Answer:
Step-by-step explanation:
[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]
= -5x² + 25xy + xy - 5y²
= 5x(-x + 5y) - y(-x +5y)
= (-x + 5y)(5x - y)
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE explain thoroughly. Chapter 9 part 1
1. How can you determine the end behaviors for a graph from the function? What are the possible behaviors?
2. How is solving a polynomial inequality different from a solving a polynomial equation? How do the solutions differ?
3. What is a composite function? How does order of the composite function play a role in solving the composition?
9514 1404 393
Explanation:
1. End behavior is the behavior of the function when the value of the independent variable gets large (or otherwise approaches the end of the domain). There are generally four kinds of end behavior:
the function approaches a constant (horizontal asymptote)the function approaches a function (slant asymptote, for example)the function oscillates between two of the above end behaviorsthe function tends toward +∞ or -∞Of these, behavior 2 will ultimately look like one of the others.
For polynomials, the function will always approach ±∞ as the independent variable approaches ±∞. Whether the signs of the infinities agree or not depends on the even/odd degree of the polynomial, and the sign of its leading coefficient.
For exponential functions, the end behavior is a horizontal asymptote in one direction and a tending toward ±∞ in the other direction.
For trig functions sine and cosine, the end behavior is the same as the "middle" behavior: the function oscillates between two extreme values.
For rational functions (ratios of polynomials), the end behavior will depend on the difference in degree between numerator and denominator. If the degree of the denominator is greater than or equal to that of the numerator, the function will have a horizontal asymptote. If the degree of the numerator is greater, then the end behavior will asymptotically approach the quotient of the two functions—often a "slant asymptote".
__
2. A polynomial inequality written in the form f(x) ≥ 0, or f(x) > 0, will be solved by first identifying the real zeros of the function f(x), including the multiplicity of each. For positive values of x greater than the largest zero, the sign of the function will match the sign of the leading coefficient. The sign will change at each zero that has odd multiplicity, so one can work right to left to identify the sign of the function in each interval between odd-multiplicity zeros.
The value of the function will be zero at each even-multiplicity zero, but will not change sign there. Obviously, the zero at that point will not be included in the solution interval if the inequality is f(x) > 0, but will be if it is f(x) ≥ 0. Once the sign of the function is identified in each interval, the solution to the inequality becomes evident.
As a check on your work, you will notice that the sign of the function for x > max(zeros) will be the same as the sign of the function for x < min(zeros) if the function is of even degree; otherwise, the signs will be different.
The solution to a polynomial inequality is a set of intervals on the real number line. The solution to a polynomial equation is a set of points, which may be in the complex plane.
__
3. A composite function is a function of a function, or a function of a composite function. For example f(g(x)) is a composite function. The composition can be written using either of the equivalent forms ...
[tex](f\circ g)(x)\ \Leftrightarrow\ f(g(x))[/tex]
It can be easy to confuse an improperly written composition operator with a multiplication symbol, so the form f(g(x)) is preferred when the appropriate typography is not available.
When simplifying the form of a composition, the Order of Operations applies. That is, inner parenthetical expressions are evaluated (or simplified) first. As with any function, the argument of the function is substituted wherever the independent variable appears.
For example, in computing the value f(g(2)), first the value of g(2) is determined, then that value is used as the argument of the function f. The same is true of other arguments, whether a single variable, or some complicated expression, or even another composition.
Note that the expression f(g(x)) is written as the composition shown above. The expression g(f(x)) would be written using the composition operator with g on the left of it, and f on the right of it:
[tex](g\circ f)(x)\ \Leftrightarrow\ g(f(x))[/tex]
That is, with respect to the argument of the composition, the functions in a composition expression are right-associative. For example, ...
for h(x)=2x+3, g(x)=x^2, f(x)=x-2 we can evaluate f(g(h(x)) as follows:
f(g(h(x)) = f(g(2x+3) = f((2x+3)^2) = (2x+3)^2 -2
It should be obvious that g(h(f(x)) will have a different result.
g(h(f(x)) = g(h(x-2)) = g(2(x-2)+3) = (2(x-2)+3)^2
Knowing that AQPT = AARZ, a congruent side pair is:
Answer:
A. QT ≅ AZ
Step-by-step explanation:
When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.
Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:
QP ≅ AR
PT ≅ RZ
QT ≅ AZ
The only correct one given in the options given above is QT ≅ AZ
Simplify 6 - (-2) - 3(-5).
Answer:
23
Step-by-step explanation:
6 - (-2) - 3(-5).
PEMDAS says multiply first
6 +2 +15
Add
23
Answer:
Answer is 23
Step-by-step explanation:
First open brackets:
[tex] = 6 + 2 + 15[/tex]
summ up:
[tex] = 23[/tex]
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim
Answer:
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that under 64% fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at least 64%, that is:
[tex]H_0: p \geq 0.64[/tex]
At the alternative hypothesis, we test if the proportion is of less than 64%, that is:
[tex]H_1: p < 0.64[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
64% is tested at the null hypothesis:
This means that [tex]\mu = 0.64, \sigma = \sqrt{0.64*0.36}[/tex]
A sample of 900 computer chips revealed that 61% of the chips fail in the first 1000 hours of their use.
This means that [tex]n = 900, X = 0.61[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.61 - 0.64}{\frac{\sqrt{0.64*0.36}}{\sqrt{900}}}[/tex]
[tex]z = -1.88[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.61, which is the p-value of z = -1.88.
Looking at the z-table, z = -1.88 has a p-value of 0.0301.
The p-value of the test is 0.0301 > 0.02, which means that there is not sufficient evidence at the 0.02 level to support the company's claim.
3. Find the least common denominator for the group of denominators using the method of prime numbers. 45, 75, 63
We have to find LCM
3 | 45,75,63
3 | 15,25,21
5 | 5,25,7
5 | 1,5,7
7 | 1,1,7
LCM=3×3×5×5×7=1575
The least common denominator for the group of denominators using the method of prime numbers is 1575.
What is least common multiple?LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers. A factor is one of the numbers that multiplies by a whole number to get that number.
For the given situation,
The numbers are 45, 75, 63
Prime factors of 45 = [tex]3,3,5[/tex]
Prime factors of 75 = [tex]3,5,5[/tex]
Prime factors of 63 = [tex]3,3,7[/tex]
Then the LCM can be found by, first take the common factors then multiple the remaining factors as,
⇒ [tex](3)(3)(5)(5)(7)[/tex]
⇒ [tex]1575[/tex]
Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.
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Enter a value that would not make relation a function (-4,0),(?,8),(9,0),(-5,2)
Answer:
Step-by-step explanation:
? = -4, 9, or -5
The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
What are zeros of quadratic function?The zero of the function is where the y-value is zero. The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
here, we have,
from the given the information , we get,
If one zero is x= 4, then one factor of the expression would be (x - 4).
Similarly if another zero is x=-9, then another factor of the expression would be (x+9)
We have two answers with these two factors and both are possible. So, the answers are b and c.
Hence, The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
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complete question:
Which function's graph has a zeros at (4,0) and (-9,0)?
3 coins Priya spends $45 on gas, $10 on dinner, and $8 on a video game. How much money did Priya spend on variable expenses?
Answer:
3x=63
Step-by-step explanation:
3 coins means a coin is x and total expenditure is equal to 63
4. Tony bought a computer, a cell
phone, and a television. The
computer costs 2.5 times as much
as the television. The television cost 5 times as much as the cell phone. If Tony spent a total of $925, how much did the cell phone
cost?
Answer:
$50
Step-by-step explanation:
Let x represent the cost of the cell phone.
Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.
Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.
Create an equation to represent the situation, and solve for x:
x + 5x + 12.5x = 925
18.5x = 925
x = 50
So, the cell phone cost $50
Answer:
$50
Step-by-step explanation:
Let x represent the cost of the cell phone.
Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.
Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.
Create an equation to represent the situation, and solve for x:
x + 5x + 12.5x = 925
18.5x = 925
x = 50
So, the cell phone cost $50
a car completes a journey in 8hours it covers half the distance at 40kms per hours and the rest at 60 km per hour. what is the total distance of the journey?
Answer:
384 kmph
Step-by-step explanation:
75% increase followed by 50% decrease is it greater than to original
Answer:
Set original amount = xAfter a 75% increase, it would become
x + 75%x = x + 0.75x = x(1 + 0.75) = 1.75x
After a 50% decrease, it would become
1.75x - 50%(1.75x) = 1.75x - 0.5(1.75x) = 1.75x - 0.875x = 0.875x = [tex]\frac{7}{8} x[/tex]
Because [tex]\frac{7}{8} x[/tex] is less than x, the new amount would be less than the original.
What is the slope of the line that passes through the points listed in the table?
x l y
8 l 3
10 l 7
A. -4
B. -2
C. 2
D. 4
Answer:
2
Step-by-step explanation:
The slope is given by
m = ( y2-y1)/(x2-x1)
= (7-3)/(10-8)
= 4/2
= 2
Please help !!! Plzzzz
Explanation:
Because we have a midsegment, this means that it is half as long as the side it's parallel to. You can think of "mid" as "middle" and that could lead to "halfway" to remember to take half.
So z = 14/2 = 7
compute (-12)+(-8)+30
Answer:
10
Step-by-step explanation:
(-12) + (-8) +30
-(12+8)+30
-20 + 30
10
What is the period of the graph of y = 5 sin (pi x) + 3?
Equate whats inside (arguments) [tex]\sin[/tex] with base period of sine function [tex]2\pi[/tex] and solve for x to get period,
[tex]\pi x=2\pi\implies x=2[/tex]
So the period of the graph of the given function is precisely 2.
Hope this helps :)
Answer:
Step-by-step explanation:
bvjvhvghj
Evaluate the line integral
Soydx + zdy + xdz,
[»= f (t)=dw= f'(t)dt
where C is the parametric curve
x=t, y=t, z=ť, Ost<1.
It looks like you're asked to compute
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz[/tex]
where C is parameterized by ⟨t, t, t⟩ with 0 ≤ t ≤ 1.
In other words, x = y = z = t, so dx = dy = dz = dt, and the integral reduces to
[tex]\displaystyle\int_C y\,\mathrm dx + z\,\mathrm dy + x\,\mathrm dz = \int_0^1 t\,\mathrm dt + t\,\mathrm dt + t\,\mathrm dt \\\\ = 3 \int_0^1 t\,\mathrm dt \\\\ =\frac32t^2\bigg|_{t=0}^{t=1} \\\\ =\boxed{\frac32}[/tex]
(x
3
+y
3
)(xy
4
+7)
Answer:
question is not proper
Step-by-step explanation:
question is
evaluate (5^0-4^-1)×3/4
Answer:
[tex](5^{0} -4^{-1} )(\frac{3}{4} )\\\\=(1-\frac{1}{4^{1}} )(\frac{3}{4} )\\\\=(\frac{4}{4} -\frac{1}{4} )(\frac{3}{4} )\\\\=(\frac{3}{4} )(\frac{3}{4} )\\\\=\frac{9}{16}[/tex]
Which subset(s) of numbers does 5 3/8 belong to ?
Answer:
Rational number
Step-by-step explanation:
Given
[tex]5\frac{3}{8}[/tex]
Required
The subset it belongs to
Express as improper fraction
[tex]5\frac{3}{8} = \frac{43}{8}[/tex]
The above number is rational because it is represented by the division of 2 integers, i.e. 43 and 8 are integers
Express as decimals
[tex]5\frac{3}{8} = 5.375[/tex]
The above number cannot be classified as integers or whole because it has decimal parts
w • (-4+ z) = mz + 17
z = ____
solve for z.
ps.. pls help me lol. i need the answer
Answer:
z = (17+4w)/(w-m)
Step-by-step explanation:
w • (-4+ z) = mz + 17
Distribute
-4w +wz = mz+17
Subtract mz from each side
-4w +wz - mz = mz+17-mz
-4w +wz-mz = 17
Add 4w to each side
-4w +4w+wz-mz = 17+4w
wz-mz = 17+4w
Factor out z
z(w-m) = 17+4w
Divide by (w-m)
z(w-m)/(w-m) = (17+4w)/(w-m)
z = (17+4w)/(w-m)
To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts.23 One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:
Answer: Hello your question is incomplete attached below is the complete question
answer:
i) 0.8 , standard error = 0.0516
ii) 0.39, standard error = 0.0425
Step-by-step explanation:
i) proportion of Juveniles reference for females ( f )
= x₁ / n₁ = 48 / 60 = 0.8
standard error = [tex]\sqrt{\frac{0.8(1-0.8)}{60} }[/tex] = 0.0516
ii) Proportion of Juveniles reference for males ( m )
= x₂ / n₂ = 52 / 132 = 0.39
standard error = [tex]\sqrt{\frac{0.39(1-0.39)}{132} }[/tex] = 0.0425
Q12 A baker wants to order crough our for 10 laves of bread weighing 750g each. She has a recipe for a 500g loaf of bread which needs 480g of flour, How many kiograms of flour does the baker need? Show your working kg (3 marks)
Answer:
i am not sure lol
Step-by-step explanation:
please help i dont wanna fail
Answer:
4
Step-by-step explanation
Plug in the numbers for x and y.
4/4 ( 2 + (6) - (4))
Remove the parenthesis. Since 4/4 is equal to 1, you can put down 1 as well.
1 (2 + 6 - 4)
Distribute the 1. When anything is multiplied by 1, it remains the same.
2 + 6 - 4
Simplify.
4
[tex]\huge\boxed{\textsf{Hey there!}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{x}{4}(2 + y - x)}}[/tex]
[tex]\huge\boxed{\mathsf{= \dfrac{4}{4}(2 + 6 - 4)}}[/tex]
[tex]\huge\boxed{\mathsf{= 1(8 - 4)}}[/tex]
[tex]\huge\boxed{\mathsf{= 1(4)}}[/tex]
[tex]\huge\boxed{\mathsf{= 4}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: 4}}\huge\checkmark[/tex]
[tex]\huge\boxed{\boxed{\textsf{Good luck on your assignment \& enjoy your day!}}}[/tex]
~[tex]\huge\boxed{\boxed{\huge\boxed{\mathsf{Amphitrite1040:)}}}}[/tex].2333 repeating as a fraction
Answer and Step-by-step explanation:
0.2333...
First, multiply the number by 10 (because there is 1 number being repeated.
2.333.....
Now subtract by the original number.
2.333...
- 0.2333...
2.10
Write this as an equation:
(10 x fraction) - fraction = 2.1 (10 x fraction) - fraction = 9 x fraction
9 x fraction = 2.1 (Divide both sides by 9)
[tex]\frac{2.1}{9}[/tex] = [tex]\frac{7}{30}[/tex]
[tex]\frac{7}{30}[/tex] is the answer.
(To check, do 7 divided by 30 in a calculator, and you will get 0.233 repeating)
#teamtrees #PAW (Plant And Water)
I hope this helps!
kofi earned 50 cedis mowing lawn. today, kofi earned 60% of what he earned yesterday mowing lawns. how much money did kojo earn mowing lawn today
Answer:
Kofi earned today = 30 cedis
Step-by-step explanation:
Given:
Kofi earned yesterday = 50 cedis
Kofi earned today = 60% of Kofi earned yesterday
Find:
Kofi earned today
Computation:
Kofi earned today = 60% of Kofi earned yesterday
Kofi earned today = 60% x 50
Kofi earned today = 0.60 x 50
Kofi earned today = 30
Kofi earned today = 30 cedis
Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?
Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls
The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
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Identify the decimals labeled with letters A B and C on the scale
Answer:
A. 37.39 B. 37.41 C. 37.27
(X^2 + 6x + 8) divided (x + 2)
Answer:
x+ 4
Step-by-step explanation:
____x__+4___
x+2 | [tex]x^2 + 6x + 8[/tex]
[tex]x^2 + 2x[/tex]
------------
[tex]4x + 8\\[/tex]
[tex]4x + 8\\[/tex]
--------
0
Answer:
x+4
Step-by-step explanation:
Given the parent graph h(x) = x, what happens when it is changed to h(x + 9)?
Answer:
If the parent graph is h(x) = x, then h(x+9) would actually be shifting the graph 9 units to the LEFT.
Let me know if this helps!
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
