Solve 2x^3-5x^2-11x-4=0
Answers
x = {-1, -0.5, 4}
The factorization will be
.. (2x+1)(x +1)(x -4) = 0
Related Questions
Which of these denominations in no longer made in the United States?
A. $1000
B. $50
C. $2
D. $100
Answers
Answer:
$1000
Step-by-step explanation:
Select the type of equations.
consistent
equivalent
inconsistent
Answers
1. Given a || b , c || d, and . Find the measure of angles 1 through 12 in the complex figure.
Answers
To solve all of the angles that are listed you are going to have to set up and solve several equation involving supplementary angles and angles around traversals around parallel lines.
For example, you could set up the equation:
3 + 4 + 69 = 180
Also, angle 9 is 116 because they are alternate interior angles.
Also, angle 11 is 116 because the are corresponding angles.
Also, angle k can be solved with the equation: k + 12 + 90 = 180.
Good luck
In summary:
- Angle 1 = Angle 2 = Angle 3 = Angle 4 = 69°
- Angle 5 = Angle 6 = Angle 7 = Angle 8 = 116°
- Angle 9 = Angle 10 = 69°
- Angle 11 = Angle 12 = 116°
Let's analyze the complex figure with parallel lines and transversals. We have two parallel lines, a and b, intersected by two transversals. I'll break down the problem step by step:
1. Angle 1: This angle is formed by the intersection of a and the transversal. It is an **alternate interior angle** with the angle measuring 69°. Therefore, **Angle 1 = 69°**.
2. **Angle 2**: It is also an alternate interior angle with the same measure as **Angle 1**. Hence, **Angle 2 = 69°**.
3. **Angle 3**: This angle is formed by the intersection of **b** and the transversal. It is a **corresponding angle** to **Angle 1**. Therefore, **Angle 3 = 69°**.
4. **Angle 4**: It is a corresponding angle to **Angle 2**. Thus, **Angle 4 = 69°**.
5. **Angle 5**: This angle is formed by the intersection of **c** and the transversal. It is an **alternate interior angle** with the angle measuring **116°**¹. Therefore, **Angle 5 = 116°**.
6. **Angle 6**: It is also an alternate interior angle with the same measure as **Angle 5**. Hence, **Angle 6 = 116°**.
7. **Angle 7**: This angle is formed by the intersection of **d** and the transversal. It is a **corresponding angle** to **Angle 5**. Therefore, **Angle 7 = 116°**.
8. Angle 8: It is a corresponding angle to Angle 6. Thus, Angle 8 = 116°.
9. Angle 9: It is a vertical angle to Angle 1. Therefore Angle 9 = 69°.
10. Angle 10: It is a vertical angle to Angle 2. Thus Angle 10 = 69°.
11. Angle 11: It is a vertical angle to Angle 5. Therefore, Angle 11 = 116°.
12. Angle 12: It is a vertical angle to Angle 6. Thus, Angle 12 = 116°.
54 is 60% of what number?
Enter your answer in the box.
Answers
I hope I helped!
Answer:The answer would be 90
Step-by-step explanation:
This is really confusing... making my head hurt. I don't understand it AT ALL. If I get this one wrong, and all the other three like this, I'm gonna fail my test.
Can you figure out number 8 please and show how you got it?
Answers
You're working with a geometric problem where the probability of success is constant in each trial. This is related to the situation where you repeatedly ask students if they live within a five-mile radius. The problems you've mentioned seem to involve figuring out specifics related to degrees and interpreting figures.
Explanation:It sounds like you're dealing with a geometric problem. Geometric problems often involve situations where the probability of success or failure stays constant across trials. For example, you inquire if a person lives within five miles of you - the probability is fixed, regardless of the number of people you ask.
Let's decipher it step by step. Firstly, visualize each instance (trial) as the asking of a question to a student and consider success as the event where the student lives within five miles. Probability of success then stays the same every time you ask.
