Answer:
[tex]x^2+1[/tex] cannot be factored, thus it's a prime polynomial
Step-by-step explanation:
A prime number or expression cannot be factored in any factor different from 1 and the number or expression itself.
One of the following expressions is prime. The rest of them can be factored.
[tex]x^3-1[/tex] is the difference of two cubes. It can be factored as:
[tex]x^3-1=(x-1)(x^2+x+1)[/tex]
[tex]x^3+1[/tex] is the sum of two cubes. It can be factored as:
[tex]x^3+1=(x+1)(x^2-x+1)[/tex]
[tex]x^2-1[/tex] is the difference of two squares. It can be factored as:
[tex]x^2-1=(x-1)(x+1)[/tex]
[tex]\mathbf{x^2+1}[/tex] cannot be factored, thus it's a prime polynomial
Compare: -7 -4
PLEASE HELP ME!
Write the rational number as a decimal -4 2/3
- 4.(6)
Step-by-step explanation:Hi there !
- 4 2/3 =
= - 4 6/9
= - 4.(6)
Good luck !
A researcher is exploring the notion that there is an economy of scale in raising children. While having one child might add to a family's financial stress, the second or third one might not be as "expensive" since they would already be sharing one roof, could share clothing, etc. The researcher has access to a large community of parents where 15% have one child under 18 in their home, 65% of parents have two children, and 20% of parents have three or more children. Rounded to the nearest whole number, the probability that any given family who is selected has two or more children at home is ________ %?
Answer:
The probability that any given family who is selected has two or more children at home is 85%.
Step-by-step explanation:
The information provided is as follows:
Number of Children Probability
1 0.15
2 0.65
> 3 0.20
Compute the probability that any given family who is selected has two or more children at home as follows:
P (At least 2 Children) = P (2 children) + P (More than 3 children)
= 0.65 + 0.20
= 0.85
Thus, the probability that any given family who is selected has two or more children at home is 85%.
HELP ME PLEASE!!!!!!!!!
Which statement describes the system of equations?
5x-3y=34
x-2y=4
It has infinitely many solutions.
It has no solution.
It has one solution (24/13, -14/13)
It has one solution (8, 2).
Answer: It has one solution (8, 2).
Step-by-step explanation:
I put both equations in Desmos and the solution was (8,2)
divide 25.84 divide by 4
Answer:
25.84 divide by 4 Is 6.46.
Find all complex solutions (real and non-real). (Enter your answers as a comma-separated list.) x3 8x2 21x 20
Answer:
The answer is "non-real solution: "i-3 and -i-3" and real solution is -2".
Step-by-step explanation:
In the given equation there is some mistype error so, its correct equation can be defined as follows:
Given value:
[tex]\bold{ f(x) = x^3+ 8x^2 +22x +20}[/tex]
use hit and trial method we put x value are -2:
[tex]f(-2) = (-2)^3+ 8(-2)^2 +22(-2) +20\\\\[/tex]
[tex]= -8 + 8 \times 4 +22 \times -2 +20\\\\= -8 + 32 -44 +20\\\\= -52 + 52\\\\=0[/tex]
So, the real solution to the equation is "-2".
In the above solution, we calculate the f(x) =-2 is its real solution. so, the calculation for non-real solution:
divide the value [tex]x^3+8x^2+ 22x +20[/tex] by ([tex]x+2[/tex]):
Quotient: [tex]x^2+6x+10[/tex]
Remainder: 0
[tex]\to x^2+6x+10 \\\\compare \ with \ ax^2+bx+c: \\\\a= 1\\b= 6\\c=10\\\\\bold{Formula:}\\\\\to D= b^2-4ac\\\\[/tex]
[tex]= 6^2- 4 \times 1 \times 10\\\\ = 36- 40\\\\ = -4[/tex]
Formula for calculate non-real solution:
[tex]\bold{\frac{-b\pm \sqrt{D}}{2}}[/tex]
non-real solution: "i-3 and -i-3"
I will give you 25 points help please
Answer:
horizontal 2 units to the right, vertical translation 3 units up, vertical stretch by a factor of 4
What is 11/9 as a decimal?
Answer:
1.2 (the 2 continuing on)
Step-by-step explanation:
Just divide the numerator by the denominator and you'll get your answer
Solve this equation -3-2[4-1]
Answer:
-15
Step-by-step explanation:
(-3-2)*(4-1)
-5*3=-15
Answer:
-15
Step-by-step explanation:
By rule of pemdas, 4-1 = 3. -3 -2= -5. -5 * 3= -15.
7 – 0.2n = -0.8n + 10
What value of n makes this equation true?
Please helpp
The answer to the equation is [tex]n=5[/tex]
First, you must add 0.8n on both sides.
[tex]0.6n+7=10[/tex]
Then, subtract 7 from both sides.
[tex]0.6n=3[/tex]
Finally, divide both sides by 0.6
[tex]n=5[/tex]
Given f(x) = 5x + 1, find f(-3).
