first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.
here,
7. (-154) ➗ (-14) =11
11. (-40) ➗10=-4
15. 90 ➗ (-15)=-6
16. 108 ➗ (-9)=-12
17. (-48) ➗ (-6)=8
18. (-105) ➗ 7=-15
hope it helps you..........
according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
Answer:
6
Step-by-step explanation:
First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.
Expanding, we get
(x³-3x+1)² = (x³-3x+1)(x³-3x+1)
= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1
= x^6 - 6x^4 + 2x³ +9x²-6x + 1
In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots
Matthew actually drew the 10 of hearts and the 3 of clubs. If he keeps those to one side and selects two more from the pack, what is the chance that he'll get a pair of 10s this time? As before, give your answer in its simplest form. 2nd Attempt: Probability of getting a pair of 10s
If the rate of inflation is 2.6% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today.
p(t)=600(1.026)t
Find the current price of the item and the price 9 years from today.
Round your answers to the nearest dollar as necessary.
Answer:
The current price of the item is $600.
The price of the item 9 years from today will be of $756.
Step-by-step explanation:
Price of the item:
The price of the item, in dollars, after t years, is given by:
[tex]p(t) = 600(1.026)^t[/tex]
Current price of the item
This is p(0). So
[tex]p(0) = 600(1.026)^0 = 600[/tex]
The current price of the item is $600.
9 years from today.
This is p(9). So
[tex]p(9) = 600(1.026)^9 = 756[/tex]
The price of the item 9 years from today will be of $756.
Which of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46
Log6^(4x-5)=Log6^(2x+1)
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Given
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Required
Solve for x
We have:
[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]
Remove log6 from both sides
[tex](4x-5) = (2x+1)[/tex]
Collect like terms
[tex]4x - 2x = 5 + 1[/tex]
[tex]2x = 6[/tex]
Divide by 2
[tex]x = 3[/tex]
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
Answer:
260% is the correct answer
Step-by-step explanation:
i hope i helped
The owner of a greenhouse wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use a random number table to select a simple random sample. She labels the violets 01–60. Refer to the given line from a random number table. Which numbers represent the first 5 plants selected?
60633 78034 99602 83440 55120 61551
33, 03, 49, 02, 40
06, 33, 03, 49, 02
60, 63, 37, 80, 34
60, 37, 34, 28, 40
Answer:
60, 37, 34, 28, 40
(D)
ED2021
Please help me out really need it
Answer:
[tex]{ \tt{hypotenuse = { \boxed{5}}}} \\ { \tt{opposite = { \boxed{3}}}} \\ { \tt{adjacent = { \boxed{4}}}} \\ \\ { \tt{ \sin \angle R = \frac{{ \boxed{3}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \cos \angle R = \frac{{ \boxed{4}}}{{ \boxed{5}}} }} \\ \\ { \tt{ \tan \angle R = \frac{ \boxed{3}}{{ \boxed{4}}} }}[/tex]
X = The set of months in a year?
there are 12 set of months in a year
Determine if the triangle is Right, Acute or Obtuse.
Answer:
I think the right answer is: Acute
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor. What is the recommended investment portfolio for this client? What is the annual return for the portfolio? A second client , also with $500,000 has been classified as aggressive. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor
Answer:
Blair & Rosen (B&R) Plc.
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total portfolio returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
Step-by-step explanation:
a) Data and Calculations:
Maximum investible savings = $500,000
Projected annual return of the internet fund = 12%
Projected annual return of the blue-chip fund = 9%
Maximum determined amount to invest in the internet fund = $350,000
Risk rating for the internet fund = 6/1,000
Risk rating for the blue-chip fund = 4/1,000
Maximum risk rating for a moderate investor = 240
Maximum risk rating for an aggressive investor = 320
Recommendation for moderate investor:
Internet fund = 96/240 * $500,000 = $200,000
Blue-chip fund = 144/240 * $500,000 = $300,000
Annual return for the portfolio:
Internet fund = $200,000 * 12% = $24,000
Blue-chip fund = $300,000 * 9% = $27,000
Total returns = $51,000
Annual returns of portfolio = $51,000/$500,000 * 100 = 10.2%
Recommendation for aggressive investor:
Internet fund = 192/320 * $500,000 = $300,000
Blue-chip fund = 128/320 * $500,000 = $200,000
What numbers are to the right of 0 on the number line?
Answer:
Positive numbers.
Step-by-step explanation:
Numbers after zero are positive numbers, which can be any number (whole or decimal/fraction). But numbers before zero are negative numbers which can be also whole or decimal fraction.
Example for numbers to the right of 0: 7, 6.5, 8/10
Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker
Two workers finished a job in 7.5 days.
