The Perimeter of the Rectangle is 144cm;
What is the Perimeter of a Rectangle?
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
According to the question
Let the length of the rectangle be x cm;
So, The breadth of the rectangle will be: (x+2) cm;
And, we have the diagonal = 52 cm;
So,
we can use the Pythagoras triangle to find the value of x cm;
⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]
⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]
⇒[tex]2x^{2} +4x = 2700[/tex]
⇒[tex]2x^{2} +4x - 2700 =0;[/tex]
By solving the above equation, we get:
x = 35 cm;
So, the length of the rectangle = is 35 cm;
Breadth of the rectangle = 37 cm;
and
Perimeter of the Rectangle = 2(35 + 37) cm;
The perimeter of the Rectangle = = 144 cm;
Hence,
The perimeter of the Rectangle = = 144 cm;
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A bookstore had 150 copies of a magazine. Yesterday the bookstore sold 2/5 of these copies. How many copies were sold yesterday
Answer:
Hi
Step-by-step explanation:
so the question is asking what is 2/5 of 150
if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.
does 150 split up into 5 even parts??
hmmm you probably are thinking, 15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30 :)
2 time 30 = 60
so there is how to figure out the answer and , the answer 60 :)
Q2.
I am thinking of two numbers.
The first number is x
The second number is 7.5 more than x.
Write down an expression, in terms of x for the second number.
For the two numbers,
the product is double the sum.
Work out the numbers I could be thinking of.
Give both possible pairs of answers.
Answer:
second number = (x + 7.5)
Since the product of the two numbers is double of their sum,
x(x + 7.5) = 2(x + x + 7.5)
x² + 7.5x = 2(2x + 7.5)
x² + 7.5x = 4x + 15
x² + 7.5x - 4x - 15 = 0
x² + 3.5x - 15 = 0
∴ x = -6 or 2.5
∴ second number
= -6 + 7.5 or 2.5 + 7.5
= 1.5 or 10
∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.
A bank employee notices an abandoned checking account. The bank charges a monthly fee for the account modeled by the function
A(m)=184-8m, where M is in months and A(m) is in dollars.
What is the domain of the function within the context? Use inequality Notation.
The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23
How to find the domain of the functionThe equation is linear equation in the slope intercept form as
y = mx + c
where
m = slope = -8
c = intercept = 184
x = input variables = m
y = output variables = A(m)
The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0
0 = 184 - 8m
8m = 184
m = 23
The maximum value of m is 23 hence the domain is m ≤ 23
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A pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins. If there are 38 pirates on the ship and they split the coins evenly, how many coins did they collect?
A. 10
B. 11
C. 380
D. 418
The number of coins that the pirates collect is A. 10.
How to calculate the value?From the information, the pirate ship found a treasure chest that contained 127 gold coins and 253 silver coins and there are 38 pirates on the ship.
The number of coins that way person will get will be:
=>Total coins / Number of pirates
= (253 + 127) / 38
= 380 / 38
= 10
Each person gets 10 coins.
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help please and thankyou
The value of x will be 24.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
For a given right triangle, the expression is,
⇒ sin (3x - 7) = cos (x + 1)
Now,
Solve for x as;
The expression is,
⇒ sin (3x - 7) = cos (x + 1)
Since, sin x= cos (90 - x)
So, We get;
⇒ sin (3x - 7) = cos (x + 1)
⇒ cos (90 - (3x - 7)) = cos (x + 1)
⇒ 90 - (3x - 7) = (x + 1)
⇒ 90 - 3x + 7 = x + 1
⇒ 97 - 3x = x + 1
⇒ 97 - 1 = x + 3x
⇒ 96 = 4x
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24
Thus, The value of x will be 24.
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mario tiene una cinta de 6 m y su amiga beatriz tiene una cinta de 8 m ¿cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz?
La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.
¿Como se comparan las longitudes?
Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.
Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:
6m/8m = 0.75
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3.6 x 10^7 + 2.1 x 10.7=
a) 14
b) 5.7
c) 3.6
d) none of these
The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:
= 3.6 x 10^7 + 2.1 x 10.^7
= 5.7 × 10^7
Therefore, the correct option is D.
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Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
1. x-int: (-2,0) , (5,0)
P (3,6)
Answer:
Below
Step-by-step explanation:
a(x-p)(x-q) p = -2 q = 5
a ( x- - 2)(x - 5) sub in the values of the point given (3,6) to calculate 'a'
6 = a (3+2)(3-5)
a = -6 /10 = - 3/5
y = -3/5 (x+2)(x-5)
Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-2, 0) and (5, 0) then:
p = -2q = 5Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-2))(x-5)[/tex]
[tex]\implies y=a(x+2)(x-5)[/tex]
To find a, substitute the given point on the curve P (3, 6) into the equation:
[tex]\implies 6=a(3+2)(3-5)[/tex]
[tex]\implies 6=a(5)(-2)[/tex]
[tex]\implies 6=-10a[/tex]
[tex]\implies a=\dfrac{6}{-10}[/tex]
[tex]\implies a=-\dfrac{3}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]
[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
What translation is made from f(x) → f(x) + 6? sliding it up reflection across the y-axis rotation around the origin reflection across the x-axis
The translation made from f(x) → f(x) + 6 is sliding it up
what is translation in geometry?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.
