The market price of the watch after a discount of 10% is $3500 .
In the question ,
it is given that
the price at which the trader sold the wrist watch = $3150
the amount of discount given by trader = 10% ,
we need to find the market price of the watch ,
let the market price of the watch be "x" .
so , the formula that can be used to calculate the market price is
selling price = market price - (discount percent)×(market price)
Substituting the values , we get
3150 = x - 10% of x
3150 = x - 0.10x ....because 10% = 0.10
(1 - 0.10)x = 3150
0.90x = 3150
Dividing both sides by 0.90 , we get
x = 3150/0.90
x = 3500
market price is $3500 .
Therefore , The market price of the watch after a discount of 10% is $3500 .
The given question is incomplete , the complete question is
A trader sold a wrist watch for $3150 after giving a 10% discount. Find the marked price of the watch ?
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DIG DEEPER! Using the figure, write an equation that represents z in terms of x and y.
Z=
We can write z = x + y using thee Exterior Angle Property of a Triangle
What is Exterior Angle Property of a triangle?
If a triangle side is constructed, the outside angle formed is equal to the sum of the two inside opposing angles.
Solution:
Using the Exterior Angle Property of a Triangle it can be observed that z = x + y
Sum of angles in a triangle is 180 degrees
w + x + y = 180 degree -----(1)
Also, using linear angle sum property
w + z = 180 degree -----(2)
From equation 1 and 2
w + x + y = w + z
Therefore, x + y = z
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What is the rate of change in the function?
Answer:
The rate of change, or slope, is 1/2.
To find the slope of a line, first, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!
Find the length of the third side. If necessary, round to the nearest tenth.
13
15
The length of the third side is 9
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) in familiar algebraic notation, a2 + b2 = c2
Given that
By using Pythagoras' theorem.
A^2+B^2=C^2
13 is c because it is the hypotenuse and across from the right angle
a is unknown and b is 15
A^2+12^2=15^2
A^2 +144 = 225
A^2 = 225- 144
A^2= 81
A = 9
Therefore the length of the third side is 9
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month of the gym
membership?
5. A train travels 16 miles in
20 minutes. At this rate, how
many minutes will it take to
travel 12 miles?
Answer: 15 minutes
Step-by-step explanation:
Let's make a proportion
16 miles - 20 minutes
12 miles - х minutes
Hence,
[tex]\displaystyle\\x=\frac{12(20)}{16} \\\\x=\frac{3(4)(4)(5)}{4(4)} \\\\x=3(5)\\\\x=15\ minutes[/tex]
Pleedadeees helppilyyy meeelili out
Answer:
Step-by-step explanation:
Answer: I Can't Read it
Step-by-step explanation: Its to far
During a session, a senate had a total of 112 Democrats and Republicans. There were 4 fewer Democrats than Republicans. How many members of each party were there?
Answer:
There are 54 Republicans, and 58 Democrats
Step-by-step explanation:
See the attached image
Write 480 ml as a fraction of 3 litres
Give your answer in its simplest form
Answer:
Step-by-step explanation:480/3000
Mike and Tom are trying to make weight for wrestling. Mike weighs 200 lbs and is
losing 2 Lbs a week. Tom weighs 160 lbs and is gaining 3 pounds a week. How many
weeks will both boys weigh the same?
Answer:
8 weeksStep-by-step explanation:
Let the number of weeks be x after which both boys have same weight.
Mike's weight after x weeks:
200 - 2xTom's weight after x weeks:
160 + 3xEquate both expressions and solve for x:
200 - 2x = 160 + 3x3x + 2x = 200 - 1605x = 40x = 8Answer:
After 8 weeks, both boys weigh same.
Step-by-step explanation:
Forming the equation,
→ 200 - 2x = 160 + 3x
Now the value of x will be,
→ 200 - 2x = 160 + 3x
→ -2x - 3x = 160 - 200
→ -5x = -40
→ x = -40/-5
→ x = 40/5
→ [ x = 8 weeks ]
Hence, the value of x is 8.
