expression.
Variable term: The term which contains variable is called variable term.
Constant term:The term which does not contain variable is called constant term.
To find the variable terms we will find the terms which contains variable.
We can see that in the given expression
There are three terms which contain variables.
Hence, the variable terms are
[tex]6x^2,3xy,4z[/tex]
The cost, c(x), for a taxi ride is given by c(x) = 2x + 4.00, where x is the number of minutes. What does the slope mean for this situation?
A. The taxi ride costs a total of $4.00.
B. The taxi ride costs $2.00 per trip.
C. The rate of change of the cost of the taxi ride is $2.00 per minute.
D. The rate of change of the cost of the taxi ride is $4.00 per minute.
Answers
Answer:
Answer is option c
Step-by-step explanation:
Given that the cost, c(x), for a taxi ride is given by c(x) = 2x + 4.00, where x is the number of minutes.
We find that whenever 1 minute increases cost increases by 2 dollars.
Hence rate of change of cost with respect to minute of taxi ride = 2 dollas
i.e. this is of the form y=mx+b where
m =2 is the slope or rate of change and
b = 4 is the fixed charge even for 0 minute.
Thus option C is right
consider the function f(x) = {(sinx)/x, x cannot equal 0
{k, , x = 0
In order for f(x) to be continuous at x - 0, the value of k must be..
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As x -> 0, Limit of [sin (x) / x ] = 1.
Then, given that f(0) = k , k must be 1.
Answer: k must be 1.
Final answer:
For the function f(x) = (sinx)/x to be continuous at x = 0, the value of k must be 1, which is the limit of the function as x approaches 0.
Explanation:
The student is asking about the continuity of a given function at x = 0. To determine what the value of k must be for the function f(x) = (sinx)/x when x is approaching 0, we need to look at the limit of the function as x approaches 0.
Although the function is not defined at x = 0 due to division by zero, we know that the limit of (sin x)/x as x approaches 0 is 1. This can be proven using L'Hospital's rule or the squeezing theorem. Hence, for the function to be continuous at x = 0, the value of k must also be 1.
Solve the system of equations.
x + 3y = −1
2x + 2y = 6 (1 point)
(−4, 1)
(2, −1)
(4, −1)
(5, −2)
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the solution to the system of equation is (5, -T
System of equationx + 3y = −1 2x + 2y = 6From equation 1;
x = -1 - 3y
Substitute x = -1-3y into equation 2
x + y = 3
-1-3y + y = 3
-1 -2y = 3
-2y = 4
y = -2
Since x + y = 3
x = 3 + 2
x = 5
Hence the solution to the system of equation is (5, -2)
what is an asymptote? ...?
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A line that the graph of a function approaches but never touches.
Which terms could have a greatest common factor of 5m2n2? Check all that apply.
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answers
Answer : [tex] 5m^4n^3[/tex] and [tex] 15m^2n^2[/tex]
Greatest common factor of [tex] 5m^2n^2 [/tex]
If we are able to factor out [tex] 5m^2n^2 [/tex] from each option then that would be our answer.
Lets check with each options
(a)[tex] m^5n^5 [/tex], we cannot take out 5.
(b)[tex] 5m^4n^3 [/tex], We can take out common factor and it can be written as [tex] 5m^4n^3=5m^2n^2(m^2n) [/tex]
(c) [tex] 10m^4n [/tex], we cannot take out n^2 because we have only 'n'
(d) [tex] 15m^2n^2[/tex], We can take out common factor and it can be written as [tex] 15m^2n^2=5m^2n^2(3) [/tex]
(e) [tex] 24m^3n^4 [/tex], we cannot take out 5 because we have 24
So answer is (b) and (d)
(1.) decide if function f is invertible.
a) f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.
b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius. ...?
Answers
f(n) is not invertible because several different days, n, may have the same number of students, f(n). Then for one specific f(n) you cannot determine a unique n.
b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius.?
f(x) is invertible because each x gives a different f(x), then you can determine unambiguously which f(x) corresponds to each x.
A cable installer charges $30.00 per hour plus a $50.00 service charge. Your father's firm hires him to hook up his company's Internet service.
Find the total charges if it takes the cable installer 8.5 hours to complete the task. ...?
Answers
Final answer:
To calculate the total charges for the cable installation, multiply the hourly rate of $30.00 by the 8.5 hours spent ($255.00) and add the $50.00 service charge, resulting in total charges of $305.00.
Explanation:
The task requires us to calculate the total charges based on the cable installer's hourly rate and a service charge. The installer charges $30.00 per hour and there's an additional $50.00 service charge. To find the total cost for 8.5 hours of work, we multiply the hourly rate by the number of hours and then add the service charge.
Calculation: Total charges = (Hourly rate × Number of hours) + Service charge = ($30.00 × 8.5 hours) + $50.00
Step 1: Calculate the hourly charge
Hourly charge = $30.00 × 8.5 = $255.00
Step 2: Add the service charge
Total charges = $255.00 + $50.00 = $305.00
The total charges for the cable installation service will be $305.00.
