Answer:
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
Step-by-step explanation:
Let be [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] a rational function armed with polynomial function. We proceed to factor the expression to the find the zeros and poles of the rational function:
1) [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] Given
2) [tex]f(x) = \frac{(x + 2)\cdot (x-2)}{x\cdot (x^{2}-3\cdot x -10)}[/tex] [tex]a^{2} - b^{2} = (a + b)\cdot (a - b)[/tex]/Associative, commutative and distributive properties.
3) [tex]f(x) = \frac{(x+2)\cdot (x-2)}{x\cdot (x-5)\cdot (x+2)}[/tex] [tex]x^{2} -(a+b)\cdot x + a\cdot b = (x-a)\cdot (x-b)[/tex]
4) [tex]f(x) = \frac{x-2}{x\cdot (x-5)}[/tex] Commutative property/Existence of multiplicative inverse/Modulative property/Result
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
bank reduces the interest rate from 12% p.a. to 10% p.a to expand its business. By how much is the yearly interest on Rs. 8,400 decreased?
Answer:
$168
Step-by-step explanation:
yearly interest = principal x time x interest rate
interest when interest rate is 12% = 8400 x 0.12 = 1008
interest when interest rate is 10% = 8400 x 0.1 = 840
decrease in interest rate = 1008 - 840 = 168
3. Solve the system of equations without graphing. Show your reasoning.
ſ 2y = x - 4
4x + 3y = 5
Answer:
X=2, y=-1
Step-by-step explanation:
2y=x-4 equation 1
4x+3y=5 equation 2
x=2y+4 isolate x in equation 1
4(2y+4)+3y=5 substitute value of x from equation 1 into equation 2
8y+16+3y=5
11y=-11
y=-1
solve for x by inputting y value into either equation
2y=x-4
2(-1)=x-4
-2=x-4
2=x
PLEASEEEE ANSWER THIS IM BEING TIMED AND SHOW YOUR WORK ILL GIVE TOU BRAINLIST IF YOU DO!!!!
pls help!!!!!!!!!!!!!!!!!!
Answer:
32 degrees.
Step-by-step explanation:
A triangle is 180 degrees.
180 - 85 - 63 = 32 degrees.
Answer:
x = 32
Step-by-step explanation:
All interior angles in a triangle equal to 180
use this to solve for x
180 = 85 + 63 + x
180 - 85 - 63 = x
32 = x
4) Which shampoo bottle size has the lowest price per ounce?*
Help plz..And No links!! I repeat No links!!
Answer:
the first
Step-by-step explanation:
i did the test
HELP ASAP PLEASE!!!!!
In 2019, Tessa earned $32000. (a) She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018. [2] (b) In 2020, Tessa's earnings increased by 7%. Work out her earnings in 2020.
Answer:
$7,680
$34,240
Step-by-step explanation:
Amount Tessa earns in 2019 = $32000
a. She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018.
Percent of tax = 24%
Amount of tax paid = 24% of $32,000
= 24/100 * 32,000
= 0.24 * 32,000
= $7,680
Amount of tax paid = $7,680
b. Tessa's earnings increased by 7%. Work out her earnings in 2020.
Percentage increase in earnings = 7%
Amount of increase in earnings = 7% of $32,000
= 7/100 * 32,000
= 0.07 * 32,000
= $2,240
Amount of increase in earnings = $2,240
Total earnings in 2020 = Amount Tessa earns in 2019 + Amount of increase in earnings
= $32,000 + $2,240
= $34,240
Total earnings in 2020 = $34,240
The trampoline park charges a $8 for kids and $4 for adults. Your extended family is going there to celebrate your birthday. Your family has at most $190 dollars to spend on entrance fees. You can invite at most 35 people. What are some possible combinations of adults and kids who could go to your party? Write a system of equations for this situation.
Answer:
a+k ≤ 35
8a+4k ≤ 190
Some possible combinations are 10 adults and 20 kids
5 adults and 29 kids
Step-by-step explanation:
Let k= number of kids
a = number of adults
a+k ≤ 35 since you can have at most 35
8a + 4k ≤ 190 since the most you can spend is 190
Some possible combinations are 10 adults and 20 kids
(10+30 < 35 and 8*10+4*20 = 80+80 =160< 190)
Another possible combination
5 adults and 29 kids
(5+29 < 35 and 5*10 + 4*29 =50+116=166)
A shop window is 6 meters long and has an area of 18m².What is the height of the window
Answer:
3 meters
Step-by-step explanation:
Assuming the window is rectangular
A = l*h
18 = 6*h
Divide each side by 6
18/6 = 6h/6
3 = h
Which shows a quadratic function?
