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Naming Polynomials
Name each polynomial by degree and number of terms.
1) 3
2) 6a3
3) 9m + 5m² + 10m3 - 5
4) -9x + 4x2 – 2x3 - 10x?
5) 5
6) -7 + 3n3
7) -a"
8) -2 + 6x - 72
9) 6
10) 10.rº
11) 6r* – 2x
12) 9+ 4m?
13) -3n
14) -ns
ans
4) -9x + 4x2 – 2x3 - 10x?
cos(4x + pi/5) - sin 2x = 0
cos(4x + π/5) - sin(2x) = 0
Since cos(x + π/2) = -sin(x), we can write
cos(4x + π/5) = cos(4x + π/2 - 3π/10) = -sin(4x - 3π/10)
Then we can absorb the negative signs into either sin expression, using the fact that sin(-x) = -sin(x):
-sin(4x - 3π/10) - sin(2x) = 0
sin(3π/10 - 4x) + sin(-2x) = 0
Recall that
• sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
• sin(a - b) = sin(a) cos(b) - cos(a) sin(b)
==> • 2 sin(a) cos(b) = sin(a + b) + sin(a - b)
We can further condense the left side in our equation if there exists a solution to
{ 3π/10 - 4x = a + b
{ -2x = a - b
We have
(a + b) + (a - b) = (3π/10 - 4x) + (-2x)
==> 2a = 3π/10 - 6x
==> a = 3π/20 - 3x
(a + b) - (a - b) = (3π/10 - 4x) - (-2x)
==> 2b = 3π/10 - 2x
==> b = 3π/20 - x
So in our equation, we have
sin(3π/10 - 4x) + sin(-2x) = 0
2 sin(3π/20 - 3x) cos(3π/20 - x) = 0
sin(3π/20 - 3x) cos(3π/20 - x) = 0
Solve for x :
sin(3π/20 - 3x) = 0 or cos(3π/20 - x) = 0
[3π/20 - 3x = arcsin(0) + nπ or 3π/20 - 3x = π - arcsin(0) + nπ]
or [3π/20 - x = arccos(0) + nπ or 3π/20 - x = -arccos(0) + nπ]
[3π/20 - 3x = nπ or 3π/20 - 3x = π + nπ]
or [3π/20 - x = π/2 + nπ or 3π/20 - x = -π/2 + nπ]
[3x = 3π/20 - nπ or 3x = -17π/20 - nπ]
or [x = -7π/20 - nπ or x = 13π/20 - nπ]
[x = π/20 - nπ/3 or x = -17π/60 - nπ/3]
or [x = -7π/20 - nπ or x = 13π/20 - nπ]
(where n is any integer)
5. * Your parents drove the family car 462 miles on 14 gallons of gas. On average, how many miles did the car travel on each gallon of gas (Write the expression and solve)?
Answer:
33 miles did the car travel on each gallon of gas
A(-1, 3), B(2, 2), and C(3, -6). If the triangle is translated 5 units to the right, what are the coordinates of A'?
Answer:
(4,3)
Step-by-step explanation:
If the triangle ABC is moved 5 units to the right, the coordinates of A will be (4,3). We can find this by using the values already given for A. We are given (-1,3) which is A's current position. Since we are moving it to the right we are only looking at the first number. If we add 5 to -1 we get 4 which we put in the place of the -1 in the coordinates to get our answer.
Sophie bought snacks for her team's practice. She bought a bag of chips for $2.49 and
a 12-pack of juice bottles. The total cost before tax was $27.57. Write and solve an
equation which can be used to determine x, how much each bottle of juice costs?
Call a bottle of juice costs is x
$2.49 + 12x = $27.57
12x = $27.57 - $2.49
12x = $25.08
x = $25.08 / 12
x = $2.09
SO each bottle of juice costs $2.09.
Mark as Brainliest If the answer is helpful!
Will give brainliest
Answer:
about 15.08
Step-by-step explanation:
Angle BAC + Angle CAH = 180 (they are supplenmentary angles), which means (12x+4)+(x-20)=180
solve:
13x-16=180
13x=196
x≈15.08
Answer:
12x+4 + x-20 = 180
13x = 196
x = 15.08
Step-by-step explanation:
The population of the world grows exponentially at a rate of 1.1% per year.
Find the number of years it takes for the population to grow from 7 billion to 7.31 billion.
