Answers
Let's factor by grouping.
2n^2 + 7n + 5
2n^2 + 2n + 5n + 5
(2n^2 + 2n) + (5n + 5)
2n(n + 1) + 5(n + 1)
(2n+5)(n+1)
If 2n^2+7n+5 is prime, then one of the factors 2n+5 or n+1 must be 1. This is because a prime number can only be factored into 1 times itself. Example: 7 = 7*1.
Let's set each factor equal to 1 and see what happens.
2n+5 = 1 leads to n = -2. But it was stated that n > 0. So we rule out this case.n+1 = 1 leads to n = 0. This is ruled out as well since n > 0.It is impossible for (2n+5)(n+1) to be prime since none of the factors is 1. Therefore, (2n+5)(n+1) = 2n^2+7n+5 is composite for positive integers n = 1, 2, 3, ...
--------------
Another way to think about it:
2n^2 + 7n + 5 = (2n+5)(n+1)
Since n > 0 both 2n+5 and n+1 are larger than 1.
This means we have two different positive factors. These factors may be prime or composite. They multiply to some composite value.
Example: If n = 4 then
(2n+5)(n+1) = (2*4+5)(4+1) = 13*5 = 65
Answer:
There are no positive integer solutions for n.
Step-by-step explanation:
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. Therefore, the factors of a prime number are limited to 1 and the number itself.
To find all positive integers n such that 2n² + 7n + 5 is a prime number, first factor the quadratic.
\(2n^2+7n+5\)
\(= 2n^2+2n+5n+5\)
\(= 2n(n+1)+5(n+1)\)
\(= (2n+5)(n+1)\)
As the factors of a prime number are limited to 1 and the number itself, set each factor to 1 and solve for n:
\(\begin{aligned}2n+5&=1\\2n&=-4\\n&=-2\end{aligned}\) \(\begin{aligned}n+1&=1\\n&=1-1\\n&=0\end{aligned}\)
Since -2 and 0 are not positive integers, it is therefore not possible for 2n² + 7n + 5 to be a prime number for any positive integer value of n.
Hence, there are no positive integer solutions for n in this case.
Related Questions
The sum of negative eight and a number divided by four is two
Answers
Answer:
x = 16 or \(\frac{-8 + x}{4} = 2\)
Step-by-step explanation:
let's start from the beginning and move along!
the sum (+) of negative eight (-8) and a number (x) ----> (-8 + x)divided by four (/4) is two = 2\(\frac{-8 + x}{4}\) = 2
to solve this...
1) multiply both sides by four to get rid of the fraction
\((4)\frac{-8 + x}{4} = 2(4)\) ------> -8 + x = 8
2) add 8 to both sides to isolate x ----> x = 16
Can someone please help me with math.
Answers
Answer:
Its C
Step-by-step explanation:
Can some one help me ASAP please
Answers
Answer:
5
Step-by-step explanation:
What is the value of in the solution of the
system of equations 3x + 2y = 12 and 5x – 2y = 4?
Answers
Answer:
x = 2
y = 3
Step-by-step explanation:
add the 2 together and the y-values drop out and you are left with:
8x = 16
x = 2
3(2) + 2y = 12
2y = 6
y = 3
In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?
Answers
Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).
In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.
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Martha has 30 cakes
she gives 13 of the cakes to Adul
what fraction of the 30 cakes does Marta have now
Answers
Marta has 17/30 of the cakes left
4
Select the correct answer.
Which of the equations below represents a line parallel to the yaxis?
A. X= -y
B. X= 4y
C.x=y
D.X= 4
HELP
Answers
Answer:
x=4
Step-by-step explanation:
The y axis is a line where the value of x does not change ( x=0)
It is a vertical line
The only line where the value of x does not change is x=4
It is a vertical line at x=4
What value of m would make parallelogram wxyz a square.
Answers
To make parallelogram WXYZ a square, the following conditions must be met:
1. All four sides of the parallelogram must have equal length.
2. The angles between adjacent sides must be 90 degrees.
Since a square is a special type of parallelogram with all sides equal and all angles equal to 90 degrees, we can determine the value of m that would make WXYZ a square by ensuring that these conditions are met. To find the value of m, we need more information about the dimensions or properties of the parallelogram WXYZ. Please provide additional details or measurements related to the parallelogram. The diagonals of a square are equal in length and bisect each other at 90-degree angles. The perimeter of a square is the sum of all four sides, and the area of a square is calculated by squaring the length of one side.In order for parallelogram WXYZ to be a square, it must have congruent sides and right angles at each vertex.
Since opposite sides of a parallelogram are congruent, we can equate the lengths of adjacent sides to find the value of m that would make it a square.
Let's assume that WX and XY are adjacent sides of the parallelogram.
If WX = XY, then the parallelogram would have congruent sides.
Let's say WX = m and XY = m.
To form a square, the angles at each vertex must be right angles. This means that WX and XY must be perpendicular to each other.
In a square, opposite sides are parallel, so the slopes of WX and XY must be negative reciprocals of each other.