I need help ASAP
Answer:
take a look ...........
What is 715 divided by 25 and what is 514 divided by 28?
Plsss help I really need it for my HW
Answer:
715 divided by 25 is 28.6, while 514 divided by 28 is 18.35. Hope this helps!
Step-by-step explanation:
Solve the literal equation xy - 4xz = 5 for x.
X=
Answer:
x = 5/(-4 z + y)
Step-by-step explanation:
Solve for x:
x y - 4 x z = 5
Hint: | Write the linear polynomial on the left-hand side in standard form.
Collect in terms of x:
x (-4 z + y) = 5
Hint: | Solve for x.
Divide both sides by -4 z + y:
Answer: x = 5/(-4 z + y)
I just need some one to explain how to do it ,
Answer:
f(x) = (x^2-16) / (x+3)
f(x) has no horizontal asymptote.
Vertical assymptote is x = -3
Dividing the numerator by the denominator gives x - 3 remainder -7. Therefore, the oblique assymptote is x - 3.
the vertical asymptotes of the function f(x) = (5x + 1) / (x^2 + x - 6) = (5x + 1)/(x - 2)(x + 3) is x = 2 and x = -3.
the zeros of the function f(x) = (3x^2 - 3x - 6 ) / (3x - 6) = (3x^2 + 3x - 6x - 6) / (3x - 6) = (3x(x + 1) - 6(x + 1)) / (3x - 6) = (3x - 6)(x + 1)/(3x - 6) = x + 1 is x = -1
the function f(x) = (x^2 + x - 12) / (x - 3) = (x - 3)(x + 4) / (x - 3) is --> disc = 3, x-int = (-4, 0), y-int = 4? basic shape = straight line
Step-by-step explanation:
Hope this helps! brainliest please
NEED HELP ASAP Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberries less than Ann and Ben together, what is the total number of strawberries the three of them ate?
Answer:
170Step-by-step explanation:
given:
Ann, Ben, and Cindy were eating strawberries.
The ratio of the numbers of berries they ate is 5:5:7.
If Cindy ate 30 strawberries less than Ann and Ben together,
find:
what is the total number of strawberries the three of them ate?
solution:
add the ratios 5 + 5 + 7 = 17
since Cindy ate 30, less than Ann and Ben together so, the equation is
7x = 5x + 5x - 30
7x - 10x = -30
x = 30/3
x = 10
ann 5 x 10 = 50
ben 5 x 10 = 50
cindy 7 x 10 = 70
total = 170
==============================================
Explanation:
A = number Ann ate
B = number Ben ate
C = number Cindy ate
Let x be some positive whole number
Since A,B,C is in the ratio 5:5:7, this means
A = 5x
B = 5x
C = 7x
Note how A:B:C = 5x:5x:7x = 5:5:7. We divide all parts by x to simplify the ratio.
-------------------
Cindy ate 30 strawberries less than Ann and Ben, so
C = A+B-30
C = 5x+5x-30
C = 10x-30
Earlier in the last section we had C = 7x, and now we found C = 10x-30
Since we're talking about the same C value, we can equate and solve
C = 7x
10x-30 = 7x ... replace C with 10x-30
10x-7x = 30
3x = 30
x = 30/3
x = 10
------------------
With this x value, we now know that...
A = 5x = 5*10 = 50
B = 5x = 5*10 = 50
C = 7x = 7*10 = 70
Cindy's count (70) is 30 less than Ann and Ben's combined count (50+50 = 100), so that helps confirm the answer.
Further confirmation comes from 50:50:70 reducing to 5:5:7 when you divide all parts by the GCF 10.
--------------------
The last step is to add the values of A, B and C.
A+B+C = 50+50+70
A+B+C = 100+70
A+B+C = 170
---------------------
Side note: since A+B+C = 5x+5x+7x = 17x, this means that the final answer is a multiple of 17.
What is 3/4 ÷ 1/2 ?
-5(2x+9)? simplify the expressions by disturbing the negatives and combining like terms
Answer:
-10x-45
Step-by-step explanation:
Write the slope-intercept form of the equation of the line described by (−1, −1), parallel to y = −2x − 4
Answer:
y = -2x - 3
Step-by-step explanation:
Slope intercept form of line is
y = mx + c
where
m is the slope and c is the y intercept
________________________________________
Given that line
y = −2x − 4
comparing it with y = mx + c
m = -2 and c = -4
Thus, slope of this line is -2
we also know that when two lines are parallel then their slopes are same
thus, slope of required line will be m = -2
___________________________________________
now let the equation of line passing through (-1,-1) be
y = mx + c
we have found m to be -2
using this in above equation we have
y = -2x + c
since (-1,-1) passes through the above line using x = -1 and y = -1
we have
-1 = -2*-1 + c
-1 = 2 + c
c = -1 - 2 = -3
using c = -3 in y = -2x + c
we have
equation of line as
y = -2x - 3 in slope intercept form.
