Answer:
Discount =40\%
Selling price of headphone =\$36
Solution --
we know that,
MP=SP * 100/(100-D\%)
putting values now we get,
MP = 36 * 100 / 60=60$
so, initial price of Headphone was =$60
The logarithmic functions, f(x) and g(x), are shown on the graph.
What is the equation that represents g(x)? Explain your reasoning.
Answer:
g(x) = log(x + 1) + 4
Step-by-step explanation:
The graph of g(x) is shifted 1 unit left and 4 units right from its parent function.
Given the system of equations, what is the solution? x 3y = 5 x - 3y = -1 {(-4, -3)} {(2, 1)} {(-2, 3)}
The solution of the equation is (2, 1).
x=2 and y=1
What do you meant by equation?A mathematical assertion that two expressions are equal is known as equating. It can be expressed as either an identity, in which case the variables can take on any value, or a conditional equation, in which case the variables can only have specific values (roots).
According to the given information:We have two options for finding the answer. The first is to solve the equations via term elimination:
x + 3y = 5 ..............1
x - 3y = -1 ...............2
2x = 4 ..............3
With the equation, we can determine x. (3)
x = 4/2
x = 2
To determine y, we may now swap out x=2 in equation (1).
x + 3y = 5
2 + 3y = 5
3y = 3
y = 1
We've discovered x and y now.
x=2
y=1
The second method involves removing x from equation 1.
x + 3y = 5
x = 5 - 3y
In the equation right now, we may substitute x = 5 - 3y......... (2)
x - 3y = -1
(5 - 3y) - 3y = -1
5 - 6y = -1
6y = -6
y = 1
Currently, we can change y=1 in equations (1), (2), or (4) to find x.
We'll apply the equation (1)
x + 3y = 5
x + 3(1) = 5
x + 3 = 5
x = 2
The two variants x = 2 and y = 1 have allowed us to confirm this.
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(08.05 MC)The following box plot shows the number of books sold each day at a bookstore for 40 days. How many days did the bookstore sell 2 to 12 books?
A box plot is drawn with end points at 0 and 16. The box extends from 2 to 12 and a vertical line is drawn inside the box at 7
2
4
10
20
Considering the given box-and-whisker plot, it is found that the bookstore sold between 2 to 12 books in 20 days.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.From the plot given in this problem, the have that:
The 25th percentile is of 2.The median is of 7.The 75th percentile is of 12.This means that the percentage of days in which between 2 to 12 books were sold is:
P = 75 - 25 = 50%.
Hence, out of 40 days, the amount of days is:
0.5 x 40 = 20 days.
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Write the first five terms of the sequence with the given nth term. an = cos n 2
The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
For given question,
We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]
We need to find the first five terms of the sequence.
For n = 1
[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]
For n = 2,
[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]
For n = 3,
[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]
For n = 4,
[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]
For n = 5,
[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]
Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0
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What is the sum in simplest form?
4 1/2 + 1 3/5=
6 1/10
5 1/10
6 1/5
5 4/7
Answer:
6 1/10
Step-by-step explanation:
In order to add fractions, we have to make the denominators equal. we can multiply 1/2 by 5/5 and get 5/10, and multiply 3/5 by 2/2 and get 6/10, to make the denominator equal. Now we add the fractions. 4 5/10 + 1 6/10 = 5 11/10 = 6 1/10
find the maximum value of c=4x+2y subject to the fallowing constraints x≥0 y≥0 2x+2y≤10 3x+y≤9
The maximum value of c=4x+2y subject to the constraints is 14
How to determine the maximum value?The objective function is given as:
c = 4x+2y
The constraints are given as:
x≥0 y≥0
2x+2y≤10
3x+y≤9
Rewrite 2x+2y≤10 and 3x+y≤9 as equations
2x+2y = 10
3x+y = 9
Divide 2x+2y = 10 through by 2
x+y = 5
Subtract x+y = 5 from 3x+y = 9
3x - x + y - y = 9 - 5
Evaluate the difference
2x = 4
Divide by 2
x = 2
Substitute x = 2 in x+y = 5
2+y = 5
Solve for y
y = 3
So, we have
(x, y) = (2, 3)
Substitute (x, y) = (2, 3) in c = 4x+2y
c = 4 * 2 + 2 * 3
Evaluate
c = 14
Hence, the maximum value of c=4x+2y subject to the constraints is 14
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Please use elimination method to solve
The answer is x = 4, y = -1 or (4, -1).
