The polynomial 3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).
To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:
1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)
Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).
To learn more on Polynomials click:
brainly.com/question/11536910
#SPJ11
A constant force of 18 newtons is being applied at a constant angle of 56° on an object at the same time that a constant force of 32 newtons at
a constant angle of 124° is acting on the object. What is the magnitude and direction of the resultant force?
The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.
What is a vector?A vector is an amount that has direction as well as magnitude and complies with the rule of vector addition.
A constant force of 18 newtons is supplied to an item at a constant angle of 56° while a constant force of 32 newtons is produced to the entity at a fixed angle of 124°.
Then the magnitude and direction of the resultant force are given as,
∑F = 0
∑F = 18 · cos 56° + 32 · cos 124°
∑F = 10.065 - 17.894
∑F = - 7.829 N
The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.
More about the vector link is given below.
https://brainly.com/question/13188123
#SPJ9
The cost of renting a canoe to use on River Y costs $25. The cost of renting a canoe to use on River Z costs $2 per hour plus a $11 deposit. The total cost, c, of renting a canoe on either river for n hours can be represented by an equation. Write and graph a system to find how many hours you have to rent a canoe for the cost to be the same on both rivers.
A teacher can grade 15 papers in 25 minutes. At this rate, how many papers can she grade in 90 minutes?
15/25 = x/90
25x = 1350
x = 54
54 papers
(w^5y^4)^3
show work pleaseee
Using the properties of the exponents, we solve the expression and found the result as [tex]w^{15} y^{12}[/tex].
What are exponents?The exponent of a number indicates how many times a number has been multiplied by itself. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. How many times we must multiply the reciprocal of the base is indicated by a negative exponent. When writing exponentiated fractions, negative exponents are employed. A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. The square root of a base is a number with a power of half.
Given,
[tex](w^5 * y^4)^3[/tex]
We have to solve this using the properties of the exponents.
Now, this can be written as:
[tex](w^5)^3 * (y^4)^3[/tex]
When the exponent is raised to another power, we can follow the power rule for exponents.
This rule states that multiply the exponent by the power to raise a number with an exponent to that power.
Then the above expression becomes
[tex]w^{(5*3)} * y^{(4*3)}[/tex] = [tex]w^{15} y^{12}[/tex]
Therefore using the properties of the exponents, we solve the expression and found the result as [tex]w^{15} y^{12}[/tex].
To learn more about exponents, follow the link.
https://brainly.com/question/11975096
#SPJ1
What is the area of the notebook paper?
Answer: 8.5 by 11 inches.
Step-by-step explanation:
The standard 8.5″ x 11″ or Letter size so prevalent in full sized notebooks.
the differenceof two numbers is -1 if twice the first number ids added to three times the second number the result is 13 what are the numbers?
The numbers are 4 and 5, as their difference is -1 and adding 2 times the first to 3 times the second results in 13.
To solve the problem, we can start by using algebra. Let x be the first number and y be the second number. Then we can write two equations based on the given information:
x - y = -1 (since the difference of the numbers is -1)2x + 3y = 13 (since adding 2 times the first to 3 times the second gives 13)We can solve this system of equations by substituting x - 1 for y in the second equation, which gives:
2x + 3(x-1) = 13Simplifying this equation, we get:
5x - 3 = 13Adding 3 to both sides, we get:
5x = 16Dividing both sides by 5, we get:
x = 4Now that we know x, we can use the first equation to find y:
4 - y = -1Adding y to both sides, we get:
4 + y = 1Subtracting 4 from both sides, we get:
y = 5Therefore, the first number is 4 and the second number is 5, which satisfies both equations.
Learn more about equations https://brainly.com/question/28871326
#SPJ11
Please help in math 75 points
Answer
10 is the answer
Please mark as brainliest HOPE IT HELPS!
What’s the value of -√22
Answer:
the answer is 22
Step-by-step explanation:
-22 x -22=22
If 3 boxes of cereal cost $4.50, what does 1 box of cereal cost?