In problem 91, it's important to understand the degrees involved. The first part mentions 88.6°. Without the full problem, it's hard to give a direct answer here, but angles often play a part in geometry and trigonometry problems, it could be related to that. As for the figures mentioned (Car X, the hash marks) they would likely be visible on a diagram accompanying your problem and would inform the solution.
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Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
(Edit I have to repost this question bc i really need it answered. I'm offering more points now!
Answers
Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)
There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
(5x ) (x ) = 5x^2 +
2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3
3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.
For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6. This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.
As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.
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Problem # 2
Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
4x^2 (x - 3) (x - 4)
To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x )(x ) and guessing for which numbers will add to -7x and multiply to 12
A recipe for punch says to use 4 1/2 of lemonade for each cup of ginger ale. If you use 1 2/5 cups of ginger ale, how much lemonade should you use?
Answers
Identify the 25th term of the arithmetic sequence 2, 1 and 3 over 5,
1 and 1 over 5 …
@ranga
Answers
1 and 3/5 = (5+3)/5 = 8/5
1 and 1/5 = (5+1)/5 = 6/5
Therefore your arithmetic sequence is 2, 8/5, 6/5, ...
In an arithmetic sequence, the difference between a given term and the preceding one is equal to the difference between the following term and the given one. In your case:
d = 8/5 - 2 = (8-10)/5 = -2/5
As a prove: d = 6/5 - 8/5 = -2/5
Now, in order to find the 25th term you need to apply the formula:
an = a + (n - 1)d
where an is the number you are looking for, a is the first term, n is the term you are looking for and d is the distance.
Hence,
a₂₅ = 2 + (25-1)(-2/5) = 2 - 24·2/5 = 2 - 48/5 = (10-48)/5 = -38/5
-7 3/5 is the correct answer simplified.
Find the area of a parallelogram with a height 15 cm and a base of 18 and 2/3 cm
Answers
The formula for area of a parallelogram is [tex]A = bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height.
You're given the values of both the base and the height, so you can just plug these values into the formula for area. It will be easier to multiply if we convert the mixed number to an improper fraction first, so I'll do that.
[tex]18 \frac{2}{3} = \frac{56}{3} [/tex]
[tex]A = bh[/tex]
[tex]A = \frac{56}{3} *15[/tex]
[tex]A= \frac{56}{3} * \frac{15}{1} [/tex]
[tex]A= \frac{840}{3} [/tex]
[tex]A=280[/tex]
Answer:
The area of the parallelogram is 280 cm².
Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.
Answers
2a^2= c^2
If we have square root
√2a^2=√c^2
a√2= c
Answer:
Step-by-step explanation:
In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem that is:
[tex]a^{2}+b^{2}=c^{2}[/tex], which in this isosceles triangle becomes [tex]a^{2}+a^{2}=c^{2}[/tex] as a=b in isosceles triangle.
By combining the like terms, [tex]2a^{2}=c^{2}[/tex]
Now, we will determine the principal square root of both sides of the equation,
[tex]c=\sqrt{2}a[/tex] (since a is positive)
Divide both sides of the equation by 2, we get
[tex]\frac{c}{2}=\frac{\sqrt{2}a}{2}[/tex]
[tex]\frac{c}{2}=\frac{a}{\sqrt{2}}[/tex]
[tex]c=\frac{2a}{\sqrt{2}}[/tex]
[tex]c=\sqrt{2}a[/tex]
Now, as a=b, then [tex]c=\sqrt{2}b[/tex]
Find the number of sides of a regular polygon if the interior angle is 150
Answers
360/30= 12.
remember that no matter what is the polygon the sum of EXTERIOR angle is 360.
and 1 exterior angle + 1 interior angle = 180.
25 points!
Answer both! please leave explanation!
Answers
sin 27 = 34/x
x = 34/sin27
x = 74.89
2) to find the value of x you'll use the tangent formula
tan 49 = x/55
55(tan49) = x
63.270
hey I really need help its a test -3x=48
5x-1=29
4(x-6)+7=23
3(x-4)+5x=4
Answers
5x-1=29 --> x=6
4(x-6)+7=23 --> x=10
3(x-4)+5x=4 --> x=2
Colinda has just purchased her first home for $125,000. She put down a 20 percent down payment of $25,000 and took out a 4 percent mortgage for the rest. Her mortgage payment is $477 per month. How much of her first monthly mortgage payment is amortization?
Answers
Colinda's first monthly mortgage payment includes $143.70 towards amortization, after subtracting the first month's interest of $333.30 from the total payment of $477.
Explanation:To determine how much of Colinda’s first monthly mortgage payment is for amortization, we must first calculate the amount of her payment that goes towards interest and then subtract this from the total monthly payment.
Colinda bought a house for $125,000, made a 20% down payment ($25,000), and took out a mortgage for the remaining $100,000 at a 4% annual interest rate. Her monthly mortgage payment is $477.
First, calculate the monthly interest rate: 4% annually means 0.04 / 12 per month = 0.003333. Therefore, the first month’s interest on the mortgage is $100,000 * 0.003333 = $333.30.
Next, subtract the interest from the total monthly payment to find the amortization portion: $477 (total monthly payment) – $333.30 (interest) = $143.70 towards amortization.
The amount of Colinda's first monthly mortgage payment that is amortization is approximately $143.67.
To separate the interest portion from the total payment.
First, let's calculate the monthly interest rate:
[tex]\text{Monthly interest rate} = \frac{4 \%}{12} = \frac{0.04}{12} = 0.00333 \text{ (approx.)}[/tex]
Next, we calculate the interest portion of the first payment:
[tex]\text{Interest portion} = \text{Principal} \times \text{Monthly interest rate}[/tex]
[tex]\text{Interest portion} = 100,000 \times 0.00333 = 333.33 \text{ (approx.)}[/tex]
Now, to find the amortization portion, we subtract the interest portion from the total monthly payment:
[tex]\text{Amortization portion} = \text{Total monthly payment} - \text{Interest portion}[/tex]
[tex]\text{Amortization portion} = 477 - 333.33 = 143.67[/tex]
What was the original price if:
a
after increasing by 30% it became $520?
Answers
130% x = 520 Change a % to a decimal
(130/100) x = 520
1.3 x = 520 Divide by 1.3
x =520 / 1.3
x = 400
So the original cost of the item was 400 dollars.
Answer:
Original price was $400.
Step-by-step explanation:
Let the original price = x dollars.
It is given that the new price is obtained by increasing the original price by 30% i.e. 0.3
As, the new price is $520.
So, we have the relation,
[tex]x+0.03x=520[/tex]
i.e. [tex]1.3x=520[/tex]
i.e. [tex]x=\frac{520}{1.3}[/tex]
i.e. x = 400
Hence, the original price was $400.
Jack just opened a checking account at the bank. Within the first month, he deposited three checks for $34.98, $51.02, and $51.22. He withdrew $3.23 for new pencils, $4.22 for cards, and $9.79 for movies from his account in the same month.
Order the rational numbers from least to greatest and explain your reasoning.
At the beginning of the month Jack’s balance was $98. What was his balance at the end of the
month after all of his deposits and withdrawals? Show your work, no credit will be given for just an
answer.
Answers
34.98
51.02
51.22
Total income = 137.22 $
Now, let's find the amount of expenses:
3.23
4.22
9.79
Total expenses = $ 17.24
The balance at the end of the month is:
Initial amount + total income-total expenses
Substituting:
98 + 137.22-17.24 = 217.98 $
Answer:
his balance at the end of the month after all of his deposits and withdrawals is:
$ 217.98
what is the product? (9t-4)(-9-4)
Answers
Answer: The product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
Explanation:
The given expression is,
[tex](9t-4)(-9-4)[/tex]
Simplify the above expression.
[tex](9t-4)(-13)[/tex]
Use distributive property t simplify the above expression.
[tex](9t-4)(-13)=9t\times (-13)-4\times(-13)[/tex]
[tex](9t-4)(-13)=117t+52[/tex]
Therefore, the product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
A certain drug is made from only two ingredients: compound a and compound
b. there are 7 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 748 milliliters of the drug, how many milliliters of compound b are needed?
Answers
A delivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 95 pounds. the truck is transporting 50 large boxes and 65 small boxes. if the truck is carrying a total of 5275 pounds in boxes, how much does each type of box weigh?
Answers
Final answer:
By setting up a system of linear equations from the given conditions, we can determine that a large box weighs 60 pounds, and a small box weighs 35 pounds.
Explanation:
To solve the problem involving the weights of large and small boxes being transported by a delivery truck, we can set up a system of linear equations. Let L represent the weight of a large box and S represent the weight of a small box. We know from the problem statement the following:
A large box plus a small box weighs 95 pounds: L + S = 95
Total weight of all boxes: 50L + 65S = 5275
Now we can solve this system of equations by substitution or elimination. If we solve the first equation for L, we get L = 95 - S. Substituting this into the second equation gives us:
50(95 - S) + 65S = 5275
Expanding and simplifying the equation, we get:
4750 - 50S + 65S = 5275
15S = 5275 - 4750
15S = 525
S = 35
Now that we have the weight of the small box, we can substitute it back into the first equation to find the weight of the large box:
L + 35 = 95
L = 60
Therefore, a large box weighs 60 pounds, and a small box weighs 35 pounds.
A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?
Please round to the tenths place.
Please show work/steps and provide units with your answer.
Answers
Mark a line going from the base of the building to the person 34 feet.
Draw another line from the person to the top of the building. Label the angle between the two lines as 74o
Tan(74) = o / a
Tan(74) = o/34
o = 34*Tan (74)
o = 34 * 3.49
o = 118.6
The building is 118.6 feet tall.
Help: Scientists think the _____ is a solid iron with a layer of liquid iron surrounding it.
1. Outer core
2. Inner core
3. Mantle
4. Crust,
Answers
What is the area of a regular hexagon with a side length of 4 m? Enter your answer in the box. Round only your final answer to the nearest hundredth.
Answers
A= a^2 (3√3)/2
we replace a with 4
A=41.57
The area of a regular hexagon with a side of 4m is 24√3.
Side of the regular hexagon = 4m
What is a regular hexagon?A Regular hexagon is a polygon with 6 equal sides.
We know that a regular hexagon with a side p comprises 6 equilateral triangles with a side p.
So, the area of a regular hexagon with side p= area of 6 equilateral triangles with side p.
So, the area of a regular hexagon with side p = [tex]6*\frac{\sqrt{3} }{4} p^{2}[/tex]
The area of a regular hexagon with a side of 4m = [tex]6*\frac{\sqrt{3} }{4} 4^{2}[/tex]
The area of a regular hexagon with a side of 4m =24√3.
Therefore, The area of a regular hexagon with a side of 4m is 24√3.
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Arrange the summation expressions in increasing order of their values.
Answers
[tex]\sum_{i=1}^{4}4(5)^{i-1} = (4(5)^{1-1}) + (4(5)^{2-1}) + (4(5)^{3-1}) + (4(5)^{4-1})[/tex]
[tex]=4+20+100+500 = 624 [/tex]
[tex]\sum_{i=1}^{5}3(4)^{i-1} = (3(4)^{1-1}) + (3(4)^{2-1}) + (3(4)^{3-1}) + (3(4)^{4-1}) + (3(4)^{5-1})[/tex]
[tex]=3+12+48+192+768=1023[/tex]
[tex]\sum_{i=1}^{2}5(6)^{i-1} = (5(6)^{1-1}) + (5(6)^{2-1})[/tex]
[tex]=5+30=35[/tex]
[tex]\sum_{i=1}^{4}5^{i-1} = (5^{1-1})+(5^{2-1})+(5^{3-1})+(5^{4-1}) [/tex]
[tex]=1 + 5+ 25+125 = 156[/tex]
So, our totals are: 624, 1023, 35, and 156. So clearly, 1023 > 624 > 156 > 35. W can write it as (your answer):
[tex]\sum_{i=1}^{2}5(6)^{i-1} <\sum_{i=1}^{4}5^{i-1} <\sum_{i=1}^{4}4(5)^{i-1} < \sum_{i=1}^{5}3(4)^{i-1} [/tex]
Hope this helps! If anything is confusing, you can always DM me.
∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)
100p for an answer please
Answers
For n=5.3
5.3+8=13.3
All that apply:
1) First, write an expression.
2) the correct expression is: n + 8
3) second, substitute 5.3 for the variable, n.
4) third, simplify by adding 5.3 and 8
5) the answer is 13.3
What is the volume of a cylinder with base radius 3 and height 8?
Answers
Answer is provided in the image attached.
Final answer:
The volume of a cylinder with a base radius of 3 and a height of 8 is approximately 226.195 cubic units, using the formula V = πr²h.
Explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where π is the constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder. For a cylinder with base radius 3 and height 8, we use the values directly in the formula:
V = π×(3²)×8
V = π×9×8
V = π×72
V = 3.14159×72
V ≈ 226.195 cubic units
Therefore, the volume of the cylinder is approximately 226.195 cubic units.
(-6)^-12(-6)^5(-6)^2
Answers
if your simplifying your answer is the same.
if your multiplying your answer is also the same.
hope i helped :D
the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 5sqrt6
Answers
A man 50 years old has 8 sons born of equal intervals. The sum of the ages of the father and sons is 186. What is the age of the eldest son if the youngest is 3 years old.,
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To find the age of the eldest son in a family where the father is 50 and has 8 sons with a total age sum of 186, and the youngest son is 3, one can determine the age difference between siblings and use the formula for the sum of an arithmetic series.
The question is asking us to determine the age of the eldest son, given that the sum of the ages of a 50-year-old father and his 8 sons is 186 years and the youngest son is 3 years old. Let's assume that the sons are born at equal intervals; we can denote the age difference between each son as 'd' years.
The sequence of the sons' ages forms an arithmetic series where the youngest son is 3 years old (the first term of the series, or 'a1'), and the eldest son's age will be 'a1 + 7d' (since there are 8 sons).
Since the sum of an arithmetic series is given by the formula 'n/2 * (a1 + an)', where 'n' is the number of terms, 'a1' is the first term and 'an' is the last term, we can set up the equation:
8/2 * (3 + (3 + 7d)) = 186 - 50 (subtract the father's age from the total sum).
This simplifies to 4 * (3 + 3 + 7d) = 136, or '4 * (6 + 7d) = 136'. Dividing both sides by 4, we get '6 + 7d = 34', which leads to '7d = 28' and thus 'd = 4'.
Therefore, the age of the eldest son will be '3 + 7*4', which equals 31 years old.
please help. i get two diff ans.
If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? A) $3900, B) $3947 C) $3,977.40 D) $4000,
Answers
Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Then, find the volume of the cylinder if the radius is increased to 10 cm. Leave your answers in term of pi.
Answers
[tex]v= \pi r^{2} h[/tex]
where v = volume of cylinder, r = radius, and h = height of cylinder.
1) Radius = 5 cm, height = 10 cm. Plug these values into the equation.
[tex]v= \pi 5^{2} (10) = 250 \pi [/tex]
2) Radius = 10 cm, height = 10 cm.
[tex]v= \pi 10^{2} (10) = 1000 \pi[/tex]
Volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
How to determine the volume of the cylinder?The volume of the cylinder can be determined by multiplying area of base with height of the cylinder.
V=πr²*h
where r is the radius of base of the cylinder and h is the height of the cylinder.
following this above formula in given problem,
radius of the base of the cylinder= 5cm
height of the cylinder=10cm
volume= V=πr²*h= π5²*10= 250π cm³
Now the radius of the cylinder is increased to 10cm.
now r=10cm
height of the cylinder=10cm
volume= V=πr²*h= π10²*10= 1000π cm³
Therefore volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
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