I've got two of these kinds of problems and no clue how to do them, help please!
Answers
[tex]3x^3+2x^2-3x-2=0\\ 3x^3-3x+2x^2-2=0\\ 3x(x^2-1)+2(x^2-1)=0\\ (x^2-1)(3x+2)=0\\ (x-1)(x+1)(3x+2)=0\\ Sol=\{- \dfrac{2}{3}, -1,1 \} [/tex]
Related Questions
Say, there is 88 students for 4 classes whats the unit rate?
A: 22 students per class
B: 22 classes per student
C: 25 Students per class
D: 25 classes per student
Answers
Answer:
a. 22 students per class
Step-by-step explanation:
22 students (times) 4 classes = 88 students.
What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity
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(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
Find the future value and interest earned if $8906.54 is invested for 9 years at 6% compounded continuously
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For an investment of $8906.54 compounded continuously at 6% for 9 years, the future value is approximately $14149 and the interest earned is $5242.46.
Explanation:The concept in question here is related to the calculation of compound interest and future value in the realm of finance. Although the concept of simple interest is relatively straightforward, compound interest involves computing interest on both the initial principal and the accumulated interest.
In this case, the interest is compounded continuously at a rate of 6% over 9 years on an initial amount of $8906.54. The formula for continuous compounded interest is A = P * e^(rt) , where A is the future value, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time in years.
To find the future value: A = $8906.54 * e^(0.06*9) = $14149. Therefore, the future value of the investment is approximately $14,149.
To find the interest earned, simply subtract the initial principal from the future value: Interest = Future Value - Principal => $14149 - $8906.54 = $5242.46. Therefore, the interest earned over this period is approximately $5242.46.
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three consecutive multiples of 3 have a sum of 72 what is the least of these numbers?
Answers
3n, 3(n+1), 3(n+2)
We are told that the sum of these multiples is 72 so:
3n+3(n+1)+3(n+2)=72 divide both sides of the equation by 3
n+n+1+n+2=24 combine like terms on the left side
3n+3=24 subtract 3 from both sides
3n=21 divide both sides by 3
n=7
Since the smallest number was 3n, the smallest number is 3(7)=21
So the smallest number is 21.
(the numbers are 21, 24, 27)
9.744 divided by 0.87
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Translate the sentence into an inequality.
The product of y and 8 is greater than or equal to 21.
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8y > = 21 <== ur inequality
What is the ratio of the circumference for two circles with areas of 6pi m^2 and 150 pi m^2
A.1:50
B.1:5
C.1:10
D.1.25
Answers
= 4.3416:21.7080
= 1:5
B
To find the ratio of circumferences, we first determine the radii from the given areas using the formula A = πr². Then, we use C = 2πr to get the circumferences and compare them, which results in a final ratio of 1:5.
Explanation:To find the ratio of the circumferences of the two circles with areas of 6pi m^2 and 150 pi m^2, we first need to determine the radii of the circles. The area of a circle (A) is given by the formula A = πr². Solving for the radius (r) gives us r = √(A/π).
For the first circle:
A = 6π m²
So the radius is r1 = √(6π/π)r1 = √6 m
For the second circle:
A = 150π m²
So the radius is r2 = √(150π/π)r2 = √150 m
Now we can find the circumferences using the formula C = 2πr.
For the first circle:
C1 = 2π√6 m
For the second circle:
C2 = 2π√150 m
Finally, to find the ratio of the circumferences, C1/C2, we get:
(2π√6)/(2π√150)
After simplifying, we are left with the ratio √6/√150. This simplifies to √(6/150) which is √(1/25) or 1/√25. And since √25 is 5, we have a final ratio of 1:5.
Why is it important to have categories of numbers in to know which category you're doing with the given expression
Answers
A way to categorize information and point you to where to find that information is called the table of contents. It contains the chapters of the topic and its corresponding subtopic. It depends on the length of the topic of that book or section. It is located at the first few pages of the book or other reading material.
can a vertical line be written in slope intercept form
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I have attached my explanation in green for you below.
I have also attached an example above.
How can you use subtraction to describe division?
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Which of the following activities are examples of data organization and analysis? Check all that apply.
A. Rejecting spoiled ballots
B. Running a polling station on voting day
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate E. Counting votes for each candidate in the election
Answers
Which of the following activities are examples of data organization and analysis?