Give your answer correct to the nearest whole number.
Answer:
4
Step-by-step explanation:
Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have
population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as
(original population)*1.011ˣ
Therefore, to get from 7 billion to 7.31 billion, we have
7 billion * 1.011ˣ = 7.31 billion
divide both sides by 7 billion to relatively isolate the x
1.011ˣ = 7.31/7
Another way of writing this is
log (base 1.011) (7.31/7) = x
≈ 3.96
Rounding to the nearest whole number, we get 4 as our answer
The number of years it takes for the population to grow from 7 billion to 7.31 billion is;
n = 4 years.
We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.
Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;
P_1 = 1.011¹ × P
After 2 years, it will be;
P_2 = 1.011² × P
Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;
P_n = 1.011ⁿ × P
Now, we are told that the population grew from 7 billion to 7.31 billion.
Thus;
P = 7 billion
P = 7 billion P_n = 7.31 billion
Thus;
7 billion × 1.011ⁿ = 7.31 billion
divide both sides by 7 billion to get;
1.011ⁿ = 7.31/7
1.011ⁿ = 1.044285
n log 1.011 = log 1.044285
n = 0.018819/0.004751156
n ≈ 4 years
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Make a sketch that matches the description: E is between F and G. H is between F and E.
Hi! I'm happy to help!
For this, you just simply follow the directions, and alter as you go. First, we need to place E between F and G, so we can put F and G on opposite sides of E.
F E G
From here, we put H between F and E
F H E G
I hope this was helpful, keep learning! :D
I need help solving this.
16 - 2t + 5t +9
Answer:
give brainliest please I need it to level up
Step-by-step explanation:
16 - 2t + 5t + 9
16 + 9 -2t + 5t=0
25 + 3t =0
3t= -25
t= -8.3
Find the area of the shape.
Either enter an exact answer in terms of π or use 3.143, point, 14 for π and enter your answer as a decimal
Answer:
84.861
Step-by-step explanation:
In the given figure, 1/4 part of Circle is missing
so, we have to find the area of 3/4 part of circle
Area of circle = πr²
Given, r = 6
Now, Area of 3/4 part of circle = (3/4)×πr²
= (3/4) × 3.143 × 6²
= 84.861
Simplify 9/12 into simplest form
SOLVE FOR Y
2x-y=3
pls help
Answer:
x = 3+y/2
Step-by-step explanation:
6+7(x+5)<-25-2x
need help
What fraction is equal to -0.37?
which is the simplified form of the expression
please help!!
Answer:
A
Step-by-step explanation:
p^-8q^-20 * p^8q^-10
=q^-30
=1/q^30
Seventeen more than twice a number is -13. What is the number?
Answer:
-15
Step-by-step explanation:
17+2a=-13
2a=-30
a=-15
Seven teenagers were asked what they charge hourly for babysitting,
The results are shown below. What is the median of these prices?
$8.00, $8.50, $9.00, $9.25, $9.50, $10.75, $11.00
Median- is the middle value whereby the values are place in order (ascending)
$9.25 is the median of these prices
Fine the measurements. Are this correctly?
Answer:
1: 5 2: 13 3: sqr root of 15 4: 1 5: 1 6: 3
Step-by-step explanation:
Follow the formula a squared plus b squared equals c squared. C is always the longest side of the equation. So figure out your variables to fill in and in the end, square root your remaining answer.
a region's average movie theater ticket price in 2007 was $6.72. For 2017, it was estimated to be $8.81. Find the percent of increase in average movie theater ticket price for this 10-year periods
Answer:
31.1011905%
Step-by-step explanation:
Take the new price and subtract the original price
8.81 - 6.72
2.09
Divide by the original price
2.09/6.72
.311011905
Change to percent form
31.1011905%
Percent of increase in average movie theatre ticket price will be 31.1%
Given prices of the ticket in two different years are,
In year 2007 price of the ticket was $6.72After 10 years price of the ticket is $8.81To calculate the percent increase in the price of an object expression to be used,
Percent increase = [tex]\frac{\text{Final price - Initial price}}{\text{Initial price}}\times 100[/tex]
= [tex]\frac{8.81-6.72}{6.72}\times 100[/tex]
= [tex]0.311\times 100[/tex]
= [tex]31.10[/tex]%
Therefore, percent of increase in the price of the ticket will be 31.1%
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helpppppppppppp fast ill mark you brainlist or whatever !!! hurry i have one try
Elisa withdrew $22 at a time from her bank account and withdrew a total of $198. Frances withdrew $45 at a time from his bank account and withdrew a total of $270. Who made the greater number of withdrawals? (select) made the greater number of withdrawals, because she made withdrawals, while (select) only made withdrawals.