Reduce 75 litres of water by 15%
Answer:
63.75 litres
Step-by-step explanation:
the original amount of water is 100%
then a reduction of 15% = 100% - 15% = 85% of original
multiply 75 litres by 85% to obtain reduction
75 × 85%
= 75 × [tex]\frac{85}{100}[/tex] = 75 × 0.85 = 63.75
75 litres reduced by 15% = 63.75 litres
the hypotenuse of a right triangle is 11 inches. if one leg is 10 inches, find the degree measure of each angle
The measure of angles are
∠A = 24.61 degrees∠B = 90 degrees∠C = 65.39 degreesThe length of the hypotenuse of the right triangle = 11 inches
The length of the one leg = 10 inches
Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square
Then the equation will be
The length of the other leg = [tex]\sqrt{11^2-10^2}[/tex]
= [tex]\sqrt{121-100}[/tex]
= 4.58 inches
Therefore AC = 11 inches
AB = 10 inches
BC = 4.58 inches
The angle B = 90 degrees
Consider the angle A
cos θ = Adjacent side / hypotenuse
cos θ = 10 /11
θ = 24.61 degrees
Consider the angle C
cos θ = Adjacent side / Hypotenuse
cos θ = 4.58 / 11
θ = 65.39 degrees
Hence, the measure of angles are
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what is the volume of the following rectangular prism? 1 1/3 units 4 1/2 units2
Answer: 6 units^3
Step-by-step explanation:
using the volume of a rectangular prism formula:
L*W*H
We are already given the AREA which is the part L*W of the previous formula.
Now we multiply:
1 1/3 units * 4 1/2 units^2
Convert the fractions into 4/3 * 9/2 for an easier multiplication.
Resulting in 36/6 which is equivalent to 36 divided by 6.
Which gives us our answer of 6.
C is a circle with centre the origin.
A tangent to C passes through the points (-20, 0) and (0, 10)
Work out an equation of C.
You must show all your working.
The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).
Equation of circle:
Equation of the circle refer the position of a circle on a cartesian plane.
Given,
C is a circle with center the origin.
A tangent to C passes through the points (-20, 0) and (0, 10)
Here we need to find the equation of the circle C.
In order to find the equation of our line:
We have to identify the y-intercept which is (0,10).
Now, we need to find the gradient of our line which is:
Than can be calculated by,
=> (10 - 0) / (0- (-20))
=> 10/20 = 0.5
Now, the equation of our line is written as,
y = 0.5x + 10
But, here we know the center of our circle is the origin:
Which is in the following form:
=> x² + y² = r²
where r refers the radius
So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.
Then the equation of the circle is written as,
=> x² + (0.5x + 10)² = r²
When we simplify it, then we get,
=> x² + (0.5x + 10)(0.5x + 10) = r²
Now, we can expand and simplify the brackets to leave us with:
=> 1.25x² + 10x + 100 = r²
=> 1.25x² + 10x + 100 - r² = 0
Here we know that this is a tangent and so it only meets the circle at one point.
So, this equation should only have one solution.
Then it can be written as,
=> b² - 4ac = 0
=> 10² - 4(1.25)(100 - r²) = 0
When we simplify this one then we get the value of
=> r² = 90
Therefore the equation of the circle is x^2 + y^2 = 80.
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what is the square root of negative numbers. define the answer
Answer:
Although square roots are generally taken to be positive, a square root can be negative as a negative number multiplied by a negative number is always positive.
Step-by-step explanation:
In general, when someone is asking for a square root, they are seeking the positive value. This is called the principal square root. However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the principal square root, but the negative version. The negative square "squared" will give the same positive result as the principal square root, for instance,
3⋅3=9 and −3⋅−3=9.
Answer: The correct answer is 0. Negative numbers don't really have any square roots since a square cannot be negative it can only be positive or a 0.
Step-by-step explanation: I hope this helps!
Khadija is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4 people. Khadija reserved 2 more small rooms than large rooms, which altogether can accommodate 48 guests. Graphically solve a system of equations in order to determine the number of small rooms reserved, x, and the number of large rooms reserved, y.
There are 8 small rooms and 6 large rooms.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Let s be the number of small rooms reserved.
Let l be the number of large rooms reserved.
Each small room can accommodate 3 guests, hence s small rooms can hold 3s guests.
Each large room can accommodate 4 guests, so all large rooms can hold 5l guests.
Thus, the total number of guests
48 =3s+4l
3s+4l=48
3s+4l=48
as, Khadija reserved 2 more small rooms than large rooms,
So, s=l+2
s=l+2
Now, solving the equations
3s+5l= 54
s=l+2
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Directions: Tell whether each is a prime factorization. Write YES or NO in the
blank.
___________1. 3 x 2 x 9 x 5
___________2. 2 x 2 x 3 x 7
___________3. 5 x 7 x 3 x 2
___________4. 7 x 2 x 12 x 3
___________5. 3 x 2 x 7 x 2
___________6. 3 x 5 x 2 x 13
___________7. 5 x 3 x 21
___________8. 7 x 3 x 5 x 11
___________9. 2 x 5 x 4 x 2
___________10. 3 x 7 x 31 x 5
The longet ide of an acute triangle meaure 30 inche. The two ide are congruent, but their length i unknown. What i the mallet poible perimeter of the triangle, rounded to the nearet tenth?
