Correct option is third option - " the original amount of the loan "
What is linear equation ? A linear equation, a first-order polynomial, that is, H. The sum of a series of terms, each of which is the product of a constant and a variable to the first power, equals the constant. In particular, linear equations in n variables have the form a0 + a1x1 + ... + anxn = c. where x1,...,xn are variables, coefficients a0,...,an are constants, and c is a constant. With multiple variables, the equation may be linear in some variables and non-linear in others. So the equation x + y = 3 is linear in both x and y, but x + y2 = 0 is linear in x but not in y. An equation of two linear variables represents a straight line in Cartesian coordinates. If the constant term c = 0, the line passes through the origin. A linear equation is an algebraic equation of the form y=mx+b. The above is sometimes called a "linear equation in two variables" where y and x are variables.Calculationx value would be the time in months and y value would be the loan amount that is left.
The y-intercept is basically the point where x is 0. So, we can say the y-intercept would be when time is 0.
That's basically when the loan started and the y-value represents the full loan amount., which is $22,000.
correct option is third option -- "the original amount of the loan".
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Each month, kaisorn deposits $50. 00 onto her public transportation card. It costs her $2. 50 per trip to ride the subway. Thom deposits $40. 00 on his public transportation card. It costs him $2. 00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2. 5x = y 40 − 2x = y 50 + 2. 5x = y 40 + 2x = y 50 − 2. 5y = x 40 − 2y = x 50 + 2. 5y = x 40 + 2y = x.
The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
The correct option is (A)
Given,
In the question:
Kaisorn deposits $50. 00 onto her public transportation card.
It costs her $2. 50 per trip to ride the subway.
Thom deposits $40. 00 on his public transportation card.
It costs him $2. 00 per trip to ride the subway.
Now, According to the question:
x → represents the number of trips
y → represents the amount remaining in each account
According to the given condition:
The system of equations represents their transportation costs is :
50 − 2. 5x = y
40 − 2x = y
Hence, The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
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what is (2 x 10 to the power of 5) divided by (4 x 10 to the power of 2)
PLEASE HELP ME AND TELL ME HOW YOU DID IT AND THANKS 25 POINTS HELP
Select the type of cross section formed when a triangular pyramid is cut parallel to its
base.
Ann and Ben tranlate document from German into Englih. A et of document that would take Ann 10 day would take Ben 12 day. Ann tart to tranlate the document. After 2 day Ann and Ben both work on tranlating the document. How many more day will it take to complete the work?
You mut how your working
After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.
A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work
She works for 2 days, hence the work done = 2 x 1/20 = 2/10
The remaining work = 1 - 2/10 = 8/10
Then Ben joins.
A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.
Each day, both Ann and Ben will complete:
1/10 + 1/12 = 11/60 unit work
The remaining work = 8/10
Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:
8/10 : 11/60 = 48/11 = 4.4 days
Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.
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A line passes through the point
(8, 7) and has a slope of 4
Write an equation in slope-intercept form for this line.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 4}(x-\stackrel{x_1}{8}) \\\\\\ y-7=4x-32\implies {\Large \begin{array}{llll} y=4x-25 \end{array}}[/tex]
Answer:
y = 4x -25
Step-by-step explanation:
y = 4x + b
we must find the y intercept
plug in the point
7 = 4(8) + b
7 = 32 + b
subtract 32 from both sides
-25 = b
the y intercept is -25
plug in -25 for b
y = 4x - 25
order the sides DEF from shortest to longest
From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.
Triangle:
The polygon with three edges known as sides and three vertices are known as triangle.
Given,
Here we have the triangle with their corresponding angle.
Now, we have to order the sides from shortest to longest.
Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.
By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.
In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.
From values, the shortest to longest the order is written as DE, DF and EF.
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Which description matches the graph of the inequality y <|x-2| + 1
A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
What is inequality?
Inequality is a relationship between two expressions or values that is not equal to each other.