The slope of WX can be represented as (change in y) / (change in x). Since it is perpendicular to XY, its slope will be the negative reciprocal of the slope of XY.
Let's assume the slope of XY is denoted as a. Then the slope of WX would be -1/a.
We can now equate the slopes of WX and XY:
-1/a = (change in y) / (change in x)
Simplifying this equation, we get:
a = -1
Therefore, the slope of XY is -1.
Now, we can equate the lengths of WX and XY:
m = m
Since WX = XY and both sides have length m, we can say that m = m.
So, any value of m would make parallelogram WXYZ a square as long as the sides WX and XY are congruent and perpendicular to each other, with a slope of -1.
hence, the value of m = -1.
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GIVING OUT BRAINLEST!!
Enter the range of values for x
Answers
Answer:
I need help w this question to answer it plz!
Answer:
Step-by-step explanation:
You will need to add a picture
What is the range of the graph? A) (3, 5) B) [3, 5] C) (2, 5) D) [2, 5]
![What is the range of the graph? A) (3, 5) B) [3, 5] C) (2, 5) D) [2, 5]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/NbWu9RSxokbm7JlqNbiomNPpRPjq0jhO.png)
Answers
Answer:
B. [3, 5]
Step-by-step explanation:
The range of a graph are the y-values that are plotted on the vertical axis (y-axis). In order words, the range values, are the possible set of output values of that are plotted on the vertical axis on the graph.
"[ ]" is usually used to denote the possible set of values.
Therefore, the range of the given graph, as we can see from the y-axis, include values from 3 to 5. Therefore, the range of the graph is [3, 5].
Jacob received 685 votes in the school election.
If he received 125 more than 2/3 of the total
number of votes, how many students voted in
the election?
Answers
Answer:
840
Step-by-step explanation:
He gets 685 votes. This is 125 more than 2/3 of the total number of votes. So 2/3 must be 125 less than 685.
2/3=560
So ÷2 to find 1/3, because 2/3 ÷2 = 1/3.
1/3=280
So then you x3 because 1/3x3=3/3, or 1 whole.
1 whole=840
840=total number of votes
if sin a=0.865 and cos b=0.529 with both angles terminal rays in quadrant 1, find the values of cos(a b sin (a b)
Answers
cos(a b) = 0.965 and sin(a b) = 0.674 .
sin a = 0.865
cos a = √(1 - sin² a)
cos a = sqrt(1 - 0.865²)
cos a = 0.502
Similarly, cos b = 0.529
sin b = √(1 - cos² b)
sin b = √(1 - 0.529²)
sin b = 0.854
Trigonometry identity
cos(a b) and sin(a b)
cos(a b) = cos ( 0.502 × 0.529 )
cos(a b) = cos 0.266
cos(a b) = 0.965
Trigonometry identity
sin(a b) = sin (0.865 × 0.854 )
sin(a b) = sin (0.739)
sin(a b) = 0.674
Therefore, cos(a b) = 0.965 and sin(a b) = 0.674
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Please help me with edge question .
Answers
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)
1
Solve for h in the mathematical formula A = (a + b)h. Drag and drop the numbers and variables into
ca
the correct boxes to complete the formula.
Answers
Answer:
h = A*2/a+b
Step-by-step explanation:
find the measure of angle y. round your answer to the nearest hundredth. (please type the numerical answer only)
Answers
The measure of angle y is 52.81 degrees.
In this geometry problem, we are asked to determine the measure of angle y. After performing the necessary calculations, we find that the measure of angle y is 52.81 degrees. This answer has been rounded to the nearest hundredth.
To arrive at this result, we likely had access to a diagram or description of the given angles and their relationships. By applying the appropriate geometric principles, such as the properties of supplementary or complementary angles, we were able to identify the relevant information needed to find the measure of angle y.
It is important to note that without a specific diagram or further context, it is challenging to provide a detailed explanation of the specific steps involved in solving this problem. The answer of 52.81 degrees represents the final outcome based on the given information, calculations, and rounding instructions.
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The number of days ahead travelers purchase their airline tickets can be modeled by an exponential distribution with the average amount of time equal to 15 days. Find the probability that a traveler will purchase a ticket fewer than ten days in advance. How many days do half of all travelers wait
Answers
Answer:
The right answer is:
(a) 0.4866
(b) 10.3972
Step-by-step explanation:
Let X be the number of days,
X is \(exp(\lambda)\),
⇒ \(\lambda =\frac{1}{15}\)
now,
⇒ \(F_x(x) = P(X \leq x)\)
\(=1-e^{-\lambda x}\)
\(=1-e^{-\frac{x}{15} }\)
or,
\(x>0\)
(a)
⇒ \(P(X<10)=F_x(10)\)
\(=1-e^{\frac{10}{15} }\)
\(=1-e^{\frac{2}{3} }\)
\(=0.4866\)
(b)
If the medium be m, then
\(P(X=m) = \frac{1}{2}\)
\(=2^{-1}\)
⇒\(1-e^{-\frac{m}{15} } = \frac{1}{2}\)
\(e^{-\frac{m}{15} } = 2^{-1}\)
\(m= 15\ ln2\)
\(=10.3972\)
Graph a line to represent the linear equation y=54x−4.