A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Any translation in a Euclidean space is an isometry.
the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units
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HELP ME PLEASE, I NEED TO FINISH THIS MATH PROBLEM!
Anna is working two summer jobs, making $9 per hour washing cars and $12 per hour landscaping. Last week Anna worked a total of 7 hours and earned a total of $78. Determine the number of hours Anna worked washing cars last week and the number of hours she worked landscaping last week.
ANSWER: ANNA WORKED _____ HOURS WASHING CARS AND ______ HOURS LANDSCAPING.
Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping
Step-by-step explanation:
i personally used a guess and check method.
i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39
i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39
39 + 39 = $78
Daniela bakes 36 cookies and gives 2 cookies to her friends
anwser: she has 34 cookies left
Use a quadratic equation to find two real numbers with a sum of 31 and a product of 210?
The quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
According to the question,
We have the following information:
The sum of roots of a quadratic equation = 31
The product of roots of a quadratic equation = 210
We know that the standard form of the quadratic equation is given as follows:
[tex]ax^{2} +bx+c = 0[/tex]
Now, the sum of roots is -b/a and the product of roots is c/a.
So, we have the following expressions:
-b/a = 31
b = -31 and a = 1
c/a = 210
c = 210 and a = 1
So, the equation will be:
[tex]x^{2} -31x+210 = 0[/tex]
Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
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Given the points A(-5,-5) and B(7, 1), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 1:5, but not necessary In that order, give two possible coordinates of point P. Graph segment AB and P in the coordinate plane.
The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
What is internal division?
When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.
The division is internally because point P lies on the line as given in the question.
The formula for the internal division is as follows:
[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]
Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].
Substute all value to obtain the coordinates.
[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]
Hence, the first cordinate is (5,0).
As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.
Now, m=5 and n=1.
Again substitute all values in to find the new coordinate.
[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]
Hence, another coordinate is (-3,-4).
Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
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In this problem we determine the first time after 10 o'clock at which the minute hand and the hour hand of a clock point in the exact same direction ( meaning when they are " on top of" each other). See if you can find the time on your own before reading the following steps. ( Assume that both hands move continously. For example, from 10 o'clock to 11 o'clock, the hour hand smoothly and gradually moves from pointing at the 10 to pointing at the 11.)
a) Let m be the number of mintues after 10 o'clock at which the minuet hand and hour hand are pointing in the same direction. In terms of m, trhough what fraction of hte entire face of the clock has the minute hand traveled during the m minutes after 10 o'clock?
b) In terms of m, what fraction of hte distance from 10 to 11 has the hour hand traveled during the m minutes after 10 o'clock?
c) Trough what farction of the entire clock's face doe sthe hour hand travel during the m minutes after 10 o'clock?
d) At what exact time do the minute hand and hour hand point in the same direction?
( GIVE BRAINLIST IF CORRECT AND ANSWER!! )
Answer:
a) 1:25 b) 2:06 c) 5:00 d) 4:10
Step-by-step explanation:
The graph below shows distance over time.
A student is walking to class. The student increases their speed for 20 seconds for 3 meters. The student then walks a constant speed for 5 seconds and then increases their speed the last 3 meters to class.
Which of these situations could be represented by this graph?
A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).
In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.
By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).
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Complete Question:
The graph below shows distance over time. Which of these situations could be represented by this graph?
answer choices
A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.
< GRADES / 2022 RATIOS AND PROPORTIONS UNIT TEST Q21
21
What percent represents the shaded part of the hundredths grid shown?
Answer: A) 0.05%
Step-by-step explanation: Converting the shaded area of the hundredths grid to a fraction would be 5/100 (or 1/20 simplified). Then convert 5/100 to a percentage by calculating 5 ÷ 100, which is 0.005%, therefor the answer is A.
Find the equation of the line passing through the given point and parallel to the given line.
( 1, 9 ), y = 4x + 2
( 5 , 2 ), y = -2x + 7
The line equation passing through the given points and parallel to the given lines are:
Line 1: y=-4x+13...(i)
Line 2: y=2x-12...(ii)
Line 1
The first line is passing through point (1,9) and parallel to the y=4x+2 line.
Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=4x+2 has:
ay = bx + c, m= -b/a
y=4x+2, m=-4
We could use the line equation formula, where:
y-y1 = m (x-x1)
we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:
y-9 = -4(x-1)
y-9=-4x+4
y=-4x+13...(i)
Line 2
The first line is passing through point (5,2) and parallel to the y=-2x+7 line.
Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=-2x+7 has:
ay = bx + c, m= -b/a
y=-2x+7, m=-2
We could use the line equation formula, where:
y-y2 = m (x-x2)
we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:
y-2 = 2(x-5)
y-2 = 2x-10
y=2x-12...(ii)
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HELP ASAP GIVING BRAINLIEST
Answer: C
Step-by-step explanation:
Kenya went to the convenience store to buy some snacks. She spent a total of $12. 00 on soda and candy. The soda cost $3. 00 and each candy bar cost $1. 50. If kenya bought one soda, how many candy bars did kenya buy?.
