Answer:
(x - 3)(x - 2)(x + 2)
Step-by-step explanation:
Given
x³ - 3x² - 4x + 12 ( factor the first/second and third/fourth terms )
= x²(x - 3) - 4(x - 3) ← factor out (x - 3) from each term
= (x - 3)(x² - 4) ← x² - 4 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
x² - 4
= x² - 2²
= (x - 2)(x + 2)
Thus
x³ - 3x² - 4x + 12 = (x - 3)(x - 2)(x + 2) ← in factored form
Answer:
(x - 2)(x - 3)(x + 2).
Step-by-step explanation:
The Factor Theorem states that if x - a is a factor of f(x) the f(a) = 0.
f(x) = x^3 - 3x^2 - 4x + 12
We try the factors of 12:
f(2) = 2^3 - 3*4 - 8 +12
= 8 - 12 - 8 + 12 = 0
- so (x - 2) is a factor of f(x)
Dividing:
x^2 - x - 6 <-----------Quotient
-----------------------------
x - 2 )x^3 - 3x^2 - 4x + 12
x^3 - 2x^2
-x^2 - 4x
-x^2 + 2x
-6x + 12
-6x + 12
So we factor x^2 - x - 6:
= (x - 3)(x + 2)
Pls don't delete just answer the ones u know pls hwlp pls
Answer:
1. 1 + 1 x 4 ÷ 1 = 8
Hope this helps.
How many shares of Lombard Incorporated traded on the 17th?
Answer:
Step-by-step explanation:
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What is x^-4/x^8??????
Answer:
1 / (x^12)
Step-by-step explanation:
x^-4 = 1/x^4
1 / (x^4)(x^8) = 1/ (x^12)
A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the width. Material for the base costs 13 dollars per square meter. Material for the sides costs 9 dollars per square meter. Find the cost of materials for the cheapest such container.
Answer:
419.25
Step-by-step explanation:
The calculation of the cost of materials for the cheapest such container is shown below:-
We assume
Width = x
Length = 2x
Height = h
where, length = [tex]2 \times width[/tex]
Base area = lb
= [tex]2x^2[/tex]
Side area = 2lh + 2bh
= 2(2x)h + 2(x)h
= 4xh + 2xh
Volume = 24 which is lbh = 24
[tex]h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}[/tex]
Now, cost is
[tex]= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}[/tex]
now we have to minimize C(x)
So, we need to compute the C'(x)
[tex]= 52x - \frac{648}{x^2}[/tex]
C"(x) [tex]= 52x - \frac{1,296}{x^3}[/tex]
now for the critical points, we will solve the equation C'(x) = 0
[tex]= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}[/tex]
[tex]C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0[/tex]
So, x is a point of minima that is
= [tex](\frac{648}{52} )^\frac{1}{3}[/tex]
Now, Base material cost is
[tex]= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}[/tex]
= 139.75
Side material cost is
[tex]= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }[/tex]
= 279.50
and finally
Total cost is
= 139.75 + 279.50
= 419.25
The cost of the side material is $279.50, the cost of the base material is $139.75 and the total cost is $419.25 and this can be determined by using the arithmetic operations.
Given :
A rectangular storage container with an open top is to have a volume of 24 cubic meters.The length of its base is twice the width.Material for the base costs 13 dollars per square meter.Material for the sides costs 9 dollars per square meter.Let the width of the rectangular storage container be 'x' then according to the given data the length is '2x' and let the height of the container be 'h'.
The base area of the rectangular storage container is given by:
Base Area = [tex]2x^2[/tex] ----- (1)
The side area of the rectangular storage container is given by:
Side Area = 2(2x)h + 2xh
= 6xh ---- (2)
Now, the volume of the rectangular storage container is given by:
Volume = lbh
Put the values of known terms in the above equation.
