Answers
The expression is simplified to x+8/x- 4
How to simply the expressionFirst, we need to know that algebraic expressions are defined as expressions that are made up of terms, variables, constants, factors and coefficients.
These expressions are also made up of arithmetic operations.
From the information given, we have that;
[tex]\frac{x^2 + 2}{x^2 - 9x + 20} - \frac{42 - 3x}{x^2 - 9x + 20}[/tex]
Now, find the lowest common multiple, we have;
x² + 2 - (42 - 3x)/x² - 9x + 20
collect the like term and expand the bracket, we have;
x² + 3x - 40/x² - 9x + 20
x² + 8x - 5x - 40/x² - 5x - 4x + 20
(x-5)(x+8)/(x-5)(x -4)
x+8/x- 4
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Related Questions
8% of the employees at a shop work part time of there are4 part time employees at the shop how many employees are there in total
Answers
There are 50 employees in total at the shop.
Let's assume the total number of employees at the shop is 'x'.
According to the given information, 8% of the employees work part-time. This means that 8% of 'x' equals the number of part-time employees.
We can set up the following equation to represent this relationship:
(8/100) * x = 4
To solve for 'x', we first simplify the equation by dividing both sides by 100:
(8/100) * x = 4
0.08 * x = 4
Next, we isolate 'x' by dividing both sides of the equation by 0.08:
x = 4 / 0.08
Performing the division, we find:
x = 50
Therefore, the total number of employees at the shop is 50.
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Please explain your answer in steps to the question in the picture.
Answers
Answer:
[tex]\begin{aligned}v &= \dfrac{33}{13} \approx 2.5\end{aligned}[/tex]
Step-by-step explanation:
First, we can reciprocate (flip) both sides.
[tex]\dfrac{13}{3}=\dfrac{11}{v}[/tex]
[tex]\implies \dfrac{3}{13} = \dfrac{v}{11}[/tex]
Next, we can multiply both sides by 11.
[tex]\implies 11\cdot \dfrac{3}{13} = \dfrac{v}{\not{11}} \cdot \not{11}[/tex]
[tex]\implies \dfrac{33}{13} = v[/tex]
[tex]\implies \boxed{v = \dfrac{33}{13}}[/tex]
Bigco Corporation is one of the nation’s leading distributors of food and related products to restaurants, universities, hotels, and other customers. A simplified version of its recent income statement contained the following items (in millions).
Cost of sales $ 11,571
Income taxes 249
Interest expense 23
Net earnings 1,442
Sales 16,400
Earnings before income taxes 1,691
Selling, general, and administration expense 3,543
Other revenues 428
Total expenses (excluding income taxes) 15,137
Total revenues 16,828
Prepare an income statement for the year ended June 30, current year. (Hint: First order the items as they would appear on the income statement and then confirm the values of the subtotals and totals.)
Answers
Step-by-step explanation:
I hope this answer is helpful ):
3 1/8 divided by (x - 4 7/28) = 17/18 + 1 5/6
(Key on how to write the mixed numbers: Three is a whole number and then the fraction is 1/8, 4 is the whole number and 7/28 is the fraction, 1 is the whole number and 5/6 is the fraction)
Please provide the work and the answer! :)
Answers
x = 301/56
Algebraic expressionsAlgebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expression
Given the algebraic expression,
[tex]3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} [/tex]
Step 1:
Simplify the expression by converting the mixed numbers into improper fractions:
25/8 ÷ ( x - 119/28) = 17/18 + 11/6
Step 2: Simplify the right side of the equation
25/8 ÷( x - 119/28) = 17/18 + 33/18
25/8 ÷( x - 119/28) = 50/18
Step 3: Multiply both sides of the equation by (x - 119/28)
25/8 = 50/18 × (x - 119/28)
Step 4: Multiply both sides of the equation by (18/50)
25/8 × (18/50) = (x - 119/28)
Step 5: Simplify the left side of the equation
9/8 = (x - 119/28)
Step 6: Add 119/28 to both sides of the equation
9/8 + 119/28 = x
Step 7: Calculate the value of x:
x = 9/8 + 119/28
= 63/56 + 238/56
= 301/56
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Fill in the table 'using this function rule.