Answer:
OPTION B IS YOUR ANSWER.
You know its a quadratic when the second difference of each y value is same.
Here's what I mean.
Option B
First all x values differ by 1. So we're good on those.
Now for the y values
Which are
3, -1, -3, -3, -1
find the difference between the second and first fod each... Then do this a second time.
If it gives the same value for all the second differences... Then its quadratic.
-1-3 = -4
-3-(-1) = -3 + 1 = -2
-3-(-3) = -3 + 3 = 0
-1-(-3) = -1 + 3 = 2.
The values are -4, -2, 0, 2.
Now find the difference of these(2nd - 1st)
-2-(-4) = -2 + 4 = 2
0-(-2)= 0 + 2 = 2
2 - 0 = 2
Since all second differences gave 2 as their answer....
Option B is your Quadratic Function!!!
Hope this helps!
What’s the answer for this
155/18 x 2
Step-by-step explanation:
[tex] \tt{} \frac{155}{18} \times 2[/tex]
[tex]\tt{} \frac{155}{9} [/tex]
[tex]\tt{}17 \frac{2}{9} \\ \\ \\ [/tex]
If I was asked to think of a number and multiply it by 2, I could write this algebraically as 2x. Write the following algebraically, using x as your unknown. "I think of a number, multiply it by 4 and add 5 to the result"
Answer:
4x + 5
Step-by-step explanation:
What are the domain and range of the function represented by the table?
Answer:
Doman is always the x-intercept.
And Range is always the y-intercept.
Domain = {-5, 0, 5, 10, 15}
Range = {-1, 0, 1, 2, 3}
So the answer is C.
what is 12.8% of 250?
Answer:
32
put 12.8% as a decimal which is 0.128 and times it by 250
Answer:
32
Step-by-step explanation:
[tex]\frac{y}{250} :\frac{12.8}{100}[/tex]
y × 100 = 250 × 12.8
100y = 3200
100y ÷ 100 = 3200 ÷ 100
y = 32
I NEED TO GRADUATE I NEED HELP NOW
Two opposing opinions were shown to a random sample of 2,150 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:
Opinion A: The issue of equal pay is more important than increasing the minimum wage.
Opinion B: Increasing the minimum wage is more important than the issue of equal pay.
Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."
The outcomes were as follows:
50% chose Opinion A, 42% chose Opinion B, and 8% chose "Neutral."
Part A: Create and interpret a 99% confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B. (5 points)
Part B: The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met? (5 points)
Answer: Answer:
A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B
= (0.51, 0.57)
This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)
B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
_________________________________________________________
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.
Critical value = 2.33
Standard error = σₓ = √[p(1-p)/n]
p = sample proportion = 0.54
n = sample size = 1500
σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287
98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.54 ± (2.33 × 0.01287)
CI = 0.54 ± 0.02998)
98% CI = (0.51, 0.57)
98% Confidence interval = (0.51, 0.57)
B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?
For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;
- The sample data must have been obtained using a random sampling technique.
- The sampling distribution must be normal or approximately normal.
- The variables of the sample data must be independent of each other.
On the second point, the condition for a binomial distribution to approximate a normal distribution is that
np ≥ 10
and n(1-p) ≥ 10
The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.
For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
Step-by-step explanation:
A store sells two different packages of soda as described below. (Standard 6.EE.9) Package A: 18 soda Package B: 10 soda Write an equation for Package A and an equation for Package B that represent the total number of sodas, g, in p packages.
Answer:
[tex]g = 18p[/tex] --- A
[tex]g = 10p[/tex] ---- B
Step-by-step explanation:
Given
[tex]Package\ A: 18\ soda[/tex]
[tex]Package\ B: 10\ soda[/tex]
Required
The equation of both packages
The given details represent the number of sodas in each package.
So, the equation of A is:
[tex]g = 18p[/tex]
And the equation of B is:
[tex]g = 10p[/tex]
Two adjacent angles form an obtuse angle measured 164°. If m<1 = 3x+5 and m<2= 5x+9, find the measurement of the larger angle. Plz help and don't answer if you don't know for sure :) thxx
Answer:
102.75
Step-by-step explanation:
The two angles add to 164
<1 + <2 = 164
3x+5 + 5x+9 = 164
Combine like terms
8x+14 = 164
Subtract 14 from each side
8x+14-14 =164-14
8x = 150
Divide by 8
8x/8 = 150/8
x = 18.75
The larger angle is 5x+9 = 5(18.75) +9 =102.75
Math question part 2 please help
Answer:
471 cm
Step-by-step explanation:
here diameter of the circle is 150cm, and we know radius is half of diameter.
therefore r = 150/2
= 75
Now,
according to formula,
Circumference of circle = 2πr
= 2 x 3.14 x 75
= 471 cm
Sunaina had three pizzas. She shared the pizzas with her friends. Each of them ate
many friends ate 3/7 of a pizza. How many friends ate the pizza
Answer:
6 friends
Step-by-step explanation:
Take 1/7 multiply by 5/6
9514 1404 393
Answer:
7 friends
Step-by-step explanation:
3 pizzas will give 3/7 of a pizza to each of ...
3/(3/7) = 3 · 7/3 = 7 . . . friends
7 friends ate the pizza.
_____
We assume that Sunaina and her 6 friends constitute 7 friends.
Please give real answers with an explaination. 30 points + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Answer:
option A
Step-by-step explanation:
The line splits the triangle ABC into two triangles with same base length.
Therefore ,
[tex]Area \ of \ ABC = Area \ of \ ABD + Area \ of \ CBD\\\\[/tex]
[tex]= (\frac{1}{2} \times base \times height) + (\frac{1}{2} \times base \times height)\\\\=(\frac{1}{2} \times AD \times BD) + (\frac{1}{2} \times CD \times BD)\\\\=(\frac{1}{2} \times AD \times BD) + (\frac{1}{2} \times AD \times BD)[/tex][tex][ \ Given : AD = \ CD \ ][/tex]
[tex]= 2 \times (\frac{1}{2} \times AD \times BD)\\\\= 2 \times Area \ of \ ABD[/tex]
plz help I need to finish this Geometry
How do you know what method (SSS, SAS, ASA, AAS) to use when proving triangle congruence?
It depends on what type of triangle you’re dealing with, and what is marked similar.
. Parallelogram ABCD,
Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
Answer:
Step-by-step explanation:
Question 1 = 2002
2002 - 2000 = 2 (the years since 2000)
y = (275 x 2) + 50
y = 875
Question 2 = 1425 likes
2005 - 2000 = 5 (the years since 2000)
y = (275 x 5) + 50
y = 1425
Question 3 = 2018
Since y = 5000
5000 - 50(the extra likes) = 4950
4950 / 275 = 18 (the years since 2000)
2000 + 18 = 2018 (the year)
It takes 4 hours for a field to be watered if there are 3 water pipes. How many long would it take for the field to be watered if there were 8 pipes?
Answer:
1.5 hours
Step-by-step explanation:
Total watering hours
4 * 3 = 12
time needed for 8 pipes
12/8 = 1.5 hours
What’s the triangle similarity theorem?
Answer:If a segment is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original and the segment that divides the two sides it intersects is proportional
Step-by-step explanation:
a+b+c=68
a-b=5
b:c=3
-------------------
a,b,c=?
-------------------
Answer:
a = 32
b= 27
c = 9
Step-by-step explanation:
a= 5+ b from the second equation
c= b/3 from the third equation
substitute the above equations to the first equation then solve for b your answer will be 27
substitute the value of b in the second equation you will solve for a
perform the same substitution to the third equation you will get the answer for c
Step-by-step explanation:
a-b=5<=>a=5+b (1)
b:c=3<=>b=3c (2)
a+b+c=68<=>5+b+3c+c=68<=>5+3c+3c+c=68
<=>7c=63<=>c=9
Fill in (2), we have b=3c=3.9=27
and in (1), we have a=5+b=5+27=32
So, a=32, b=27, c=9
John gets paid $76 a day at his new job printing t-shirts. He also earns $2.50 for every t-shirt sold. Create
and equation to describe how much money John makes in a day. Write the equation for this problem in
function notation. Then interpret how much money John would makes in one day after selling 32 t-shirts.
Make sure to define your variables and show all of your work.I swear who ever answers this I will Give them brainlist please help
Answer:
y=76+2.5x where y is the amount he earns in a day and x is the number of tshirts sold
y=76+2.5(32)
y=76+80
y=156
he earns 156 dollars if he sold 32 tshirts
Step-by-step explanation:
5. One side of a triangle is 14 cm and another side is 11 cm, therefore, the
third side must be greater than ___
cm and less then ____
cm.
Can someone help me with this please :,)
Answer: 43.07
Step-by-step explanation:
