Answer:
x + 9y²
Step-by-step explanation:
A prime polynomial is simply an irreducible polynomial.
x + 9y² is a prime polynomial
First, we test the options.
x + 9y²
The above function cannot be reduced further.
Hence, x + 9y² is a prime polynomial
3m + 9n
Factor out 3
3 (m + 3n)
3m + 9n is not a prime because it can be factored as 3 (m + 3n)
8x^7 - 9x + 12x²
Factor out x
x(8x^6 - 9 + 12x)
8x^7 - 9x + 12x² is not a prime because it can be factored as x(8x^6 - 9 + 12x)
Hence, x + 9y² is a prime polynomial
10, 18, 26, 34, 42, ...
Write the simplified formula (expression) for the given Arithmetic Sequence
Answer:
[tex]10 + (n - 1) 8[/tex]
Step-by-step explanation:
All arithmetic sequence can be written as:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So in our sequence we have [tex]a_{1} = 10[/tex] and for find the difference substract two sequence terms.
[tex]d = a_{n+1} - a_{n} = 18 - 10 = 8[/tex]
Now replace the knowns terms in the general form:
[tex]a_{n} = 10 + (n - 1)8[/tex]
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The common difference between any two consecutive terms in an arithmetic sequence is constant.
In this case, the common difference is 8, as each term is obtained by adding 8 to the previous term.
Let the first term of the sequence be 'a', then the second term is 'a + 8', the third term is 'a + 16', and so on.
Therefore, the nth term of the sequence can be expressed as:
a + (n-1)d
where d is a common difference, which is 8 in this case.
So, the simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
where a is the first term of the sequence and n is the position of the term in the sequence.
Thus,
The simplified formula for the given arithmetic sequence is:
a(n) = a + 8 (n - 1)
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ang Find any three rational numbers between 2 and 3
Answer:
5/2, 9/4 and 19/7.
Step-by-step explanation:
Rational numbers can be written as a/b where a and b are integers ( b not = 0).
Find the slope of the line that passes through (75, -83) and (-11, -85).
please I'm in soccer and our last game is Saturday I wont be able to play if I fail this report card so please answer as soon as possible. Please and Thank You.
Slope = (y₂ - y₁) ÷ (x₂ - x₁)
= (-85 - (-83)) ÷ (-11 - 75)
= -2 ÷ -86
= ¹/₄₃
Checking my answer:
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.
⇒ y - (-83) = ¹/₄₃ (x - 75)
⇒ y + 83 = ¹/₄₃ (x - 75)
I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given.
approximate 79.75 to the nearest hundred, ten, whole number, thenth
Answer: ten - 80(?)
hundred - 100
whole number - 80
tenth - 79.8
Is 500 x 30 a good estimate for the number of tickets sold at the number of tickets sold at the theater in one month
Answer:
It depends if business is steady. If they make about 500 a day that is a fair estimate. Make sure that the month you are talking about has 30 days.
Which graph represents the following equation 2x - 4y = 12
I took screen shots of my work here you go!
Which is not a zero of the function?
HELP please AGAIN
Answer:
2
Step-by-step explanation:
The zeroes of a function, or the x-intercepts, are just where the line intersects the x-axis. For this function, you can see the line intersects the x-axis at these 3 points:
x = -4
x = 0
x = 5
Those 3 are the zeroes of this function. 2 is not one of them, so that is your answer.
which one of those equations match the graph
Incase you didn't get the notification on your other post.
Answer:
It's D)
C is incorrect because the constant is + 1, not - 8
A is incorrect because the f doesn't go up by 2 for every x value
B is incorrect because 2/3 * 2 would be 4/3 which is 1 1/3, which is wrong because g goes up by 2 every x.
D is correct because f goes up by 1/3, and the y-intercept is 1 (Where the line meets when the x-axis is 0) and 1/3 * 6x is 6x/3 which is 2x, then add the y-intercept to the equation, which should be 2x + 1
Help guys I need this right now lol I lose credit
Answer:
Answer Below
Step-by-step explanation:
7: Not congruent; Only one angle and only side is shown for each triangle
8: ASA; Two angles shown with a side put in-between
9: SSS; Should be self-explanatory (only sides are shown)
10: ASA; Angles with side shoved between
11: Not Congruent; Triangles are separated and only one side are shown
12: Not Congruent; Angles said to be congruent are on different angles
What is the fourth equivalent fraction to 6/7
Answer:
3/4 is equivalent to 6/7
Hey there!
Equivalent fractions have the same value. Here are some fractions that are equivalent to 6/7:
[tex]\frac{6}{7} =\frac{12}{14} =\frac{18}{21} =\frac{24}{28} ...[/tex]
Hope it helps. Please let me know if you have any questions.