This inequality may be written in two ways:
(a) y < x - 2 + 1
or
y < x - 1
(b) y < -x +2 + 1
or
y < -x + 3
A graph of the inequality is shown below. The shaded region satisfies the inequality.
Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
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Pls help me thank you
The value of y is x/2 + c/5
Given,
In the question:
5x - 7y = 3y - 2c
To find the value of y.
Now, According to the question:
The equation is given as:
5x - 7y = 3y - 2c
Combine the like terms:
-7y - 3y = -5x - 2c
Calculate the sum or difference:
-10y = -5x - 2c
y = -5x/-10 - 2c/-10
Calculate the product or quotient :
y = x/2 + c/5
Hence, The value of y is x/2 + c/5
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I need help with this
The value of the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9
What is a Function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5
(f+g)(x) = f(x) + g(x)
So by adding the two functions
(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5
(f + g)(x) = [tex]x^{2}[/tex] -5x + 9
In conclusion, the value of [tex]x^{2}[/tex] -5x + 9
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P(AIB) can be read as "the probability that A occurs given that B has
occurred."
OA. True
OB. False
SUBMIT
P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.
Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.
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HELP WHATS 565 divid by 000000.666 x X -k
Answer:
565/0.666=848.348
Step-by-step explanation:
if you needed variables added to the equation then show a picture and I can answer it.
solve the equation by elimination method 4x-2y=8,5x+3y=6
Answer:
Point form:
(18/11 , -8/11)
Equation form:
x=18/11 , y=-18/11
Match each number with its estimated power of 10
The matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
What are Exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
We have to match the following terms :
1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵
2) 219,000 = 2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵
3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶
4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵
5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶
Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
7, 7/1
Step-by-step explanation:
The ratio 7:49 can be simplified to 1:7.
Please help pleaseee
According to the Pythagoras theorem, the value of x is 13.76
Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.
Given,
Here we have the triangle with the side values.
Now, we have to find the value of x through this given values.
In order to calculate the value of x,
First, we need the value of the side KM.
Let us consider the value of KM is y.
Then according to the concept of Pythagoras theorem,
The value of y is calculated as,
=> (12.3)² = y² + (5.4)²
=> 151.29 = y² + 29.16
=> y² = 122.13
=> y = 11.05
Therefore, the value of the hypotenuse x is calculated as,
=> x² = (11.05)² + (8.2)²
=> x² = 122.13 + 67.24
=> x² = 189.37
=> x = 13.76
Therefore, the value of x is 13.76.
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A robot can complete 4 tasks in hour. Each task takes the same amount of time.
5/6
a. It takes the robot
(Simplify your answer.)
-
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
hour(s) to complete one task.
1 task will complete in 12.5 minutes
The robot can complete 9.6 task in 1 hour
Given,
Number of task a robot can complete = 4
Time taken by robot = 5/6 of 1 hour
5/6 of 1 hour = 5/6 × 60 minutes
= 300/6
= 50 minutes
Then,
4 task takes 50 minutes
1 task = 50 minutes / 4 task
= 12.5 minutes
So,
1 task = 12.5 minutes
x task = 60 minutes
1 : 12.5 = x : 60
1/12.5 = x / 60
1*60 = 12.5*x
60 = 12.5x
x = 60/12.5 = 4.8
x= 4.8
Therefore,
The robot can complete 4.8 task in 1 hour
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Type the missing number to complete the proportion.
18 orders in 2 days = 9 orders in
days
Answer:
18 orders in 2 days 9 orders in 1 day
Answer:
Step-by-step explanation:
9x2=18 which is 2 days so 9x1= 9 which is one day
square root of 81 divided by 3
Answer: Yes
Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications
For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.
56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.