The smallest possible perimeter of the triangle is, 72.4 inches.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.
As given the longest side of an acute triangle measure 30 inches.
The two remaining sides' combined length must be longer than the opposite side.
The sum of the two remaining sides should be greater than 30 inches if the side is 30.
Assume the other two sides add up to 31 inches.
So, The perimeter of a triangle is equal to the sum of its three sides, which comes to 30 + 31 = 64 inches.
Consequently, the circumference must be greater than 64 inches.
Hence, based on the possibilities, the triangle's smallest conceivable perimeter is 72.4 inches.
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Write a numerical expression to model the situation Kristen read her book for 2 hours after school.Then she read for another hour before she went to sleep.
The numerical expression to model the situation when Kristen read her book is 2 + 1.
What is a numerical expression?A numerical expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, Kristen read her book for 2 hours after school, then she read for another hour before she went to sleep. The expression will be:
= 2 + 1
= 3
She read for 3 hours.
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suppose that a set of scores has a mean of 5 and standard deviation of 2. what score corresponds to a z score of -2.0?
The set of scores has a mean of 5 and a standard deviation of 2. The score which corresponds to a z score of -2.0 is 1.
Given in the question,
Mean (m) = 5
Standard deviation σ =2
Z-score = -2
The score x,
= Z = x - m / σ
= -2 = x - 5 / 2
= -4 = x - 5
= x = 1
Standard deviation in statistics means the amount of dispersion or variations in the set of values. A lower standard deviation means the value is closer to the mean while a higher standard deviation means the value is farther away from the mean.
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The circumference of a circle is 15 in. What is the area, in square inches? Express
your answer in terms of pie
Answer:
The area is 225/(4π) in²Step-by-step explanation:
Area of circle equation:
A = πr²Circumference of circle equation:
C = 2πrGivenC = 15 inTo Find Area of circleSolutionUse circumference equation to find the radius:
2πr = 15r = 15/(2π)Find the area:
A = π*[15/(2π)]² = 225/(4π)A biker cycles 9 miles in 2/3 of an hour. Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours 3 hours and 3.5 hours
Answer:
27 miles, 40.5 miles, and 47.25 miles
Step-by-step explanation:
9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5
We now have a unit rate which is 13.5 miles each hour.
Now lets solve for 2 hours.
13.5*2= 27 miles
Now lets solve for 3 hours.
13.5*3=40.5 miles
Now lets solve for 3.5
13.5*3.5= 47.25 miles
Write an inequality using variables x and y whose graph is described by the given information. The points (2,5) and (-3,-5) lie on the boundary line. The points (6,5) and (-2,-3) are solutions of the inequality.
The inequality using variables x and y which satisfy the points are; y>-3x+3.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given that the points (2,5) and (-3,-5) lie on the boundary line.
The system of inequality is given by:
y>-3x+3-
Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies the inequality.
a) (6, 5)
when x=6 and y= 5
then we have:
y>-3x+3
6 > -3×5 + 3
6>- 15+3
5 > -12
This means that the point will lie in the solution set.
Also, (-2, -3) when x= -2 and y= -3
then we have:
5 > -3×(-2) + 3
5> 6 + 3
5> 9
Hence, the inequality using variables x and y which satisfy the points are; y>-3x+3.
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PLEASE HURRY
I am having trouble
Answer:
12
Step-by-step explanation:
(5+7)/7=12/7.
Green box = 12.
Vertical asymptote at x=5 and x=-5. X intercept at (2,0) (-1,0) Y intercept at (0,4). Write an equation for a rational function with the given information. I'll gave brainillst!!!
The rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
What is rational function equation?
A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
The function has vertical asymptote at x = 5 and x = -5
So , the denominator of the fraction of rational function contains the terms (x - 5) and (x + 5)
The x intercept is at ( 2 , 0 ) and ( -1 , 0 )
The y intercept is at ( 0 , 4 )
So , the numerator of the fraction of the rational function contains the terms
( x- 2 ) and ( x + 1 )
So , the rational function is of the form
f ( x )=P( x ) / Q( x )
f ( x ) = A ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
Now , we have the y intercept at ( 0 , 4 )
So , f ( 0 ) = 4
Substituting the value of f ( 0 ) in the above equation , we have
4 = A ( 0 + 1 ) ( 0 - 2 ) / ( 0 - 5 ) ( 0 + 5 )
4 = A ( -2 ) / ( -25 )
4 = 2A / 25
Multiply 25 on both sides , we get
2A = 100
Divide by 2 on both sides , we get
A = 50
Therefore , the rational function becomes
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
Hence , the rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
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Find the value of y.
