For which values of x and y is line p parallel to line q?
X=5,y=3
x=1, y=5
x=3, y=5
x=3, y=6
Answers
Step 1
Find the value of x
we know that
If lines p and q are parallel
then
[tex](45x-5)+(16x+2)=180\°[/tex] ------> by consecutive interior angles
Solve for x
[tex](45x-5)+(16x+2)=180\° \\61x=180+3 \\x=3\°[/tex]
Step 2
Find the value of y
we know that
If lines p and q are parallel
then
[tex](26y)=(45x-5)[/tex] ------> by corresponding angles
substitute the value of x and solve for y
[tex](26y)=(45*3-5)[/tex]
[tex](26y)=130[/tex]
[tex]y=5\°[/tex]
therefore
the answer is the option
[tex]x=3\°[/tex] , [tex]y=5\°[/tex]
Related Questions
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]
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.
What is the simplified form of each expression?
A. 729x33
B. 3x33
C. 729x29
D. 3x29
Answers
99
21141
87
These are the correct answers.
The simplified form of each expression is as follows:
[tex]A. \( 729 \times 33 \) simplifies to \( 3^6 \times 33 \) B. \( 3 \times 33 \) simplifies to \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \). C. \( 729 \times 29 \) simplifies to \( 3^6 \times 29 \). D. \( 3 \times 29 \) simplifies to \( 3 \times 29 \).[/tex]
To simplify these expressions, we recognize that 729 is a power of 3, specifically [tex]\( 3^6 \)[/tex], and that 33 and 29 are prime numbers. Therefore, we can express each product in terms of its prime factors.
A. For the expression [tex]\( 729 \times 33 \)[/tex] , we know that 729 is [tex]\( 3^6 \)[/tex] and 33 is a prime number. Thus, the simplified form is [tex]\( 3^6 \times 33 \)[/tex].
[tex]B. For the expression \( 3 \times 33 \), we can further break down 33 into \( 3 \times 11 \), since 33 is the product of these two prime numbers. Therefore, the simplified form is \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \).[/tex]
[tex]C. For the expression \( 729 \times 29 \), similar to expression A, 729 is \( 3^6 \) and 29 is a prime number. Hence, the simplified form is \( 3^6 \times 29 \).[/tex]
[tex]D. For the expression \( 3 \times 29 \), both 3 and 29 are prime numbers, so the expression is already in its simplest form and cannot be simplified further. Thus, the simplified form remains \( 3 \times 29 \).[/tex]In summary, the simplified forms are:
[tex]A. \( 3^6 \times 33 \) B. \( 3^2 \times 11 \) or \( 3 \times 3 \times 11 \) C. \( 3^6 \times 29 \) D. \( 3 \times 29 \)[/tex]
13x - 7 = 136
11
15
8
9
Answers
x = 11
The line y = –2x – 8 is graphed. Which ordered pairs are solutions to the equation? Check all that apply.
A) (–8, 8)
B) (–6, 2)
C) (–2, 4)
D) (0, –4)
E) (2, –12)
Answers
you have: y=-2x-8
Simply plug in the coordinates-->>
A.) (-8,8)
8= -2(-8)-8
8=16-8
8=8 (Yes/True)
B.) (-6,2)
2=-2(-6)-8
2=12-8
2=4 (No)
C.) (-2,4)
4=-2(-2)-8
4=4-8
4=-4 (No)
D.) (0,-4)
-4=-2(0)-8
-4=0-8
-4=-8 (No)
E.) (2,-12)
-12=-2(2)-8
-12=-4-8
-12=-12 (Yes/True)
Thus, your answer.
(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.
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.
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..
Answers
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.
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
what is an asymptote? ...?
Answers
A line that the graph of a function approaches but never touches.
∠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
Answers
A commuter must pass through five traffic lights on her way to work, and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.
X= # of red P(x)
0 0.05
1 0.25
2 0.35
3 0.15
4 0.15
5 0.05
a. How many red lights should she expect to hit each day?
b. What's the standard deviation?
c. Find the mean and standard deviation of the number of red lights the commuter should expect to hit on her way during a 5 day work week.
Answers
Answer:
a) 2 red lights
b) SD = 1.26
c) mean = 10, SD = 1.26
Step-by-step explanation:
a) The number of red lights she expects to hit by day can be gotten by calculating the mean of the distribution.
[tex]E(X) = \sum xP(x)[/tex]
[tex]E(X) = (0*0.05) + (1*0.25) + (2*0.35) + (3*0.15) + (4*0.15) + (5*0.15)\\E(X) = 2.25[/tex]
Since the number of lights cannot be a decimal, she expects to hit 2 lights each day
b)
Variance, [tex]V(X) = \sum(x- \mu)^{2} P(x)[/tex]
[tex]V(X) = [(0-2.25)^{2}*0.05] + [(1-2.25)^{2}*0.25] + [(2-2.25)^{2}*0.35] + [(3-2.25)^{2}*0.15] + [(4-2.25)^{2}*0.15] + [(5-2.25)^{2}*0.05][/tex]
V(X) = 0.253 + 0.391 + 0.022 + 0.084 + 0.459 + 0.378
V(X) = 1.587
Standard Deviation, [tex]SD = \sqrt{V(X)}[/tex]
[tex]SD = \sqrt{1.587}[/tex]
SD = 1.26
c) In a 5 day work week, the commuter is expected to hit an average of 5* 2 red lights, i.e. mean = number of red lights hit per day * number of days
mean = 2 * 5
mean = 10
The standard deviation will not change, SD = 1.26
How many solutions are there to this equation?
5(x + 10)- 25= 5x + 25
a. 1
b. 0
c. infinitely many
Answers
Solve the system of equations.
x + 3y = −1
2x + 2y = 6 (1 point)
(−4, 1)
(2, −1)
(4, −1)
(5, −2)
Answers
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)
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
Determine algebraically all points where the graphs of xy=10 and y=x+3 intersect
Answers
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!
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.
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].
6) If sec theta+tan theta = P. PT sin theta=P^2-1/P^2+1 ...?
Answers
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.
How many solutions to this equation?
145 = 10x - 8x
A. 2
B. 1
C. infinitely many
Answers
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
Answers
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
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? _________________________
Answers
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 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}
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
What is 7 40/81 rounded to the nearest whole number
Answers
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:
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].
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)
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