24 = [tex]2x^2h[/tex]
[tex]h = \dfrac{12}{x^2}[/tex]
Now, the cost is given by:
[tex]\rm C(x)=13(2x^2)+9(6xh)[/tex]
[tex]\rm C(x)= 26x^2 + \dfrac{648}{x}[/tex]
Now, to minimize C(x) differentiate the C(x) with respect to x.
[tex]\rm C'(x)=52x -\dfrac{648}{x^2}[/tex] ---- (3)
Now, equate the above equation to zero.
[tex]0 = 52x =\dfrac{648}{x^2}[/tex]
[tex]x = \sqrt[3]{\dfrac{648}{52}}[/tex]
Now, differentiate equation (3) with respect to x.
[tex]\rm C"(x) = 52+\dfrac{1296}{x^3}[/tex]
Now, put the value of x in the above equation.
[tex]\rm C"(x) = 52+\dfrac{1296}{\dfrac{648}{52}}[/tex]
[tex]\rm C"(x) = 52+104[/tex]
[tex]\rm C"(x) = 156 > 0[/tex]
Therefore, 'x' is the point of minima.
Now, the cost of the base material is:
[tex]= 13\times 2 \times (\dfrac{648}{52})^\frac{2}{3}[/tex]
= $139.75
Now, the cost of the side material is:
[tex]=\dfrac{648}{\sqrt[3]{\dfrac{648}{52}} }[/tex]
= $279.50
Therefore, the total cost is given by:
= 139.75 + 279.50
= $419.25
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What is the relationship between centimeters and inches?
Answer:
What do you mean like the the ratio of cm to inches?
Step-by-step explanation:
?
Sachiko is framing the border of a square picture. If she knows the area of the picture, how could Sachiko determine the amount of framing material she needs to buy? Divide the area by 2, and then multiply the quotient by 4. Set the area equal to x2, solve for x, and then multiply the value of x by 4. Set the area equal to x3, and then solve for x. Set the area equal to x2, solve for x, and then divide the value of x by 4.
Answer:
Set the area equal to x2, solve for x, and then multiply the value of x by 4.
Step-by-step explanation:
The area of the picture is given by
A = s^2 where s is the side length
Let the side length be x
A = x^2
Take the square root of each side
sqrt(A) = sqrt(x^2)
x = sqrt(A)
We want to find the perimeter since we are framing the border
P = 4s since the picture is a square
P = 4 * x
Answer:
B.
Step-by-step explanation:
Let's let x represent the side length of the square.
Since the picture is a square, all the lengths are the same. Moreover, the area of the square is x times x or x squared. Thus:
[tex]A=x^2[/tex]
The amount of framing Sachiko needs is represented by the perimeter of the square. The perimeter of a square is determined by the formula:
[tex]P=4x[/tex]
Now, if Sachiko knows the area and she wants to find the perimeter, she can do the following:
First, the area is equal to x^2. So, she should first just find the length itself. So her first step should be to set the area equal to x^2 and then solve for x.
Then, when she has found her length, she just need to multiply it by 4 to get the perimeter or the amount of framing she needs.
Thus, the answer is choice B.
plz answer it, plz answer it, plz answer it.
Given that :-
x+y < 5 3 < x < 5To Find :-
Value of ySolution :-
The fist expression x + y < 5 states that sum of x and y could be any rational number less than 5 .
And the second expression 3 < x < 5 states that value of x could be any rational number between 3 and 5.
Let's check which option suits best.
Is it possible to have value of 8/3 by y ?
→ x + 8/3 < 5
→ x < 5 - 8/3
→ x = 7/3
7/3 is a rational number . So y as 8/3 is possible value.
→ 7/3 = 2.33
But value of x should be greater than 3 .
So option A is wrong.
Is it possible to have value 2 by y ?
→ x +2 < 5
→ x < 5-2
→ x < 3 .
But value of X should be greater than 3.
So option B is also incorrect.
Is it possible to have value 0 by y?
→ x +0 <5
→ x < 5
It also fullfill 2nd expression that X should have value less than 5 and greater than 3.
So option C is valid .
Value of y is 0 .
What is the median of the following numbers?
6,4,1,9, 3, 8,3,5, 10
Answer: The median is 5
Step-by-step explanation:
The median is the middle number after being arranged from least to greatest.
So arrange the numbers from least to greatest.
1,3,3,4,5,6,8,9,10
So the middle number in this set is 5
Ao cobrar uma falta em um jogo de futebol, uma jogador imprime à bola a uma velocidade de 43,2 km/h. Sabendo que a bola gasta 3 s até atingir as redes, determine a distância percorrida? A)16m B)36m C) 30m D)12m E) 24m
Answer:
B
Step-by-step explanation:
Nesta questão, estamos interessados em calcular a distância percorrida se um jogador correr a uma velocidade de 43,2 km / h por 3 segundos.
Matematicamente; a distância percorrida = velocidade * tempo
O problema que temos aqui é que nossas unidades não são consistentes.
A melhor maneira de fazer isso é ter unidades consistentes em metros por segundos e segundos, pois nossa resposta está em metros.
Portanto, a conversão que precisamos fazer aqui é converter 43,2 km / h em metros por segundo Matematicamente, sabemos que existem 1000 m em um quilômetro.
Da mesma forma, uma vez que 60 segundos fazem um minuto e 60 minutos fazem uma hora, o número de segundos em uma hora é 60 * 60 = 3.600 segundos
Assim, convertendo 43,2 km / h em m / s, temos; (43,2 * 1000) / 3600 = 12 m / s
Portanto, a distância percorrida em metros seria agora; velocidade em m / s * tempo em segundos = 12 m / s * 3 segundos = 36 m
Help on both questions please!! Ty
What is the value of x in the figure below? In this diagram, AABD - ACAD.
===================================================
The right triangles are similar, allowing us to form the proportion below
BD/AD = AD/DC
5/AD = AD/9 .... substitution
5*9 = (AD)*(AD) .... cross multiply
45 = (AD)^2
(AD)^2 = 45
AD = sqrt(45) ... apply square root
We could simplify but your teacher has decided not to. If you want to simplify, then
AD = sqrt(45)
AD = sqrt(9*5)
AD = sqrt(9)*sqrt(5)
AD = 3*sqrt(5)
--------
Segment AD is the geometric mean of BD and DC.
AD = sqrt(BD*DC)
which is the result of solving BD/AD = AD/DC for AD
So,
AD = sqrt(BD*DC)
AD = sqrt(5*9)
AD = sqrt(45)
Please help with #32
Answer:
The temperature at 10 pm was -1 degrees and the arrows helped you understand when the temperature increased and decreased.
Step-by-step explanation:
At 8 am, we know that the temperature is -3 degrees, or 3 degrees below zero. By 1 pm, the temperature has risen by 14 degrees and is now 11 degrees. We know this because -3+14=11. Now by 10 pm, the temperature has dropped 12 degrees which means that it's -1 degrees. (11-12=-1) The plot points would be all of the temperatures, or -3, 11, and -1. The arrows you need to draw are from -3 to 11 (an increase) and from 11 to -1 (a decrease). Drawing the arrows this way represents the temperature at different times and how it changed over time.
A price increases from $50 to $120. What is the percentage change?
Answer: 140%
Step-by-step explanation:
From the question, we are informed that price increases from $50 to $120. The percentage change will be:
= (New price - Old price)/Old price × 100
= (120 - 50)/50 × 100
= 70/50 × 100
= 1.4 × 100
= 140%
Wendy thinks the perfect chocolate chip cookie has 353535 chocolate chips for every 555 ounces of dough. Cookie Club makes batches of chocolate chips cookies with 100100100 chocolate chips and 151515 ounces of dough.
Answer:
Wendy will think cookie club chocolate cookies are not chocolatey enough
Step-by-step explanation:
Wendy thinks the perfect chocolate chip cookie has 35 chocolate chips for every 5 ounces of dough. Cookie Club makes batches of chocolate chips cookies with 100 chocolate chips and 15 ounces of dough. What will Wendy think about Cookie Club's cookies?
