Fill in the missing numbers to complete the factorization. Some of the numbers could be negative. Type the numbers in increasing order.
x 3 + 2x 2 - x - 2 = (x +
Answers
Answer:
[tex]x^3+2x^2-x-2=(x+1)(x-1)(x+2)[/tex]
Step-by-step explanation:
We have given equation : [tex]x^3+2x^2-x-2=(x+[/tex]
To find : the missing numbers
We have given that missing numbers complete the factorization
so, we find the factors of the given equation
[tex]x^3+2x^2-x-2=0[/tex]
with the help of graph(attached) we find the roots of the equation or you can also take help of hit n trial method.
Roots of the equation are = 1,-1,-2
therefore the factors are (x+1)(x-1)(x+2)
and the missing terms are the factors of the equation = (x+1)(x-1)(x+2)
Answer:
[tex](x-1)>(x+1)>(x+2)[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^3+2x^2-x-2[/tex]
Factorizing the above equation, we get
[tex](x+1)(x^2+x-2)[/tex]
[tex](x+1)(x^2+2x-x-2)[/tex]
[tex](x+1)(x(x+2)-1(x+2))[/tex]
[tex](x+1)(x-1)(x+2)[/tex]
which is the required factorized form of the given equation.
Now, the numbers in increasing order are:
[tex](x-1)>(x+1)>(x+2)[/tex]
Related Questions
An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.
Answers
width: 20 - 2x
length: 40 - 2x
height: x
Volume = width x length x height
1500 = x(20 - 2x)(40 - 2x)
1500 = x(800 + 4x² - 120x)
1500 = 4x³ - 120x² + 800x
0 = 4x³ - 120x² + 800x - 1500
0 = x³ - 30x² + 200x - 375
Solving the cubic equation:
x = 5 (only integer root)
Length = 30 cm
Width = 10 cm
Height = 5 cm
find two consecutive odd integers whose sum is -88
Answers
first number is x. Second number is the next (or consecutive) odd number so its x+2 (can also do x-2)
Using (x+2)
x + (x+2) = -88
2x = -90
x = -45
and the other number will be -43
Using (x=2)
x + (x-2) = -88
2x = -86
x = -43
and the other number will be -45
______________________
Explanation:
_________________________________
Let "x" = one of the odd integers.
Let "x + 2" = the other odd integer.
_________________________________
x + (x + 2) = - 88 ;
x + x + 2 = - 88;
2x + 2 = - 88 ; Now, subtract "2" from EACH side of the equation:
_______________________
2x + 2 - 2 = - 88 - 2 ; to get:
______________________________
2x = -90 ; Now, divide EACH side of the equation by "2"; to isolate "x" on one side of the question; and solve for "x";
_________________________________
2x/2 = -90/2 ;
______________
x = -45
_________
So one of the integers is -45. It is an odd number? Yes!
The next consecutive integer is: "(x+2)" ; or, (-45 + 2) = -43. Its it an odd number? Yes!
Are "-45", and "-43" consecutive odd integers? Yes!
_______________________________
The two consecutive integers are: -45 and -43.
_________________________
To check our work:
___________________
Do the sum of our two consecutive integers equal -88?
___________
-45 + (-43) =? -88 ? Yes!
___________________________
can someone please explain?
Show that the point (7/25, 24/25) is on the unit circle
Answers
d = √(x² + y²)
d = √[(7/25)² + (24/25²)]
d = 1
So this point does lie on the unit circle.
To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.
Explanation:To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.
The distance between two points, (x1, y1) and (x2, y2), is given by the formula: √((x2-x1)² + (y2-y1)²).
In this case, the distance between the point (7/25, 24/25) and the origin (0, 0) can be calculated as: √((7/25-0)² + (24/25-0)²) = √((49/625) + (576/625)) = √(625/625) = 1.
Since the distance between the given point and the origin is indeed equal to 1, we can conclude that the point is on the unit circle.
If 3x-1=11, then 2x=?
Answers
To find 2x, we first need to solve for x in the equation 3x - 1 = 11. We isolate x by adding 1 to both sides and divide by 3 to obtain x = 4. Finally, multiplying x by 2 gives us 2x = 8.
Explanation:To solve the equation 3x - 1 = 11 for 2x, we need to isolate x first. Adding 1 to both sides, we get 3x = 12. Dividing both sides by 3, we find that x = 4. Now, to find 2x, we simply multiply x by 2, which gives us 2(4) = 8.
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Find the area of the region. Use a graphing utility to verify your result.
y = 6 sin(x) + sin(6x)
the graph goes from x=0 to x=pi ...?
Answers
To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval. Using a graphing utility, we can plot the function and verify the result.
Explanation:To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval.
Using a graphing utility, we can plot the function and verify the result. The integral will give us the area under the curve.
A graphing utility like Desmos or Wolfram Alpha can be used to plot the function and find the area under the curve.
NEED YOUR HELP!! I WILL UPVOTE!
Combining Like Terms:
Solve the equations by combining like terms. Show all the steps.
Then write two of your own problems where you combine like terms. Show all steps, as well as your solution.
1. 16x − 4x = -48
Answers
x=-4
10y-13y=30
-3y=30 (divide -3 from both sides)
-10=y
10x+14x=48
24x=48 (divide 24 from both sides)
x=2
Which of the following is the best estimate for the capacity of a bottle of salad dressing?
1 fl oz
1 gal
1 pt
I'm just having trouble picturing a bottle of salad dressing... I don't use it that often. ...?
Answers
1 fl oz is the best estimate for the capacity of a bottle of salad dressing.
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Answer:
1 gal
Step-by-step explanation:
Find the missing number in this proportion.
7 / 35 = ? / 28
Answers
To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. The missing number is 5.6.
Explanation:To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and then setting the two products equal to each other. In this case, we have 7 * 28 = ? * 35. Solving for the missing number, we get:
7 * 28 = ? * 35
196 = ? * 35
? = 196 / 35
? = 5.6
So, the missing number is 5.6.
isabella bought 1.1 kilograms of top quality hamburger meat at $5.00 per kilogram. how much did it cost?
Answers
The cost of 1.1 kilograms of hamburger meat at $5.00 per kilogram is $5.50
Multiply the weight of the meat (1.1 kg) by the price per kilogram ($5.00):
1.1 kg x $5.00/kg = $5.50.
Therefore, it cost Isabella $5.50 to buy 1.1 kilograms of top-quality hamburger meat.
A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?
$2
$4
$30
$36
Answers
10 percent = 10/100 = 0.10
10% of $40 = 0.10*40 = 4
You save $4
The old price is $40 and changes to $36 after the discount is applied. This is ignoring any taxes or other surcharges
Anyways I'm going a bit off tangent. The final answer is choice B) $4
Answer:
B) $4
Step-by-step explanation:
A triangle has side length of 14 cm 48 cm and 50 cm classify it as acute obtuse or right
Answers
The triangle with side lengths of 14 cm, 48 cm, and 50 cm is a right triangle.
Explanation:The lengths of the sides of the triangle are 14 cm, 48 cm, and 50 cm. To classify the triangle, we need to determine if it is acute, obtuse, or right.
Using the Pythagorean theorem, we can check if it satisfies the condition for a right triangle. If the square of the length of the longest side (50 cm) is equal to the sum of the squares of the other two sides (14 cm and 48 cm), then it is a right triangle.
In this case, (50)^2 = (14)^2 + (48)^2, which is true. Therefore, the triangle is a right triangle.
Final answer:
A triangle with side lengths of 14 cm, 48 cm, and 50 cm is classified as an acute triangle.
Explanation:
A triangle with side lengths of 14 cm, 48 cm, and 50 cm can be classified as an acute triangle.
To determine this, we need to check if the square of the longest side (50 cm) is less than the sum of the squares of the other two sides (14 cm and 48 cm).
502 < 142 + 482
2500 < 196 + 2304
2500 < 2500
This inequality is not true, so the triangle is not obtuse or right. Thus, it is classified as an acute triangle.
3. Brinn’s rectangular kitchen has an area of 81 square feet. The kitchen is 9 times as many square feet as Brinn’s pantry. If the rectangular pantry is 3 feet wide, what is the length of the pantry?
Answers
The length of the pantry is 3 feet.
To find the length of the pantry, we need to determine its area first. According to the question, the kitchen is 9 times the size of the pantry. With the kitchen's area being 81 square feet, the pantry's area would be 81 square feet divided by 9, which equals 9 square feet. Since we are given that the width of the pantry is 3 feet, we divide the total area of the pantry by its width to find the length.
The calculation is as follows:
Area of kitchen: 81 sq ft
Area of pantry: 81 sq ft / 9 = 9 sq ft
Width of pantry: 3 ft
Length of pantry: Area of pantry / Width of pantry = 9 sq ft / 3 ft = 3 feet long.
If Anton can carry 3 boxes per trip, how many trips will it take him to move 51 boxes? 17 27 30 37
Answers
so, for 51 boxes, it would be: 51/3 = 17
So, option A is your answer.
Hope this helps!
Answer:
17 trips will it take him to move 51 boxes
Step-by-step explanation:
Given: Anton can carry 3 boxes per trip.
That's mean for 1 trip he carry 3 boxes .
To carry 51 boxes he make , [tex]\frac{51}{3}=17[/tex] trip
Therefore, 17 trips will it take him to move 51 boxes.
find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9) find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9)
Answers
Substituting y = 3 to the expressions yields:
(3)^2/(-3(3)+9)
9/0, which is undefined.
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Simplify by combining like terms step by step
- (3x - 4y) + x
Solve each formula for the indicated variable. step by step
h = vt -5t^2 , for v
Answers
-3x + 4y + x.....combine like terms
-2x + 4y
h = vt - 5t^2....add 5t^2 to both sides
h + 5t^2 = vt....divide both sides by t
(h + 5t^2) / t = v
find the zero of the function. state the multiple zero . y=9x^3 -9x
Answers
The zeros of the function y = 9x³ - 9x are x = 0, x = 1, and x = -1. There are no multiple zeros for this function.
The question seeks to identify the zeros of the function y = 9x^3 - 9x. To find the zeros, we set the function equal to zero and solve for x.
Step 1: Set the function equal to 0: 0 = 9x³ - 9x.Step 2: Factor out a common term: 0 = 9x(x² - 1).Step 3: Factor further using difference of squares: 0 = 9x(x - 1)(x + 1).Step 4: Set each factor equal to zero: x = 0, x = 1, x = -1.Step 5: Identify the multiple zero, if any. In this case, there are no multiple zeros.The zeros of the function are x = 0, x = 1, and x = -1.
Therefore, as per the above explaination, the correct answer is x = 0, x = 1, and x = -1.
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
(State wether the graph of the linear relationship is a solid line or a set of unconnected points.
Answers
Angle ABD and angle BDE are supplementary. Find the measures of both angles.
m angle ABD =5x degrees, m angle BDE = (17x-18)degrees
Answers
∠ABD + ∠BDE = 180
5x + 17x - 18 = 180
22x = 198
x = 9
∠ABD = 5(9) = 45°
∠BDE = 180 - 45 = 135°
What is the general term for the sequence 1,6,11,16,...?
n + 5
5n - 4
5n + 1
Answers
Just plug numbers into it. Make this a table.
n 0 1 2 3
y 1 6 11 16
Answer:
Step-by-step explanation:
The given sequence is:
1,6,11,16,...
Since, the sequence is Arithmetic progression, therefore
The general term for the sequence is:
[tex]A_{n}=a+(n-1)d[/tex]
where a is the first term of the sequence and d is common difference.
Substituting the given values, we get
[tex]A_{n}=1+(n-1)5[/tex]
[tex]A_{n}=1+5n-5[/tex]
[tex]A_{n}=5n-4[/tex]
which is the required general term.
Thus, option B is correct.
The sales tax rate in jans town is 7.5.if she buys 3 lamps for $23.59 each and a sofa for $769.99 , how much sales tax does she own ?
Answers
Now, lets we total the money that she must pay without tax ( just for 3 lamps and 1 sofa ) :
3 lamps = 3 . $23.59 = $70.77
1 sofa = $ 769.99
Total amount = $769.99 + $70.77 = $840.76
We have to find tax amount, the tax amount of the total amount is about 7.5% of the price. Then we have to adding the tax amount into the total amount. So that we have the Total amount including the tax.
tax amount = 7.5% . 840.76 = $63.057
Total amount (inc. tax amount) =
$840.76 + $63.057 = $903.817
Therefore, she must pay those sofa and lamps about $903.817. So expensive huh? =))
Which function has the greatest y-intercept? (2 points)
f(x)
g(x)
h(x)
All three functions have the same y-intercept.
Answers
The function h(x) has the greatest y-intercept of 8, as it crosses the y-axis at the highest point.
Explanation:The function that has the greatest y-intercept is the one that crosses the y-axis at the highest value. The y-intercept is the point where the graph of a function intersects the y-axis, which is when x = 0. So, to find the function with the greatest y-intercept, we need to evaluate the y-value when x = 0 for each function.
Let's consider the functions f(x), g(x), and h(x). If f(x) has an equation of y = 3x + 5, g(x) has an equation of y = x - 2, and h(x) has an equation of y = -2x + 8, we can plug in x = 0 and see which function gives us the greatest y-value.
For f(x), when x = 0, y = 3(0) + 5 = 5. For g(x), when x = 0, y = 0 - 2 = -2. And for h(x), when x = 0, y = -2(0) + 8 = 8. Thus, h(x) has the greatest y-intercept because it crosses the y-axis at the highest point, which is 8.
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If x =4 calculate the value of 2x squared - 5
Answers
= 2(x)^2 - 5
= 2(4)^2 - 5
= 2(16) - 5
= 32 - 5
= 27
The number 72 is between what two perfect squares? Enter a numerical answer only.
Answers
6 x 6
2 x 2
So the number 72 is between the PRODUCT of two perfect squares such as those.
One product has to be above 72, and the other below it.
So lets multiply.
8 x 8 = 64
9 x 9 = 81
Oh look at that, 72 is between 64 and 81.
64=8^2
81 = 9^2
72 is between what two perfect squares 64=8^2 and 81 = 9^2
Find the area of a regular hexagon with the given measurement.
2 sqrt3 apothem
A =
...?
Answers
[tex]\sf tan(x^o)=\dfrac{Opposite}{Adjacent}[/tex]
[tex]\sf tan(30^o)=\dfrac{x}{2\sqrt{\sf 3}}[/tex]
We know that [tex]\sf tan(30^o)=\dfrac{1}{\sqrt{\sf 3}}[/tex]:
[tex]\sf \dfrac{1}{\sqrt{\sf 3}}=\dfrac{x}{2\sqrt{\sf 3}}[/tex]
Multiply [tex]\sf 2\sqrt{\sf 3}[/tex] to both sides:
[tex]\sf x=\dfrac{2\sqrt{\sf 3}}{\sqrt{\sf 3}}[/tex]
Simplify:
[tex]\sf x=2[/tex]
So half the side length of the hexagon is 2. That means the entire side length is 2 * 2 = 4.
Now use the formula:
[tex]\sf A=\dfrac{1}{2}ap[/tex]
This is used to calculate the area of any regular polygon. Where 'a' is the apothem and 'p' is the perimeter. The side length is 4, a hexagon has 6 sides, so the perimeter is 6 * 4 = 24. Plug in what we know:
[tex]\sf A=\dfrac{1}{2}(2\sqrt{\sf 3})(24)[/tex]
Simplify:
[tex]\boxed{\sf A=24\sqrt{\sf 3}}[/tex]
Answer:
41.57 unit²
Step-by-step explanation:
We know,
Area of a regular hexagon = [tex]3\times (sidelength)\times (apothem)[/tex].
The length of the apothem = [tex]2\sqrt{3}[/tex] units.
Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.
As, the apothem of the regular hexagon = height of the equilateral triangle
So, height of the equilateral triangle = [tex]2\sqrt{3}[/tex] units.
As, in the equilateral triangle, 'One of the side length is the S, other will be [tex]\frac{S}{2}[/tex] and height is [tex]2\sqrt{3}[/tex] units'.
So, using Pythagoras Theorem, we have,
[tex]hypotenuse^{2}=perpendicular^{2}+base^{2}[/tex]
i.e. [tex]S^{2}=(\frac{S}{2})^{2}+(2\sqrt{3})^{2}[/tex]
i.e. [tex]S^{2}=\frac{S^2}{4}+12[/tex]
i.e. [tex]S^{2}-\frac{S^2}{4}=12[/tex]
i.e. [tex]\frac{3S^2}{4}=12[/tex]
i.e. [tex3S^2=48[/tex]
i.e. [texS^2=16[/tex]
i.e. S= 4 units
That is, the side length of the hexagon = 4 units.
Thus, the area of the hexagon is given by,
Area of a regular hexagon = [tex]3\times (4)\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]12\times (2sqrt{3})[/tex]
i.e. Area of a regular hexagon = [tex]24sqrt{3}[/tex]
i.e. Area of a regular hexagon = 41.57 unit²
Hence, the area of the regular hexagon is 41.57 unit².
What does the inequality x + 3 ≤ 2 say?
A number and three is at most two.
A number and three is less than two.
A number and three is at least two.
A number and three is no less than two.
Answers
Answer:
A number and three is at most 3.
Step-by-step explanation:
What is the circumference of a circle whose area is 121 pi square meters?
Answers
Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4
Answers
Answer:
AC = BD = 1 unit
Step-by-step explanation:
Given : length of diagonal of rectangle ABCD [tex]AC=\frac{3y}{5}[/tex] and [tex]BD=3y-4[/tex]
We have to find the length of diagonal.
We know In rectangle diagonal are of equal lengths.
Therefore, for rectangle ABCD diagonals AC= BD
Substitute the values, we get,
[tex]\frac{3y}{5}=3y-4[/tex]
Cross multiply , we get
[tex]3y=5(3y-4)[/tex]
On simplyfy , we get
[tex]3y=15y-20[/tex]
Solve for y , we get
[tex]15y-3y=20[/tex]
[tex]12y=20[/tex]
Divide both side by 12, we get,
[tex]y=\frac{20}{12}=\frac{10}{6}[/tex]
Thus, put the values of y in AC and BD to find the length of diagonals , we get,
[tex]AC=\frac{3y}{5}=\frac{3}{5}\times\frac{10}{6}=1[/tex]
Similarly for BC, we get,
[tex]BD=3y-4=3(\frac{10}{6})-4=5-4=1[/tex]
Thus, AC = BD = 1 unit
how do you graph this function rule: y = |X| - 7
Answers
to graph it
graph x=y for all x≥0
now reflect that line across y axis
you get a v
move that whole graph 7 units down
done
A painting measures 15 cm long by 24 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 45 cm long by 72 cm high. The second poster measures 97.5 cm long by 156 cm high. Which of the following is true? (Hint: To be an accuarate representation of the painting, would the the poster be similar to the painting?)
Answers
I had the same thing. Please mark as Brainiest Answer.
Answer:
Both posters ARE accurate representations of the painting
Step-by-step explanation:
Gradpoint
Solve the system by substitution.
2x - y + z = -4
z = 5
-2x + 3y - z = -10
Answers
2x - y + 5 = -4
y = 2x + 9
Substituting y and z into the third equation
-2x + 3(2x + 9) - 5 = -10
4x + 27 = -5
x = -8
y = 2(-8) + 9 = 7
z = 5
Answer: a
Step-by-step explanation: that person coulda said that