Answers
Using function concepts, it is found that:
a) Point (3,-13) is not on the graph, because substituting x = 3 on the equation does not result in 13.
b) If x = 1, f(x) = -3, hence point (1,-3) is on the graph of f.
c) if f(x) = 2, x = 16, so point (16,2) is on the graph of f.
d) The domain is all real numbers except x = 4.
e) The x-intercept is of x = -8.
f) The y-intercept is of y = -2.
What are the points on the graph?The function is given by:
f(x) = (x + 8)/(x - 4).
Hence, when x = 3:
f(3) = (3 + 8)/(3 - 4) = 11/-1 = -11.
Hence:
Point (3,-13) is not on the graph, because substituting x = 3 on the equation does not result in 13.
When x = 1, we have that:
f(1) = (1 + 8)/(1 - 4) = 9/-3 = -3.
If x = 1, f(x) = -3, hence point (1,-3) is on the graph of f.
For f(x) = 2, we have that:
2 = (x + 8)/(x - 4)
2x - 8 = x + 8
x = 16.
Hence:
if f(x) = 2, x = 16, so point (16,2) is on the graph of f.
What is the domain of the function?The domain of a function is the set that contains all possible input values of the function.
This function is a fraction, meaning that the denominator cannot be zero, so:
x - 4 = 0 -> x = 4.
Hence:
The domain is all real numbers except x = 4.
What are the intercepts of the function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.For this problem, we have that:
f(x) = 0.
(x + 8)/(x - 4) = 0.
x + 8 = 0
x = -8.
f(0) = 8/-4 = -2.
Hence:
e) The x-intercept is of x = -8.
f) The y-intercept is of y = -2.
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Related Questions
Find the equation of the horizontal line through the point (5,−5) and (5,-5).
Answers
Answer:
Step-by-step explanation:
A horizontal line is given by an equation of the form Y = b
Notice that in both points the Y coordinate is the same no matter what value you choose for x
Y = -5
Please help me solve this I need a step by step solution that isn't too complicated, and I need to find an inequality that is written and the solved. Here's the question:
Neil and Yuki run a data entry service. Neil starts at 9:00am and can type 45 words per minute. Yuki arrives at 10:30am and can type 60 words per minute. Write and solve an inequality to find at what time Yuki will have typed more words than Neil. Let x represent the time in minutes.
Answers
Answer:
45*90+45*x and Yuki would have typed 60*x.
Words typed by Yuki > Words typed by Neil
45 \times 90 + 45 \times x < 90 \times x45×90+45×x<90×x
Solving above inequality would give
x > 90x>90
it means that 90 minutes after 10:30 AM
Yuki would type more than Neil.
24 over 80 equivalent
Answers
The equivalent expression of 24 over 80 is 3/10
How to determine the equivalent?The expression is given as
24 over 80
Rewrite the expression properly
So, we have
24/80
Divide the numerator and the denominator by 8
So, we have
3/10
Hence, the equivalent expression of 24 over 80 is 3/10
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Anna and Connor are in different math classes in NYC. Anna's teacher is always giving exams with 30 questions on them, while Connor's teacher gives more frequent exams with 24 questions on them. Anna's teacher also gives 3 projects. Even though two classes take different number of exams, the teachers told them the they will have the same total number of exam questions this year. What is the minimum amount of exam questions Anna and Connor will expect this year?
Answers
Dave and his brother, Theo, are selling cookies by the pound at the school bake sale. Dave sold 14.84 pounds of cookies and Theo sold 21.45 pounds of cookies. How many pounds did they sell altogether?
Answers
I think this is the answer
During a giveaway, every fourth customer gets a coupon and every tenth customer gets a free item. If 60 customers participate, how many get both the coupon and free item? A. 2 people B. 10 people C. 20 people D. 3 people
Answers
every 5th person to get a coupon also gets a free item
Use the graph of the function shown below to find:
A. The value of y when x is equal to each of the following: -3, -2, 0, 2, 4.
B. The value of x when y is equal to each of the following: -1.5, 0, 2, 2.5.
C. The domain of the function.
D. The range of the function.
Answers
Part A: 0, 2.4, 2.4, 1, 2
Find the y coordinate of the point on the graph with the given x coordinate.Part B: -2.5, 6, 0.5, N/A
Find the x coordinate of the point on the graph with the given y coordinate.
Part C: [-3, 7]
The domain is the set of x values.Part D: [-1, 2.4]
The range is the set of y values.A. The value of y, when x is equal to -3, -2, 0, 2, 4, is 0, 2.4, 2.4, 1, 2 respectively.
B. The value of x, when y is equal to -1.5, 0, 2, is -2.4, -3, and 4 respectively.
C. The domain of the function is {-3, -2, 0, 2, 4}.
D. The range of the function is {0, 1, 2.4}.
A. To find the value of y at x is equal to -3, -2, 0, 2, 4 is found by the graph given.
x: -3 -2 0 2 4
y: 0 2.4 2.4 1 2
B. To find the value of x at y is equal to -1.5, 0, 2, is found by the graph given.
y: -1.5 0 2
x: -2.4 -3 4
C. The domain of a function is the set of all possible input values (in this case, x values) for which the function is defined.
From the given x values, we can see that the function is defined for all of these values: -3, -2, 0, 2, 4.
So, the domain of the function is {-3, -2, 0, 2, 4}.
D. The range of the function:
The range of a function is the set of all possible output values (in this case, y values) that the function can produce.
From the given y values, we can see that the function produces these y values: 0, 1, 2.4.
So, the range of the function is {0, 1, 2.4}.
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write an expression equilavant to a + a + a + a + a + a + a
Answers
Hello,
[tex]a + a + a + a + a + a + a= 7 \times a = 7a[/tex]
Answer:
7a
Step-by-step explanation:
SOLVE this equation.
0.5r+5=r-8
Answers
Answer:
r = 26
Step-by-step explanation:
Let's solve the problem,
→ 0.5r + 5 = r - 8
→ r - 0.5r = 5 + 8
→ 0.5r = 13
→ r = 13/0.5
→ [ r = 26 ]
So, the value of r is 26.
Gimme brainlliest
y = 3x - 1 on a graph
Answers
Answer:
See explanation
Step-by-step explanation:
How do you write -4 and 4/25 as a decimal
Answers
Answer: -4.16
Step-by-step explanation:
100/25=4
-4 4/25=
-4 4*4/(25*4)=
-4 16/100= -4.16
0.4 x 0.17 i need a answer plsss
Answers
Answer:
0.068
Step-by-step explanation:
calculator
Answer:
0.068
0.4x0.17= 0.068
Step-by-step explanation:
8p-1-2q+7q identify the constant
Answers
Answer:
In equation 8p-1-2q+7q, 1 is the constant
Step-by-step explanation:
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Example: in "8p-1-2q+7q", 1 is the constants.
Let's simplify step-by-step.
8p−1−2q+7q
=8p+−1+−2q+7q
Combine Like Terms:
=8p+−1+−2q+7q
=(8p)+(−2q+7q)+(−1)
=8p+5q+−1
=8p+5q−1
the total of the ages of andrew, caren and barbara is 68 years. what was the total of their ages five years ago?
Answers
Sum of their ages= 53
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away,
a-b = c (c may be a positive or negative value it may be 0 too)
given that, total of the ages of andrew, caren and barbara is 68 years
asked about their total 5 years back so we have to subtract five years from three of them then we will get,
3x5=15
subtract 15 from 68 to get total of their ages five years ago
68-15=53
this gives the total age of andrew , caren and barbara 5 years ago
which is equal to 53
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Answer:
Ages together equal 53.
Step-by-step explanation:
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. For instance, the adjacent image shows 5 2 peaches, or 5 peaches with 2 subtracted.
a-b = c (c may have a positive, negative, or even zero value.)
Given that, Andrew, Caren, and Barbara's combined age is 68 years.
asked them how many years back in total they had, so we had to take away five years from three of them to get,
3x5=15
In order to calculate their ages five years ago, take 15 out of 68.
68-15=53
this reveals Andrew, Caren, and Barbara's combined ages. five years ago
which is equal to 53.
D. Highway I-10 is having an extension added
on. It will then be 3,000 miles long. How long
is the extension?
I-10 2,460
Answers
Answer:
the extension is 540 miles long
Step-by-step explanation:
I-10=2460
2460+x=3000
subtract 2460 from both sides
x=540
the extension is 540 miles long
sells pens with a company's logo printed on the pens. Writing World charges a standard price per box of pens when the customer purchases 200 or fewer boxes. Each box over 200 that the customer purchases is sold at a discounted rate. A customer purchases x boxes of pens,where x ≥ 200. The average cost of a single box of pens purchased by this customer is 1600+6(x-200) represented by X What is the meaning of the parts of this rational expression in the context of the situation?
Answers
What is Algebra?
The analysis of mathematical representations is algebra, and the
handling of those symbols is logic.
Division means the separation of something into different parts,
sharing of something among different people, places, etc.
Use the digits nine, six, and three one time each in the following Multi-
digit division problem then rewrite the problem.
Then the problem whose result is 40 will be given as the division of
3600 by 90.
3,600 / 90 = 40
The number in the problem whose result is 40, will be 3,600 and 90.
Complete the table of values below and use it to graph the equation y − x = − 6.
x
1
2
3
Answers
Can someone tell me the answer pls
Answers
Step-by-step explanation:
a normal function expresses y (the functional result) in terms of x (and constants).
we need to transform this to express now x in terms of y (and constants).
at the end we only rename x into y and y into x to make it an actual function.
h(x) = y = (-5x + 6)/(3x + 4)
y(3x + 4) = (-5x + 6)
3xy + 4y = -5x + 6
4y - 6 = -5x - 3xy = x(-5 - 3y)
x = (4y - 6)/(-5 - 3y)
and after renaming we get therefore the function
y = h-1(x) = (4x - 6)/(-3x - 5)
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true on edeginuity. Please help!!!
Answers
Answer:
x = 2/3
Step-by-step explanation:
If f(x) = -3x + 4, f(x) = g(x), and g(x) = 2, by the Transitive Property, -3x + 4 = 2
From here we can solve for x.
-3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
3x = 2
3x/3 = 2/3
x = 2/3
Layla has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $319.28. She buys 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94. She plans to spend some or all of the money she has left to buy new biking outfits for $77.02 each.
Answers
The inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].
As per the question statement, Layla has a budget of $680 to spend at a bicycle store for some new gear and biking outfits, and she buys a new bicycle for $319.28, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94.
We are required to express the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget if a new biking outfit costs $77.02
First, let us calculate the total spending Layla has already done before going for new biking outfits, which is $319.28 on bicycle, 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94, summed up as [tex][319.28+(4.90*3)+37.94]=(319.28+14.7+37.94)=371.92[/tex]
And supposing that she buys "x" new biking outfits, of $77.02 each, the total spending has to be equal to, or less than $680, i.e.,
[tex][680\geq (371.90+77.02x)][/tex]
Hence, the inequality that can be used to determine "x", the maximum number of outfits that Layla can purchase while staying within her budget is [tex][680\geq (371.90+77.02x)][/tex].
Inequality: In mathematics, an inequality is a relation which makes comparison between two inequal numbers or other mathematical expressions.To learn more about Inequality, click on the link below.
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Can someone help me! Please this assignment is due today.
Answers
The simplified form of the expression 5(3/5 x + 8y²) - 4x - (6y² + 10) will be 34y² - x - 10.
What is simplification?Simplicity is the quality of making anything less complicated and more manageable in terms of both execution and comprehension.
The expression is given below.
⇒ 5(3/5 x + 8y²) - 4x - (6y² + 10)
Simplify the expression, then we have
⇒ 5(3/5 x + 8y²) - 4x - (6y² + 10)
⇒ 3x + 40y² - 4x - 6y² - 10
⇒ 34y² - x - 10
The simplified form of the expression 5(3/5 x + 8y²) - 4x - (6y² + 10) will be 34y² - x - 10.
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What is three subtracted by 4/7
Answers
Answer:
2.42
Step-by-step explanation:
3 - 4/7 = 2.42
3 - 8/14 = 2.42
3 - 0.57 = 2.42
3 - 57.1 = 2.42
Breaking things down like this will make it easier to solve and get you answers faster!
I’m so confused! Can someone please help.
Answers
For the given kite DCBA, the value of AD as 22 units and CB as 30 units.
We know that the two longer sides and the two shorter sides of the kite are equal to each other.
So, we get that:
AD = CD
Substituting the values, we get that:
11 y - 22 = 7 y - 6
11 y - 7 y = 22 - 6
4 y = 16
y = 16 / 4
y = 4
AD = 11 y - 22 = 44 - 22 = 22 units
AB = BC
Substituting the values, we get that:
3 x + 12 = 5 x
5 x - 3 x = 12
2 x = 12
x = 12 / 2
x = 6
CB = 5 x = 30 units
Therefore, we get that, for the given kite DCBA, the value of AD as 22 units and CB as 30 units.
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Suppose you make hot chocolate. It's too hot to drink, so you put it in the freezer to cool it off. If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit, what will the temperature of the hot chocolate be after 4 minutes? (k = 0.12)
307.05
272.33
132.56
117.57
Answers
If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.