Given,
The mean of the population, μ = 15.1 kg
Standard deviation, σ = 2.2 kg
We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;
Here,
z score = x - μ / σ
The z-score calculates how far the measure deviates from the mean by standard deviation.The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.
x = 16.5
z score = x - μ / σ
z = (16.5 - 15.1) / 2.2 = 0.64
Z = 0.64 has a p-value of 0.7389.
x = 13
z score = x - μ / σ
z = (13 - 15.1) / 2.2 = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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wilma can mow a lawn in 120 minutes. vanessa can mow the same lawn in 80 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
Working together, they can mow the yard in 48 minutes.
Given data;
A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?
Let 't' is their time in minutes working together.
Add their rates of working to get their rate working together,
Wilma's rate: [ 1 lawn ] / [ 120 min ]
Vanessa's rate: [ 1 lawn ] / [ 80 min ]
Rate working together: [ 1 lawn ] / [ t min ]
1/120 + 1/80 = 1/t
Multiply both sides by 240t;
2t + 3t = 240
5t = 240
t = 48
It takes them 48 min to mow the lawn working together.
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a coin is flipped eight times. each result is either a heads or a tails. how many possible outcomes contain at least 33 tails ?
The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.
The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:
[tex]\frac{8!}{3!5!} + \frac{8!}{4!4!} + \frac{8!}{5!3!} + \frac{8!}{6!2!} + \frac{8!}{7!1!} + \frac{8!}{8!0!}[/tex]56 + 70 + 56 + 28 + 8 + 1= 219Hence, the possible outcomes that contain at least three tails are 219.
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A rectangle is 25 cm on one side and 6 cm on another side. What is the perimeter?
Answer:
31
Step-by-step explanation:
A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If ( x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.
Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:
(x, y) → (SFx, SFy) = (0.4x, 0.4y)
Where:
x and y represents the data points.SF represents the scale factor.Read more on dilation here: brainly.com/question/20482938
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Complete Question:
A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
answer choices
(0.4x, 0.4y)
(x + 20, y + 20)
(x + 0.4, y + 0.4)
(20x, 20y)
Complete the sentence…?
is 10 times as much as 0.11
Answer: 1.1
Step-by-step explanation:
10 * .11 is 1.1
When multiplying decimals by ten you move the decimal place once to the right.
Answer:
1.1
Step-by-step explanation:
0.11 x 10 = 1.1
You are moving the decimal point over once (x 10).
The scatterplot shows the relationship between the length of a pendulum and the time it takes to complete one full swing.
Which transformations would linearize these data using a power model? Check all that apply.
ln(Length), ln(Time)
ln(Length), Time
log(Length), log(Time)
Length, log(Time)
Length, Time2
Answer:
a) ln(Length), ln(Time)
c)log(Length), log(Time)
e)Length, Time²
Step-by-step explanation:
Answer:
the person above me is correct!
Step-by-step explanation:
Choose the equation that represents the graph shown
Answer:
[tex]y=|x|-4[/tex]
Step-by-step explanation:
The vertex of the graph is at (4, 0).
This eliminates all of the options except for [tex]y=|x|-4[/tex].
Math help needed (grade 9)
Step-by-step explanation:
volume = base area × height
= (1/2×12×16)×10
=960cm3
surface area:
1. triangle area = 1/2×12×16=96cm2
2.bottom area = 12×10=120cm2
3.side area = 16×10=160cm2
4.slope area = 10×20=200cm2
5.add everything and remember you have two triangle
surface area= 96×2+120+160+200 =672cm2
In the following figure, AD is the bisector of ZBAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that AAEG = AAFG by the AAS congruence postulate. Do you agree or disagree? Explain.
I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent
The AAS have it that the two triangles being compared should have their two angles and the side not included being equal
The Angle - Angle - Side = AAS, here include
< FA,G - < AFG - AG
< EAG - < AEG - AG
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necesito saber como se resuelve
La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.
¿Cómo resolver un ecuación exponencial?
Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.
Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:
f(x) = 9ˣ⁺¹ - 28.3ˣ - 3
g(x) = 0
La solución es todo punto tal que f(x) = g(x).
A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.
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