How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?
let t = time required by one worker to complete the job alone
then
(t+8) = time required by the other worker (shirker)
let the completed job = 1
A typical shared work equation
7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1
multiply by t(t+8), cancel the denominators, and you have
7.5(t+8) + 7.5t = t(t+8)
7.5t + 60 + 7.5t = t^2 + 8t
15t + 60 = t^2 + 8t
form a quadratic equation on the right
0 = t^2 + 8t - 15t - 60
t^2 - 7t - 60 = 0
Factor easily to
(t-12) (t+5) = 0
the positive solution is all we want here
t = 12 days, the first guy working alone
then
the shirker would struggle thru the job in 20 days.
Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15
Step-by-step explanation:
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,
y'' - 6y' + 9y = 0
If y = C₁ exp(3x) + C₂ x exp(3x), then
y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))
y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))
Substituting these into the DE gives
(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))
… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))
… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))
= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))
… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))
… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)
= 0
so the provided solution does satisfy the DE.
Please help!!! Find the domain of the function y = 2 cot(5∕8x).
A) All real numbers except odd integer multiples of 8π∕5
B) All real numbers except 0 and integer multiples of 8π∕5
C) All real numbers except 0 and integer multiples of 4π∕5
D) All real numbers except odd integer multiples of 4π∕5
Answer:
B) All real numbers except 0 and integer multiples of 8π∕5
Step-by-step explanation:
Cotangent function:
The cotangent function is given by:
[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]
Domain:
All real values except those at which:
[tex]\sin{ax} = 0[/tex]
The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]
In this question:
[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.
Simplify to the extent possible
(logx16)(log2x)
Answer:
[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]
Change base x to base 2:
[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]
How many tens are in 6 hundreds
Answer:
60
Step-by-step explanation:
10 x 6 = 60
Hope this helped! :)
HELP ANYONE PLZZZ ?
1sr.
z(x)=x+1
If you input a 3 into z(x), what do you get for the output?
2nd.
n(x)=2/x
n(x) will give you an output for any number you use as an input except which of the following?
A. 0
B .3
C. 5
D. Trick question- you can get an output for every number you use as an input .
9514 1404 393
Answer:
4A. 0Step-by-step explanation:
1. Input 3 for x and do the arithmetic.
z(x) = x+1
z(3) = 3+1 = 4 . . . . . the output is 4
__
2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.
What is the endpoint of a line segment if the midpoint M( – 3, 4) and the other endpoint is E(7, – 2)?
Answers
(– 13, 10)
(10, – 13)
(– 1, 2)
(2, – 1)
9514 1404 393
Answer:
(-13, 10)
Step-by-step explanation:
If M is the midpoint of segment DE, then ...
D = 2M -E
D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)
The other end point is (-13, 10).
please help, it’s urgent !!!
D
A
B
C
for more explanation please don't hesitate to just respond
Hi, help with question 18 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle y^2 = 1 + \sin x[/tex]
And we want to prove that:
[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]
Find the first derivative by taking the derivative of both sides with respect to x:
[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]
Divide both sides by 2y:
[tex]\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}[/tex]Find the second derivative using the quotient rule:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]
Combine fractions:
[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]
Simplify:
[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]
Cancel:
[tex]\displaystyle -\sin x + y^2 = 1[/tex]
Substitute:
[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]
Simplify. Hence:
[tex]1\stackrel{\checkmark}{=}1[/tex]
Q.E.D.
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew $60 from his bank account 3 times.
what is the change in mikes account balance after all 3 withdrawals?
a+b=60000
[tex]\frac{a}{b}=\frac{4}{1}[/tex]
a=?
b=?
Answer: a = 25.67
Step-by-step explanation:
I need the answer to this
Answer:
[tex]A)\:x<12[/tex]
[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]
OAmalOHopeO
Answer:
x < 12.................................
Solve 60 ÷ 5(1 + 1(1 + 1))
Answer:
Creo que es 36
Step-by-step explanation
:D
Answer:
36
Step-by-step explanation:
Find the lateral area of this square based pyramid. 10in 5in (in the image)
Answer:
100 in²
Step-by-step explanation:
4 triangles, each of them has area = 10*5/2
so total area = (10*5/2)*4
= (10*5*2)
= 100 in²
Answered by GAUTHMATH
The lateral surface area of the pyramid is 100 in²
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.
4 triangles, each of them has an area = 10 x ( 5/2 )
So total area = (10 x 5/2) x 4
Total area = (10 x 5 x 2)
Total area = 100 in²
Therefore the lateral surface area of the pyramid is 100 in²
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use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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work out the equasion 39+(−13)
Answer:
39-13=26
Step-by-step explanation:
plus(minus)=minus
The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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