Answers
The solutions using the relevant theorems are:
13. x = −3 or x = 4
14. x = 12
15. x = 12
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6
What is the Triangle Midsegment Theorem?The midsegment of a triangle that joins two sides of a triangle divides the two sides proportionally based on the triangle midsegment theorem.
What is the Angle Bisector Theorem?
The angle bisector of a triangle, according to the angle bisector theorem divides the opposite angles sides in a proportional manner.
What is the Parallel Lines and Proportionality Theorem?The theorem states that when three or more lines that are parallel is cut across by two transversals, they are divided by the transversal proportionally.
13. Apply the angle bisector theorem:
x/3 = (x + 4)/(x + 2)
Cross multiply
x(x + 2) = 3(x + 4)
x² + 2x = 3x + 12
x² + 2x - 3x - 12 = 0
x² - x - 12 = 0
Factorize
x = −3 or x = 4
14. Apply the angle bisector theorem:
16/x = 12/9
x(12) = (16)(9)
12x = 144
x = 12
15. Apply the angle bisector theorem:
(x - 4)/6 = x/9
9(x - 4) = 6x
9x - 36 = 6x
9x - 6x = 36
3x = 36
x = 12
16. Apply the triangle midsegment theorem:
3x/(x + 4) = (x - 1)/(x - 2)
Cross multiply
3x/(x + 4) = (x - 1)/(x - 2)
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² + 3x - 4 - 3x² + 6x = 0
-2x² + 9x - 4 = 0
Factorize
x = 1/2 or x = 4
17. Apply the Parallel Lines and Proportionality Theorem:
(x + 3)/(2x + 2) = (2x + 2)/(4x - 2)
Cross multiply
4x² + 10x - 6 = 4x² + 8x + 4
4x² + 10x - 6 - 4x² - 8x - 4 = 0
2x - 10 = 0
2x = 10
x = 5
18. Apply the angle bisector theorem:
(2x + 3)/x = (x + 4)/(x - 2)
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize
x = −1 or x = 6
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Related Questions
The first quartile of the dataset {1, 2, 3, 4, 5, 6} is _______. (give your answer as a whole number.
Answers
The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.
Given data set: {1,2,3,4,5,6}
Median of the given data set =3.5
The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.
Thus, the first quartile is 2.
The quarter divides the distribution into four groups and calculates the range of values above and below the mean.
A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.
The interquartile range, a measurement of variation around the median, is calculated using quartiles.
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Please help and explain.
Answers
Answer:
B
Step-by-step explanation:
It's B
Answer:
Option B
Step-by-step explanation:
The equation is:
[tex]y=10-2x[/tex]
when x=2
[tex]y=10-2(2)010-4=6[/tex]
When x = 3
[tex]y=10-2(3)=10-6=4[/tex]
When x=4
[tex]y=10-2(4)=10-8=2[/tex]
Hope this helps
I really need help ASAP! thx
Let f(z)=z-8 and g(z)=4z-9
Find (f+g)(2)
Answers
Answer:
(f +g)(2) = -7
Step-by-step explanation:
Functions are added by adding their values.
Application(f +g)(2) = f(2) +g(2)
= (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2
= -6 +(-1)
(f +g)(2) = -7
No matter what the value of s, 1s? is equal to the
value of s.
Answers
The complete statement is no matter what the value of s, √s² is equal to the absolute value of s?
How to complete the blank?The statement is given as:
No matter what the value of s, √s² is equal to the ______ value of s?
The above statement can be split as follows:
No matter what the value of s, √s² is equal to the ______ value of s?This means that, irrespective of the value of s, what would be the value of the square root of the square of s.
Assume that s is negative (say s = -2), the value of the square root of the square of s would be
√s² = √(-2)²
Evaluate the square
√s² = √4
Evaluate the square root
√s² = 2
See that s = 2 is the positive equivalent or absolute value of s = -2
Now, assume that s is positive (say s = 4), the value of the square root of the square of s would be
√s² = √4²
Evaluate the square
√s² = √16
Evaluate the square root
√s² = 4
See that s = 4 is the positive equivalent or absolute value of s = 4
Hence, the complete statement is no matter what the value of s, √s² is equal to the absolute value of s?
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Complete question
No matter what the value of s, √s² is equal to the ______ value of s?
graph: g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2
Answers
[tex]g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2[/tex]
generate by: Amplitude:5 Period:4
Phase shift:(3 to the right) Vertical shift:-2
x=3,g(x)= 3
x=4,g(x)= -2
x=5,g(x)= -5
x=6,g(x)= -2
x=7,g(x)= 3
the graph is like cos(x)
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If p(x) = x² - 1 and g(x)= 5(x-1), which expression is equivalent to (p - q)(x)?