y = -5x+2
x
-1
0
1
2
y
0
0
0
X
4
S
Answers
Answer:
7, 2, -3, -8
Step-by-step explanation:
y = -5x + 2 Substitute in -1 for x
y = -5(-1) + 2
y = 5 + 2
y = 7
y = -5x + 2 Substitute in 0 for x
y = -5(0) + 2
y = 0 + 2
y = 2
y = -5 + 2 substitutes in 1 for x
y = -5(1) + 2
y = -5 + 2
y = -3
y = -5x + 2 Substitute in 2 for x
y = -5(2) + 2
y = -10 + 2
y = -8
Helping in the name of Jesus.
when you answer the question in the picture, make sure to explain your answer in steps. Thank you.
Answers
Answer:
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{-10}{6 +6} \implies \cfrac{ -10 }{ 12 } \implies - \cfrac{5}{6}[/tex]
[tex]\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}{4}=\stackrel{m}{- \cfrac{5}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -4 = - \cfrac{5}{6} ( x +6) \\\\\\ y-4=- \cfrac{5}{6}x-5\implies {\Large \begin{array}{llll} y=- \cfrac{5}{6}x-1 \end{array}}[/tex]
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
b) [tex]MN = 6\frac{3}{4}[/tex]
Step-by-step explanation:
In ΔPQN and ΔLMN,
∠PQN = ∠LMN (given)
∠PNQ = ∠LNM (vertically opposite angles)
Since two angles in the triangles are same, the third angle must alos be same
Therefore,
∠QPN = ∠MLN
By AAA property, the two triangles are similar
Therefore,
[tex]\frac{PQ}{LM} =\frac{QN}{MN} =\frac{PN}{LN} \\\\\implies \frac{8}{6} =\frac{9}{MN} =\frac{PN}{LN} \\\\\implies \frac{8}{6} =\frac{9}{MN}\\\\\implies MN =\frac{9*6}{8}\\\\\implies MN =\frac{54}{8}\\\\\implies MN =\frac{27}{4}\\\\\implies MN =6\frac{3}{4}[/tex]
Marvin ran 7 1/4 miles on Saturday and 6 1/4 miles on Sunday. How many miles did Marvin run in all?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer: 13 1/2
Step-by-step explanation:
There are a few methods to complete this problem, but here is one of the simplest methods by separating the parts:
First, we rewrite our equation with parts separated
7 + 1/4 + 6 + 1/4
Next, we solve the whole number parts
7 + 6 = 13
Solving the fraction parts and reducing the result to the lowest terms
1/4 + 1/4 = 2/4
2/4 = 1/2
Combining the whole and fraction parts
13 + 1/2 = 13 1/2
Hope this helps! Please feel free to ask any questions if needed :)
Answer is 13 1/4
Explanation
because 7+6=13 and 1x1=1 and 4x1=4
1x4=4 and 1x4=4 so that equals 5/4
But
4 go into 5 one time so the answer will be
13 1/4
In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answers
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= [tex]\frac{18}{36}[/tex]
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
(B) reduction
Step-by-step explanation:
A dilation with a scale factor of 1/4 is a reduction.
A dilation is a transformation that enlarges or reduces a figure by a certain scale factor. The scale factor is a number that tells you how much bigger or smaller the image will be compared to the original figure. A scale factor of 1/4 means that the image will be 1/4 the size of the original figure. This is a reduction, because the image is smaller than the original figure.
X+5<5x-3 solve the equation.
Answers
x+5<5x-3
x+8<5x
8<5x-x
8<4x
2
That means, all numbers in the (right-) open interval (-infty , 2) are solutions. On the numberline, this would correspond to all numbers LEFT of 2 (NOT INCLUDING 2)
7.) According to the quantity equation, changes in the money supply will lead directly to
changes in the price level if velocity and real GDP are unaffected by the change in the
money supply. Will velocity change over time? What factors might lead to changes in
velocity? Are those changes related to changes in the money supply?
Answers
According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.
For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.
For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.
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Complete the frequency table for the following set of data. You may optionally click a number to shade it out.
Answers
The completed frequency table is:
Interval | Tally | Frequency
0-2 | ||| | 6
3-5 | ||| | 6
6-8 | |||||| | 8
9-11 | | | 1
12-14 | || | 2
To complete the frequency table, we need to count the frequency of each interval. We can start by organizing the data in ascending order:
0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 13, 13
Now, let's count the frequency for each interval:
0-2: 6 (0, 1, 1, 2, 2, 2)
3-5: 6 (3, 3, 4, 4, 5, 5)
6-8: 8 (6, 6, 6, 6, 6, 6, 7, 8)
9-11: 1 (9)
12-14: 2 (10, 10, 13, 13)
Now we can complete the frequency table:
Interval | Tally | Frequency
0-2 | ||| | 6
3-5 | ||| | 6
6-8 | |||||| | 8
9-11 | | | 1
12-14 | || | 2
The tally marks represent the frequency count in each interval, where each vertical line represents one count. The total frequency is obtained by counting the number of tally marks in each interval.
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What is the meaning of "Then B = {f(X) ⊂ P(n) : X ∈ A} is nonempty, and has a ⊂-maximal element"?
Answers
B is the set made of all the sets f(X) where X is a subset of A.
A is a subset of the powerset of F. That means A includes some subsets of F, e.g. X.
Now P(n) is the powerset of the first n natural numbers. So P(n) includes all the possible sets including 1 to n of the first n natural numbers (and the empty set, though not important here).
Now, f is a function that maps any element of f ONE TO ONE to a natural number k.
Then we define f(X), where X={a,b,c,…} (element of A, therefore a subset of F), so f(X)={f(a), f(b),…..} which is a set of natural numbers :)
So subset maximal means, there is some X in A for which f(X) (by definition an element of B) is the biggest element of B by size. They want to differentiate “Maximum size set” from “set with Maximum size element” I think :)
Two different students decide to compare their businesses. Scooter makes his own t-shirts,
while Karissa does computer repairs. For both models, x represents the number of sales made
each month and f(x) represents total money for each individual. The two functions below model
their respective businesses:
Scooter: f(x) = 200 + 15x
Karissa: f(x) = 80 + 35x
a. Describe what the slope and y intercept represent for both models based on the context.
Compare the two functions. What is one statement you could say about each?
b.
C.
In one month, Scooter sells 20 shirts. That same month, Karissa does 12 repairs. Who had
the better month?
Answers
a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
How to Describe what the slope and y intercept represent for both models based on the contexta) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.
In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.
Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.
b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.
For Scooter, with x = 20 (number of shirts sold):
f(x) = 200 + 15x
f(20) = 200 + 15 * 20
f(20) = 200 + 300
f(20) = 500
For Karissa, with x = 12 (number of repairs):
f(x) = 80 + 35x
f(12) = 80 + 35 * 12
f(12) = 80 + 420
f(12) = 500
Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
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Provide reasons for the proof of the triangle proportionality theorem. 25 points
Answers
The two column proof is completed below
Statement Reason
1. line KI parallel to line MN Given
2. ∠ JKL ≅ ∠ JMN and ∠ JLK ≅ ∠ JNM Corresponding angles are equal
3. Δ JKL ~ Δ JMN Similar triangles
4. (JM)/(JK) = (JN)/(JL) Ratios of corresponding sides are
equal
5. JM = JK + KM and JN = JL + LN Segment Addition Postulate
6. (JK + KM)/(JK) = (JL + LN)/(JL) Substitution property
7. (JK)/(JK) + (KM)/(JK) = (JL)/(JL) + (LN)/(JL) Addition of fractions
8. 1 + (KM)/(JK) = 1 + (LN)/(JL) Simplify
9. (KM)/(JK) = (LN)/(JL) Simplify (the required proof)
What are similar triangles?Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.
The equality of corresponding sides of similar triangles is used in the proof and it helped to state that: (JM)/(JK) = (JN)/(JL).
Further calculations were substitution and simplifying
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100 Points! Geometry question. Find x and y. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer: 35x/2 + 9y −5
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic charged $75
per hour, and the second mechanic charged $95
per hour. The mechanics worked for a combined total of 20
hours, and together they charged a total of $1800
. How long did each mechanic work?
Answers
Answer:
The first mechanic worked 5 hours
The second mechanic worked 15 hours
======================================================
Work Shown:
x = number of hours the 1st mechanic worked
y = number of hours the 2nd mechanic worked
75x = total amount charged by the 1st mechanic
95y = total amount charged by the 2nd mechanic
75x+95y = total charged both mechanics combined
75x+95y = 1800 is the first equation to set up
The other equation is x+y = 20 since the total combined time spent was 20 hours.