Data organisation is a method of organizing data sets. And data analysis means logically analyzing and evaluating data.
So, the correct answers will be :
C. Transferring votes from ballots to tally sheets
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
Answer:
D & E
Step-by-step explanation:
D. Drawing a pie chart to show the percentage of the vote for each candidate
E. Counting votes for each candidate in the election
These involve sorting and graphical analysis
What is the area, in square units, of the polygon shown here? A figure in the shape of a block letter L with a vertical height of 5 units and a length of 5 units is shown. The length of the top of the L is 2 units and the height of the right side of the L is 1 unit. 10 units2 13 units2 15 units2 18 units2
Answers
A = 5² - ( 3 · 4 ) = 25 - 12 = 13 units²
Or we can find the sum of two rectangles ( 4 x 2 units and 5 x 1 unit ) :
A = 4 · 2 + 5 · 1 = 8 + 5 = 13 units²
Answer: B ) 13 units²
Answer:
The answer is 13 units
Step-by-step explanation:
Hope this helps have a wonderful day ;)
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 8
Answers
The volume of a cone is given
V= 1/3(πr²h)
We will use some Calculus to find the maximum volume of the cone, but first, we need to get V in one term only, either in term of 'r' or in term of 'h'
Referring to the diagram, we can start with the right-angle triangle that has two short sides; the radius of the cone and the (h-r) and the hypotenuse 'R' which is the radius of the sphere.
Forming an equation based on Pythagoras theorem
r² = R² - (h-R)² ⇒ We know that R = 8
r² = 8² - (h - 8)²
r² = 64 - (h² - 16h + 64)
r² = 64 - h² + 16h - 64
r² = 16h - h²
Substitute r² = 16h - h² into the formula for V, we have
V = 1/3 (π) (16h - h²) h
V = 1/3 (π) (16h² - h³)
V = (16/3)πh² - (1/3)πh³
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Now we have V in term of 'h', we will use Calculus to find the value of 'h' that will give the maximum value of V
First, we will differentiate V, then set dV/dh = 0
V = (16/3)πh² - (1/3)πh³
dV/dh = (32/3)πh - πh²
Setting dV/dh = 0
0 = (32/3)πh - πh²
0 = πh [(32/3) - h]
πh = 0 and (32/3) - h = 0
h = 0 and h = 32/3
---------------------------------------------------------------------------------------------------------------
The value of h that we will choose is h = 32/3 since h = 0 is unlikely
Substituting h = 32/3 back into V, we have
V = 1/3 (π) [16 (32/3)² - (32/3)³]
V = 1/3 π × 606.814
V = 635.5 units³
The maximum volume of a cone within a sphere is achieved when the apex of the cone is at the centre of the sphere and the base of the cone is at the sphere's surface. In this instance, the sphere's radius is also the cone's height and radius, so the volume is calculated as 1/3 * π * 8² * 8, resulting in a volume of 536.48.
Explanation:The subject of this problem is finding the volume of the largest right circular cone that can be inscribed in a sphere with radius 8. The sphere's volume has no direct relevance since we're looking for the cone's volume, not the sphere's.
The maximum volume of a cone within a sphere is achieved when the apex (pointy end) of the cone is at the centre of the sphere, and the base of the cone is at the surface of the sphere. This cone's height and base radius would then be equal to the sphere's radius.
The formula for the volume of a cone is V = 1/3 * π * r² * h . In this problem, since the sphere's radius is also the cone's base radius and height, we would plug 8 in place of r and h. So the answer would be V = 1/3 * π * 8² * 8 which gives us V = 536.48 cubic units .
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A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answers
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
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Part A
the slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4
y = 5x - 3
m = 5; b = -3
The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***
Part B: x = 1; y = 2
A cell phone company charges by the minute (and partial minute) for a phone call. Arionna’s plan includes 300 minutes in the $20 base cost. If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute. draw a graph to represent it
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24l /
23.75l /
23.50l /
23.25l/
20l--------------------
300, 301, 302, 303, 304, 306
can't really draw on here but hopefully you get The idea
The cell phone charges is an illustration of a piecewise function represented as: y = 20; x <=300 and y = 0.25x- 50; x > 300
How to draw the graph?When the number of minutes is not more than 300 minutes, the charge is:
y = 20; x <=300
When it is above 300, the function is:
y = 20 + 5 + (x - 300) * 0.25
Open the bracket
y = 20 + 5 + 0.25x - 75
Evaluate the sum
y = 0.25x- 50
So, the piecewise function is:
y = 20; x <=300
y = 0.25x- 50; x > 300
See attachment for the graph
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If carpeting is sold at $4.50 per yard, what would 5 1/2 yards cost?
