Answer:
Step-by-step explanation:
Solving 3x2-5x-1 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C number, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = -5
C = -1
B2 - 4AC =
25 - (-12) =
37
Applying the quadratic formula :
5 ± √ 37
x = —————
6
√ 37, rounded to 4 decimal digits, is 6.0828
So now we are looking at:
x = ( 5 ± 6.083 ) / 6
Two solutions:
x =(5+√37)/6= 1.847
x =(5-√37)/6=-0.180
What is 2 3 as an exponent?
2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times. 2^3 = 2 * 2 * 2 = 8
In the notation 2^3, the number 2 is the base and the number 3 is the exponent. The exponent tells you how many times the base is being multiplied by itself. In this case, 2 is multiplied by itself 3 times.
It's important to note that the exponent is also known as the power, so 2^3 is also read as 2 to the power of 3.
In summary, 2 3 as an exponent is written as 2^3 and it represents 2 multiplied by itself 3 times, or 2 to the power of 3 which is equal to 8. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.
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Find the value of each variable in the following parallelogram
Answer:
a = 2
b = 7
Step-by-step explanation:
The given rectangle is a parallelogram.
WZ = XY10b + 1 = 9b + 8
Transfer like terms to the same side of the equation10b - 9b = 8 - 1
Add/Subtract like termsb = 7
2. WX = ZY
6a + 4 = a + 14
Transfer like terms to the same side of the equation6a - a = 14 - 4
Add/Subtract like terms5a = 10
Divide both sides by 5a = 2
find the area of shaded region
Answer:
119 cm²
Step-by-step explanation:
Area of shaded region:Area of white triangle:
base = 9 cm
height = 14 cm
[tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base *height}[/tex]
[tex]\sf =\dfrac{1}{2}*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\[/tex]
Area of trapezium:
[tex]\sf \boxed{Area \ of \ trapezium =\dfrac{(a+b)*h}{2}}[/tex]
Here, a and b are the parallel sides of trapezium & h is the height.
a = 9 cm ; b = 17 cm and h =14 cm
[tex]\sf Area \ of \ trapezium = \dfrac{(9+17)*14}{2}[/tex]
[tex]= \dfrac{26*14}{2}\\\\\\=13*14\\\\= 182 \ cm^2[/tex]
Area of shaded region = area of trapezium - area of white triangle
= 182 - 63
= 119 cm²
Answer:
area of shaded region = 119 cm²
Step-by-step explanation:
the outer figure has one pair of parallel sides and is a trapezium.
the shaded area (A) is calculated as
A = area of trapezium - area of white triangle
the area of a trapezium is calculated as
area = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 14 , b₁ = 9 , b₂ = 17 , then
area = [tex]\frac{1}{2}[/tex] × 14 × (9 + 17) = 7 × 26 = 182 cm²
the area of the triangle is calculated as
area = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 9 and h = 14 , then
area = [tex]\frac{1}{2}[/tex] × 9 × 14 = 4.5 × 14 = 63 cm²
then area of shaded region (A) is
A = 182 - 63 = 119 cm²
Is it 3 pair or 3 pairs?
It is "3 pairs" not "3 pair", because a pair is a set of two things, so if you have 3 of them it would be 3 sets of two things or 3 pairs.
A 500 g packet of Healthy Flakes costs €3.20.
A 750 g packet of Healthy Flakes costs €4.50.
Which size packet is the better buy?
Show all your calculations and explain your answer clearly.
The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.
what is unitary method ?The unit technique is a method of problem-solving that entails calculating the value of a single unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single unit value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, linear algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.
given
The price of a 500 g packet of Healthy Flakes is €3.20.
Healthy Flakes come in packets of 750 g for €4.50.
A better size packet of 500 g costs €3.20. A two-pack of 750 g costs €166.66.
The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.
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The measures of the angles of a triangle are shown in the figure below. Solve for x. (3x)° 58° 80°
Answer:
x=14
Step-by-step explanation:
The angles inside a triangle add up to 180 degress all the time, therefore
58+80+3x=180
simplify
138+3x=180
subtract 138 from both sides of the equation
3x=42
divide both sides by 3
x=14
what are the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down, given T(-1,-1), U (-1,2), and V(2,1)?
The coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down can be found by following the transformation sequence.
What are the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down, given T(-1,-1), U (-1,2), and V(2,1)?The first transformation to be applied is the dilation with a scale of 5. This transformation enlarges the coordinates of the original points by a factor of 5. The coordinates of T, U, and V become (5(-1,-1)), (5(-1,2)), and (5(2,1)) respectively. The coordinates of the dilated points are (T’(-5,-5)), (U’(-5,10)), and (V’(10,5)).The next transformation to be applied is the translation 3 units right and 2 units down.This transformation adds 3 to the x-coordinate and subtracts 2 from the y-coordinate of each point. After the translation, the coordinates of T’, U’, and V’ become (T’(-2,-7)), (U’(-2,8)), and (V’(13,3)) respectively.Therefore, the coordinates of V’ in the image of TUV under a dilation centered at the origin with scale 5 followed by a translation 3 units right and 2 units down are (13,3).The coordinates of V' can be found by first applying the dilation with scale 5 to the original points, followed by a translation 3 units right and 2 units down. Using the coordinates of T, U, and V as starting points, the coordinates of the points after the dilation with scale 5 can be found. T(-1,-1) becomes (-5,-5), U(-1,2) becomes (-5,10), and V(2,1) becomes (10,5). Applying the translation of 3 units right and 2 units down to the new points, the coordinates of V' can be found. T(-5,-5) becomes (-2,-7), U(-5,10) becomes (-2,8), and V(10,5) becomes (13,3). Therefore, the coordinates of V' are (13,3).To learn more about a dilation and a translation refer to:
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Figure 3 of a tile pattern has 11 tiles, while figure 4 has 13 tiles The patter grows at a constant rate.
A write a equation to represent this situation
B which figure will contain 1015 tiles
Answer:
y = 2x + 5
Figure 505
Step-by-step explanation:
(3,11) ( 4,13)
Find the slope
Change in y over the change in x
[tex]\frac{13-11}{4-3}[/tex] = [tex]\frac{2}{1}[/tex] = 2
slope (m) is 2.
Part A
Find the y -intercept
m = 2
x = 3 from the point (3,11)
y = 11 from the point (3,11)
y = mx + b Substitute what I know and solve for b
11 = (2)(3) + b
11 = 6 + b Subtract 6 from both sides
11 - 6 = 6 -6 + b
5 = b
The y intercept (b) is 5
y = mx + b
y = 2x + 5
Part B
y = 2x + 5
1015 = 2x + 5 Subtract 5 from both sides
1015 - 5 = 2x + 5 - 5
1010 = 2x Divide both sides by 2
505
Moira needs a total of 214 hours to finish reading a book. Yesterday, she read for 178 hours. Supply the correct numbers to complete the equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book.
h + =
An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:
Let the variable h represent the number of hours.Let the variable T represent the total number of hours.Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;
h + 178 = T
Substituting the given parameters into the algebraic equation, we have the following;
h + 178 = 214
Solving for h, we have the following;
h = 214 - 178
h = 36 hours.
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A medical school student opens a credit card to pay for living expenses during their first year of medical school. The student expects to pay $12,500 in living expenses. The credit card company charges an annual interest rate of 15.99% compounded
continuously. I no payments are made for three years, what will be the balance on the card rounded to the nearest penny?
O$20,194.87
$20.129.60
O$18.406.25
O$14.667.42
The balance on the credit card after three years would be $20,111.25.
What is continuous compound interest?
Continuous compounding means that there is no limit to how often interest can compound. Compounding continuously can occur an infinite number of times, meaning a balance is earning interest at all times.
The balance on the credit card after three years can be calculated using the formula for continuous compound interest:
A = P * e^(rt)
where A is the final balance, P is the initial principle (the amount of the loan), r is the annual interest rate as a decimal, and t is the number of years.
In this case, P = $12,500, r = 0.1599 (15.99% as a decimal), and t = 3.
Plugging these values into the formula:
A = $12,500 * e^(0.1599 * 3)
A = $12,500 * e^0.4797
A = $12,500 * 1.6089
A = $20,111.25
Rounded to the nearest penny: $20,111.25
Hence, the balance on the credit card after three years would be $20,111.25.
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Compared to lat year, the population of Boom Town ha increaed by 25%. The population i now 6,000. What wa the population lat year
The population of the Boom town increased by 25% compared to last year, present population is 6000 then last year population is equal to 4800.
As given in the question,
Given population of the present year is equal to 6000
Let us consider 'x' be the last year population.
Increased in population compared to last year = 25%
Required equation is given by :
x + (25/100)x = 6000
⇒ (125 / 100 )x = 6000
⇒ x = ( 6000 × 100 ) / 125
⇒ x = 4800
Therefore, the population of the last year as per given data of the present year is equal to 4800.
The above question is incomplete, the complete question is:
Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?
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What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?
1. Substitute the values into the Pythagorean theorem and show that a false statement results.
2. Determine the sum of the side lengths and compare it to the Pythagorean theorem.
3.Calculate the difference between the horizontal and vertical coordinates of each pair of measurements to show the triangle is equilateral.
4.Use the coordinate plane to draw the triangle and show that it is an acute triangle.
Substitute the values into the Pythagorean theorem and show that a false statement results.
What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?The best way to show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle is to substitute these values into the Pythagorean theorem and show that a false statement results.The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.In this case, 8^2 + 16^2 = 64 + 256 = 320, which does not equal 22^2 = 484.This disproves the possibility of the triangle being a right triangle. As an alternative, one could also determine the sum of the side lengths and compare it to the Pythagorean theorem.In this case, the sum of the side lengths is 8 + 16 + 22 = 46, which again does not equal the square of the longest side.Both these methods show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle.To learn more about Pythagorean theorem refer to:
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(2x²-3x+1)-(-2x²-3x+2)
If the expression above is written in the form
ax²+bx+c, in which a, b, and c are constants,
what is the value of a+b+c?
in the form ax²+bx+c, in which a, b, and c are constants, the value of given quadratic equation a+b+c is 0.
What is simplification?Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.
For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as [tex]2x^2 + 4x = 2x(x+2).[/tex]
Simplifying an equation might involve isolating a variable on one side of the equation, or solving for the value of an unknown.Simplifying a fraction might involve finding a common denominator and canceling out common factors in the numerator and denominator.Simplifying a square root might involve expressing it in simplest radical form.The goal of simplification is to make the expression or equation easier to understand, manipulate, or solve.
The expression given is already in the form ax^(2) + bx + c, so we can simply add the coefficients of the x^(2), x and constant terms to find the value of a+b+c:
[tex](2x^{(2)} -3x+1)-(-2x^{(2)}-3x+2) = 2x^{(2)} - (-2x^{(2)}) + (-3x) - (-3x) + 1 - 2[/tex]
a+b+c = 2 - (-2) + (-3) - (-3) + 1 - 2 = 2 + 2 - 3 - 3 + 1 - 2 = 0
Therefore, the value of a+b+c is 0.
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Solve 3x^2+16x-5 using quadratic equation
Using quadratic equation, the value of x is 5 and -1/3
How to calculate the value of x using quadratic equation?3x²+16x-5
3x² +16x -5= 0
Split the middle term using two factors
3x² -15x -x -5= 0
Take out the common factors
(3x-1)(x-5)= 0
3x+1= 0
3x= 0-1
3x= -1
x= -1/3
x-5= 0
x= 0+5
x= 5
Hence x = 5 and x= -1/3
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What is the value of exponential 2?
The value of exponential 2 is 2^2, or 4. This means two multiplied by itself two times or squared.
Exponential notation is a way of expressing a number, usually greater than 10, as a base number, the number 2 in this case, raised to a power, which in this case is 2. Therefore, exponential 2 is written as 2^2, which means two multiplied by itself two times or squared.
For example, if we wanted to find the value of exponential 8, we could easily calculate 2^8, or 256, which is much faster than multiplying 2 by itself 8 times. Exponential notation is also helpful when calculating exponents with variables.
For example, if we wanted to find the value of 3^x, we could use exponential notation to find the answer quickly. In summary, exponential notation is a useful tool for quickly finding the value of a number raised to a power.
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Use the graph below to fill in the blank with the correct number:
f(1) = ________
The function's value at x = 1, y = - 1 Or f(1) = -1.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
The x-coordinate represents the input and the y-coordinate represents the output.