Answer:
$1.50
Step-by-step explanation:
3 boxes = $4.50
1 box= $4.50÷3
1box= $1.50
Answer:$1.50
Step-by-step explanation:
What is the solution for 3 1/4 + 3/8
Result in decimals: 3.625
Step-by-step explanation:
Answer:
29/8 or 3 5/8
Step-by-step explanation:
first turn 3 1/4 to 13/4
now change 13/4 to get 26/8
now add 26/8+ 3/8 and get 29/8 or 3 5/8
increase 72 in the ratio 3:5
Answer:
75:77
Step-by-step explanation:
5 is 2 more than 3
3+72=75
5+72=77
therefore: 3:5 = 75:77
If that's not what you meant, then I don't understand the question
Using Pythagorean theorem, solve for x. Please, please help.
Answer: 14.6
Step-by-step explanation:
Kate buys a greeting card for 3.79. She then buys 4 postcards that all cost the same amount. The total cost is 5.11. How much is each postcard? Show your work.
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32÷4=.33
The line 8-2y=x is dilated by a scale factor of 1/4 about the center. What is the equation of the image
The equation of the image is x = 32 - 2y which is dilated by a scale factor of 1/4 about the center.
What is dilation?Dilation is a process for creating similar figures by modifying the dimensions.
To dilate a line by a scale factor of 1/4 about the center, we can first find the coordinates of the center of dilation.
Since no center is given in the problem, we can assume that the center is the origin (0,0).
To find the equation of the image, we need to apply the dilation to the original line. The dilation multiplies all distances by the scale factor, so the image of the point (x, y) is (1/4)x, (1/4)y).
So, the image of line 8 - 2y = x under this dilation is:
8 - 2(1/4)y = (1/4)x
8 - (1/2)y = (1/4)x
32 - 2y = x
Therefore, the equation of the image is x = 32 - 2y.
Learn more about the dilation here:
brainly.com/question/13176891
#SPJ9
Direction in your noteook solve following mindline theorem show your solution
The midline or midsegment theorem calculate the value of P. the value of the variable, P that base length in the trapezoid is equals to the 13.
A trapezoid is a 4-sided (square) shape in which some sides are parallels and others not. The midsection of a trapeze is the line that runs from the middle of one leg to the middle of the other. The midsection or Midsegment theorem of a trapezium states that if a line parallel to the two bases passes through the middle of one leg, it also passes through the middle of the other leg. Also, the length of the middle fragment is half the length of two bases. Now we see a trapezoid in the image above, the length of the midsegment = 25
One of the bases of the trapezium = 37
We need to calculate the value of the other base length P Using Midsigment or Midline Theorem, Midsigment = length of two bases/2
=> 25 = (37 + P)/2
=> 50 = 37 + P
=> P = 50 - 37
=> P = 13
Hence, required length is 13.
For more information about Midsegment , visit :
https://brainly.com/question/29512883
#SPJ4
Complete question:
Use the midline theorem to find the value of the variable in the trapezoid. See the above figure.
V varies partly as D and partly as the square of D when Vequals to 5 ,D equals to 2, and when V equal to 9 and D equals to 3
write this law connecting V and D
[tex]\stackrel{ \textit{Partial Variation} }{V=aD+bD^2}\qquad \impliedby \begin{array}{llll} \textit{V\textit{ varies partly}}\\ \textit{with D and partly with }D^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} V=5\\ D=2\\[-0.5em] \hrulefill\\ V=9\\ D=3 \end{cases}\implies \begin{array}{llll} 5=a2+b2^2&\qquad &5=2a+4b\\\\ 9=a3+b3^2&&9=3a+9b \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{5=2a+4b}\implies 5-2a=4b\implies \cfrac{5-2a}{4}=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{9=3a+9b}\implies \stackrel{\textit{substituting from above}}{9=3a+9\left( \cfrac{5-2a}{4} \right)}\implies 9=3a+\cfrac{45-18a}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(9)=4\left( 3a+\cfrac{45-18a}{4} \right)}\implies 36=12a+45-18a\implies -9=-6a[/tex]
[tex]\cfrac{-9}{-6}=a\implies \boxed{\cfrac{3}{2}=a}\hspace{5em}b=\cfrac{5-2\left( \frac{3}{2} \right)}{4}\implies \boxed{b=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V=\cfrac{3}{2}D+\cfrac{1}{2}D^2~\hfill[/tex]
I need help guys
I need this by friday plsss
The length of the midsegment of the given trapezoid is 16.
What is a trapezoid?
A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid.
Given is a trapezoid TUVW, with bases UV and TW given by expressions, 3x-1, 8x and the midsegment XY is 3x+7.
