Answers
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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ΔABC≅ ΔCDA By ASA Congruence, therefore m∠ BAC ≅ m∠ DCA, hence proved using parallelogram side theorem.
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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Related Questions
What is the complete factorization of the polynomial below?
x³+3x²-x-3
O A. (x-1)(x-1)(x+3)
O B. (x+1)(x-1)(x+3)
OC. (x + 1)(x-1)(x-3)
O D. (x-1)(x-1)(x-3)
Answers
Find the z* values based on a standard normal distribution for an 86% confidence interval for a proportion, for a 78% confidence interval for a mean.
Answers
The z values are-
confidence interval 86 % = 1.0confidence interval 78% = 0.8Describe the term confidence interval?The likelihood that a parameter might fall between two values near the mean is shown by a confidence interval.Confidence intervals quantify when certain or uncertain a survey method is.They are also utilized in regression analysis and hypothesis testing.P-values and confidence intervals are commonly used by statisticians to determine statistical significance.They are often built with 95% or 99% confidence levels.Although they are related, confidence level and confidence interval are not the same thing.Obtain the z values from the t-distribution table for 0.86 and 0.78 confidence interval.
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write an equation of the passing through point p that is perpendicular to the given line .
p(3,1) y= 1/3x -5
Answers
Answer:
y = -3x + 10
Step-by-step explanation:
slope of perpendicular line = -3
y-1 = -3(x-3)
y-1 = -3x + 9
y = -3x + 9 + 1
y = -3x + 10
what is
m=-(4+m)+2
thank you
Answers
The value of m in the equation m=-(4+m)+2 is -1.
How are linear equations solved step-by-step?
Clear decimals or fractions.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.Remove the variable term from the equation's other side.Divide each side of the equation to find the solution.Verify your response.One of the easiest methods for resolving a system of linear equations is graphing. Simply plot each equation as a line on a graph and identify the point or points where the lines converge to find the value. These equations are simple to graph because they are already expressed in slope-intercept form.
m = -(4+m)+2
m = -4 -m + 2
m = -2 - m
m + m = -2
2m = -2
m = -1
Hence, the value of m in equation m=-(4+m)+2 is -1.
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Jason is a high school basketball player. He made some free throws (worth one point each) and some two-point shots in a particular game. Jason made a total of 13 photos altogether and scored a total of 20 points. Write a system of equations that could be used to determine the number of free throws Jason made and the number of two-point shots he made. Define the variables that you use to write the system.
Answers
Answer:
Let x be the number of free throws Jason made, and y be the number of two point shots he made.
The system of equations will be
x+ 2y = 20x+2y=20
x + y = 13x+y=13
Solving these using elimination method we get,
x + 2y = 20x+2y=20
----------------------------
y = 7y=7
x = 6⇒x=6
The number of free throws Jason made are 6, and the number of two point shots he made are 7.
A coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. write an equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.
Answers
The equation to express the total cost, c, to use the Internet at the coffeehouse for t hours is c = rt.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. An equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.
The equation will be:
c = r(t)
c = rt
where c = cost
t = number of hours
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Calculate the distance between the points C=(-9, 7) and Q=(-1, 3) in the coordinate plane. Round your answer to the nearest hundredth.
Answers
The distance between the points C = (-9, 7) and Q = (-1, 3) in the coordinate plane will be;
⇒ D = 10
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).
Now,
Since, Two points on the coordinate plane are C = (-9, 7) and Q = (-1, 3).
Hence, The distance between the points C = (-9, 7) and Q = (-1, 3) in the coordinate plane will be;
⇒ D = √(3 - 7)² + (- 1 - (-9))²
⇒ D = √ (-4)² + (8)²
⇒ D = √36 + 64
⇒ D = √100
⇒ D = 10
Thus, The distance = 10
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For each of these relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)) b) {(1,1), (1,2), (2,1), (2,2). (3,3), (4,4)} c) {(2,4), (4,2)) d) {(1,2), (2,3), (3,4)} e) {(1,1), (2,2), (3,3), (4,4)} f) {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}
Answers
Relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive.
Given :
a )
= { ( 2, 2 ),( 2, 3 ),( 2, 4 ),( 3, 2 ),( 3, 3 ) ,( 3, 4 ) }
Not reflexive because we do not have (1, 1), (3, 3), and (4, 4).
Not symmetric because while we we have (3, 4), we do not have (4, 3).
Not anti symmetric because we have both (2, 3) and (3, 2).
Transitive because if we have (a, b) in this relation, then a will be either 2 or 3. Then (2, c)
b )
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 3),(4, 4)}
Reflexive because (a, a) is in the relation for all a = 1, 2, 3, 4.
Symmetric because for every (a, b), we have a (b, a).