We are given :
2x + 7y = 13x + 4y = 8Multiply the 1st equation with 3 and 2nd equation with 2.
3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3
4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16
Now, subtract : Equation 3 - Equation 4.
6x + 21y - 6x - 8y = 3 - 1613y = -13y = -1Substitute in the 1st equation.
3x + 4(-1) = 83x - 4 = 83x = 12x = 4Answer:
(4, - 1 )
Step-by-step explanation:
2x + 7y = 1 → (1)
3x + 4y = 8 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate x
6x + 21y = 3 → (3)
- 6x - 8y = - 16 → (4)
add (3) and (4) term by term to eliminate x
0 + 13y = - 13
13y = - 13 ( divide both sides by 13 )
y = - 1
substitute y = - 1 into either of the 2 equations and solve for x
substituting into (1)
2x + 7(- 1) = 1
2x - 7 = 1 ( add 7 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
solution is (4, - 1 )
The function f(x) = x2 4 is defined over the interval [-2, 2]. if the interval is divided into n equal parts, what is the height of the right endpoint of the kth rectangle?
the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.
= -2 +k*(5/n)
What is Coordinate geometry?The study of geometry utilizing coordinate points is referred to as coordinate geometry (or analytic geometry). Finding the distance between two points, dividing lines in the m:n ratio, locating a line's midpoint, and computing the area of a triangle in the Cartesian plane can all be done using coordinate geometry.
The range for the definition of the function f(x) = x^2 + 4 is (-2, 2).
Between this interval, there are a total of 5 equal pieces.
Height of each rectangle's right endpoint equals if the interval is divided into n equal pieces. k=(5/n)
Therefore, the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.
= -2 + k*(5/n)
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Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?
Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
What was the relationship between the lines with equations 4x − 8y = 9 and 8x − 7y = 9?Given: 4x - 8y = 9 ............(1)
8x - 7y = 9 ............(2)
To be the same line, the equations have to be multiples of each other.
Multiplying (1) by 2, we get
2(4x - 8y = 9) = 8x - 16y = 18
From (1) solve the value of y, we get
4x - 8y = 9 ............(1)
-8y = -4x + 9
The value of y = (1/2)x - 9/8
From (2),
8x - 7y = 9
solve the value of y, we get
-7y = -8x + 9
The value of y = (8/7)x - 9/7
To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
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The vertices of an isosceles triangle are A(3, 6), B(7, 2), and C4, 3).
What is the equation of the triangle's line of symmetry?
Answer:
[tex]y=x-1[/tex]
Step-by-step explanation:
The line of symmetry of an isosceles triangle is perpendicular to its base.
Given vertices of the isosceles triangle:
A = (3, 6)B = (7, 2)C = (4, 3)By sketching the triangle with the given points, we can see that AB is its base. (See attached graph).
To find the equation for the line of symmetry, first find the slope of the line AB. To do this, use the coordinates of points A and B and the slope formula.
Define the points:
[tex]\textsf{Let }(x_1,y_1)=(7, 2)[/tex][tex]\textsf{Let }(x_2,y_2)=(3, 6)[/tex][tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1[/tex]
As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.
Therefore, the slope of the line of symmetry = 1.
The line of symmetry will pass through point C (4, 3).
Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=1(x-4)[/tex]
[tex]\implies y-3=x-4[/tex]
[tex]\implies y=x-1[/tex]
Therefore, the equation of the given isosceles triangle's axis of symmetry is:
[tex]y = x - 1[/tex]
If we graph the points
then we will get AC=CB
That means C is the point from where the axis of symmetry passes
Foot of perpendicular is midpoint of AB
Midpoint of AB
((3+7)/2,(6+2)/2)(10/2,8/2)(5,4)Find equation of C and foot of perpendicular
Slope
m=(4-3)/(5-4)=1Equation
y-3=1(x-4)y-3=x-4y=x-1It is October and that means it is State Fair time again! Your uncle took you and 2 of your friends to the
fair. Admission for everyone to get into the fair was $20.00. You then went to the Midway, where they
have all of the rides, and he bout all-day ride passes for you and your friends. If your uncle spent a total
of $65.00 at the fair, how much did each of the all-day ride passes cost?
Answer: All-day ride passes cost $15 each
Step-by-step explanation:
It was $20 in total for everyone to get in, so subtract that from $65 to just focus on the all day passes
65-20=45
So the all day passes all together cost $45
Since your uncle bought it for you and 2 friends that's 3 people in total so divide 45 by 3
45 divided by 3 = 15
So each of the all day passes cost $15
Hope this helped :)
Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:
A. 19 p
B. 20 p
C. 21 p
D. 18 p
Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.