The base of a triangle is 12 inches greater than the height. If the area is 80 square inches, find the length of the base
PLEASE HELP
Answer:
Step-by-step explanation:
Because the area of a triangle you have to divide by 2 and then you get the area right so we multiply 80 x 2 = 160 is the area of the square which you divide by 2 but we are not going to do that. now we have to get 2 lengths with 12 difference so we have to just do trial and error method.
208+8x−718+2x SIMPLIFY PLEASE
Answer:10x-510
Step-by-step explanation:
math
The sign of the leading coefficient for the polynomial equation of the graph is negative positive zero
Answer:
The sign of the leading coefficient for the polynomial equation of the graph is NEGATIVE
Hope this helps!
Answer: 1 turning point
Step-by-step explanation:
What is the equation of the line that passes through the point (4, -3) and has a slope of 1?
Answer:
y=x-7
Step-by-step explanation:
y=mx+b
(-3)=(1)(4)+b
-3=4+b
-3=4+b
-4=-4+b
-7=b
then y=1x-7
then simplify and it gives you y=x-7
Siobhan earned $45 babysitting on Friday. On Saturday, she babysat for 5 hours at $4 per hour. On Sunday she bought a DVD for $32. How
much money did she have left after buying the DVD?
$30
Work: 45+20=65
65-35=30
A fast-food restaurant has a cost of production C(x)=12x+114 and a revenue function R(x)=6x. When does the company start to turn a profit?
Step-by-step explanation:
Given data
C(x)=12x+114
R(x)=6x.
The company will start to run on profit just when revenue equals the production cost, that is
C(x)=R(x)
equating the two expressions we have
12x+114=6x
solving for x we have
12x-6x+114=0
6x+114=0
6x=-114
x=-114/6
x=-19
Hence the company will start to run on proft when they start to produce above 19 items
Profit is the difference between the revenue and cost functions
A production greater than 19 will turn a profit
From the question, we have:
[tex]\mathbf{R(x) = 6x}[/tex]
[tex]\mathbf{C(x) = 12x + 114}[/tex]
So, the profit function is:
[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]
Substitute known values
[tex]\mathbf{P(x) = 6x - 12x - 114}\\[/tex]
[tex]\mathbf{P(x) = - 6x - 114}[/tex]
Equate to 0
[tex]\mathbf{- 6x - 114 = 0}[/tex]
Collect like terms
[tex]\mathbf{- 6x= 114}[/tex]
Divide both sides by -6
[tex]\mathbf{x= -19}[/tex]
The above equation means that: A production greater than 19 will turn a profit
Read more about profit functions at:
https://brainly.com/question/16866047
Susan's grandpa was fibbing again: "your grandma and I, together, we are over 150
years old!" If her grandpa is 71, and her grandma is 68, what's the real sum of their ages?
Easy as pie.
Just add em.
Making it.
71
+68
------
139
Meaning both of em are 139 years.This also means they are not over 150.
Fifteen more than three times a number is the same as ten less than six times
the number. What is the number?
Answer:
The number: x
Step-by-step explanation:
15+3x = 6x-10
3x = 25
Answer:
40
Step-by-step explanation:
15 + 3x = 6x - 10
15 + 10 = 6x - 3x
25 = 3x
25/3 = x
To check
15 + 3(25/3) = 6(25/3) - 10
15 + 25 = 50 - 10
40 = 40
When you reverse the digits in a certain two-digit number you decrease its value by 45. What is the number if the sum of its digits is 9?
Answer:
72
Step-by-step explanation:
x+y=9 possible numbers
1 and 8
2 and 7
3 and 6
4 and 5
9 and 0
so
81-18=63
72-27=45 so this is the right number
63-36=27
54-45=9
90-9=81
The average of 4,-8,6,14,-3 is
Answer: The average is 2.6
Step-by-step explanation:
The average is the same as the mean so to find the mean of the numbers add them up and divide it by the number of values.
(4) + (-8) + (6) + ( 14) + (-3) = 13
13/5 = 2.6
I need help plz hurry
Answer:
a. 7
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Define
y - (x - z)
x = -4
y = 5
z = -2
Step 2: Substitute and Evaluate
5 - (-4 - (-2))
5 - (-4 + 2)
5 - (-2)
5 + 2
7
Answer:
A. 7
Step-by-step explanation:
Plug in the values of x, y, and z: 5 - (-4 - -2)Simplify: 5 - (-4 + 2)-4 + 2 = -2Plug -2 in: 5 - (-2)Simplify: 5 + 25 + 2 = 7I hope this helps!
Analyzing a Linear Function Expressed in Different Ways Choose the true statements. A linear function is expressed by a graph of a line that crosses both axes at the origin. An equation is written in slope-intercept form to express the same function as shown in the graph. From just this information, what statements can be made? A) The slope of the equation must be positive. B)The y-intercept of the equation is zero. C) It is possible that the line on the graph is horizontal. D) The slope of the equation must be negative.
Answer: The answer is option B and option C.
Answer:
B and C
Step-by-step explanation: