Answer: The answers are (-8,8) and (2,-12)
Step-by-step explanation: I substituted the coordinates into the equations and on both sides they matched!
Hope this helps! :3
What is the equation of the slant asymptote of the rational function?
f(x)=10x3−15x2+x−15x2−2
Responses
y=x−3
y equals x minus 3
y=2x−115
y equals 2 x minus fraction 11 over 5
y=2x−3
y equals 2 x minus 3
y=x−115
y equals x minus fraction 11 over 5
Using division of polynomials, the equation of the slant asymptote of the rational function is given by:
y = 2x - 3.
How to find the slant asymptote of a rational function?Suppose a rational function given by a division of two functions, as follows:
r(x) = f(x)/g(x).
The slant asymptote of the function is nothing more than the quotient of functions f(x) and g(x), that is, the division of functions f(x) and g(x).
For this problem, the function is:
r(x) = (10x³ - 15x² + x - 1)/(5x² - 1).
Hence:
f(x) = 10x³ - 15x² + x - 1.g(x) = 5x² - 1.Using a calculator, the division of these two functions is:
y = 2x - 3 + (3x - 4)/(5x² - 1)
3x - 4 is the remainder, but we consider only the quotient, hence the equation of the slant asymptote of the rational function is given by:
y = 2x - 3.
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If two angles
complementary, then their measures sum to 90
It is necessary that the for complementary angles then their measures sum to 90 degree.
According to the statement
We have to explain all about the complementary angles.
So, For this purpose, we know that the
Complementary angles are pair angles with the sum of 90 degrees.
From the given information:
We have to prove that the If two angles complementary, then their measures sum to 90.
Then
Contrapositive of p → q is ~q → ~p where p is that the hypothesis and q is that the conclusion.
Hypothesis (p) = Two angles are complementary
~p = Two angles aren't complementary
Conclusion (q) = The sum of their measures is 90°
~q = The sum of their measures isn't 90°
~ p → ~q = If the sum of the measures of two angles isn't 90°,
then they're not complementary angle.
So, It is necessary that the for complementary angles then their measures sum to 90 degree.
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Teacher Guided 1. In a book club, the ratio of male to the number of female members was 2:7. After 12 male members left the club, the ratio became 1:4. How many member were there in the book club at first?
Answer:
16
Step-by-step explanation:
Answer:
teacher guided 1 in a book
Step-by-step explanation:
At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot un 48 22 Cold 8 12 5 What is the probability that a customer ordered a small given that he or she ordered a larg drink? Rounded to the nearest percent, [? ]% Enter
The probability that a customer ordered a large given that he or she ordered a hot drink is 88 % .
What is Probability ?
The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail).The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Probability Formula = f/n
where,
f is the number of times an event occurs
n is the total number of trial
The probability is represented as:
P(Large | Hot)
This is calculated using:
P(Large | Hot) = n(Large and hot)/n(hot)
Using the data on the given table, we have:
P(Large | Hot) = 22/(8 + 12 + 5)
P(Large | Hot) = 0.88
In percentage
P(Large | Hot) = 88%
Hence, the probability that a customer ordered a large given that he or she ordered a hot drink is 88 % .
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Find the degree of the polynomial and determine whether it is a monomial, binomial, trinomial, or none of these.
13x²-x³-13x4
What is the degree of the polynomial?
Find the 69th term of the following arithmetic sequence.
2, 7, 12, 17, ...
Step-by-step explanation:
a=2
d=12-7=5
[tex]sn = \frac{n(2a + (n - 1)d)}{2} \\ s69 = \frac{69(2(2) + (69 - 1) \times 5)}{2} \\ s69 = 11868[/tex]
HOPE THIS HELPS!!
You drive 15 miles North and then head East and drive an additional 25 miles. What is your total dis- tance?
Answer: 40
Step-by-step explanation: the answer is only 40 if you are doing addition. and i did 15 + 25. 15 +25 is 25 + 10 = 35+5 =40
I really don’t understand Exponents Much. Could someone explain the subject to me? I learn best with examples!
Tysm <3
Exponentiation is a mathematical operation denoted by the symbol bn that consists of two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n."
What are exponents?Exponentiation is a mathematical operation denoted by bⁿ the symbol bn that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bⁿ is the product of multiplying n bases:[tex]b^n=\underbrace{b \times b \times \cdots \times b \times b}_{n \text { times }}[/tex]
Typically, the exponent is shown as a superscript to the right of the base. In that case, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or simply "b to the nth."Several other properties of exponentiation follow directly from the basic fact stated above that, for any positive integer display style n, display style bⁿ is displayed style n occurrences of display style bb all multiplied by each other. More specifically:[tex]\begin{aligned}b^{n+m} &=\underbrace{b \times \cdots \times b}_{n+m \text { times }} \\&=\underbrace{b \times \cdots \times b}_{n \text { times }} \times \underbrace{b \times \cdots \times b}_{m \text { times }} \\&=b^n \times b^m\end{aligned}[/tex]
For example, the number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 2³) means: 2 x 2 x 2 = 8.Therefore, exponentiation is a mathematical operation denoted by the symbol bn that consists of two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n."
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Regan swims for the Sharks swim team. Last season, the Sharks won 5 swim meets for every 3 they lost.
Pick the diagram that models the ratio in the story.
If the Sharks had 16 swim meets in all, how many did they win?
If the Sharks had 16 swim meets in all, they won 10 swims.
Given,
Regan swims for the Sharks swim team. Last season, the Sharks won 5 swim meets for every 3 they lost.
We need to find out if the Sharks had 16 swim meets in all, and how many did they win.
How to compare two units?Example:
2 cups = 4 eggs
To find for 4 cups.
We need to multiply 2 so that 2 cups becomes 4 cups.
4 cups = 2 x 4 eggs = 8 eggs
We have,
5 sims own for every 3 swims lost.
We can write it as:
5 own = 3 lost
Multiply 2 on both sides
2 x 5 own = 2 x 3 lost
10 own = 6 lost
We have,
16 swims in total.
It can be written as,
10 own = 6 lost
And we see that,
10 + 6 = 16 swims
Thus,
If the Sharks had 16 swim meets in all, they won 10 swims.
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The two stadiums with the largest capacities are Marshfield Stadium and Bowden Stadium. Marshfield Stadium has a capacity of 6,427 more than Bowden. If the combined capacity for the two stadiums is 210,355, find the capacity for each stadium.
The capacity for the Bowden and Marshfield Stadiums are 101, 954 and 108, 381 respectively.
How to determine the valueLet the Bowden Stadium be x
From the information given, we have that;
Bowden Stadium = xMarshfield Stadium = x + 6,427Sum of both Bowden and Marshfield Stadiums = 210,355This can be represented as;
x + x + 6,427 = 210,355
collect like terms
2x + 6427 = 210,355
2x = 210, 335 - 6427
2x = 203, 908
Make 'x' the subject
2x/2 = 203, 908/ 2
x = 101, 954
Then,
Bowden Stadium = x = 101, 954
Marshfield Stadium = x + 6,427 = 101, 954 + 6,427 = 108, 381
Thus, the capacity for the Bowden and Marshfield Stadiums are 101, 954 and 108, 381 respectively.
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Precipitation for the month of March was 4 3/4 inches less than average. I’m April, the precipitation was 1 1/2 inches less than average. How many inches below average was the precipitation for both March and April?
The inches below average was the precipitation for both March and April is 6 1/4 inches
How to compute the value?From the information given, the precipitation for the month of March was 4 3/4 inches less than average. In April, the precipitation was 1 1/2 inches less than average.
Therefore, the inches below average will be:
= 4 3/4 + 1 1/2
= 4 3/4 + 1 2/4
= 6 1/4
The inches is 6 1/4 inches.
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Find the domain of the function g(x)= 4/x^2 +3x +2. Write your answer in set builder notation
Answer:
[tex] \{x|x \neq -2, -1 \}[/tex]
Step-by-step explanation:
The denominator cannot equal 0 because division by zero is undefined.
[tex]x^2 + 3x+2 \neq 0 \implies (x+1)(x+2) \neq 0 \implies x \neq -1, -2[/tex]
[tex]\therefore \{x|x \neq -2, -1 \}[/tex]
Answer:
[tex] \{x|x \neq -2, -1 \}[/tex]
Step-by-step explanation:
The denominator cannot equal 0 because division by zero is undefined.
[tex]x^2 + 3x+2 \neq 0 \implies (x+1)(x+2) \neq 0 \implies x \neq -1, -2[/tex]
[tex]\therefore \{x|x \neq -2, -1 \}[/tex]
Davis is trying to decide between two part time jobs on Saturdays. He could make $16.25 per hour working
at the city's ice arena, but getting to work and back would cost him $7.50 round trip for travel. His other
option is to work as a dog walker in his neighborhood for $12.50 per hour but he can ride his bike or walk
there for free. He estimates he could work up to 7 hours at the arena but up to 10 hours walking dogs. He
always works at least 1 hour if he goes to the arena.
1. Write two different functions that represent Davis's gross wages, where h is the number of
hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and
d(h) is his gross wages from walking dogs.