Solve for y to get y = 20-x
Then plug it into the first equation to solve for x.
75x+95y = 1800
75x+95( y ) = 1800
75x+95(20-x) = 1800 ....... replace y with 20-x
75x+1900-95x = 1800
-20x+1900 = 1800
-20x = 1800-1900
-20x = -100
x = -100/(-20)
x = 5
Now we can determine the value of y
y = 20-x
y = 20-5
y = 15
The first mechanic worked 5 hours.
The second mechanic worked 15 hours.
Expand and simplify (2x - 1)(x + 3)(x - 5)
Answers
Answer:
2x^3-5x^2-28x+15 -------------------------expanded
2x^3-5x^2-28x+15--------------------simplified
Step-by-step explanation:
\left(2x-1\right)\left(x+3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
simplyfied
\left(2x^2+5x-3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
=2x^3-5x^2-28x+15
Scenario The graph below is provided by a ride-sharing service in your area showing the cost, in dollars, of a ride by the mile. Assessment Instructions Show and explain all steps in your responses to the following parts of the assignment using the Algebra concepts and explain All mathematical steps and explanations. • Part 1: Calculate the base fee (in dollars) charged by the ride-share service. - Part 2: Calculate the rate of increase in cost in dollars per mile. - Part 3: Identify the slope and -intercept of the equation in the graph. - Part 4: Write the slope-intercept equation of the line in the graph. • Part 5: Use your equation from part 4 to extrapolate the cost of a 20-mile ride.
Answers
Part 1: The base fee charged by the ride-share service is $4.
Part 2: The rate of increase in cost in dollars per mile is $2.7.
Part 3: The slope and y-intercept of the equation are $2.7 and $4 respectively.
Part 4: The slope-intercept equation of the line in the graph is y = 2.7x + .
Part 5: The cost of a 20-mile ride is $58.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Part 1.
The base fee is the initial fee or y-intercept, and based on the graph, it is equal to $4.
Part 2.
Rate of increase = (y₂ - y₁)/(x₂ - x₁)
Rate of increase = (12 - 4)/(3 - 0)
Rate of increase = $8/3 or $2.7.
Part 3.
The slope and y-intercept of the equation in this graph are $2.7 and $4 respectively.
Part 4.
Next, we would write the slope-intercept equation of the line as follows;
y = mx + b
y = 2.7x + 4
Part 5.
When x = 20 miles, the cost is given by;
y = 2.7x + 4
y = 2.7(20) + 4
y = $58.
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In a bank, 20 customers on the average, are served by a cashier in an hour. If
the service time has exponential distribution, what is the probability that;
(i) It will take more than 10 minutes to serve a customer?
(ii) A customer shall be free within 4 minutes
Answers
(i) The probability that it will take more than 10 minutes to serve a customer is approximately 0.1353.
(ii) The probability that a customer shall be free within 4 minutes is approximately 0.4866.
To solve this problem, we can use the exponential distribution formula. The exponential distribution is often used to model the time between events occurring at a constant average rate. In this case, we want to find the probability of specific service times.
Let's denote λ as the average number of customers served per hour. Given that 20 customers are served on average, we can determine λ by dividing the average number of customers by the time taken to serve them, which is 1 hour. Therefore, λ = 20 customers/hour.
Now, we can calculate the probability using the exponential distribution formula:
(i) To find the probability that it will take more than 10 minutes to serve a customer, we need to convert 10 minutes to hours, which is 10/60 = 1/6 hour. Let's call this value x.
The probability can be calculated as P(X > x) = 1 - P(X ≤ x), where X follows an exponential distribution with rate parameter λ.
P(X > 1/6) = 1 - P(X ≤ 1/6)
= 1 - (1 - [tex]e^{(-\lambda x))[/tex] [Using the cumulative distribution function (CDF) of the exponential distribution]
= [tex]e^(- \lambda x)[/tex]
= [tex]e^{(-20/6)[/tex]
≈ 0.1353
(ii) To find the probability that a customer shall be free within 4 minutes, we convert 4 minutes to hours, which is 4/60 = 1/15 hour. Let's call this value y.