Not antisymmetric because we have (1, 2) and (2, 1).
Transitive because while we have (1, 2) and (2, 1), we also have (1, 1) and (2, 2) in the relation.
c )
{(2, 4),(4, 2)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Symmetric because for every (a, b), we have a (b, a).
Not antisymmetric because we have both (2, 4) and (4, 2).
Not transitive because we are missing (2, 2) and (4, 4)
d )
{(1, 2),(2, 3),(3, 4)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Not symmetric because we do not have (2, 1),(3, 2), and (4, 3).
Antisymmetric because for every (a, b), we do not have a (b, a).
Not transitive because we do not have (1, 3) for (1, 2) and (2, 3)
e )
{(1, 1),(2, 2),(3, 3),(4, 4)}
Reflexive because we have (a, a) for every a = 1, 2, 3, 4.
Symmetric because we do not have a case where (a, b) and a 6= b.
Antisymmetric because we do not have a case where (a, b) and a 6= b.
Transitive because we can satisfy (a, b) and (b, c) when a = b = c.
f )
{(1, 3),(1, 4),(2, 3),(2, 4),(3, 1),(3, 4)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Not symmetric because the relation does not contain (4, 1), (3, 2), (4, 2), and (4, 3).
Not antisymmetric because we have (1, 3) and (3, 1).
Not transitive because we do not have (2, 1) for (2, 3) and (3, 1).
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Sasha put $3,500 into a savings account that earns 2.3% annual compound
interest If she makes no other deposits or withdrawals, what will her balance be after 12 years ? Round to the nearest cent. SHOW ALL WORK TO RECEIVE CREDIT.
Answers
Sasha's balance after 12 years, if she makes no other deposits or withdrawals would be $ 4, 598. 07
How to find the balance ?Sasha's balance after 12 years will be the future value of her savings after 12 years at a rate of 2. 3% per year.
This future value can be found by the formula :
Amount after 12 years = Amount deposited by Sasha x ( 1 + annual compound interest ) ^ number of years
= 3, 500 x ( 1 + 2 .3 % ) ¹²
= 3, 500 x 1.3137344983996021269289886802331
= $ 4, 598. 07
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Compute mean for list of values and return mean for python
Answers
Python is a dynamic, high-level, free open source, and interpreted programming language.
What are basics of Python?So let's begin by looking at them:Properties. Python is implicitly and dynamically typed, so you do not have to declare variables. ...Data types. Let's move ahead to data types. ...Strings. Let's move on to strings. ...Flow control statements. ...Functions. ...Classes. ...Exceptions. ...File I/O.Python 3 was used for the above code.Each function in the above code is defined starting with the keyword def, the name of the function (mean, median, mode, main) and a pair of parentheses containing the parameter.The various defined functions in the module are saved as stats.py in the text editor.#definition of "median" function
def median(list):
#checking median condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#sort the list
list.sort()
#find middle element
mid = len(list) / 2
#check the condition
if len(list) % 2 == 1:
return list[mid]
else:
return (list[mid] + list[mid - 1]) / 2
#definition of "mean" function
def mean(list):
#checking mean condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#sort the list
list.sort()
#set the value
total = 0
#initiate a for loop
for num in list:
#then we calculate the total
total += num
#return the value
return total/ len(list)
#definition of "mode" function
def mode(list):
#checking mode condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#declare the variable
num_Dictionary = {}
#check the condition
for digit in list:
num = num_Dictionary.get(digit, None)
if num == None:
num_Dictionary[digit] = 1
else:
num_Dictionary[digit] = num + 1
#getting the maximum value
max_Value = max(num_Dictionary.values())
mode_List = []
for k in num_Dictionary:
if num_Dictionary[k] == max_Value:
mode_List.append(k)
return mode_List
#definition of main function
def main():
#set the list
num_list = [7, 4, 8, 10, 9]
#call the "mean" function with a parameter
print ("Mean of the given list: ", mean(num_list))
#call the "mode" function with a parameter
print ("Mode of the given list:", mode(num_list))
#call the "median" function with a parameter
print ("Median of the given list:", median(num_list))
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Look at the grid below.
a) What equation best represents the red line on the grid below?
b) What equation best represents the blue line on the grid below?
c) Find and list two co-ordinates on the red line
d) Find and list two co-ordinates on the blue line
Answers
a) The linear function that best represents the red line is given as follows: y = -4x + 4.
b) The linear function that best represents the blue line is given as follows: y = x - 2.
c) Two coordinates of the red line are given as follows: (0,4) and (1,0).
d) The coordinates of the blue line are given as follows: (0,-2) and (2,0).
What are the linear functions?The slope-intercept definition used to define a linear function from it's graph is given as follows:
y = mx + b.
