Answer:
1) 11x + 9x
= 20x
2) 8y - 7y
= 1y
= y
3) 5t - 7t
= -2t
4) -n + 4n
= 3n
5) 5w² + 12w²
= 17w²
6) 2x² - 9x²
= -7x²
7) -4y² + 9y²
= 5y²
8) 6c - 4 + 2c - 7
= 8c - 11
9) 5 - 3x + y + 6
= 11 - 3x + y
Given z = 4 (cos (pi/ 2) + i sin (pi/2 ) ) , what is z3?
a)12 (cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction pi Over 2 EndFraction) )
b)64 (cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction pi Over 2 EndFraction) )
c)12 (cosine (StartFraction 3 pi Over 2 EndFraction) + I sine (StartFraction 3 pi Over 2 EndFraction) )
d)64 (cosine (StartFraction 3 pi Over 2 EndFraction) + I sine (StartFraction 3 pi Over 2 EndFraction) )
Answer:
D
Step-by-step explanation:
The value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.
What is a complex number?A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.
For the given situation,
The complex number, z = 4 (cos (pi/ 2) + i sin (pi/2 ) )
[tex]z=4(cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )[/tex]
⇒ [tex]z^{3}=4^{3} (cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )^{3}[/tex]
By De Moivre's theorem,
[tex]{\displaystyle {\big (}\cos x+i\sin x{\big )}^{n}=\cos nx+i\sin nx}[/tex]
Thus, [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex]
Hence we can conclude that the value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.
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Abigail wants to attend a community college. Suppose x represents the number of credits she takes and y represents her total fees in dollars. Which of these statements are correct? Select all that apply.
A.
If tuition amounts to $125 plus $150 per credit, the function that would model this situation is y = 150x + 125.
B.
If tuition amounts to $200 plus $175 per credit, the function that would model this situation is x = 175y + 200.
C.
If tuition amounts to $175 plus $150 per credit, the function that would model this situation is y = 175x + 150.
D.
If tuition amounts to $250 plus $275 per credit, the function that would model this situation is x = 250y + 275.
E.
If tuition amounts to $225 plus $200 per credit, the function that would model this situation is y = 200x + 225.
F.
If tuition amounts to $100 plus $125 per credit, the function that would model this situation is y = 125x + 100.
Answer:
ddddddddddxdddxsddddddddD
Step-by-step explanation:
i hope it helps you
What is the annual interest for a principle of $3,500 at a simple annual interest rate of 2.3%?
Answer:
80.5
Step-by-step explanation:
factorise the following: x*2-2x-3
should i use dy\dx (normal differentiation) or d²y\dx² (differentiation of the differentiation)?
Use both!
You want to minimize P, so differentiate P with respect to x and set the derivative equal to 0 and solve for any critical points.
P = 8/x + 2x
dP/dx = -8/x² + 2 = 0
8/x² = 2
x² = 8/2 = 4
x = ± √4 = ± 2
You can then use the second derivative to determine the concavity of P, and its sign at a given critical point decides whether it is a minimum or a maximum.
We have
d²P/dx² = 16/x³
When x = -2, the second derivative is negative, which means there's a relative maximum here.
When x = 2, the second derivative is positive, which means there's a relative minimum here.
So, P has a relative maximum value of 8/(-2) + 2(-2) = -8 when x = -2.
Jan jdjnznxwjzn help
Answer:
A.
Step-by-step explanation:
it is due in very soon and i don’t wanna fail math. can someone plz help. :/
Answer:
y= -1 , 0 , y = -2
x= 10 , infinity , x = 7
x= -4 , infinity , x= 7
1.
A. SSS
B.T SAS
C. ASA
D. AAS
E. HL
F.. Not
Answer:
ASA
Step-by-step explanation:
Simplify the expression.
-3a + (-5a) – 7 + 6a
A. 14a + 7
B. -2a + 7
C. 2a - 7
D. -2a - 7
SHOW YOIUR WORK PLZSSSSSS
Please Help Quick ASAP Hurry This is Pre-Algebra 1 i need the answer now please ASAP
Which Word Best describes the numbers 10 and -10?
A.Opposites
B.Coordinate
C.Absolute Value
D.Expression
Answer:
Part A
Step-by-step explanation:
is the point (-2,3) a solution to y<2x+1?
Answer:
No it is not
Step-by-step explanation:
Plug it in
3 < 2(-2) + 1
3 < -4 + 1
3 < -3
3 is not less than -3
PQR is an isosceles triangle in which PQ=PR
M and N are points on PQ and PR such that angle MRQ=angle NQR
Prove that triangles QNR and RMQ are congruent
9514 1404 393
Explanation:
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Solve 3/5k-5=7/10k by eliminating the fraction. Explain how you determine what to multiply each term by and all the steps to solving the equation.
9514 1404 393
Answer:
k = -50
Step-by-step explanation:
The fraction denominators are 5 and 10. The least common multiple of those values is 10. This means we can eliminate fractions by multiplying both sides of the equation by 10:
6k -50 = 7k
Subtracting 6k from both sides of the equation leaves you with the solution:
-50 = k
What is the estimated product?
86 × 32
Answer:
2,752
Step-by-step explanation:
86x32 = 2752
Product: It means to multiply.
Answer:
I believe the estimated product is 2749
PLEASE ANSWER ASAP For the Christmas and holiday season, every student in Mrs. Perri’s class decided to send a card to each student in the class and to Mrs. Perri. There are 31 students in the class. How many cards were sent that day?
Find the slope of the line containing the pair of points.
(-8,-2) and (6,3)
Answer:
5/14
Step-by-step explanation:
3--2=5
6--8=14
In GHJ, GH = 21 inches, HJ = 24 inches, and GJ = 9 inches. Which statement is true? A. G is smallest B. J is smallest C. H is largest D. G is largest
Answer:
G is the smallest
H is the largest
Step-by-step explanation:
Given
[tex]GH = 21[/tex]
[tex]HJ = 24[/tex]
[tex]GJ = 9[/tex]
Required
Which of the statements is true
First, we need to solve for G, H and J as follows:
[tex]G + H = 21[/tex] --- (1)
[tex]H + J = 24[/tex] --- (2)
[tex]G + J = 9[/tex] --- (3)
Make G the subject in (1)
[tex]G = 21 - H[/tex]
Substitute 21 - H for G in (3)
[tex]21 - H + J = 9[/tex]
Collect Like Terms
[tex]-H + J = 9 - 21[/tex]
[tex]-H + J = -12[/tex]
Make J the subject
[tex]J = H - 12[/tex]
Substitute H - 12 for J in (2)
[tex]H + H - 12 = 24[/tex]
[tex]2H - 12 = 24[/tex]
Collect Like Terms
[tex]2H = 24 + 12[/tex]
[tex]2H = 36[/tex]
Solve for H
[tex]H = 18[/tex]
Substitute 18 for H in [tex]J = H - 12[/tex]
[tex]J = 18 - 12[/tex]
[tex]J = 6[/tex]
Substitute 18 for H in [tex]G = 21 - H[/tex]
[tex]G = 21 - 18[/tex]
[tex]G = 3[/tex]
So, we have that:
[tex]G = 3[/tex] [tex]J = 6[/tex] [tex]H = 18[/tex]
Hence, we can conclude that:
G is the smallest
H is the largest
Find the recursive rule, explicit rule, and f(20)
Answer:
Recursive:
[tex]f(1)=4, f(n)=f(n-1)-4[/tex]
Explicit:
[tex]f(n)=4-4(n-1)[/tex]
And the 20th term f(20) is -72.
Step-by-step explanation:
We have the sequence:
4, 0, -4, -8...
Let’s find the recursive and explicit rule for the sequence.
Recursive Rule:
Let’s determine the factor by which the sequence is decreasing by. We see that each subsequent term is 4 less than the previous term. In other words, our common difference is -4.
So, this is a arithmetic sequence.
The standard format for an recursive rule for an arithmetic sequence is:
[tex]f(1)=a , f(n)=f(n-1)+(d)[/tex]
Where a is the initial term and d is our common difference.
From our sequence, we know that our initial term a is 4.
We also determined that our common difference is -4.
Substitute. Hence, our recursive rule is:
[tex]f(1)=4, f(n)=f(n-1)-4[/tex]
Explicit Rule:
The standard format for an explicit rule for an arithmetic sequence is:
[tex]f(n)=a+d(n-1)[/tex]
Where a is the initial term and d is the common difference. So, again, let’s substitute 4 for a and -4 for d. Hence, our explicit formula is:
[tex]f(n)=4-4(n-1)[/tex]
To find f(20), we can use the explicit formula. It is possible to use the recursive formula, but it gets tedious. Therefore, we will substitute 20 for n for our explicit formula:
[tex]f(20)=4-4(20-1)[/tex]
Evaluate:
[tex]\begin{aligned} f(20)&=4-4(19) \\ f(20)&=4-76 \\ f(20)&=-72 \end{aligned}[/tex]
Hence, our 20th term is -72.
Solve for x -1 + 18x 16x + 9
Answer:
[tex]288 {x}^{2} + x + 18[/tex]
Step-by-step explanation:
Ayan po ang answer sana po makatulong
Paki heart nalang po kung nakatulong
#carrying learning
Osama buys some notebooks and some pens.
Each notebook costs $12 more than each pen.
The total cost of 5 notebooks and 2 pens is $64.20.
Find the cost of one pen.
Answer:
$2.10
Step-by-step explanation:
12*5=60
64-60.20=4.20
4.20 is for 2 pens
4.20/2=2.10
=$2.10
What is the equation of the line shown in this graph?
Answer:
y = 1
hope that helps you
What are the vertical asymptotes of 10/X-1
Answer:
Enter a problem...
Algebra Examples
Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)
f
(
x
)
=
10
x
2
−
1
Find where the expression
10
x
2
−
1
is undefined.
x
=
−
1
,
x
=
1
Since
10
x
2
−
1
→
∞
as
x
→
−
1
from the left and
10
x
2
−
1
→
−
∞
as
x
→
−
1
from the right, then
x
=
−
1
is a vertical asymptote.
x
=
−
1
Since
10
x
2
−
1
→
−
∞
as
x
→
1
from the left and
10
x
2
−
1
→
∞
as
x
→
1
from the right, then
x
=
1
is a vertical asymptote.
x
=
1
List all of the vertical asymptotes:
x
=
−
1
,
1
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
0
m
=
2
Since
n
<
m
, the x-axis,
y
=
0
, is the horizontal asymptote.
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
1
,
1
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
image of graph
The vertical asymptotes of the given function are x = 1 and x = -1,
We have given the rational function is 10/(x²-1).
We need to find the vertical asymptotes of this function.
Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.
To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.
x²-1=0
x²=1
x=±√1
x=±1
Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.
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What is the slope of this line?
Enter your answer as a fraction in simplest term in the box.
Can someone help me with this pls?
Answer:
1/4 is the simplest form
Step-by-step explanation:
Answer:
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MARK ME BRAINLIESTMARK ME BRAINLIEST
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second. y=-16x^2+242x+73
Answer:
t = 15.42 s
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
[tex]y=-16x^2+242x+73[/tex]
We ned to find the time when the rocket will the ground. For this, y = 0
[tex]-16x^2+242x+73=0[/tex]
It is a quadratic equation whose solution is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Here, a = -16, b = 242 and c = 73
[tex]x=\dfrac{-b+ \sqrt{b^2-4ac} }{2a}, x=\dfrac{-b-\sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-242+ \sqrt{(242)^2-4(-16)(73)} }{2(-16)}, x=\dfrac{-242- \sqrt{(242)^2-4(-16)(73)} }{2(-16)}\\\\=-0.295\ s, 15.42\ s[/tex]
Neglecting negative value.
So, it will hit the ground in 15.42 s.
Answer:
t = 15.42 s
Step-by-step explanation:
for what value of X is ABCD a rectangle ? explain your answer
Answer:
10
Step-by-step explanation:
If ABCD is a rectangle, then AB=CD and AC=BD.
AC=BD, so x+6=2x-4Subtract, -x+6=-4Subtract, -x=-10Make positive, x=10Check work:
10+6=2(10)-410+6=20-416=16I need help on this thx
The price of some medication was increased from $8 to $12. By what percentage was the price of the medicine increased?
Answer: 25 percent
Step-by-step explanation:
The price of the medicine was increased by 50%.
Given,
The price of some medication was increased from $8 to $12.
We need to find by what percentage the price of the medicine increased.
How do we find a percentage increase?The formula used is given as:
Percentage increase = [tex]\frac{Final~amount - Initial~amount} {Initial ~amount}[/tex] x 100
Find the initial amount.
= $8
Find the final amount.
= $12
Find the percentage increased.
= ($12 - $8) / $8 x 100
= 4/8 x 100
= 1/2 x 100
= 50%
Thus the price of the medicine was increased by 50%.
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Of all the items on the pizza, enter the fraction that is mushrooms.
---------------
Answer:
2/3
Step-by-step explanation:
A cheetah ran 60/4 and a gazelle ran 100/8 which won is higher
Answer:
The cheeta is slow, the gazelle
Step-by-step explanation:
The cheeta x2 is 120/8 making the gazelle higher
Answer:
Cheetah
Step-by-step explanation:
One: Cheetah's have always been known as the fastest animals on earth.
Mathematically:
60 / 4 = 15 (cheetah)
100 / 8 = 12.5 (gazelle)
15 is higher than 12.5
Can you tell me whether this represents a function or not? (For both questions, just say ‘Yes or No’)
Answer:
No for both
Step-by-step explanation:
If 2 x values that are the same but different y values for them then its not a function