How many points did Lewis score?Lewis is the player who scored the least amount of points as they are first in the order.
To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.
If Lewis scored 19 points as the lowest then the total points would be:
= 19 + 20 + 21 + 22
= 82 points
If Lewis scored 20 points, the total points would be:
= 20 + 21 + 22 + 23
= 86 points
Lewis therefore scored less than 19 points.
If Lewis scored 18 points, the total is:
= 18 + 19 + 20 + 21
= 78 points
Lewis therefore scored 18 points.
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escribe la ecuacion de la circunferencia que tiene como diametro AB donde A(3,-4) y B(-2,-4
La ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².
¿Cómo derivar la ecuación estándar de la circunferencia?
En este problema debemos derivar la ecuación estándar de la circunferencia, cuyo diámetro está comprendido por el segmento de recta entre los puntos A(x, y) = (3, - 4) y B(x, y) = (- 2, - 4). La ecuación estándar de la circunferencia se presenta a continuación:
(x - h)² + (y - k)² = r² (1)
Donde:
(h, k) - Coordenadas del centro.r - Radio de la circunferencia.El centro de la circunferencia es el punto medio del segmento de recta AB:
(h, k) = 0.5 · (3, - 4) + 0.5 · (- 2, 4)
(h, k) = (1.5, - 2) + (- 1, 2)
(h, k) = (0.5, 0)
Y el radio de la circunferencia es la mitad de la longitud del segmento de recta AB:
[tex]r = \frac{1}{2}\cdot \sqrt{(-2 - 3)^{2}+[-4 - (-4)]^{2}}[/tex]
r = 2.5
Por tanto, la ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².
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What is the value for x when solving the equation –x (–1) = 3x (–5) using algebra tiles? x = –1 x = 1 x = 2 x = 3
The value of x in the equation –x (–1) = 3x (–5) is x = 1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
–x (–1) = 3x (–5)
Remove the bracket in the above equation
-x - 1 = 3x - 5
Collect the like terms in the above equation
3x + x = 5 - 1
Evaluate the like terms in the above equation
4x = 4
Divide both sides by 4 in the above equation
x = 1
Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1
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Answer:
-3, or D
Step-by-step explanation:
Select all the ways that express the number 32.148.
A 32 tens + 14 tenths + 8 hundredths
B 32 ones + 14 hundredths + 8 thousandths pauodt er
C 321 tenths + 48 thousandths
D 32,148 hundredths
E 32,148 thousandths
Answer: B, C, E
Step-by-step explanation: a is wrong 32 tens is 320. B is right. 321 tenths is 32.1 and 48 thousandths is 0.048 so C is correct. 32,148 hundredths is too much but 32,148 thousandths is 32.148
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the function representing the number of people, f(x), at the fair x hours after the gates open.
The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x
What is the function that represent the number of people at the fair?
The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.
Linear functions can be represented by : y = mx + c
Where:
y = dependent variable c = constantf(x) = 68 + (1.5x)
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"if i purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would i owe after the 8.75% tax is applied?" employee: "your total would be __________."
Answer:$96.98
Step-by-step explanation: all you just do is to add it all up to the total amount.
Answer: $105.47
I hope you get the job!!!!!
Solve the equation. Write the smaller value of x. x^2-4x-5=0
Use the figure to the right to list all of the pairs of angles that fit each description.
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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does someone mind helping me with this question? thank you!
Answer:
100
Step-by-step explanation:
to turn whole numbers to a fraction it is whatever numbers out of 100
Answer:
99
Step-by-step explanation:
r(x) = a sinx
what is the value of a
please help i need
this asap!! drag each measure to the correct location on the table classify each measure as a measure of center or a measure or variation
The measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
what is measure centre and measure of variation?A measure of central tendency (measure of centre) is a value that attempts to describe a set of data by identifying the central position of the data set.
The measure of central tendency includes the mean, median and mode.
The measure of variation describes the amount of variability or spread in a set of data.
The common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.
Therefore, the measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
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Determine the qualities of the given set. (select all that apply. ){(x, y) | x > 0, y > 0}
The qualities of the set {(x,y): x>0,y>0} is as under:
All points lie in first quadrant.All values are positive and greater than zero.Given a set {(x,y),x>0,y>0}.
We are required to determine the qualities of the set.
We know that a set is a collection of things,numbers, fractions, etc.