In which the coefficients are listed as follows:
m is the slope, representing by how much y changes when x is increased by one.b is the y-intercept, representing the value of y when the graph of the function crosses the y-axis.For the red line, two points are given as follows:
(0,4) and (1,0)
Hence the parameters are of:
b = 4, a when x = 0, y = 4.m = -4, as when x increases by one, y decays by 4.Thus the equation is of:
y = -4x + 4.
For the blue line, the equation is of:
y = x - 2.
As:
When x = 0, y = -2.When x increases by 2, y also increases by 2, hence the slope is of m = 2/2 = 1.More can be learned about linear functions at https://brainly.com/question/24808124
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Which equation represents the linear relationship between the x-values and the y- values in the table
Answers
The equation of a line that represents the table is y = 6x - 5.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
To obtain the linear equation first we need slope(m) = (y₂ - y₁)/(x₂ - x₁)
= (1 + 11)/(1 + 1) = 12/2 = 6.
Now, we'll take any one of these coordinate points and construct an equation in slope-intercept form,
- 11 = 6(-1) + b.
- 11 = - 6 + b.
b = - 5.
∴ y = 6x - 5 is our equation.
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Please help, I don't understand this.
Answers
Answer:
-0.3
Step-by-step explanation:
just sum -0.66x and 0.36x
Answer: -21
Step-by-step explanation:
To begin, we can combine like terms, -0.66 and 0.36 are coefficients with the same variable.
This gives us -0.66x+0.36x= -0.30x, and the equation becomes -0.30x=6.3.
Next, we can simply solve for x by dividing 6.3 by -0.30, and that gives us x=-21.
Help I need a formula to know what I am doing
Answers
Answer:
2((2x+2)+3x)=124 units
Step-by-step explanation:
We know that the formula for perimeter is 2(b+h) and since we know this, we just substitute the values for this and solve.
B. Find an equivalent fraction of 3/4 and 9 is numerator
Answers
Answer:
9/12
Step-by-step explanation:
The easiest way to do this would to multiply the numerator and the denominator.
We need to find out how to get the numerator (3) to 9.
We can do this equation.
3 × 3 = 9
Now that we have multiplied the numerator by 3, we now need to multiply the denominator by 3.
4 × 3 = 12
The new fraction is 9/12.
Find the equation of the line passing through pl7, -2) and (5, 3).
Answers
The equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.
What is two point equation form?
The equation of a line in the coordinate plane can be expressed in two point form. Depending on the facts at hand, there are different ways to find a line's equation. One of the ways is the two-point form. When two locations along a line are known, this is used to determine the equation of the line. Slope intercept form, intercept form, point slope form, and others are crucial ways to describe a line equation.The equation of the line passing through two points is
(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)
Here, (x₁,y₁) ∈ (7, -2)
(x₂, y₂) ∈ (5, 3).
y - (-2) / 3 -(-2) = x - 7/ 5 - 7
(y + 2) / 5 = x-7 / -2
-2y - 4 = 5x - 35
5x + 2y - 31 = 0
Hence, the equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.
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Find the missing angles
m∠1=
m∠2=
m∠3=
m∠4=
m∠5=
Answers
Answer:
m1= 35
m2= 65
m3= 29
m4= 115
m5=65
For the following, find the arc length:
(Use pi=3.14 and round your final answer to the hundredths.)
X=
Answers
[tex]\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47[/tex]
Pls answer its for my finall
Answers
The non-real complex number is [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].
We have,
To find a non-real complex number,
What is not a real number?
Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i.
A non-real complex number is an imaginary number containing negative numbers in the root.
Here,
[tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex]
In this option, it includes the negative term that is in the root so this is imaginary, therefore, the answer is "Option B".
Hence, the non-real complex number is [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].
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What is the solution set of the equation( 6/m)+2 = (m+3)/(m−1)?
Answers
Solution set of the equation is -3,-1, and 2 by simplifying the equation we get m³+2m²-5m-6 = 0
What is equation ?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Mathematical algebraic equations typically have one or more variables.
Given equation is: (6/m)+2 = (m+3)(m-1)
multiply with m both sides,
⇒6+2m = m(m²+2m-3)
⇒m³+2m²-3m = 6+2m
So we get,
m³+2m²-5m-6 = 0
Solving we get, m = -3, m = -1, m = 2 as solution of given equation.
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A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 5 hours.
Answers
average speed = 3 3/4 km/h
In order to find how many kilometers the hiker will walk in 5 hours, you'll need to multiply the average speed by the hiker's hours.
[tex]3\dfrac{3}{4} \times5[/tex]
[tex]=\fbox{18.75 km}[/tex]
Express cos U as a fraction in simplest terms.