1. State the domain and range for each function.
2. If Davis works 1 hour, what would be his gross pay at each job? What if he worked 6 hours?
3. Davis wants to know what his net pay, also called take-home pay, is going to be. Assume that
10.5% of just his paycheck, not his travel expenses, is withheld for taxes at the arena. Because
dog walking is a self-employed activity, Davis estimates he needs to set aside 18% of his income
for taxes. Modify your functions from question 1 to model net pay including these tax
withholdings.
4. State the domain and range for each of these new functions.
1) Two different functions that could represent Davis' gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs are:
Function A: a(h) = 16.25h - 7.50
Function B: d(h) = 12.50h
2) If Davis works 1 hour, his gross pay at each job is:
1 Hour 6 Hours
a) $16.25 $97.50
b) $12.50 $75
3) To find Davis' net pay after tax, the modified functions in question 1 are as follows:
Function A: a(h) = (16.25h - 7.50)(1 - 0.105)
Function B: d(h) = 12.50h(1 - 0.18)
4) The domain and range for each of these new functions are:
Domain Range
a) Function A [1, 2, ... 7] [7.83, 15.66, ... 54.81]
b) Function B [1, 2, ... 12] [10.25, 20.5, ... 123]
What are the domain and range of a function?The domain refers to all the possible values of the independent (input) variables.
The range refers to the possible values of the dependent (output) values.
Data and Calculations:Arena Dog Walking
Pay rate per hour $16.25 $12.50
Travel expense $7.50 $0
Maximum hours worked 7 hours 10 hours
Gross pay for one hour $16.25 $12.50
Gross pay for 6 hours $97.50 $75
After
Tax 10.5% 18%
After-tax factor (1 - 0.105) (1 - 0.18)
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−7.94 + 2.5
−5.44
−8.19
−10.44
54.40
Answer:
−5.44
Step-by-step explanation:
−7.94 + 2.5
Calculate
−5.44
describe the relationshipbetween the values of the digits in the 9,999,999
Answer:
You can multiply 10 to get each place value 9 x 10 = 90
90 x 10 = 9000
9000 x 10 = 90,000
Step-by-step explanation:
Sorry if it doesn't help
Emergency helppppp mee one questionn plsss yikessss!!!
Answer:
It is the last answer shown where the absolute value of -4 is the greatest
-2.47, -2, -1 3/4, -3/8, | -4 |
Step-by-step explanation:
Absolute value indicates how far away a value is from zero. The sign is not relevant in that context.
Given the function, complete the table of values then graph the ordered pairs.
Answer: a
Step-by-step explanation:
Kayla wants to coach basketball. The Lady Falcons will pay her a monthly salary of
$2250 plus a bonus of $75 for every game they win. Their rival, the Lady Hornets
offered her a greater monthly salary of $2750 but only gives a bonus of $25 for every
game they win. Write a system of linear equations to determine how many games they
would have to win in order to receive the same pay from either team.
Write the system. You do not need to solve.
Answer:
[tex]$ \left \{ {{y= 2250 + 75x} \atop {y=2750 + 25x}} \right. $[/tex]
If Kayla's team wins 10 games on each team, she would be paid the same amount.
Step-by-step explanation:
Hello!
Let the amount of money earned be y, and the number of games they win be x.
For the Lady Falcons, the equation would be y = 2250 + 75x.
For the Lady Hornets, the equation would be y = 2750 + 25x.
The system would be [tex]\left \{ {{y= 2250 + 75x} \atop {y=2750 + 25x}} \right.[/tex].
_______________________________________________________
The question says not to solve, but we are going to solve it anyway for practice.
Solve the Systemy = 2250 + 75xIf Kayla's team wins 10 games on each team, she would be paid the same amount.
Convert -56 degree c to Kelvin
How do you find the surface area of the pyramid
The pyramid's surface area is = 409.6 cm2.
The provided pyramid's surface area is equal to its square base plus its lateral sides.
The square base's area is given by (Side)2
= (8)2
= 64 cm2.
Area of the lateral side = 1/2 (Lateral height)(Base)
= √4² + (9.2)
2 [By applying Pythagoras theorem]
82.81+36
= √100.64
= 10.8 cm
Area of the lateral side = (8)(10.8)
= 86.4 cm²
The provided pyramid's surface area is calculated as follows:
Area of the base + 4(Area of one lateral side)
= 64 + 4(86.4)
= 409.6 cm2.
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Using the following information about the family’s assets and liabilities, calculate the total assets: Checking account: $3,000 Savings account: $13,000 Credit card balance: $5,500 Utility bill: $500 Home: $320,000 Mortgage (30 years): $210,000 Car: $25,000 Car loan (60 months): $18,000 Student loan (7 years): $25,000 Household items: $15,000 Retirement account: $64,000 Other assets: $39,000
The net worth of a given family is $227500.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Assets are simply subtracted from liabilities to determine net value. Your money and investments, your home and other properties you own, your automobiles, and any other valuable possessions you own are all considered assets.