From the given points in the graph, we can conclude that when x = 1, y = -1.
Therefore, The value of the function f(1) = -1.
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How would the graph change if she already had $5 saved AND started saving $2.50 a week? Use the color blue
to represent this situation on the graph provided. Write the equation of the line represented in the graph.
Describe how the components of the equation represent the situation.
The linear function to model this problem is y = 2.50x + 5
What is Linear FunctionA linear function is a type of mathematical function that describes a straight line. A linear function is defined by an equation of the form:
y = mx + c
Where y is the dependent variable (the variable being measured or predicted), x is the independent variable (the variable being used to make the prediction or explanation), m is the slope of the line (the rate of change of y with respect to x), and c is the y-intercept (the value of y when x is zero).
The linear function to model this problem is given as;
y = 2.50x + 5
We can use a graphing calculator to represent this.
Kindly find the attached graph below
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A rectangular box has the length of [tex]\sqrt{90}[/tex] inches, width of [tex]\sqrt{14}[/tex] inches, and height of [tex]\sqrt{70}[/tex] inches.
a. What is the volume of the box?
b. What is the area of the top of the box?
c. What is the ratio of the height of the box to the length of the box?
Don't answer in decimals.
The volume, surface area, and ratio of the height of the box to the length will be 296.98 cubic inches, 292.35 square inches, and 0.88, respectively.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
A rectangular box has a length of √90 inches, a width of √14 inches, and a height of √70 inches.
The volume of the box is given as,
V = LBW
V = (√90) x (√14) x (√70)
V = 296.98 cubic inches
The area of the top of the box is given as,
SA = 2(LW + WB + BL)
SA = 2(√90 x √14 + √14 x √70 + √70 x √90)
SA = 292.35 square inches
The ratio of the height of the box to the length of the box is given as,
H / L = √70 / √90
H / L = 0.88
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In the diagram, △OA′B′ is a scale drawing of △OAB . What is the length of AB ?
Answer:
2.4
Step-by-step explanation:
2/5=AB/6
=>AB=2.4
which is the proper way to enter the following piece wise function into Desmos
The proper way to enter the piece-wise function into Desmos is given as follows:
y = 5x - 1 {x < -2}.y = x - 4 {x ≥ -2}.What is a piecewise function?A piecewise function is a function that has different definitions, based on the input of the function.
The definitions for this problem are given as follows:
Left of x = -2.Right of x = -2.The correct command to enter an interval in Desmos is between {}, hence the intervals are given as follows:
Left of x = -2 -> {x < -2}.Right of x = -2 -> {x ≥ -2}.The definitions of f(x) are entered using y = f(x), hence the correct option is given by the second option.
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whats the equation of the line in slope-intercept form
The equation in slope intercept form is
y = 5/2x + 5
What is Slope intercept form ?One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.
Any location that is not on the line will not fulfill the coordinates.
This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.
Two points on the line are (-2,0) and (0,5)
The slope intercept form is
y = mx + c
so when y = 0 and x = -2
0 = -2(m) + c
or, 2m -c = 0 ..(i)
again when x= 0 y = 5
5 = 0*m + c
c = 5
so putting c= 5 in equation (i) we get
m = 5/2
so the equation in slope intercept form is
y = 5/2x + 5
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What is HJ? correct answer gets brainliest
For the given line segment, the value of HJ is 32 and hence option a is the correct answer.
What is a line segment?Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places.
Given that:
GJ = 56
[tex]\frac{GH}{HJ} =\frac{3}{4}[/tex]
The line segment GHJ = GJ can be written as follows:
GJ= GH +HJ
From the given ratio we know that:
GH = 3x and
HJ = 4x
Thus, the value of GJ = 3x + 4x
GJ = 7x
56 = 7x
x = 8
Substitute the value of x = 8 in GH = 3x and HJ = 4x.
GH= (3)(8) = 24
HJ = (4)(8) = 32
Hence the value of HJ = 32 and option a is the correct answer.
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it's overlapping triangles, high school 10th grade math.
the statements need to be matched to the reasons.
In the overlapping triangles, the statements needed to be match to the reasons are explained below.