In any set the values of x represents the domain of the function and the values of y represents the value of codomain of the function with which the set belongs to.
Set={(x,y): x>0,y>0}
From the above set we can find the qualities stated below:
All points lie in first quadrant as the first quadrant only contains positive values of x and y.All values are positive because it is given that they are greater than zeroHence the qualities of the set {(x,y): x>0,y>0} are that all values should be in first quadrant and all the values are positive.
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Which values below belong in this table? Select all that apply.
The possible value of y are 16, 32 and 64
How to find the values of an exponential table?The table above is an exponential table.
Therefore, let's confirm the ratio of the y axis.
8 / 4 = 2
4 / 2 = 2
Therefore, the other y axis can be gotten as follows:
y = 8 × 2 = 16
y = 16 × 2 = 32
y = 32 × 2 = 64
y = 64 × 2 = 128
Therefore, the possible value of y are 16, 32 and 64
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Help me with this problem, random answer will be reported and you won’t get points
Answer:
A = 49B = 41 C = 90 a = 17.255526 (approximate)b = 15c = 22.863796 (approximate)Round the decimal values however needed.
Step-by-step explanation:
The uppercase letters represent the angles, while the lowercase counterparts are the side lengths opposite said angle. For example, side b is opposite angle B.
Angle B is 41 and angle C is 90 because of the square marker. The remaining angle A is...
A+B+C = 180
A+41+90 = 180
A+131 = 180
A = 180-131
A = 49
Or note that
A = 90 - B = 90 - 41 = 49
This shortcut works since we have a right triangle.
---------
That takes care of the angles. Now onto the sides.
We'll need to use trig ratios to determine the missing sides. There are a few approaches, but this is one you could take
tan(angle) = opposite/adjacent
tan(A) = a/b
tan(49) = a/15
a = 15*tan(49)
a = 17.255526 approximately
Furthermore,
sin(angle) = opposite/hypotenuse
sin(B) = b/c
sin(41) = 15/c
c*sin(41) = 15
c = 15/sin(41)
c = 22.863796 approximately
There is another trig function (cosine) that you could use. Also, you could use the pythagorean theorem once you know two sides of the right triangle.
The pythagorean theorem is a^2+b^2 = c^2
The answers have been confirmed with GeoGebra which is a useful geometry app.
1) A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4sqrt(7) - f feet high, how far away from the base of the building is the bottom of the ladder located? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the exact answer
Answer:
12√2.
Step-by-step explanation:
You can do this by the Pythagoras theorem:
20^2 = x^2 + (4sqrt7)^2 where x is the distance required.
x^2 = 20^2 - (4sqrt7)^2
= 400 - 112
= 288
x = √288
= √144 *√2
= 12√2.
2. G.CO.9 Look at the diagram below showing two parallel lines being cut
by two transversals. If m24 = 70 and m412 = 130, which of the following
statements are true? SELECT ALL THAT APPLY.
The statements that are true regarding the angles formed by the transversal and parallel lines are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
How to Find the Angles Formed by a Transversal and Parallel Lines?Given the following angle measures formed when two parallel lines ( being cut by two transversals:
m∠4 = 70° m∠12 = 130°Using relevant theorems, let's determine which of the statements are true:
Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.
m∠4 = m∠1
m∠1 = 70°.
m∠2 = 180 - m∠4 [linear angles theorem]
m∠2 = 180 - 70
m∠2 = 110°
m∠6 = m∠4 [base on the alternate interior angles theorem]
m∠6 = 70°.
m∠9 = 180 - m∠12 [based on the linear angles theorem]
m∠9 = 180 - 130
m∠9 = 50°
m∠16 = m∠12 [based on the corresponding angles theorem]
m∠16 = 130°
The statements that are true are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
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A weaver bought a bundle of grass of 50.00 dollars from which he made 8 mats if each mats was sold for 15.00 dollars find the percentage profit
The percentage profit is 140%
What is percentage?
Percentage can be described as the expression of a number in hundredth.
The formula for calculating percentage profit is
profit/cost price × 100
cost price= $50
selling price= $15
number of mats produced= 8
selling price of the mat= 15 × 8
= 120
Profit= selling price-cost price
= 120-50
$70
Therefore the percentage profit can be calculated as follows
= 70/50 × 100
= 1.4 ×100
= 140
Thus, the percentage profit is 140%
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103h=7(
7
2
−
7
3
h)−103
Answer:
I think its -10 or -8
Step-by-step explanation:
what is Rational Number
Answer:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.