The probability can be calculated as P(X ≤ y), where X follows an exponential distribution with rate parameter λ.
P(X ≤ 1/15) = 1 - [tex]e^{(-\lambda y)[/tex]
= 1 - [tex]e^{(-20/15)[/tex]
≈ 0.4866
Therefore, the probability that a customer shall be free within 4 minutes is approximately 0.4866.
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question is in the picture, please explain your answer step by step.
Answers
Answer:
Step-by-step explanation:
the two other notations can be any from the following,
6/7, 6to7, 6<7
GEOMETRY 100 POINTS CHALLENGE
Answers
Answer:
∠D = 44
Step-by-step explanation:
Since EF║DG, ED is a transversal
⇒ ∠E + ∠D = 180
⇒ ∠D = 180 - ∠E
= 180 - 136
= 44
⇒ ∠D = 44
How many roots do the functions have in common?
�
(
�
)
=
�
2
−
9
f(x)=x
2
−9f, left parenthesis, x, right parenthesis, equals, x, squared, minus, 9
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens up. The function has a y-intercept at zero, eight, an x-intercept at two, zero, a minimum around six, negative six point five, and another x-intercept at ten, zero.
Answers
There are no roots of the given functions in common.
To find the roots of the functions in common, the two given functions will have to be equated to each other. So the answer to the given question will be determined by finding the roots of the given equations. The given equations are: (�)=�2−9f(x)=x2−9
Here, the first equation is a linear equation and the second one is a quadratic equation. The number of roots of these two functions in common will be the number of solutions to the equation obtained by equating these two given equations.
Now, equating the given equations, we have (�) = f(x)2 - 9 ⇔ � - f(x)2 = 9.The equation obtained by equating the two given equations is a quadratic equation. Let p(x) = � - f(x)2, then the above equation can be written as p(x) = 9.
Since the discriminant, D = b^2 - 4ac = 0 - 4(1)(9) = - 36 < 0, this means the quadratic equation doesn't have any real solutions. Hence, there are no roots of the given functions in common.
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6) 1,1,3,8,19, 41
a) 60
b) 81
c) 90
d) 101
Analogias
Answers
The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.
To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:
1 1 3 8 19 41
0 2 5 11 22
Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.
Let's check if the differences between consecutive terms are square numbers:
2 = 1²
5 = 2² + 1²
11 = 3² + 2²
22 = 4² + 3²
Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:
41 + 57 = 98
Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.
Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.
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If 400 x 300 = 120,000
And 40 x 30 is 1,200
Fill in the blanks and show your work
*_____ x ______ = 12,000?
Answers
Answer:
this list
Step-by-step explanation:
1×12000=12000
2×6000=12000
3×4000=12000
4×3000=12000
5×2400=12000
6×2000=12000
8×1500=12000
10 ×1200=12000
12 ×1000=12000
PLEASE HELP AS SOON AS POSSIBLE
Answers
A. The slope intercept form of the graph is y = -10x + 100.
B. The slope intercept form equation can be gotten using two points to find the slope and the y-intercept.
C. The slope represents the change in the percentage of battery remaining with respect to the change in number of hours.
How to represent equation in slope intercept form?
The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the (0, 100) and (1, 90). Hence,
m = 90 - 100 / 1 - 0
m = -10 / 1
m = -10
Therefore,
y = -10x + b
y = -10x + 100
B. The slope intercept form equation can be found using two points in the graph.
C. The slope in this situation represent the change in the percentage of battery remaining with respect to the change in number of hours.
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3.1 Which basic property of operations was used in each of the following
calculations?
3.1.1 25 x 4 = 4 x 25 = 100
3.1.2 412 412 412 + (-412) = 0
3.1.3 25 +37
-
=
= 20 + 5+ 30+7
= 20 +30 +5+7
= 50+ 12 = 62
Answers
3.1.1 The basic property of operations used is the commutative property of multiplication.
3.1.2 The basic property of operations used is the additive inverse property.
3.1.3 The basic property of operations used is the associative property of addition.
3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.
3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.
3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.
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The electrical resistance varies directly as the square of the voltage (V
) and inversely as the electric power (P
). If the voltage is 20
volts and the electric power is 5
watts, then the electrical resistance is 80
ohms.
Answers
The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.
In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.
The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.
According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms
Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.
Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
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