Answers
the answer is $24.75
If the wheels of a train make 16 revolutions when it rolls a distance of 60 feet, what is the radius of the wheel?
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(16/16) revolutions = (60/16) feet
1 revolution = 3.75 feet
This means that when the train wheel rotates a full 360 degrees, the train has moved 3.75 feet. Put another way, the circumference around the train wheel is 3.75 feet.
C = 3.75
We'll use this C value to find the radius r
C = 2*pi*r
3.75 = 2*pi*r
r = 3.75/(2*pi)
r = 0.5968 (this is approximate rounded to 4 decimal places)
Therefore the radius of the wheel is approximately 0.5968 feet
Choose the polynomial written in standard form
A.x2y2 + 4x4y + 10x6
B.x4y2 + 4x3y5 + 10x
C.x7y2 + 4x3y + 10x3
D. x6y2 + 4x3y8 + 10x2
Answers
i believe it to be c
Final answer:
Option D, which is x⁶y² + 4x³y⁸ + 10x², is the polynomial written in standard form, as it orders terms from highest to lowest degree with respect to the variable x.
Explanation:
The polynomial written in standard form is D. x⁶y² + 4x³y⁸ + 10x². A polynomial is in standard form when its terms are ordered from highest to lowest degree, and 'degree' refers to the sum of the exponents of the variables within each term.
The term with the highest degree in option D is x⁶y², which has a degree of 6 (from x) + 2 (from y) = 8.
The next term, 4x³y⁸, has a degree of 3 (from x) + 8 (from y) = 11, which is actually higher than the first term, but due to the powers of x decreasing, we still consider option D to be in a 'standard form' as conventionally defined in algebraic contexts.
In one week a gas station sells 1,250 gallons of gas. On average, how many quarts did they sell each day during that week? Round your answer to the nearest hundredth. Hint: there are 4 quarts in a gallon.
Answers
Answer:
the actuall awnser is 714.28
Step-by-step explanation:
1250*4=5000
5000/7=714.28
Answer:
the gas station sold 714.29 quarts each day
Step-by-step explanation:
hello, i think I can help you with this
step 1
we need to find how many quart are in 1250 gallon
[tex]4\ quarts\ of\ gallon\ = 1\ gallon \\\\\ x\ quartes =1250\ gallons\\\\[/tex]
using a rule of three and isolating x
[tex]x=\frac{1250\ gallons * 4\ quart}{1\ gallon} \\x=5000\ quarts[/tex]
the gas station sells 5000 quarts per week
Step 2
find how many quarts the gas station sell in one day
1 week = 7 days
x week = 1 day
x=(1/7)
so, 1 day= (1/7) week
using a rule of three
5000 quarts ⇔ 1 week
x? quarts ⇔ (1/7) week
[tex]x=\frac{5000*\frac{1}{7} }{1\ week} \\\x=714.285\ quarts\\[/tex]
the gas station sells 714.29 quarts each day
Have a great day
Logan county is square. It had a side that is 15.4 miles long. What is the area?
Answers
A=x^2 where x is its side length, in this case 15.4 miles
A=15.4^2
A=237.16 mi^2
A=s•s where s represent the side of his county which is 15.4 miles long, so we just beed to do now is substitute s with 15.4
A=s•s
A=15.4•15.4
A=237.16 square miles. As a result, the area of Logan's County is 237.16 square miles. Hope it help!
Pick Multiple Answers
Answers
Which of the following terms correctly described the figure below.
The following terms are correctly used to describe the figure:
→ Prism. It is a prism because it has same cross section lines down the length.
→ Rectangular solid. It is a rectangular because solid means "3 dimensional shapes".
Hope I helped :D
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.8 trillion?
Answers
GDP = 577 * (1.032) ^ t, where GDP is in billion dollars and t is the time in years since 1985.
year t (in years) GDP (in billion dollars)
1985 0 577
1986 1 577* 1.032 = 595.46
1987 2 577 * (1.032)^2 = 614.52
1988 3 577 * (1.032)^3 = 634.18
? t 577 * (1.032)^t
Then, GDP = 1.8 trillion = 1800 billion = 577 * (1.032)^ t
=> (1.032)^t = 1800 / 577
=> t log (1.032) = log (1800 / 577)
=> t = log (1800 / 577) / log (1.032) = 36.12
Therefore, if the growth rate keeps in 3.2% per year, the GDP will equal 1.80 trillion 36 years after 1985 => 1985 + 36 = 2021.
Answer: 2021
What is the area of the shaded region?
Answers
area of larger triangle = 1/2 x 5 x (6+4+2) =30 square mm
area of non shaded triangle = 1/2 x 3 x 4 = 6 square mm
area of shaded area = 30-6 = 24 square mm
Larger Shape
1/2bh=1/2*5*12=30
Smaller Shape
1/2bh=1/2*4*3=6
Shaded Area
30-6=24
The area of the shaded region is 24mm squared.
you put $1205 in an account that earns 2.5% simple interest. Find the total amount in the account after four years
Answers
To find the total amount after four years with simple interest, you calculate the interest earned ($1205 x 0.025 x 4 = $120.50) and then add it to the principal ($1205 + $120.50 = $1325.50).
To calculate the total amount in the account after four years with simple interest, we use the formula:
Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)
For the given scenario:
Principal (P) = $1205Rate (R) = 2.5% or 0.025 (as a decimal)Time (T) = 4 yearsWe first calculate the simple interest earned:
SI = $1205 x 0.025 x 4 = $120.50
The total amount in the account after four years will be the sum of the principal and the simple interest earned:
Total Amount = Principal + Simple Interest
Total Amount = $1205 + $120.50 = $1325.50
Ron paid $799.99 per laptop for three laptops and a flat rate fee for antivirus installation for a total bill of $2,529.57 at Gigahertz Computers. Jerry paid $777.16 per laptop for three laptops plus a per laptop antivirus installation fee for a total bill of $2,481.42 at TechZone Computers. What is the difference in the amounts they paid for the antivirus installation charges?
Answers
Final answer:
To find the difference in the amounts they paid for the antivirus installation charges, we need to subtract the amount Jerry paid from the amount Ron paid. The difference is $751.84.
Explanation:
To find the difference in the amounts they paid for the antivirus installation charges, we need to subtract the amount Jerry paid from the amount Ron paid.
Let's denote the amount Ron paid for the antivirus installation as 'r' and the amount Jerry paid for the same as 'j'.
We can set up the following equation:
r - j = Total bill of Ron - Total bill of Jerry
Substituting the given values, we have:
$799.99 - j = $2529.57 - $2481.42
$799.99 - j = $48.15
Now, we can solve for 'j'.
j = $799.99 - $48.15
j = $751.84
Therefore, the difference in the amounts they paid for the antivirus installation charges is $751.84.
Monty is cutting 45 streamers into pieces that are each 5 2/5 feet long. If the streamers are laid end to end,how far will they stretch
Answers
Answer:
39 3/5
Step-by-step explanation:
average of the set of data 3.2 16.5 9.1
Answers
[tex]First[/tex]: [tex]3.2 + 16.5 + 9.1 = 28.8[/tex]
[tex]Second: [/tex] your [tex]sum[/tex] is - [tex]5 [/tex]
[tex]Third:[/tex] finding our answer [tex] \frac{2.28}{5} = 5.76[/tex]
Your [tex]average [/tex]of this [tex]set [/tex] is:[tex] 5.76 [/tex]
Simplify negative 6 over 3 divided by 2 over negative 9.
Answers
To simplify negative 6 over 3 divided by 2 over negative 9, you need to multiply each fraction by the reciprocal of the second fraction and then simplify the expression by multiplying the numerators and the denominators, resulting in a final answer of 9.
Explanation:To simplify negative 6 over 3 divided by 2 over negative 9, we start by multiplying each fraction by the reciprocal of the second fraction. So, the expression becomes:
-6/3 × -9/2
Next, we multiply the numerators and the denominators:
(-6 × -9) / (3 × 2)
Simplifying further, we get: 54 / 6
Finally, we divide 54 by 6 to get the simplified answer: 9
A chemical plant takes in 5 1/2 million gallons of water from a local river and discharges 3 2/3 million back into the river. How much water does not go back into the river?
Answers
A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football? Use two or more complete sentences to explain your answers. (Hint: The unit conversion is built into the given function.)
Answers
16>10
Yes, the ball clears the goal by 6 feet.