~An excited gal
[tex]MagicalNature[/tex] here to help
d+(-9)=-5
i need to solve for d. thank u
Answer:
4
Step-by-step explanation:
d - 9 = -5
Add 9 to -5, and you will get 4.
4 - 9 = -5
Answer:
d=4
Step-by-step explanation:
d+(-9)=-5
d=-5+9
d= 4
Evaluate the expression when x=−4/5 and y=1/3.
2x+6y
Answer:
2
--
5
Step-by-step explanation:
Start by multiplying 2 and -4/5 as fractions
2 -4 -8
------ x ------ = -------
1 5 5
Then multiply 6 and 1/3 as fractions
6 1 6 2
------ x ------ = ------- = -----
1 3 3 1
Lastly,add the two results after converting 2/1 to 10/5 to use the Greatest Common Factor so you can add.
-8 10 2
------- + ------ = -------
5 5 5
How many times farther is Jupiter from the Sun than Venus? How many times farther is Saturn from the Sun than Mars? Round your answers to the nearest tenth.
The Jupiter is 6.93 times farther from the Sun than Venus
The Saturn is 6.29 times farther from the Sun than Mars
Distance between the sun and Jupiter = 748.02 million km
Distance between the sun and venus = 108.01 million km
Ratio of the distance between the sun and Jupiter to the distance between the sun and Venus = 748.02/108.01
Ratio of the distance between the sun and Jupiter to the distance between the sun and Venus = 6.93
Therefore, the Jupiter is 6.93 times farther from the Sun than Venus
Distance between the Sun and Saturn = 1.4823 billion km = 1482.3 million km
Distance between the Sun and Mars = 235.66 million km
Ratio of the distance between the Sun and Saturn to the distance between the Sun and Mars = 1482.3/235.66
Ratio of the distance between the Sun and Saturn to the distance between the Sun and Mars = 6.29
Therefore, the Saturn is 6.29 times farther from the Sun than Mars
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use the table to work out the values of a, b, c and d
PLEASE HELP!!!
Answer:
a = 10, b = 5, c = 14, d = 25
Step-by-step explanation:
Plug in -2 for x ....
y = 2(-2)^2 + -2 + 4
y = 2(4) + 2
y = 10
Plug in -1 for x ....
y = 2(-1)^2 + -1 + 4
y = 2(1) + 3
y = 5
Plug in 2 for x ....
y = 2(2)^2 + 2 + 4
y = 2(4) + 6
y = 8 + 6
y = 14
Plug in 3 for x ....
y = 2(3)^2 + 3 + 4
y = 2(9) + 7
y = 18 + 7
y = 25
1,2
2,6
3,12
4, 20
Is the function Linear or Nonlinear, and explain why
Explanation:
The variable x increases by 1 each time we move down the rows. This increase is constant or the same jump each time.
However, the variable y increases by different amounts. From y = 2 to y = 6, we have +4. Then from y = 6 to y = 12 is +6. This mismatch of increases is sufficient to prove we don't have a linear function. The function is nonlinear.
Visually, we can plot all of the points on the same xy grid. Notice that a straight line does not go through all four points. Rather, a parabola does, and the equation of the parabola is y = x^2+x which is the same as y = x(x+1).
5y-3=-23
ttttttttttttttttttttttttttttttttt
[tex]5y-3 = -23\\\\\implies 5y = -23 +3 = -20\\\\\implies y = -4[/tex]
sin6x-cos6x=[tex]\sqrt{2}[/tex]
Condense the right side a single sine expression:
sin(6x) - cos(6x) = R sin(6x - t)
Expanding the right side gives
sin(6x) - cos(6x) = R sin(6x) cos(t) - R cos(6x) sin(t)
Then we have
R cos(t) = 1
R sin(t) = 1
Solve for R and t:
(R cos(t))² + (R sin(t))² = 1² + 1²
R² = 2
R = √2
and
(R sin(t))/(R cos(t)) = 1/1
tan(t) = 1
t = arctan(1) = π/4
So we rewrite the equation as
√2 sin(6x - π/4) = √2
Solve for x :
sin(6x - π/4) = 1
6x - π/4 = arcsin(1) + 2nπ
(where n is any integer)
6x - π/4 = π/2 + 2nπ
6x = 3π/4 + 2nπ
x = π/8 + nπ/3
Which point could be used to find f(2)?
point A will represent the input-output values of the function.
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
In the graph of y = f(x),
For every x-value (input value), value of the function is the y-value (output value).
For the input value x = 2,
Output value of the function will be,
y = f(2)
Therefore, point A will represent the input-output values of the function.