M
51
12y+7
L
Q
51
43
P
Answer:
y = 3Step-by-step explanation:
Given is a kite because:
one pair of congruent sides ML and LP,second pair of sides also congruent since OQ is perpendicular bisector of angle Q, making MPQ an isosceles triangle, hence MQ = QP.Since MQ and QP are congruent, set equation and solve for y:
12y + 7 = 4312y = 36y = 3Answer:
y = 3
Step-by-step explanation:
Forming the equation,
→ 12y + 7 = 43
Now the value of y will be,
→ 12y + 7 = 43
→ 12y = 43 - 7
→ 12y = 36
→ y = 36/12
→ [ y = 3 ]
Hence, the value of y is 3.
Write an equation of the line that passes through (-3,-3) and is perpendicular to the line 3x+4y=8
Answer:
[tex]5x-4y=-3[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Triangle XYZ has vertices X: (0,2) Y: (3,8), and Z: (6,2). Show that the triangle is isosceles by determining the length of each side.
Please help!!!
Sides XY and YZ are both equal to √45 units, therefore, triangle XYZ is an isosceles triangle.
What is an Isosceles Triangle?If a triangle has two side lengths that are equal to each other, the triangle is called an isosceles triangle. Therefore, two of the sides of an isosceles triangle must be equal.
Given the vertices of triangle XYZ as:
X(0, 2)
Y(3, 8)
Z(6, 2).
Find the length of each side using the distance formula, [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
XY = √[(3−0)² + (8−2)²]
XY = √45
XZ = √[(6−0)² + (2−2)²]
XZ = √36
XZ = 6
YZ = √[(6−3)² + (2−8)²]
YZ = √45
The triangle has two equal sides YZ and XY, therefore it is an isosceles triangle.
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Write the equation of a line that i parallel to y=1/2x4 and goe thru the point(-3,4)
1000 to the power of m divided by 100 to the power of n can be written as 10 to the power of z.
Express z in terms of m and n.
Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]
Exponentiation is the process of expressing large numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself. For example, 6 is multiplied by itself four times, yielding 6 6 6 6. This is written as [tex]6^{4}[/tex]. The exponent is 4 and the base is 6.
Given that 1000 to the power of m divided by 100 to the power of n
When powers of the equal base are divided, the same base is placed and the exponents are subtracted, which is an important mathematical property of powers.
Then, as powers of the same base, we can write 1000m and 100n:
1000m = [tex](10^{3})^{m}[/tex] = [tex]10^{3m}[/tex]
100n= [tex](10^{2)^{n} }[/tex] = [tex]10^{2n}[/tex]
Now we perform the division of powers of the same base (10)
103m/102n
= 103m-2n
Finally
103m-2n = 10z
z = 3m-2n
Therefore Z in terms of m and n is z = [tex]3^{m} -2^{n}[/tex]
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Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
The rule that describes the function is (c) Output = (0.5)(Input) + 1.5
How to determine the rule?The points on the coordinate plane are given as
(negative 1, 1), (1, 2), (3, 3), (5, 4)
Express as numbers
So, we have
(-1, 1), (1, 2), (3, 3), (5, 4)
Divide the input values by 2
So, we have
0.5(Input) => (-1/2, 1), (1/2, 2), (3/2, 3), (5/2, 4)
Add 1.5 to the input values
So, we have
0.5(Input) + 1.5 => (1, 1), (2, 2), (3, 3), (4, 4)
So, we have
Output = 0.5(Input) + 1.5
Hence, the equation is (c)Output = 0.5(Input) + 1.5
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does the graph of a power function and the graph of its inverse demonstrate
symmetry? Explain your reasoning.
Yes, the graphs of a power function and its inverse are symmetric about the line y=x.
What is an inverse function?
A function that "undoes" another function is called an inverse. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.
What is a power function?
Any function where y = xⁿ, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here,
The graphs of self-inverse functions are symmetrical about the line y=x. The domain of a one-to-one function f is the same as the range of its inverse f⁻¹ and the range of f is the same as the domain of f⁻¹.
Hence, the graphs of a power function and its inverse are symmetric about the line y=x.
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