A.5(x-1)-x²-1
B.(5x-1)-(x² - 1)
C.(x²-1)-5(x - 1)
D.(x²-1)-5x - 1
Answers
The expression which is equivalent to the required expression (p - q)(x) is; Choice C; (x²-1)-5(x - 1).
Which expression is equivalent to (p - q)(x) given that p(x) = x² - 1 and g(x)= 5(x-1)?It follows from the task content that the premise functions as given in the task content are;
p(x) = x² - 1
g(x)= 5(x-1).
Consequently, the required expression for the function operations; (p - q)(x) is simply;
p(x) - q(x) and is equivalent to;
(x² - 1) - 5(x - 1)
Therefore, the expression which is equivalent to the required expression (p - q)(x) is Choice C; (x²-1)-5(x - 1).
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Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s?
Answers
The distance between points S' and S is 2.5 units.
What is proportionality theorem in triangles?If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
Given that,
line segment ST is dilated to create line segment S'T' using the dilation rule DQ.
Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5 units, SS' = x units.
We need to find the value of x, the distance between points S' and S.
Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.
We know that the corresponding sides of two similar triangles are proportional.
So, from ΔSTQ and ΔS'T'Q, we get
[tex]\frac{SQ}{S'Q} =\frac{TQ}{T'Q}[/tex]
[tex]\frac{SQ}{SQ+S'S} =\frac{TQ}{TQ+T'Q}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{1.2+1.5}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{2.7}[/tex]
[tex]\frac{2}{2+x} =\frac{12}{27}[/tex]
[tex]\frac{1}{2+x} =\frac{6}{27}[/tex]
12+6x = 27
6x = 15
x = 2.5
Hence, Thus, the required value of x is 2.5 units.
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Find the length of the radius of a circle with a center at –7 2i and a point on the circle at 33 11i.
Answers
The length of the radius of a circle exists 41 units.
How to estimate the length of the radius of a circle?
Given: The center exists at -7+2i and a point in the circle at 33+11i.
The radius of the circle exists given by the following formula;
The radius of the circle [tex]$=\sqrt{x^{2}+y^{2}}$[/tex]
The center exists at -7 + 2i and a point in the circle at 33 + 11i.
[tex]$&x(33-(-7)), y(2 \mathrm{i}-11 \mathrm{i}) \\[/tex]
simplifying the equation, we get
[tex]$&\mathrm{x}(33+7), \mathrm{y}(-9 \mathrm{i}) \\[/tex]
[tex]$&\mathrm{x}(40), \mathrm{y}(-9(-1)) \\[/tex]
[tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex]
The center of the circle exists at [tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex].
The length of the radius of a circle exists,
Radius [tex]$}=\sqrt{x^{2}+y^{2}} \\[/tex]
substituting the values of x and y, we get
Radius[tex]$}=\sqrt{40^{2}+9^{2}} \\[/tex]
Radius [tex]$}=\sqrt{1600+81} \\[/tex]
Radius [tex]$=\sqrt{1681} \\[/tex]
Radius = 41 unit
Therefore, the length of the radius of a circle exists 41 unit.
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QP=
Help please thanks so much
Answers
Answer:
QP = | a - d |
Step-by-step explanation:
since the y- coordinates of P and Q are equal , both b
then PQ is the absolute value of the difference of the x- coordinates, that is
QP = | a - d | = | d - a |
HELP PLS WHAT IS X
Darn
Answers
Answer:
x = 55°
Step-by-step explanation:
x , 35° , 90° lie on a straight line and sum to 180° , that is
x + 35° + 90° = 180°
x + 125° = 180° ( subtract 125° from both sides )
x = 55°
A regular octagon has side lengths of 8 centimeters. what is the approximate area of the octagon?
Answers
Answer:309
Step-by-step explanation:
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
Answers
The approximate year at which two revenues were equal is; 7.5 years
How to interpret Revenue Graphs?From the graph attached, we see that in the year 10, the revenue for printed ads was 2 million dollars & 3 million dollars for printed ads and online ads revenue respectively.