SOLVE. (2ax + 1/2 bx)2 ...?
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Explanation of how to expand and simplify the given quadratic expression Hence answer is 4a²x² + abx² + 1/4b²x²,
Solve the equation: (2ax + 1/2 bx)²
Expanding the given expression:
(2ax + 1/2 bx)²
= (2ax)² + (2ax) (1/2 bx) + (1/2 bx)²
= 4a²x² + 2abx² + 1/4b²x²
= 4a²x² + abx² + 1/4b²x²
Answer: 4a²x² + abx² + 1/4b²x²
The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Answers
Ratio = hotDogs/Chicken = 4/10 = 2/5
voted for pizzas:chicken:hot dogs
10:4=5:2
chicken:hot dogs
∠1 is decomposed into two nonoverlapping angles, ∠2 and ∠3. let m∠1 = 130° and m∠3 = 75°. what type of angle is ∠2?
a. acute
b. obtuse
c. right
d. straight
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In a basic sine curve, where can the zeros NOT be found
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where n is any number.
13x - 7 = 136
11
15
8
9
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x = 11
The circumference of a circle is defined to be the _________.
A. the width of the circle
B. length of the radius
C. distance around the circle
D. area of the circle
Answers
Answer:
it is the distance of a circle
Step-by-step explanation:
Find f(6) if f(x) = x2 ÷ 3 + x.
Answers
A function is denoted as y = f (x), where x is the argument or input of the function. This means that from f(6) follows that x= 6, and to get the answer we should replace x with 6.
f(6)=6^2÷ 3 + 6= 36÷ 3 + 6= 12+6= 18
f(6)=18
Answer:
The value of f(6) is, 18
Step-by-step explanation:
Given the function:
[tex]f(x) = x^2 \div 3+ x[/tex] .....[1]
We have to find the value of [tex]f(6)[/tex].
Put x = 6 in [1] we have;
[tex]f(6) = 6^2 \div 3+ 6[/tex]
⇒[tex]f(6) = 36 \div 3 +6[/tex]
⇒[tex]f(6) = \frac{36}{3}+6[/tex]
Simplify:
[tex]f(6) = 12 +6 = 18[/tex]
Therefore, the value of f(6) is, 18
in 2000 the average cost for a gallon of gasoline was 1.40 in 2007 the average cost for a gallon of gasoline is 2.60 what is the percent of increase rounded to the nearest whole number
Answers
Then, take 1.2 and divide it by 1.40 and then multiply by 100
hope you got it :))
So basically the answer would be 86%
A $15,000, 6 percent , 50-day note ,dated November 8, is discounted at 5 percent on November 28, the proceeds of the note would be?
A. $14,936,46
b. $ 15,610,64
c. $63,54
d. $15,061,98
Answers
Answer:
D. $15061.98
Step-by-step explanation:
In order to calculate the proceeds we will using the following computation:
Principal + {Principal * Discounted rate * Frequency of a year on Maturity Date}
15,000 + {15,000 * 5% * (30/365)}
Hence, the proceeds of note would be $15,061.98
How many solutions to this equation?
145 = 10x - 8x
A. 2
B. 1
C. infinitely many
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What is 7 40/81 rounded to the nearest whole number
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Therefore, you look at the digit after the decimal point that is 1 so it will be 9 since it's less than 5
So the answer is 9
Answer:
9
Step-by-step explanation:
which phrase best defines a rhombus? a.a parallelogram with four congruent anglesb.a parallelogram with four congruent sidesc.a quadrilateral with exactly one pair of parallel sides d.a quadrilateral with no congruent sides
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A baseball team plays in a stadium that holds 51,000 spectators. With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000. Find the demand function (price p as a function of attendance x), assuming it to be linear?? ...?
Answers
Answer:
[tex]p(x)=-0.0005x+29[/tex]
Step-by-step explanation:
It is given that a baseball team plays in a stadium that holds 51,000 spectators.
Let x be the attendance and p be the price.
With ticket prices at $10, the average attendance had been 38,000. When ticket prices were lowered to $8, the average attendance rose to 42,000.
Assuming that the demand function is linear. It means, the demand line passes through the points (38000,10) and (42000,8).
The equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-10=\dfrac{8-10}{42000-38000}(x-38000)[/tex]
[tex]y-10=\dfrac{-2}{4000}(x-38000)[/tex]
[tex]y-10=-0.0005(x-38000)[/tex]
[tex]y-10=-0.0005x-0.0005(-38000)[/tex]
[tex]y-10=-0.0005x+19[/tex]
[tex]y=-0.0005x+19+10[/tex]
[tex]y=-0.0005x+29[/tex]
Substitute y=p(x).
[tex]p(x)=-0.0005x+29[/tex]
Therefore, the demand function is [tex]p(x)=-0.0005x+29[/tex].
South middle school has 750?students. North middle school has 13/15 times as many students as South. Does north middle school have more or fewer than 750 students?