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Need help on this! Please help
Answer:
PDR= 127
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Answer:
this question is a very simple. you should start with the biggest triangle then follow the steps to find each side of other triangles. THE ANSWER İS ROOT FORTY ONE
Step-by-step explanation:
these are all right-angled triangles. even the smallest one with the x side.
so, we need to apply Pythagoras to get the missing sides and finally x.
c² = a² + b²
c is the Hypotenuse, the baseline of the triangle opposite of the 90 degree angle. a and b are the legs of the triangle enclosing the 90 degree angle.
so,
52² = 48² + side1²
2704 = 2304 + side1²
400 = side1²
side1 = 20
20² = 12² + side2²
400 = 144 + side2²
256 = side2²
side2 = 16
13² = 5² + (larger part of side2)²
169 = 25 + (larger part of side2)²
144 = (larger part of side2)²
larger part of side2 = 12
that means the smaller part of side 2 = 16-12 = 4.
x² = 5² + 4² = 25 + 16 = 41
x = sqrt(41)
So, D is the right answer option.
Write 1.42 as a mixed number in simplest form.
1.42=
The decimal is repeating
Answer:
71/50
Step-by-step explanation:
If you bought 12.6 gallons of gasoline as $1.20 per gallon, how much did the gasoline cost?
Answer:
15.12$
Step-by-step explanation:
Gallons = 12.6
Cost = $1.20
Gasoline Cost = ??
12.6 ×1.20
=15.12
Hence, gasoline will cost 15.12 $
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The ratio of the angles in a quadrilateral are 7:4:5:2. What is the smallest angle?
Answer:
Step-by-step explanation:
The smallest angle in the quadrilateral with a ratio of 7:4:5:2 is 40 degrees.
To find the smallest angle in the quadrilateral, we need to determine the ratio of the angles and find the corresponding value for the smallest angle.
Given the ratio of the angles as 7:4:5:2, we can assume that the smallest angle corresponds to the ratio of 2.
To calculate the smallest angle, we can consider the sum of the ratio values as a whole, which is 7 + 4 + 5 + 2 = 18.
Now, we can find the value of the smallest angle:
Smallest angle = (2/18) * 360 degrees
= (1/9) * 360 degrees
= 40 degrees.
Therefore, the smallest angle in the quadrilateral is 40 degrees.
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You want to buy some noodles. A 6-ounce package costs $1.92. A 14-ounce package costs $4.62
A 20-ounce package costs $6.20. Which package is the best buy?
Answer:
The 20 ounce is the best package to buy.
Step-by-step explanation:
Divide the cost of the noodles by the ounces and you'll get your answers and then you have to pick the one with the least cost per noodles.
The 6 ounce costs .32 each
The 14 ounce costs .33 each
And the 20 ounce costs .31 each
Someone plsss help with this one
Answer:
B) The amount of service fee, in dollars
Step-by-step explanation:
Look for words relating to "one time," as that indicates the constant
3 candidates run for president of the club and 5 candidates run for vice-president. How many different possibilities for
filling the two positions are there?
b. 5
c. 8
d. 3
a. 15
Evaluate the expression for b = 3 and c = 5.
b2c − 11 =
Answer:
34Step-by-step explanation:
b = 3 and c = 5Substitute and evaluate:
b²c - 11 =3²*5 - 11 = 9*5 - 11 =45 - 11 =34Answer:
[tex]b = 3 \ \: \: : c = 5 \\ \\ b {}^{2} c - 11 = \\ \\ \\ {3}^{2} \times 5 - 11 = \\ \\ 9 \times 5 - 11 = \\ \\ 45 - 11 = \\ \\ = 34[/tex]
At the sewing store, Brittany bought a bag of mixed buttons. The bag included 30 buttons, of
which 10% were large. How many large buttons did Brittany get?
Answer:
3 large buttons
Step-by-step explanation:
Multiply 30 by .10 to get 3 large buttons
(100,160), (500,680) in slope intercept form
Answer:
520/400
so y = 520/400 + b
Step-by-step explanation:
5,8,6,9,7,10,8 what is the 20th term
Answer:
17
Step-by-step explanation:
the sequence is plus 3 minus 2. I forgot the actual formula for these kinds of questions but i vaguely remember
an = d (n - 1) + c
I was never able to remember how to use the formula but the sequence would be
5,8,6,9,7,10,8,11,9,12,10,13,11,14,12,15,13,16,14,17,15,18,16,19
if you'll notice, every other number is just one more than the last number...
so the 20th term is 17
Answer:
5,8,6,9,7,10,8,11,9,12,10,13,11,14,12,15,13,16,14,17...
20th term is 17
Step-by-step explanation:
add 3, subtract 2