Thus, printed ad. Revenue line equation is;
(y - 2) = (3 - 2)(x - 10)/(0 - 10)
y - 2 = (x - 10)/-10
x - 10 = -10(y - 2)
x - 10 = -10y + 20
x - 10 = -10y + 20
x + 10y = 30 -----(1)
At x = 12 years from the graph, we have;
12 + 10y = 30
10y = 18
y = 1.8
Thus, online ad. Revenue line equation is;
(y - 0) = ((3 - 0)/(10 - 0))(x - 0)
y = 3x/10
10y = 3x
10y - 3x = 0 -----(2)
At x = 12, we have;
10y = 3*12
10y = 36
y = 3.6
In year '12' the online ad revenue got doubled as that of printed ad revenue and afterward more than doubled.
B) The approximate year at which two revenues were equal is gotten by solving equation 1 and 2 simultaneously to get;
x = 7.5
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Joel wanted his mom to buy a super-sized box of his favorite cereal, but his mom didn't think it would fit in her cupboard. The box had a volume of 6900 cm3, and the base was 23, the depth, 10. How high was it?
Answers
The height of the box would be = 30cm.
How to calculate the height of the box from the given volume?The volume of the box = 6900 cm3
The base of the box = 23 cm
The depth of the box = 10cm
Therefore the height of the box can be gotten from the formula used to calculate the volume of the box. That is;
Volume = base×depth×height
6900 = 23×10×h
make h the subject of formula;
height = 6900/230
= 30cm
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exponential growth and decay real-world word problems
Answers
The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.
What is exponential growth?Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.
There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.
One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.
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suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.
a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464
Answers
In quadrant IV, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258[/tex]
Then by the definition of tangent,
[tex]\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}[/tex]
What is the slope?
What is the slope?
What is the slope?
What is the slope?
What is the slope?
Answers
Answer:
okay it's name is Muhammad Deco alfansia ( ◜‿◝ )
Answer:
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.
Step-by-step explanation: Hope this helps you!
Victor spent 1/2 of his salary on rent, 1/4 of the remainder on food and saved \mbox{Sh 1500). How much was his salary?
Answers
Nag basa nito walang jõwa
Estimate √50 to the hundredths place.
Answers
Answer:
7.07
Step-by-step explanation:
Answer:
7.07
Step-by-step explanation:
Hello!
Let's find two perfect square numbers that are directly before and after 50.
[tex]\sqrt{49} < \sqrt{50} < \sqrt{64}[/tex][tex]7 < \sqrt{50} < 8[/tex]Since the square of 7 is the closest, we can use that as our whole number.
To find the decimal...49 is 1 away from 50, and 64 is 14 away. Rewriting it as a fraction and we get [tex]\frac{1}{14}[/tex]. The decimal is 0.07142857142.
Now, put 7 and 0.07142857142 together and we get 7.07142857142. Rounding that, we get 7.07.
The real value of Root 50 is 7.071067811865475, so the decimals were really close.
help me with this.
Calculate angles in a triangle
Answers
Step-by-step explanation:
Total Angle in a triangle is 180°
so D = 140 + 25 = 165°
D = 190° - 165° = 15°
Your answer is 15°.
Answer:
angle d = [tex]\boxed{15}^ {\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠d + 25° + 140° = 180°
⇒ ∠d + 165° = 180°
⇒ ∠d = 180° - 165°
⇒ ∠d = 15°
What is the area of the triangle shown below?
Answers
Answer: the area of the triangle is 5.
Step-by-step explanation:
[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]
What is a31 of the
arithmetic sequence for
which a5 = 12.4 and
ag = : 22.4?
Answers
The value of a₃₁ of the arithmetic sequence exists 77.4.
How to find the value of a₃₁ of the arithmetic sequence?Given: a₅ = 12.4 and a₉ = : 22.4
For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists
where d = common difference
a₅ = 12.4,
a₁ + 4d = 12.4 .........(1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 .........(2)
Subtract (1) from (2), we get
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Dividing throughout by 4, we get
d = 2.5
From (1), we get
a₁ = 12.4 - 4 [tex]*[/tex] 2.5 = 2.4
a₃₁ = 2.4 + 30 [tex]*[/tex] 2.5 = 77.4
Therefore, the correct answer is a₃₁ = 77.4
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Write an expression containing x2-terms, x-terms and constants. The
x2-terms should combine to −2x2 the x-terms should sum to 3x,
and the constants should sum to 3.
Answers
[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 12^{\circ}. At some later time, the crew measures the angle of elevation from point B to be 8^{\circ}. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Bearing is a topic that deals with distance and measure of the angle in locating the position of an object. The distance required in the question is 692 feet.
