Which polynomials are prime? Check all of the boxes that apply.x² +9
x²_9
x2 + 3x + 9
-2x² +8
Answers
Final answer:
A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.
Explanation:
In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:
- x² +9 is a prime polynomial because it is a sum of squares and cannot be factored into real polynomials of lower degree.
- x² -9 is not a prime polynomial because it can be factored into (x-3)(x+3).
- x² + 3x + 9 is a prime polynomial because it cannot be factored into real polynomials of lower degree.
- -2x² +8 is not a prime polynomial as it can be factored into -2(x²-4).
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Answer: x^2+9 and x^2+3x+9
Step-by-step explanation:
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From the records of a health-insurance companies in Pennsylvania, it is known that 58% of the accounts include dental coverage. A researcher would like to take a random sample of 500 accounts to review. Find the standard deviation of the sample proportion in this situation. Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."
Convert each measure to the equivalent metric unit.8 cm = mm7 km = m18 g = kg43 kg = g234 L = mL1 346 mL = L0.81 km = cm0.05 dm = dam1.32 cg = kg3.7 mcg = mg
CAN SOMEONE HELP ME PLEASEEEplease and thank u
Help! due in a min!Find the angle measures for the following:m<1=___ m<4=___
Answers
Answer:
1 : 54
Step-by-step explanation:
5 men to 270 women
5 (men) : 270 (women)
make the ratio as small as you can by dividing the same number on both sides.
5 : 270. both sides can be divided by 5
1 : 54
It means for every 1 man working, there are 54 women working
Final answer:
The ratio of men to women in the factory is calculated by dividing the number of men by the number of women and simplifying the result. In this case, the ratio is 1:54, meaning for every man, there are 54 women.
Explanation:
The question asks to find the ratio of men to women in a factory where there are 5 men and 270 women working. To calculate the ratio of men to women, we simply divide the number of men by the number of women.
The calculation would be as follows:
- Number of men: 5
- Number of women: 270
- Ratio of men to women: 5 ÷ 270
However, ratios are typically expressed in simplest form. Since both 5 and 270 are divisible by 5, we divide each by 5:
- 5 ÷ 5 = 1
- 270 ÷ 5 = 54
- So, the simplified ratio of men to women is 1:54.
This means that for every man in the factory, there are 54 women.
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2x² – 5x + 3 = m(x)
Answers
Answer:
- vertex: (1.25, -0.125)
- axis of symmetry: x = 1.25
- minimum: -0.125
- domain: all real numbers
- range: y ≥ -0.125
Step-by-step explanation:
For quadratic ax² +bx +c, the axis of symmetry is x = -b/(2a). For your function, a=2, b=-5, c=3 and the axis of symmetry is ...
x = -(-5)/(2(2)) = 5/4 = 1.25
The vertex is on the axis of symmetry. The y-value there is ...
m(5/4) = (2(5/4) -5)(5/4) +3 = (-5/2)(5/4) +3 = -25/8 +24/8 = -1/8
The vertex is (5/4, -1/8).
The axis of symmetry is x = 5/4.
The leading coefficient is positive, so the parabola opens upward. The vertex is a minimum.
The minimum is -1/8.
The function is defined for all values of x, so ...
the domain is all real numbers.
Values of y can only be -1/8 or greater, so ...
the range is y ≥ -1/8.
Answers
Answer:
your answer is 3/2x.
Step-by-step explanation:
13/2x-5/x
-multiply 5/x by 2 to get common denominators.
13/2x-10/2x
-subtract numerators and keep the denominators the same.
3/2x
hope this helped !!
Answer:
3/2x
Step-by-step explanation:
Answers
The perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
What is area?
The area is the amοunt οf space within the perimeter οf a 2D shape. It is measured in squareunits, such as cm², m², etc.
Yοu can think οf area as the area inside a given shape οr space. It refers tο hοw much space is taken up. The larger the shape, the larger the area and perimeter οf the shape will be. Nοt tο be cοnfused with vοlume, area οnly refers tο space taken up by a flat οr 2Dοbject.
The perimeter is sum of all sides
Here,
sum of all sides = 1/2 × 2πr + 6 + 8
= 1/2 × (2×3.14×5) + 6 + 8
= 29.7 ft
Area = 1/2 × πr² + 1/2 × 8 × 6
= 1/2 × (3.14×5×5) + 1/2 × 8 × 6
= 63.25 ft²
Thus, the perimeter of the given figure is 29.7 ft while the area is 63.25 ft².
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Answers
Answer:
3003
Step-by-step explanation:
We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)
The number of different lineups you can have can be found by using combination:
There are 3003 different lineups that can be chosen.
Final answer:
To determine the number of starting lineups, we use combinations in probability. We first choose a goalie from 16 players, then 10 regular players from the remaining 15, giving us 48048 unique lineups.
Explanation:
This problem can be solved by using the concept of combinations in probability and statistics. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.
Firstly, we need to choose a goalie. There are 16 players, so the number of ways to choose a goalie is C(16, 1) = 16.
After choosing the goalie, we are left with 15 players. Then we need to choose 10 players to fill in the rest of the team. Thus, the number of ways to choose the 10 regular players is C(15, 10).
The total number of unique starting lineups is then the product of these two results. Hence, the solution would be C(16, 1) * C(15, 10) = 16 * 3003 = 48048 different starting lineups.
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Answers
Answer:
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes
Step-by-step explanation:
Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.
50ft³ = the volume
0.5ft³/min = rate
There is a key future missing which is the time it will take to fill the 50 ft³ container
Time = volume/rate
Time= 50 ft³/0.5ft³/min
Time= 50/0.5 min
Time = 100 min
The key features are
50ft³ = the volume
0.5ft³/min = rate
Time= 100 minutes