Perfect chocolate chip cookie=35 chocolate chips for every 5 ounces of dough
Wendy's perfect chocolate chip cookies = 35 chocolate chips for every 5 ounces of dough
= 35 : 5
=7:1
Cookie club chocolate chips cookies=100 chocolate chips for every 15 ounces of dough
=100 : 15
=20 : 3
Cookie club chocolate cookies have 3 times the amount of dough
Therefore,
Wendy will think cookie club chocolate cookies are not chocolatey enough
Answer:
Not choclatey enough
Step-by-step explanation:
Can someone please help me?
Answer:
the angle EBA is 25
Step-by-step explanation:
abc is an straight angle it means 180 , so if DBC is 130 you should make a substraction ( abc- dbc) it will give you the other part that acomplish the 180 of abc , and if it is divided by the half it hould be 25 each
How is 0.02 the same and different from 0.002
Answer:
0.02 is different from 0.002 because 0.02 is greater than 0.002
0.02 and 0.002 are the same because they are both decimal numbers
Step-by-step explanation:
0.02 = 2 / 100
0.002 = 2 / 1000
0.02 < 0.002
0.02 is different from 0.002 because 0.02 is greater than 0.002
0.02 can also be written as 2 × 10^2
0.002 can also be written as 2 × 10^3
0.02 and 0.002 are the same because they are both decimal numbers
Graph the line with slope -3 passing through the point (5,1) .
Answer:
Step-by-step explanation:
Graph a line given a point and a slope
Plot the given point.
Use the slope formula to identify the rise and the run.
Starting at the given point, count out the rise and run to mark the second point.
Connect the points with a line.
X^3 divided by X^2=?
Answer choices:
A)x
B)xX^5
C)x^6
D)x^10
Answer:
x
Step-by-step explanation:
you subtract
what is the distance between -2 and 5
Answer:
7
Step-by-step explanation:
To find distance on a number line you add and 2+5=7
Write a fraction equivalent to 3/5 that has a denominator of 100.
Answer:
60/100
Step-by-step explanation:
We know that 20 goes into 100 5 times, so we multiple numerator and denominator by 20 to get an equivalent fraction:
[tex]\frac{3}{5} (\frac{20}{20} )=\frac{3(20)}{5(20)} =\frac{60}{100}[/tex]
A bee flies at 20 feet per second directly from a flowerbed to its hive. The bee stays at the flowerbed for 13 minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 15 minutes. Write and equation let d be the distance from the flowerbed to the hive.
Answer:
The flowerbed is 1066.7 feet away from the hive.Noor brought 212121 sheets of stickers. She gave \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction of a sheet to each of the 454545 students at recess. She wants to give teachers 1\dfrac{1}{2}1 2 1 1, start fraction, 1, divided by, 2, end fraction sheets each.
Answer:
12 teachers will get 1/2 sheets each
Step-by-step explanation:
Noor bought 21 sheets of stickers
She gave 1/3 sheets to each 45 students
She wants to give teachers 1/2 of sheets
The question should be: how many teachers will she give
Total sheets=21
Students gets= 1/3 × 45
=45/3
=15 sheets
Remaining sheet= total sheets - students sheets
=21-15
=6 sheets
There are 6 sheets remaining for teachers
She wants to give 1/2 to each teacher
Then,
The number of teachers that will get =Remaining sheets ÷ each teacher's share
=6 ÷1/2
=6 × 2/1
=12 teachers
12 teachers will get 1/2 sheets each
Answer:
12 teachers will get 1/2 sheets each
Step-by-step explanation:
help me find x please
Answer:D
Step-by-step explanation:
Hope that helped
Answer:
its in the balls
Step-by-step explanation:
Evaluate: 6x2 + (9y-2)+y when x= 3 and y=8.
Answer:
98
Step-by-step explanation: All you have to do is multiply 6 by 3 and then multiply that answer by 2. Then you multiply 9 by 8 and subtract 2, then you add all that together and finally, subtract it by 8
Answer:
The answer is 402.