T
6
U
84
S
Answers
Answer:
cosU = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
cosU = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TU}{ST}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
A Circle Has An Equation of (x - 5)^2 + (y - 1)^2 = 30. What Is The Center And Radius Of The Circle?
Answers
the center of the circle is at (5, 1) and the radius is approximately 5.48 units.
Why it is and what is perimeter of a circle?
The standard equation of a circle with center (a,b) and radius r is:
(x - a)²2 + (y - b)²2 = r²2
Comparing this equation to the given equation, we can see that the center of the circle is (5, 1) and the radius is the square root of 30. Therefore, the center of the circle is at (5, 1) and the radius is approximately 5.48 units.
The perimeter of a circle is also known as its circumference, and it can be calculated using the formula:
C = 2πr
where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.
Alternatively, you can also use the formula:
C = πd
where d is the diameter of the circle.
So if you know the radius or diameter of a circle, you can use either of these formulas to calculate its circumference (perimeter).
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The piecewise function h(x) is shown on the graph.
7
S
5
3
N
-7-6-5-4-3-2-1₁
-2-
7 ? 9 9 9 7
-6
23 4 5 6 7 X
What is the value of h(2)?
O-2
O -1
0
3
Answers
The value of the piecewise function h(x) at x = 2 is (b) -1
How to evaluate the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
Part 1:
h(x) = x cubed for x less than negative 3
Part 2:
h(x) = 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4,
Part 3
h(x) = 5 times x plus 4, for x greater than or equal to 4
When the above statements are represented properly, we have the following equations
Part 1: h(x) = x³ for x < -3
Part 2: h(x) = 2x² - 9 for -3 ≤ x < 4
Part 3: h(x) = 5x + 4, for x ≥ 4
To calculate the function h(2), we use the domain -3 ≤ x < 4
So, we have the following function
h(x) = 2x² - 9
Substitute the known values in the above equation, so, we have the following representation
h(2) = 2(2)² - 9
Evaluate the expression
h(2) = -1
Hence, the value is (b) -1
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Complete question
The piecewise function h(x) is shown on the graph.
the function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4
What is the value of h(2)?
Value: 10
Which of the following equations represent exponential functions?
f(x)=2x²-3x+1
g(x)=0.875*
h(x)=1.75x+2
j(x)=1095.6-2x
Answers
Answer:
The first one, due to the x being raised to the power of 2
Step-by-step explanation:
Jon, Mona and Weber went to the local craft store to purchase supplies for making decorations for the upcoming dance at the high school. Jon purchased 2 sheets of craft paper, 4 boxes of markers and 5 glue sticks. His bill, before taxes was $36. Mona spent $32 when she bought 6 sheets of craft paper, 4 boxes of markers and 2 glue sticks. Weber, purchases totaled $16 when he bought 3 sheets of craft paper, 2 boxes of markers and 1 glue stick. Determine the unit cost of craft paper, marker and glue stick.
Answers
We have "No Solutions" or "Infinite Solutions" case.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the unit cost of Craft paper be x.
let the unit cost of boxes of markers be y.
let the unit cost of glue sticks be z.
So, the system of equations are
2x+ 4y + 5z= 36
6x+ 4y +2 z = 32
3x+ 2y+ z= 16
Now, solving the above three equation we get using Matrix method
All determinants are zero we have "No Solutions" or "Infinite Solutions" case.
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Question 1 (1 point)
A bacteria culture started with 200 bacteria at 2 p.m. After 1 hour, the population
has grown to 240 bacteria. Assume the population grows exponentially.
1. Find an explicit formula the gives the number of bacteria n hours after 2 p.m.
2. Use your formula to find the number of bacteria at 9 p.m. Round your answer
to nearest integer.
Answers
Hello, Elyna. ,
The formula would be:
200+200x=b
Step-by-step formula:
1.) x equals hours, whereas b equals bacteria.
2.) There are 24 hours in one day.
3.) 24*5= 120
4.) Connect it.
5.) 200+200(120)= 6.) 24200= 5 bacterium days
Hope I could help.
What amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period?
Answers
The required amount of $799.90 will reduce the amount by $842.
Given that,
The amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
For 5/10 and n /30
The discount would be 5% if paid in the 30-day span,
Amount = amount invoiced [1 - 5%/100]
Amount = $842[0.95]
Amount = $799.9
Thus, the required amount of $799.90 will reduce the amount by $842.
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Graph the line with slope −2 and y-intercept −4
Can you also mark the two points on the graph.
Answers
Answer:
Below
Step-by-step explanation:
See image below:
Simplify and write the answer
(3x²y⁴)³
Answers
Answer:
27x^6y^12
Step-by-step explanation:
3^3×x^2(3)×y^4(3)
=27^6y^12