The number of candy bar that she bought is 6
The total amount that she spend for soda and candy= $12
The cost of one soda = $3
The cost of one candy bar = $1.50
Number of soda that she bought = 1
Consider the number of candy bar that she bought as x
Then the equation will be
3×1 + 1.50 × x = 12
Multiply the terms
3 + 1.50x = 12
Move 3 to right hand side of the equation
1.50x = 12 - 3
1.50x = 9
Move 1.50 to the right hand side of the equation
x = 9 / 1.50
x = 6
Hence, the number of candy bar that she bought is 6
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This is part B to my last question
The y-intercept of the graph of the function g(n) represents the height of the flower.
We are given:
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.
g(n) = 10(1.02)^n
which is an exponential function.
We need to find what the y-intercept of the graph of the function g(n) represents.
We have the exponential function;
g(n) = 10(1.02)^n
where,
x-coordinate of the graph represents the number of days.
y-coordinate of the graph represents the height of the flower.
Thus, the y-intercept of the graph of the function g(n) represents the height of the flower.
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If a-b=-5 and ab=0 then find a³-b³
What’s the answer?
If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.
In the question ,
it is given that ,
the value of a - b = -5 and ab = 0
we need to find the value of the expression (a³-b³) ,
we know the identity that a³-b³ = (a - b)(a² + b² + ab)
we first need the value of a² + b² .
given that a - b = -5
squaring both the sides , we get
(a - b)² = 25
a² + b² - 2ab = 25
given ab = 0, so a² + b² = 25
Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,
we get ,
a³-b³ = (-5)(25 + 0)
a³-b³ = -5 × 25
a³-b³ = -125
the answer is -125 .
Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.
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1. Find the y-intercept of the line paing through the point A (3, -2) and B (-1, 3). (5 pt)
What is the constant rate of change in this equation? Write only the number as your answer y=5x + 12
Answer:
The slope (constant rate of change) is 5.
Does y vary directly with x? If it does, what is an equation for the direct variation?
The variable y varies directly with x and the variation equation is (b) y = -1/2x
How to determine the equation of the variation?The graph represents the given parameter
On the graph, we can see that:
The values of x are divided by -2 to get y
This means that the graph represents a direct variation
Recall that we stated that:
The values of x are divided by -2 to get y
This means that the constant of variation is -1/2
The direct variation equation is represented as:
y = kx
Where k represents the constant of variation i.e. k = -1/2
Substitute the known values in the above equation So, we have the following equation
y = -1/2x
Hence, the equation of variation is y = -1/2x
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find the annual salary of a person who is paid $835.50 per week
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5 × 52 = 43446
Find the perimeter of triangle ABC. Round your answer to two decimal places.
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-7}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) ~\hfill AB=\sqrt{(~~ 3- (-7)~~)^2 + (~~ -8- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 10)^2 + ( -10)^2} \implies \boxed{AB=\sqrt{ 200 }}[/tex]
[tex]B(\stackrel{x_1}{3}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-9}) ~\hfill BC=\sqrt{(~~ -4- 3~~)^2 + (~~ -9- (-8)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( -7)^2 + ( -1)^2} \implies \boxed{BC=\sqrt{ 50 }} \\\\\\ C(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-9})\qquad A(\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -7- (-4)~~)^2 + (~~ 2- (-9)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (11)^2} \implies \boxed{CA=\sqrt{ 130 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\LARGE perimeter}}{\sqrt{200}~~ + ~~\sqrt{50}~~ + ~~\sqrt{130}} ~~ \approx ~~ \text{\LARGE 32.61}[/tex]
What is 125 in simplest form?
Answer:
125 in simplest form is 1/8.
Step-by-step explanation:
Jon needs to buy a backpack and several folders for school. If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each. Write and solve an inequality to find the number of folders Jan would need to buy for the Supply Guys to be the cheaper option
Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality is true.
Inequality in this caseIn this case, you know that:
If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each.The Supply Guys is the cheaper option.Being "x" the number of folders, the inequality that expresses the previous relationship is
45 + 0.45x > 50.40 + 0.15x
Solving:
0.45x - 0.15x > 50.40 -45
0.30x> 5.4
x> 5.4÷ 0.3
x> 18
Finally, the number of folders Jan would need to buy is more than 18.
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Riley found a receipt for a pair of jeans for $142.95, tax included. If the sales tax rate was 6%, what was the list price of the jeans? Round your answer to the nearest cent.
Answer:
$134.86
Step-by-step explanation:
Let the original price before tax be x.
A whole amount is 100% of the amount, so x is 100% of the original price without tax.
The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.
106% of x = $142.95
106/100 × x = 142.95
1.06x = 142.95
x = 142.95/1.06
x = $134.86
Answer: $134.86
help please!!! asap!
Answer:
The registration fee is $28
Step-by-step explanation:
5,600/100=56 which is 1% of 5,600.
56/2=28 which is 0.5% of 5,600.
;)
Answer: $28
Step-by-step explanation:
you calculate what 0.5 percent is of 5,600 :)