Answers
Answer : The north middle school have fewer than 750 students.
Step-by-step explanation:
Let the number of students in south middle school be, x
and the number of students in north middle school be, y
Given:
Number students in south middle school = x = 750
and,
North middle school has 13/15 times as many students as South. That means,
[tex]y=\frac{13}{15}\times x[/tex] ........(1)
Now put the value of 'x' in expression 1, we get:
[tex]y=\frac{13}{15}\times 750[/tex]
[tex]y=650[/tex]
Thus, number of students in north middle school = y = 650
From this we conclude that north middle school have fewer than 750 students.
Hence, the north middle school have fewer than 750 students.
Calculate the slope of the line given the points (2, 1) and (1, -4).
A. 1/5
B. 5
C.-3
D. none of the above
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Determine algebraically all points where the graphs of xy=10 and y=x+3 intersect
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y1=10/x. y2=x+3
10/x=x+3
x=2 clearly => (2,5)
therefore x=-5=>(-5,-2)
You can use substitution and plug in the y value given as x+3 into xy=10.
x(x+3)=10
or
x^2+3x=10
or
x^2+3x-10=0
Then you divide the -10 into two different factors, I did 2 and -5.
x^2 is equal to xx, so now you have one x for each factor of the -10:
(x+2)(x-5)=0
This means x is either 2 or -5, and when you plug in these values to the equation y=x+3, you get:
(2,5)
and
(-5,-2)
Which are your two intersecting points!
6) If sec theta+tan theta = P. PT sin theta=P^2-1/P^2+1 ...?
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Then the problem is, given sec(x) + tan(x) = P, show that
sin(x) = [P^2 - 1] / [P^2 + 1]
I am going to take a non regular path.
First, develop a little the left side of the first equation:
sec(x) + tan(x) = 1 / cos(x) + sin(x) / cos(x) = [1 + sin(x)] / cos(x)
and that is equal to P.
Second, develop the rigth side of the second equation:
[p^2 - 1] / [p^2 + 1] =
= [ { [1 + sin(x)] / cos(x) }^2 - 1] / [ { [1 + sin(x)] / cos(x)}^2 +1 ] =
= { [1 + sin(x)]^2 - [cos(x)]^2 } / { [1 + sin(x)]^2 + [cos(x)]^2 } =
= {1 + 2sin(x) + [sin(x)^2] - [cos(x)^2] } / {1 + 2sin(x) + [sin(x)^2] + [cos(x)^2] }
= {2sin(x) + [sin(x)]^2 + [sin(x)]^2 } / { 1 + 2 sin(x) + 1} =
= {2sin(x) + 2 [sin(x)]^2 } / {2 + 2sin(x)} = {2sin(x) ( 1 + sin(x)} / {2(1+sin(x)} =
= sin(x)
Then, working with the first equation, we have proved that [p^2 - 1] / [p^2 + 1] = sin(x), the second equation.
The students at Monroe Junior High sponsored a canned food drive. The seventh-grade class collected 129% of its canned food drive goal.
a. ABOUT how many canned foods did the seventh-graders collect if their goal was 200 cans? _____________________
b. ABOUT how many canned foods did the seventh-graders collect if their goal was 595 cans? _________________________
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260 cans
b. ABOUT how many foods did the seventh-graders collect if their goal was 595 cans?
770 cans
B)768 (rounded up)
The integer n3 + 2n is divisible by 3 for every positive integer n
prove it by math induction
is it my proof right ?
Answers
Let's show that P(n) holds for n = 1
P(1) = 1^3 + 2(1) = 1 + 2 = 3 which is divisible by 3.
Now assuming, that p(k) is true, let's show that p(k + 1) is also true
p(k + 1) = (k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2 = k^3 + 3k^2 + 5k + 3 = k^3 + 2k + 3k^2 + 3k + 3 = k^3 + 2k + 3(k^2 + k + 1), since P(k) is true => k^3 + 2k is true and 3(k^2 + k + 1) is divisible by 3 for all values of k wich shows that P(k + 1)is also true.
Therefore, P(n) is true for all positive integer value of n.
By the principle of mathematical induction, we have shown that for all positive integers n, n^3 + 2n is divisible by 3.
Proof by Induction: n^3 + 2n is divisible by 3 for all positive integers n.
Base Case:
For n = 1, n^3 + 2n = 1^3 + 2(1) = 3, which is divisible by 3.
Induction Hypothesis:
Assume that for some positive integer k, k^3 + 2k is divisible by 3. We can write this as: k^3 + 2k = 3m, where m is an integer.
Induction Step:
We need to show that (k + 1)^3 + 2(k + 1) is divisible by 3. Expanding the expression:
(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2
= (k^3 + 2k) + (3k^2 + 3k + 3)
Substituting the induction hypothesis:
= 3m + 3(k^2 + k + 1)
= 3(m + k^2 + k + 1)
Since k^2 + k + 1 is an integer (sum of three integers), and m is an integer, their sum (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.