Assets = 3,000 + 13,000 + 5,500 + 15,000 + 64,000 + 320,000 + 25,000 + 39,000 = 484500
Liabilities = 500 + 210,000 + 18,000 + 25,000 = 257000
Net worth = Assets - Liabilities
Net worth = $484500- $257000 = $227500
Thus, the net worth of a given family is $227500.
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1. A honeybee leaves the hive and travels 2 KM before returning. What distance did the
honeybee travel and what was the honeybee's displacement
Total distance travelled by the honey bee is 4km and honeybee’s displacement is 0
Displacement is defined as the shortest distance travelled by the object.
According to the question we have been given that the honeybee travelled 2km before returning to the hive.
Thus the total distance travelled by the honeybee is = 2 + 2 km
= 4 km
And the honeybee’s displacement = 0
Because the bee has returned to the same from where she had left and displacement is a vector quantity that has magnitude and direction and depends upon the initial and final position. So as the initial and final destination is same for the honeybee. Thus the displacement will be zero.
Hence total distance = 4km
And displacement = 0
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In the triangles below, m/B = m/P and m/T = m/J. What is the length of pq
Answer:
5 1/3
Step-by-step explanation:
Apply +133.3% to the sides
NO LINKS!
Please help me
Reason:
If we were asked to compute log(ab), then we could use this log rule
log(ab) = log(a) + log(b)
However, we aren't multiplying the 'a' and b, so we cannot use the log rule above. There's not enough information to be able to compute log(a+b)
Choice C is a trick answer I've seen many students fall for since the erroneous thinking would be log(a+b) = log(a)+log(b) = 1.2+5.6 = 6.8
Answer:
b) Not enough information
Step-by-step explanation:
Given the logs of two values, you want to know the log of their sum.
Rules of logarithmsThe logarithm function cannot be applied to a sum. The purpose of the logarithm function is to turn the log of a product into a sum of logs. The logarithm function cannot be applied to a sum.
The only way to determine the log of the sum is to take the antilogs of the given values, add them, then take the log of the result.
Log(a+b)Assuming the base of the logarithms is 10, using the strategy just described, we can compute ...
log(a +b) = log(10^log(a) +10^log(b)) = log(10^1.2 +10^5.6)
≈ log(15.848932 +398,107.17) ≈ log(398,123.02)
≈ 5.6000173 . . . . using base 10 logs
If these are natural logs, which are also often written as log(x), as well as ln(x), then the log of the sum is about
log(e^1.2 +e^5.6) ≈ 5.6122026 . . . . using base e logs
The short answer is, there is not enough information. (The base of the logarithms must be known.)
89 children were at a party. When 50% of the girls and 20% of the boys left, there were 55 children remaining at the party. How many boys were at the party at first?
Answer:
Step-by-step explanation:
x: boy
y: girl
x+y=89 & 89-(0.2x+0.5y)=55
⇒x+y=89 & 0.2x+0.5y=34
⇒ x=35 & y=54
Natasha treats herself to some choco-vanilla ice cream. She prepares the treat with
1
8 scoops of chocolate ice cream and 2- times as much vanilla ice cream as chocolate.
2
How much vanilla ice cream does she use?
Answer:
Step-by-step explanation:
A whole number rounded to the nearest hundred is 9,452,600. What is the greatest possible value for that number?
Answer: 9,452,599
Step-by-step explanation:
it is the closest number to the 100th place without going into decimals
5,270÷59 what is IT brbr.rnrr
Answer:
89.3220338983
Step-by-step explanation:
good luck
Simplify this question
Answer:
10.5
Step-by-step explanation:
1 + 5 = 6
6 * 7 = 42
3 - 1 = 2
2^2 = 4
42 / 4 = 10.5
Answer:
[tex] = { \rm{ \frac{1 + 5.7}{ {(3 - 1)}^{2} } }} \\ \\ = { \rm{ \frac{1 + 5.7}{4} }} \\ \\ = { \rm{ \frac{6.7}{4} }} \\ \\ = { \rm{1 \frac{27}{40} }}[/tex]
At a toy company every fourth stuffed animal has its eyes inspected, and every tenth stuffed animal has its tag inspected. Which animal will be the first to have both its eyes and tag inspected?
Answer:
the 20th animal
Step-by-step explanation:
we need to find the least number dividable by 4 and 10
20 is the lowest number divided by both
20 divided by 4 = 5
20 divided by 10 = 2