Properties of a triangle.A triangle is sometimes referred to as trigon because it is bounded by three straight sides, and has a measure of internal angles which add up to 180^o.
Considering the overlapping triangles given in the question, the statements to be matched to the reasons are given below:
STATEMENT REASON
1. ΔRTN ≅ ΔSTM Side-Angle-Side (SAS)
2. <T ≅ <T Betweenness
3. RN = SM Reflexive property
4. RM = SM, TM = TN Given
5. RT = ST Substitution
6. RM + TM = TN + SN CPCTE
7. RM + TM = SN + TM Addition property of equality
The match of statements with the reasons are required to proof that RN = SM
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you decide to buy a custom frame for painting which measures 6 by 14 inches. if the framing material cost 6$ per inch, what is the total(
The total cost of the rectangular frame is C = $240.
How to find the total cost?After a small search online, I found the original question, it is written at the end of the answer.
Remember that for a rectangle of length L and width W, the perimeter is given by:
P = 2*(L + W)
In this case, we know that the frame is 6 inches by 14 inches, then the perimeter will be:
P = 2*(6in + 14in)
P = 2*20in = 40in
And we know that the framing material costs $6 per inch, then the total cost of the frame will be:
cost = 40*$6 = $240
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After a small search online, I found that the complete question is:
"You decide to buy a custom frame for a painting which measures 4 by 6 inches. If the framing material costs $2 per inch, what is the total cost of framing material?"
213.5 miles in 3.5 hours. At that rate, how many miles will he travel in 7.2
hours?
Answer: 439.2 miles
Step-by-step explanation:
213.5/3.5=61
61*7.2=439.2 miles in total
HELPPPPPPPPPPPPPP
In Shawn's class, all the students have pets. Of those pets, 1/5 are cats. Of those cats, 2/3 are alley cats. What fraction of the pets are alley cats?
Answer: Would it just be 2/3? It says 2/3 are alley cats.
Step-by-step explanation:
Answer:
1/3 of them are alley cats
Step-by-step explanation:
Question 4 In the equation y=3x+5 , the number represents the slope and the number represents the y-intercept. Question 4 In the equation y=3x+5 , the number represents the slope and the number represents the y-intercept.
The slope and the y-intercept of the line are 3 and 5 respectively.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation of a straight line → y = 3x + 5
The equation of the straight line given is -
y = 3x + 5
We can compare and conclude that -
m = 3
c = 5
Therefore, the slope and the y-intercept of the line are 3 and 5 respectively.
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What are exponents give examples?
Answer:
An exponent refers to the number of times a number is multiplied by itself.
Step-by-step explanation:
For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
What is the inequality formula?
Inequality formula:
A < B or A > BThe inequality formula is a mathematical statement that compares two values using the less than (<) or greater than (>) symbols.
The inequality formulaThe inequality formula is used to determine if one value is greater than, less than, or equal to another value. It can be written in the form of A < B or A > B, with A and B representing any two values. This is useful for solving problems that involve comparison, such as determining whether a number is greater than another or if a certain value is within a certain range. The inequality formula can also be used to graph inequalities on a number line, which is useful for visualizing the relationships between two values.
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The assets and liabilities of a salesperson are listed below.
Home Value $264,500
Retirement Portfolio $473,906
Credit Card Balances $58,236
Bank Loan $35,275
Mortgage $187,632
Car Value $22,750
Investments $139,664
Home Furnishings $23,100
What is the value of the liquid assets?
$139,664
$264,500
$473,906
$613,570
The value of the liquid assets of the salesperson is; D: $613,570
How to find the Liquid asset?Liquid assets are defined as a set of property or investment that can be converted easily into cash. These liquid assets include raw cash, fast selling and marketable securities that can be traded and converted into cash within a short time.
Hence the liquid assets of the person, along with their values, are listed as follows:
The returns from someone's retirement portfolio will supplement your Social Security benefits, and it can even prevent you from having to live squarely on a fixed income. Due to the fact that a retirement portfolio is diversified, it can protect you from market volatility by balancing different income classes. Retirement Portfolio in this question is given as $473,906 (It is called the Retirement fund)
Investments = $139,664
The total value of the person's liquid assets is given by the sum of the values of each of these two assets, hence:
473,906 + 139664 = $613,570
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