Bearing is a topic that relates the distance and measure of an angle so as to determine the accurate position of a given object. The angle with respect to the object is measured clockwise with respect to the North pole.
From the first part of the question, the height of the lighthouse, h, can be determined by applying the trigonometric function. So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 12 = [tex]\frac{h}{1315}[/tex]
h = Tan 12 x 1315
= 279.51
Thus the height of the lighthouse is approximately 280 feet.
Thus, let the distance between points A and B be represented by l. This implies that the distance from point B to the lighthouse is (l + 1315) ft.
So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 8 = [tex]\frac{280}{(l+1315)}[/tex]
Tan 8 x (l + 1315) = 280
0.141l + 185.415 = 280
0.141 l = 280 - 185.415
= 97.585
l = [tex]\frac{97.585}{0.141}[/tex]
= 692.092
l = 692 feet
Therefore, the distance between points A and B is 692 feet.
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A construction worker is pouring concrete stairs. The first step requires 1.7 cubic feet of concrete, and the first 4 steps require a total of 17 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps
Answers
Based on the given parameters of a = 1.7 cubic feet and concrete for first 4 steps as 17 cubic feet, the concrete is required for the first 12 steps is 132.6 cubic feet
Arithmetic progressionFirst term, a = 1.7 cubic feetSum of first four terms = 17 cubic feetSn = n/2 {2a + (n - 1) d}
17 = 4/2{2×1.7 + (4 - 1)d}
17 = 2{3.4 + (3)d}
17 = 2(3.4 + 3d)
17 = 6.8 + 6d
17 - 6.8 = 6d
10.2 = 6d
d = 10.2/6
Common difference, d = 1.7Concrete required for first 12 steps;
Sn = n/2 {2a + (n - 1) d}
= 12/2{2×1.7 + (12-1)1.7}
= 6{3.4 + (11) 1.7}
= 6(3.4 + 18.7)
= 6(22.1)
= 132.6
Concrete required for first 12 steps = 132.6 cubic feet
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Answer:
132.6 cubic feet
Step-by-step explanation:
Figure A is a scalr image of figur B. Figure A maps to Figure B with scale factor of 2/3. what is tge value of x?
Answers
Answer:
7
Step-by-step explanation:
You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.
Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex] and that can be changed to [tex]\frac{21}{2}[/tex]
([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex]) The two's cancel out and we are left with [tex]\frac{21}{3}[/tex] Which is the same as 7.
50 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 31 pupils use the swimming pool. 28 pupils use the gym. 7 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
Answers
Using it's concept, it is found that there is a 0.3 = 30% probability to select a pupil that uses the swimming pool but not the gym.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 50 - 7 = 43 pupils use at least one of the pool or the gym.
We use the following relation, considering the numbers of each:
Both = Pool + Gym - At least one
Hence:
Both = 31 + 28 - 43 = 16.
From this, we have that out of 50 pupils, there are 31 - 16 = 15 pupils who use the pool but not the gym, hence the probability is:
p = 15/50 = 0.3 = 30%.
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Find the quotient.
18.)97.2
Answers
Answer:
540
Step-by-step explanation:
540 =18% of 97.2
Done please
it's quotient it's a synthax error..
Tina wrote a check for $35 on Monday. On Tuesday she made of withdrawal of $60 and on
Wednesday she deposited $75. What is the change in Tina's account after the three days?
Answers
The change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25
Deposit and withdrawalDeposit is a sum of money or other asset given as an initial payment, to show good faith, or to reserve something for purchase.
Withdrawal on the other hand, is to extract money from an account.
Check = $35Withdrawal = $60Deposit = $75Change in Tina's account after the three days = - 35 - 60 + 75
= -95 + 75
= $-20
Therefore, the change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25.
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divide $800 between kofi and kweku so that kofi gets three times what kweku gets
Answers
Answer:
600 and 200
Step-by-step explanation:
kofi : kweku is 3 :1
so Kofi gets 3 out of ( 3 +1) = 3/4 of 800 = 3/4 * 800 = 600
kweku get s the rest 800- 600 = 200
The store has a 30% discount on every item in stock. how much is the 5% sales tax reduced on an item that regularly sells for $10?
i need help on this question
Answers
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
How much money should we pay in sales tax?
In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:
t = (r / 100) · (1 - d / 100) · c (1)
Where:
d - Discount rater - Sales tax ratec - Item pricet - Sales tax totalIf we know that d = 30, r = 5 and c = 10, then the sales tax total is:
t = (5/ 100) · (1 - 30 / 100) · 10
t = 0.35
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
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