Answer:
Given an equation: [tex]3x^3-21x^2-27x[/tex]
A given equation is trinomials have three terms( i.e, [tex]3x^3[/tex] , [tex]21x^2[/tex] and [tex]27x[/tex] )
Factoring is the division of the polynomial terms to the simplest forms.
A greatest common factor (GCF) identifies a factor that all terms within the polynomial have in common.
[tex](3x)(x^2) - (3x)(7x) - (3x)(9)[/tex]
now, 3x can be removed from the polynomial to simplify the factoring process.
i.e,
[tex]3x(x^2-7x-9)[/tex]
Therefore, the factor completely of [tex]3x^3-21x^2-27x[/tex] is,[tex]3x(x^2-7x-9)[/tex]
To factor the expression 3x³ - 21x² - 27x, we first factor out the common term 3x, which leaves us with 3x(x² - 7x - 9). The quadratic expression does not factor any further.
The expression 3x³ - 21x²- 27x can be factored by looking for common factors in each term. First, we can see that each term has a factor of 3x. We can factor out this common term which gives us:3x(x² - 7x - 9)
Next, we can factor the quadratic expression within the parentheses. However, this quadratic expression does not factor neatly, and it seems we've reached the simplest form by just factoring out 3x. Therefore, the completely factored form of the expression is:3x(x² - 7x - 9)
Line QR bisects angle PQS. Solve for x and find measure PQS:
m
Line QR bisects angle
PQS. Solve for x and find measure PQS:
m<PQS = 4x - 6, m<PQR = x + 11 ...?
m<PQR = (1/2) (m<PQS) = (1/2)( 4x - 6)
so x + 11 = 2x - 3 implies x =14
and then m<PQS = 4x - 6 =50°
on a number line, what is the distance between -5 and 2, it keeps saying i'm wrong.
If x equals 3 calculate the value of 2x squared plus x
What is the vertex of the following parabola?
y=(x-2)^2+3
A box of rice is 19 centimeters long, 12 centimeters wide, and 3.5 centimeters deep. The volume of the box is the product of its length, width, and height. What is the volume of the box?
A rectangle has a length of 5.50 m and a width of 12.0 m. What are the perimeter and area of this rectangle?
The perimeter of the rectangle is 35.0 meters, and the area is 66.0 square meters, using the formulas for perimeter (2(length + width)) and area (length × width).
Explanation:To calculate the perimeter and area of a rectangle, we apply the formulas: Perimeter = 2(length + width) and Area = length × width. In this case, the rectangle has a length of 5.50 m and a width of 12.0 m.
Calculating the Perimeter
Perimeter = 2(5.50 m + 12.0 m) = 2(17.5 m) = 35.0 m
Calculating the Area
Area = 5.50 m × 12.0 m = 66.0 m²
The perimeter of this rectangle is 35.0 meters, and the area is 66.0 square meters.
Please explain this problem.
# of Songs:Cost
6:$7.20
7:$8.40
8:$9.60
Cedric buys songs at a store that charges $1.20 per song. Shumeka buys songs at a different store. The table shown here gives the cost when she buys 6, 7, and 8 songs.
Are songs more expensive at Cedric’s store or Shumeka’s store?
A) Cannot be determined
B) Cedric's store is more expensive.
C) Shumeka's store is more expensive.
D) Songs cost the same at both stores.
Answer:
Songs cost the same at both stores.
Step-by-step explanation:
I would like to purchase 20 products at a cost 65.00 per product. what will be my total? your state has 3.5% sales tax
The total is: $ 1345.5
Step-by-step explanation:It is given that:
I would like to purchase 20 products at a cost 65.00 per product.
This means that the cost of 20 products will be:
[tex]20\times 65=\$\ 1300[/tex]
Also, there is a sales tax of 3.5%
This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.
i.e. he need to pay 3/5% on $ 1300
This means that the amount of tax he need to pay is: 3.5% of 1300
= 3.5%×1300
= 0.035×1300
= $ 45.5.
Hence, the total cost is: $ 1300+$ 45.5
This means that the total cost is: $ 1345.5
Two consumers borrowed 10000 for five years bob has credit score of 650 and has an intrest rate of 11.5% while tyree has a credit score of 710 and has an intrest rate of 8.0% what will be the total diffrence between what the two men pay?
...?
Calculating the total difference between what Bob and Tyree will pay over five years for borrowing $10,000 each involves simple interest calculation. Bob, with an 11.5% interest rate, pays $1,750 more than Tyree, who has an 8.0% interest rate. This demonstrates how credit scores affect loan costs.
Explanation:The question involves calculating the total difference between what two consumers, Bob and Tyree, will pay for borrowing $10,000 each over five years, given their respective interest rates based on their credit scores.
First, to solve this, we'll use the simple interest formula I = PRT, where I is the interest, P is the principal amount (the initial amount borrowed), R is the annual interest rate, and T is the time in years.
For Bob (credit score of 650 and an interest rate of 11.5%), the total interest paid is calculated as: $10,000 * 0.115 * 5 = $5,750.For Tyree (credit score of 710 and an interest rate of 8.0%), the total interest paid is calculated as: $10,000 * 0.080 * 5 = $4,000.The total difference between what Bob and Tyree pay is $5,750 - $4,000 = $1,750. Therefore, Bob will pay $1,750 more than Tyree over the five years due to his lower credit score and higher interest rate.
7.25 cm plus 7.2 cm plus 8cm equals what
integrate t sec^2 (2t) dt
Answer:
[tex]\int {t\times \sec^2(2t)} \, dt \\\\ \text{Integrating by parts}\\\\=\frac{t\times \tan 2t}{2}-\int{(\frac{d}{dt}(t) \times \int{{\ sec^{2}(2t)}}) dt}\\\\=\frac{t\times \tan 2t}{2}-\int{\frac{\tan 2t}{2}} dt\\\\=\frac{t\times \tan 2t}{2}-\frac{\log sec 2t}{4}+C[/tex]
Where C is Constant of Proportionality.
What is the converse of the statement “If an angle is a right angle, then it measures 90 degrees”? ...?
The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.”
Explanation:The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.” The converse of a conditional statement swaps the hypothesis and conclusion of the original statement. In this case, the original statement states that if an angle is a right angle (hypothesis), then it measures 90 degrees (conclusion). The converse states that if an angle measures 90 degrees (hypothesis), then it is a right angle (conclusion).
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a family of two adults and four children is going to and an amusement park. admission is 421.75 for adults and $15.25 for children. what is the total cost of the family's admission
Express answer in exact form.
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.
help me please ...?
the price of a car increases in the ratio 11:8. What is the new price of a car which originally cost 25600?
please help me with this problem thanks!
Give the excluded value(s) for the following fraction.
y+5/y^2+4y-32
Answer:
y is -8 and 4.
Step-by-step explanation:
The sum of two consecutive integers is at most 223.
What is the larger of the two integers?
Answer:
112
Step-by-step explanation:
What is the value of x?
x+58=6x+58=6
Enter your answer in the box in simplest form.
x =
Answer: The required value of x is -52.
Step-by-step explanation: We are given to find the value of x from the following equation :
[tex]x+58=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the value of x, we need to solve the equation (i).
The solution of equation (i) is as follows :
[tex]x+58=6\\\\\Rightarrow x=6-58\\\\\Rightarrow x=-52.[/tex]
Thus, the required value of x is -52.
Joel walked 2/5 of a mile to the store, 3/10 of a mile to the library, and 1/20 of a mile to the post office. Let x = the total distance Joel walked. Hw far did he walk? Draw a picture.
The total distance Joel walked is 3/4 of a mile.
To find the total distance, we add up the individual distances:
Distance to the store: 2/5 of a mileDistance to the library: 3/10 of a mileDistance to the post office: 1/20 of a mileTo add these fractions, they must have a common denominator. The least common denominator for 5, 10, and 20 is 20. So we convert the fractions:
2/5 = 8/20 (because 2x4 = 8 and 5 x 4 = 20)3/10 = 6/20 (because 3 x 2 = 6 and 10 x 2 = 20)1/20 remains the same, as its denominator is already 20.Now we add the fractions:
8/20 + 6/20 + 1/20 = 15/20
Finally, we can simplify 15/20 by dividing both the numerator and the denominator by 5:
15/20 = 3/4
Therefore, the total distance Joel walked is 3/4 of a mile.
Assume 3 in every 1000 students at a local community college have quit due to serious health issues. An insurance company offers them an $8000 policy for $50 a year. What is the amount the insurance company should expect to make on average on every student that pays?
Answer: if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:
3/1000 = 0.003
Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.
and a 0.997 probability to choose a student with no health issues.
Now, the company wins $50 for the healthy students, and lose ($50 - $8000) = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).
Then the insurance company should expect to make in average:
0.997*$50 - 0.003*($7950) = $26
So the company should expect to make 26 dollars per student in a year.
Substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place. Use the approximation 3.14 for pi. C=44. C stands for circumference.
then d= 44/3.14
r= 22/3.14
Solve using the quadratic formula.
3x^2+6x+7=0
The quadratic equation 3x^2+6x+7=0 has two complex solutions which is x=-1±√(48)i/6.
To solve the quadratic equation 3x^2+6x+7=0 using the quadratic formula, we first need to identify the coefficients a, b, and c from its standard form, which is ax^2+bx+c=0. In this case, a=3, b=6, and c=7.
The quadratic formula is given by x=(-b±√(b^2-4ac))/(2a).
Now, we will calculate the discriminant which is b^2-4ac. In this case, it is 6^2 - 4*3*7, which equals 36 - 84, or -48. Since the discriminant is negative, this means that there are no real solutions to the equation, but two complex solutions.
Applying the quadratic formula, we get the solutions:
x=(-6 ± √(-48))/(2*3)
This simplifies to:
x=(-6 ± √(48)i)/6
Therefore, the solutions are x=-1±√(48)i/6. The quadratic formula helped us to find the complex roots of the quadratic equation.
According to the chart, one milliliter of water would have a density of _____.
100 g/cm3
10 g/cm3
1 g/cm3
cannot be determined
Answer:
1gm/ cm^3
Step-by-step explanation:
Katie is selling lemonade for 1.50 pee cup. she decides to put them on sale for 0.90. what percent discount did she give her on the lemonade
20 is 50% of what number? If necessary, round to the nearest tenth.
Is it 10.0?
20 is 50 percent of the number 40.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let 20 is 50% of the number x.
Now, 50% of x=20
0.50×x=20
0.5x=20
x=20/0.5
x=40
Therefore, 20 is 50 percent of the number 40.
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What is the cost of 25.00 watch with a 5.00 discount and a 5.5% sales tax?
Factor completely: 21x3 + 35x2 + 9x + 15 ...?
Answer:
The complete factored form of given polynomial [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]
Step-by-step explanation:
Given polynomial [tex]21x^3+35x^2+9x+15[/tex]
We have to factorize the given polynomial completely.
Consider the given polynomial [tex]21x^3+35x^2+9x+15[/tex]
We will solve it by grouping of terms,
Grouping is collecting terms having some factors common
Taking [tex]7x^2[/tex] common from first two term and 3 from last two terms , we have,
[tex]21x^3+35x^2+9x+15[/tex]
[tex]\Rightarrow 7x^2(3x+5)+3(3x+5)[/tex]
Now taking (3x +5) common from both terms , we have,
[tex]\Rightarrow (7x^2+3)(3x+5)[/tex]
Thus, the complete factored form of given polynomial [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]
The total cost in dollars to produce q units of a product is C(q). Fixed costs are $13000 . The marginal cost is C'(q)=0.006q^2-q+50.
Estimate C(170) , the total cost to produce 170 units.Find the value of C'(170). Then combine these to find C(171).
To find the cost of production for 170 units, consider both fixed costs and variable costs (the integral of the marginal cost function). The cost of producing 171 units can be estimated by adding the marginal cost for the additional unit.
Explanation:The quantity of interest is C(170), the total cost to produce 170 units. To estimate this value, you can calculate the fixed costs plus the integral of the marginal cost from 1 to 170 (the number of items produced).
So, first, calculate the fixed costs which is given as $13000.
Next, estimate the total variable costs, which is the integral of the marginal cost function over the range from 1 to 170 units. Given marginal cost function is C'(q) = 0.006q^2-q+50. Use the power rule to integrate the function, then evaluate it at q=1 and q=170 and subtract.
The value of C'(170) is simply the value of the marginal cost function at q=170.
After finding the value of C(170) and C'(170), the total cost to produce 171 units, C(171), is approximately the total cost to produce 170 units plus the marginal cost to produce the 171st unit.
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