Temperature of the hot chocolateGiven:
k=0.12
Original or initial temperature=190 degrees Fahrenheit
Freezer temperature = 0 degrees Fahrenheit
Using Newton's Law of cooling to find the temperature of the hot chocolate
Temperature (t)= Temperature of surrounding environment T1 +(initial temperature of object T0-Temperature of surrounding environment T1)e-^kt
Hence,
T(t)=0+(190-0)e^-0.12t
T(t)=190e^-0.12t
Where t=4
T(t)=190e^-0.12(4)
T(t)=190e^-0.48
T(t)=117.5688
T(t)=117.57 (Approximately)
Therefore if the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit the temperature of the hot chocolate be after 4 minutes is: 117.57.
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If 4 liters of a 15% vinegar solution is mixed with x liters of a 30% vinegar solution, the result is a 20% vinegar solution. How many liters of the 30% vinegar solution were mixed?
The mixture required _ liter(s) of the 30% solution
Answers
An amount of 2 liters of the 30 % vinegar solution to obtain a 20 % vinegar solution.
How to determine the required addition to obtain a given measure of a vinegar solution
According to the statement, a vinegar solution with a given concentration must be prepared by using two vinegar solutions with different concentrations. We can find the required addition of the 30 % vinegar solution by weighted averages, whose respective formula is:
(20 / 100) · (4 + x) = (30 / 100) · x + (15 / 100) · 4
0.2 · (4 + x) = 0.3 · x + 0.15 · 4
0.8 + 0.2 · x = 0.3 · x + 0.6
0.1 · x = 0.2
x = 2
An amount of 2 liters of the 30 % vinegar solution to obtain a 20 % vinegar solution.
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1. A restaurant has three pieces of apple pie, five pieces
of cherry pie, and four pieces of pumpkin pie in its
dessert case. How many ways are there to arrange the
pies in a line? (note every pie is a unique work of art).
Answers
there are a total of 7983360 way of arrangements of the pies.
As we are provided we three pieces of apple pie, five pieces of cherry pie, and four pieces of pumpkin pie, in total 12 pies
So total combination will be
12! = 1*2*3*4*5*6*7*8*9*10*11*12
= 479001600
In the event that there was 1 pie, at that point it would be fair 1 in its line. If we had 2 pies A and B, at that point we have 2 combinations AB and BA. Adding a 3rd pie C would multiply those combinations by 3, ABC, ACB, BAC, BCA, CAB, and CBA. If each pie piece may be a unique work of craftsmanship at that point 12! is the proper amount of combinations. On the off chance that you need combinations that disregard setups where for illustration two cherry pie pieces are compatible, meaning you want uniqueness at that point you divide 12! by 5 at that point by 3 and after that by 4.
Usually 12! / (5*3*4) = 7983360 exceptionally interesting combinations.
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A sign by the pears reads, "Buy 1/4 pound for only 1/2 dollar!" Ms. Morales thought that the pears cost more than $1.00 per pound. Her daughter, Jasmine, thought that the pears cost less than $1.00 per pound. Who is correct?
Answers
Answer:Ms. Morales is right
Step-by-step explanation: it is 1/2 a dollar = to 50 cents 50 cents x 4 =2.00$
The scale on a blueprint says that 1 cm is the equivalent of 3 ft. A particular line on the blueprint representing a wall measures 12 cm. How long should the wall be?
Answers
The scale on a blueprint says that 1 cm is the equivalent of 3 ft. A particular line on the blueprint representing a wall measures 12 cm. Wall is 36 ft long.
Given,
Scale on a blueprint says that 1 cm is the equivalent of 3 ft
1cm = 3ft
A particular line on the blueprint representing a wall measures 12 cm.
12cm = 12(3) ft
= 36ft
Wall is 36 ft long.
The act or system of measuring is referred to as measurement. It may be viewed as a procedure for utilizing numbers to define physical objects. "This rod is bigger than that rod," for instance.
Since we don't know anything about the specific characteristics of the provided rods, this statement only serves a very narrow function of comparison. However, if we claim that the first rod is 20 inches long and the second is 15 inches, the first rod will be 5 inches longer than the second. This claim provides us with support for our deduction and makes greater sense mathematically.
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Add: 1/(x-3) + 4/(x+5)
Simplify answer
Answers
The expression can be simplified as 4x-12/x-3
How to simplify the expression ?The expression is
1/(x-3) + 4/(x+5)
= (x+5) + 4(x-3)/(x-3)(x+5)
= 4x-12/x-3
Hence the expression can be simplified as 4x-12/x-3
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During track practice any walks three minutes for every eight minutes of running at this rate how many minutes will she walk in a total if she runs 32 minutes