Step-by-step explanation:
First thing to do is substitute the variables.
6(3)^2+(9(8)-2)+8
Now, multiply and subtract what is in the parenthesis.
6(3)^2+(72-2)+8
6(3)^2+70+8
Now, multiply once again.
18^2+70+8
Now, simplify the exponents.
324+70+8=402
Find the missing factor 8^3=(-2x)(A)
-256.
how? 8 times 8 times 8 is 512.
512/2 is 256. But two negatives make a positive. So, it's -256.
The distance between 4 and 17 is _____
Answer:
The answer is 13
Step-by-step explanation:
The distance between 4 and 17 is 13 because addition
The distance between 4 and 17 is 13 units.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that the two numbers are 4 and 17.
The distance between 4 and 17 is calculated as below:-
To calculate the distance subtract the value 4 from the value 17.
Distance = 17 - 4 = 13 units.
Therefore, the distance between 4 and 17 is 13 units.
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the sum of a number and 4 is 6 1/2
Answer:
X=2
Step-by-step explanation:
let say x is the variable that we want to found .
x + 4 =6 1/2
X + 4 = 6
X= 2
The number is [tex]2\frac{1}{2}[/tex].
What is a sum?A summation, also called a sum, is the result of arithmetically adding numbers or quantities.
Given that, the sum of a number and 4 is [tex]6\frac{1}{2}[/tex]
Let the number be x
x + 4 = [tex]6\frac{1}{2}[/tex]
x [tex]x= 6\frac{1}{2} - 4\\= 2\frac{1}{2}[/tex]
Hence, the number is [tex]2\frac{1}{2}[/tex].
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Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00. How long will he have to wait to withdraw the money?
Answer:
Daniel has to wait around 5.24 years to withdraw the money.
Step-by-step explanation:
We are given that Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00.
Let the Principal sum of money be represented by 'P'.
The rate of interest be represented by 'R'.
The time period be represented by 'T'.
The final amount of money be represented by 'A'.
Assuming the interest given is compound interest.
So, the formula for calculating the amount of money is given by;
[tex]\text{A} = \text{P} \times (1-\text{R})^{\text{T}}[/tex]
Here, A = $1,150, P = $750, R = 8.5% and let the time he have to wait to withdraw the money be 'n'.
So, putting these values in the above formula we get;
[tex]\text{A} = \text{P} \times (1+\text{R})^{\text{T}}[/tex]
[tex]\text{\$1,150} = \text{750} \times (1+\text{0.085})^{\text{n}}[/tex]
[tex](1+\text{0.085})^{\text{n}} = \frac{\$1,150}{\$750}[/tex]
[tex](1+\text{0.085})^{\text{n}} = 1.533[/tex]
Taking log on both sides;
[tex]\text{n} \times ln(1+\text{0.085}) = ln(1.533)[/tex]
[tex]n = \frac{ ln(1.533)}{ ln(1.085)}[/tex]
n = 5.24 years
Hence, he has to wait around 5.24 years to withdraw the money.
Rearrange the equation so q is the independent variable. -7q + 12r = 3q - 4r
Answer:
q = 8/5r or q = 1.6r
Step-by-step explanation:
-7q + 12r = 3q - 4r
+7q +7q
12r = 10q - 4r
+4r +4r
16r = 10q
/10 /10
16/10 = 8/5 8/5 = 1.6
q = 8/5r or q = 1.6r
find the midpoint of the line segment joining points A(6,-5) and B(,6,1)
Explanation:
The two given points have x coordinates of x = 6 each. They add to 6+6 = 12. Divide this in half to get 12/2 = 6. Since the x coordinates were both the same, the midpoint x coordinate is the same as well.
The y coordinates are a bit more interesting. Add them up to get -5+1 = -4. Then cut this in half to get -4/2 = -2. The y coordinate of the midpoint is -2.
Overall, the midpoint is (6, -2)
Answer:
the answer is (6.-2)...