Step-by-step explanation:
Elisa made the greater number of withdrawals, because she made 9 withdrawals, while Frances only made 6 withdraws.
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
x = x + 3
The equation has ____.
(options are no solution, one solution, or infinite solutions)
A value of x that makes the equation false is ___, which when substituted into the equation and simplified makes the equation turn into ___ = ____.
Another value of x that makes the equation false is ___, which when substituted into the equation and simplified makes the equation turn into ___ = ___.
Answer:
There are no solutions.
The left side of the equation will always be three less than the right side of the equation since both sides have the same variable.
Explain how to evaluate f (2) to a student that is
absent today.
Verify the following (-23) { ( -5) + (19) } = ( -23) x -5 + (-23) x (19)
explanation needed fast pls
hey please help i’ll give brain new question sorry
Answer:
12. This is because of the commutative property of addition.
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Using the commutative property of addition
8+4 = 12
4+8 = 12
why reason distance cannot be negative?
Answer:
Distance cannot be negative because no matter which direction you travel, you will never travel negative units.
Step-by-step explanation:
Distance cannot be negative in the same way that when you put a car in reverse, the odometer does not go backwards.
If you have a mailbox 30 feet east of your house and a park 30 feet west of your house, you can think of it like a number line: your house is 0, the park is -30 and the mailbox is 30. But, if you walk to your park, you have not walked -30 feet.
HELP! WILL GIVE BRAINLIEST!!! I think it's D please check
Factor completely x3 + 5x2 − 3x − 15.
(x − 5)(x2 − 3)
(x + 5)(x2 + 3)
(x − 5)(x2 + 3)
(x + 5)(x2 − 3)
Answer:
(x + 5) (x^2 -3)
Step-by-step explanation:
[tex]x^{3} +5x^{2} - 3x - 15[/tex]
Do the grouping:
[tex]x^{3} +5x^{2} - 3x - 15 = (x^{3} +5x^{2}) + (-3x - 15)[/tex]
Then factor out [tex]x^{2}[/tex] in the first and −3 in the second group.
[tex]x^{2}(x+5) - 3(x+5)[/tex]
Factor out the common term x + 5 by using the distributive property.
Polynomial [tex]x^{2}-3[/tex] is not factored in since it does not have any rational roots, thus getting the following:
[tex](x+5)(x^{2} -3)[/tex]
Answer:
the fourth option (x+5)(x²-3)
Step-by-step explanation:
the "-15" tells us we need a 3 and a 5 with different signs.
that eliminates the first and the second options.
and the "5x²" tells us it has to be +5, as there is only one part in the whole multiplication that delivers a x² term (5×x²).
it is also confirmed for the same reasons by "-3x" that the other number has to be -3.
15 L + 2% please help
Answer:
15.3 L
Step-by-step explanation:
1% of 15 is 15÷100=0.15
0.15×2=0.3, so 2% is 0.3
15+0.3=15.3
Is there a answer to this
Answer:
mean=71
Step-by-step explanation:
Mean x¯¯¯x¯
71
Median x˜x~
72
Mode
64, 83, 79, 38, 81, 90, 59, 93, 70, 73, 71, 51
Range
55
Minimum
38
Maximum
93
Count n
12
Sum
852
Quartiles
Quartiles:
Q1 --> 61.5
Q2 --> 72
Q3 --> 82
Interquartile
Range IQR
20.5
Outliers
none
Y=3x-5 please help ASAP
Therefore, a linear equation in two variables has infinitely many solutions. Thus, y = 3x + 5 has infinitely many solutions. Hence (iii) is the correct answer.
Please help me one question left
Answer:
thanks for points
Step-by-step explanation:
too easy boi
How do you do this ? Anyone who know how and can explain this
Answer:
G. 105.
Step-by-step explanation:
Percentage of cars with 3 or more people
= 15 + 7 + 3
= 25%,
25% of 420
= 0.25 * 420
= 105.