Answers
Answer:
yes it represents it because the linear equation
Which expressions are equivalent to (1/3 x + 2x - 5/3x) - ( - 1/3x + 5)?
Select all correct expressions
O x - 5
O 4x - 5 - 3x
O 5 - x
O -4x + 5 + 3x
Answers
Answer: Options 1 and 2
Step-by-step explanation:
\(\frac{1}{3}x+2x-\frac{5}{3}x+\frac{1}{3}x-5\\\\=x-5\\\\=4x-5-3x\)
Please answer this question! It’s almost due!
(Answer Number 8)
Answers
Answer:
its incorrect.
Step-by-step explanation:
Use a formula to find the amount of wrapping paper you need to wrap a gift in the cylindrical box shown. You need to cover the top, bottom, and all the way around the box. Use 3.14 for pi. 9 radius 5 height
Answers
Yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
One needs apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
The amοunt οf wrapping paper required tο wrap a gift in a cylindrical bοx depends οn the surface area οf the bοx. Tο find the surface area οf a cylinder, we use the fοrmula:
Surface Area = 2πr² + 2πrh
where r is the radius οf the cylinder and h is the height οf the cylinder.
In this case, the given cylinder has a radius οf 9 and a height οf 5. Therefοre, we can substitute these values intο the fοrmula and simplify:
Surface Area = 2 * 3.14 * 9² + 2 * 3.14 * 9 * 5
Surface Area = 1017.96
Therefοre, yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
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The area for the circle below is
in.2.
Use 3.14 for π and type your answer to the nearest tenth.
D = 5in
I NEED HELP OR I WILL FAIL
Answers
Answer:
19.63 inches
Step-by-step explanation:
The area of a circle is found by using the formula
A = πr²
r is the radius of the circle, which is the diameter divided by two.
D = 5 in so r = D ÷2
5 ÷ 2 = 2.5 inches for the radius.
A = π (2.5)²
A = π (6.25)
A = (3.14)(6.25)
A = 19.625 inches
the population of metroville is 123,000 and is decreasing by 2.4 each year
a. write a function that models the population as a function of time t
b. predict when the population will be 90,000
Answers
The function is given as P = 123000e^ -0.024t and the time taken is 13 years.
What is the function?We have to know that as we deal with the population that we are dealing with an exponential function. In the exponential function, we can see that the data can be increasing or it can be decreasing as we can se here.
We know that;
P= Poe^-rt
P = population at time t
Po= Initial population
r = rate of decrease
t = time taken
then;
P = 123000e^ -0.024t
The population would 90 000 when;
90000/123000= e^ -0.024t
0.73 = e^ -0.024t
ln0.73 = lne^ -0.024t
ln0.73 = -0.024t
t = ln0.73/-0.024
t = 13 years
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3. Find the volume of this rectangular prism in cm³
Answers
what is the answer to -5 - (-9) =
Answers
Answer: 4
Step-by-step explanation:
= Multiply -1 by -9 to change 9 to a positive number
= Add -5 to 9 (-5 + 9 = 4)
= 4
Can someone pls help me!
Answers
Answer:
x is -3
Step-by-step explanation:
What is the volume of a sphere with a radius of 6.1 m, rounded to the nearest tenth of a cubic meter?
Answers
Answer:
V≈950.78m³
Step-by-step explanation:
can someone please someone please help me solve the following?
Answers
We need to solve the following equation:
\(\frac{5x}{x-1}+5=\frac{15}{x-1}\)Notice that x ≠ 1, since x = 1 makes zero the denominators. Then, multiplying all the terms by x-1, we obtain:
\(\begin{gathered} \frac{5x}{x-1}\cdot(x-1)+5(x-1)=\frac{15}{x-1}\cdot(x-1) \\ \\ 5x\cdot\frac{x-1}{x-1}+5x-5=15\cdot\frac{x-1}{x-1} \\ \\ 5x+5x-5=15 \\ \\ 10x-5=15 \\ \\ 10x-5+5=15+5 \\ \\ 10x=20 \\ \\ \frac{10x}{10}=\frac{20}{10} \\ \\ x=2 \end{gathered}\)-10x+10y=-10 10x-10y=10
Answers
Answer:
X=-Y
Step-by-step explanation:
...........................
What is the weight of a 24 square foot 2 inch thick aluminum plate with a unit weight of 15 lbs?
Answers
Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Weight of 1 square foot, 1 inch thick plate = 15 lbs.To find: weight of a 24 square foot, 2 inch thick aluminum plate
Finding:
By unitary method, we get:
Weight of 1 square foot aluminum plate = 15 lbs.
Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.
Again, by unitary method, we get:
Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.
Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.
Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.
Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.
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∣1/12 − 5/6∣ − (2/5 + 1/10)
I WILL GIVE BRAINLYST
Answers
Answer:
forst mark me as a brainleast