We need to find the length of the midsegment,
We know,
Midsegment = (base 1 + base 2) / 2
Therefore,
XY = UV+TW / 2
3x+7 = 3x-1 + 8x / 2
6x+14 = 11x-1
5x = 15
x = 3
XY = 3(3)+7 = 16
Hence, the length of the midsegment of the given trapezoid is 16.
Learn more about trapezoid click;
https://brainly.com/question/12623349
#SPJ1
Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. 31. tan a cot(a + 10°) 32. cos θ = sin(2 θ -30°) 33. sin(2θ +10°) = cos(3 θ - 20°) 34. sec (B+10°) = csc (2B + 20°) 35. tan(3B+ 4°) = cot(5B-10°) 36. cot(5 θ +2°)=tan(2 θ +4°)
By applying trigonometric function concept, it can be concluded that the solutions are:
31. tan a = cot(a + 10°), a = 40°
32. cos θ = sin(2θ - 30°), θ = 40°
33. sin(2θ + 10°) = cos(3θ - 20°), θ = 20°
34. sec(B + 10°) = csc(2B + 20°), B = 20°
35. tan(3B + 4°) = cot(5B - 10°), B = 12°
36. cot(5θ + 2°) = tan(2θ + 4°), θ = 12°
Two angles are said to be complementary angles if their sum is 90°. Sin and Cosine are complementary, Tan and Cot are complementary, and sec and cosec are complementary.
Trigonometric functions of complementary angles:
sin(90° - θ) = cos θ
cos(90° - θ) = sin θ
tan(90° - θ) = cot θ
cot(90° - θ) = tan θ
sec(90° - θ) = csc θ
csc(90° - θ) = sec θ
31. To find one solution for the equation tan a = cot(a + 10°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:
tan a = cot(a + 10°)
cot(90° - a) = cot(a + 10°)
90° - a = a + 10°
2a = 80°
a = 40°
32. To find one solution for the equation cos θ = sin(2θ - 30°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:
cos θ = sin(2θ - 30°)
sin(90° - θ) = sin(2θ - 30°)
θ + 2θ - 30° = 90°
3θ = 120°
θ = 40°
33. To find one solution for the equation sin(2θ + 10°) = cos(3θ - 20°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:
sin(2θ + 10°) = cos(3θ - 20°)
sin(2θ + 10°) = sin(90° - (3θ - 20°))
sin(2θ + 10°) = sin(110° - 3θ)
2θ + 10° = 110° - 3θ
5θ = 100°
θ = 20°
34. To find one solution for the equation sec (B + 10°) = csc(2B + 20°), we can use the fact that sec θ = csc(90° - θ). Therefore, we can rewrite the equation as:
sec(B + 10°) = csc(2B + 20°)
csc(90° - (B + 10°)) = sec(2B + 20°)
80° - B = 2B + 20°
3B = 60°
B = 20°
35. To find one solution for the equation tan(3B + 4°) = cot(5B-10°), we can use the fact that tan a = cot(90° - a). Therefore, we can rewrite the equation as:
tan(3B + 4°) = cot(5B - 10°)
cot (90° - (3B + 4°)) = cot(5B - 10°)
86° - 3B = 5B - 10°
8B = 96°
B = 12°
36. To find one solution for the equation cot(5θ + 2°) = tan(2θ + 4°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:
cot(5θ + 2°) = tan(2θ + 4°)
tan (90° - (5θ + 2°)) = tan(2θ + 4°)
88° - 5θ = 2θ + 4°
7θ = 84
θ = 12°
To learn more about trigonometric functions, click here: https://brainly.com/question/3418378
#SPJ11
Find the area of each shaded region.
You are planning to sell children's fairy wings at a craft fair. It costs you $5 in supplies to make each set of fairy wings and you will sell them for double your cost.
You have 100 sets of fairy wings and sell 60 of them by 2pm. The craft fair ends at 4pm and you want to sell the rest of your wings faster so you mark the price down by 30%.
With c = supply cost to make a set of wings, and P(c) = price, the equation for the price you first sell the wings is A) P(c)=2c B) P(c)=.7c C) P(c)=.5c D) P(c)=1.5c
The new equation to sell the wings faster with N(p)=new price is A) N(p)=.3p B) N(p)=p-.3 C) N(p)=.7p D) N(p)=.5p
The composed equation N(P(c) is A) .9c B) 1.4c C) .7c D) 2.7c
and represents A) the markup of the discounted price over your supply cost B) your markup profit on all the wings C) how much money you will lose by selling the wings at a lower price
The domain of all the functions is A) [0, infinity) B) (-infinity, 0] C) (-infinity, infinity)
because A) the prices will always be positive numbers B) the wings make it possible to fly C) you can hace any possible answer in these questions D) anything is possible
Answer: Dragonfly wings for the boys cost $1 while fairy wings for the girls cost $2. Phoebe's mom spent $18 on the gifts. How many dragonfly wings and fairy wings
Step-by-step explanation:
Answer:
The answer to the first question is A) P(c) = 2c, because the wings will be sold for double the cost of supplies.
The answer to the second question is B) N(p) = p - 0.3, because the price will be marked down by 30%.
The answer to the third question is A) 0.9c, which represents the markup of the discounted price over the supply cost.
The domain of all the functions is A) [0, infinity), because prices and costs must be positive numbers. Therefore, options B, C, and D are incorrect.
A water park sold 2,640 child tickets and 1,360 adult tickets. What percentage of the tickets sold were child tickets?
Answer:
66%
Step-by-step explanation:
"of the" something = means denominator of a fraction
of the tickets sold = denomination here
question asked about child tickets , so child tickets = numerator here
what percentage? = fraction x 100%
answer:
2640 / (2640+1360) x 100
Nine children want to feed the birds they eash have 2 bags of seed. How many bags of seed are there in all
Answer: 18
Step-by-step explanation:
9 kids each have two bags
9 x 2 = 18
9 + 9 = 18
Find the missing number to create a perfect-square binomial
9x2+ X+25
Missing number to make the binomial 9x² + X + 25 a perfect square is 30x.
What is quadratic equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Given expression
9x² + X + 25
It can be written as
(3x)² + X + 5²
Comparing with a² + 2ab + b²
a = 3x
b = 5
X = 2ab
X = 2(3x)(5)
X = 30x
Hence, 30x is the missing number to create a perfect-square binomial.
Learn more about quadratic equation here:
https://brainly.com/question/30098550
#SPJ9
in a certain town there were 171 robberies last year . this year the number of robberies has gone down 39%. how many robberies were there this year , to the nearest whole number ?
The robberies that took place this year to the nearest whole number is 104 robberies.
What distinguishes a percent reduction from a percent difference?A value's percentage change from its initial value is expressed as a percent reduction, but the percentage difference between two values is expressed as a % change from their average.
Let us suppose the number of robberies this year = x.
Given that,
This year the number of robberies has gone down 39%.
x = 171 (1 - 39/100)
x = 171 (1 - 0.39)
x = 104.31
Hence, the robberies that took place this year is 104 robberies.
Learn more about percentage decrease here:
https://brainly.com/question/10168902
#SPJ1
Part A
By the end of its fourth week, a movie had grossed $9.2 million. Assume the revenue y in millions of dollars is
proportional to the week x.
Movie Sales
Revenue (millions of dollars)
987654321
y
X
0 1 2 3 4 5 6 7 8 9
Week
Graph the equation on your own paper. Which of the following ordered pairs does your graph pass through? Select
all that apply.
A) (4,9.2)
B) (9.2,4)
C) (1,9.2)
D) (9.2,1)
E) (0,0)
F) (1,2.3)
The ordered pair which the graph pass through include the following:
A) (4, 9.2)
E) (0, 0)
F) (1, 2.3)
How to determine the constant of proportionality?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled by the following mathematical expression:
y = kx
Where:
x represent the number of week.y represent the revenue (in millions of dollars).k represent the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 9.2/4
Constant of proportionality (k) = 2.3
Therefore, the required equation is given by:
y = kx
y = 2.3x
In conclusion, we would use an online graphing calculator to determine the ordered pairs that the line passes through.
Read more on proportional relationship here: brainly.com/question/28350476
#SPJ1
Simplify. Assume ((3c^(2))/(2d^((8)/(5))))^(4) Write your answe that have no varia
The answer is ((81c^(8))/(16d^((32)/(5)))).
To simplify ((3c^(2))/(2d^((8)/(5))))^(4), we can use the power of a power rule and distribute the exponent of 4 to each term inside the parentheses.
((3c^(2))/(2d^((8)/(5))))^(4) = (3^(4))(c^(2*4))/(2^(4))(d^((8*4)/(5)))
Simplifying further, we get:
= (81)(c^(8))/(16)(d^((32)/(5)))
= (81c^(8))/(16d^((32)/(5)))
This is the simplified answer with no variables. It cannot be simplified further. Therefore, the answer is ((81c^(8))/(16d^((32)/(5)))).
Learn more about power rule
brainly.com/question/23418174
#SPJ11
4. Use the Variation of parameters to find a particular solution for the ODES et 22 (a) y" – 2y' + y = (b) y" + y = = sec(x) (C) y" + y = sin?(x) =
The Variation of Parameters is a method used to find a particular solution for ordinary differential equations (ODES). The method involves finding the general solution to the homogeneous equation and then using that to find a particular solution to the non-homogeneous equation.
For the given ODES:
(a) y" - 2y' + y = et^2
First, we need to find the general solution to the homogeneous equation y" - 2y' + y = 0. The characteristic equation is r^2 - 2r + 1 = 0, which has a repeated root r = 1. Therefore, the general solution to the homogeneous equation is yh = c1e^t + c2te^t.
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1e^t + u2te^t, where u1 and u2 are functions of t. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(b) y" + y = sec(x)
Similarly, we first find the general solution to the homogeneous equation y" + y = 0. The characteristic equation is r^2 + 1 = 0, which has complex roots r = i and r = -i. Therefore, the general solution to the homogeneous equation is yh = c1cos(x) + c2sin(x).
Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1cos(x) + u2sin(x), where u1 and u2 are functions of x. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.
(c) y" + y = sin^2(x)
The general solution to the homogeneous equation y" + y = 0 is the same as in part (b). We use the Variation of Parameters to find a particular solution in the same way as in part (b), but with the right-hand side of the equation being sin^2(x) instead of sec(x).
Know more about Variation of Parameters here:
https://brainly.com/question/13258421
#SPJ11
A polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed so that p(x)=q(x)*(x-1)+R What is the value of R ?
The value of R is -10.
The polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed as p(x)=q(x)*(x-1)+R. To find the value of R, we need to divide the polynomial p(x) by (x-1) using synthetic division.
Set up the synthetic division by writing the coefficients of the polynomial p(x) in a row and placing the divisor (x-1) to the left of the row.
1 | 1 -3 4 -12
|_____________
Bring down the first coefficient (1) and multiply it by the divisor (1) to get 1. Place this value below the second coefficient (-3) and add them to get -2.
1 | 1 -3 4 -12
| 1
|_____________
1 -2
Multiply the new value (-2) by the divisor (1) to get -2. Place this value below the third coefficient (4) and add them to get 2.
1 | 1 -3 4 -12
| 1 -2
|_____________
1 -2 2
Multiply the new value (2) by the divisor (1) to get 2. Place this value below the fourth coefficient (-12) and add them to get -10.
1 | 1 -3 4 -12
| 1 -2 2
|_____________
1 -2 2 -10
The final value (-10) is the remainder, or the value of R.
Therefore, the value of R is -10.
Learn about Polynomial
brainly.com/question/11536910
#SPJ11
HELP ASAP
Find the missing angles in this rhombus
1
2
41°
3
measure of angle 1
measure of angle 2
measure of angle 3
By the properties of rhombuses, m∠1 = 90°, m∠2 = 41°, and m∠3 = 49°.
What is a rhombus?A quadrilateral with all equal sides is a rhombus.
Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
A rhombus has 360° of interior angles total.
A rhombus's adjacent angles add up to 180°.
A rhombus's diagonals are perpendicular to one another and cut each other in half.
From the given figure and properties of the rhombus, m∠1 = 90°, As the diagonals bisect each other perpendicularly.
Now, The two diagonals have created 4 congruent right-angled triangles,
Therefore, m∠2 = 41°.
And m∠3 = 180° - (41° + 90°).
m∠3 = 49°.
learn more about rhombuses here :
https://brainly.com/question/16547718
#SPJ1
please help with easy math triangle question
Answer:
not sure but i think its 12
Step-by-step explanation:
if you look carefully one side witch is 6 is have of side x and 6 x 2 is 12
hope this helps.
Answer:I think its 15 but I'm not sure
Step-by-step explanation: