2n^2+3n-9 factoring trinomials
The trinomial [tex]2n^2[/tex]+3n-9 cannot be factored using integers as no two numbers exist that multiply to give -18 (the product of the leading coefficient and the constant term) and add up to 3 (the middle coefficient).
To factor the quadratic trinomial [tex]2n^2[/tex]+3n-9, one must find two binomials that, when multiplied together, give the original trinomial. Factoring complex trinomials can sometimes be achieved by finding two numbers that multiply to give the product of the leading coefficient (2 in this case) and the constant term (-9 in this case), and add to give the middle coefficient (3 in this case). However, for this particular trinomial, such numbers do not exist, and it cannot be factored using integers. This means that either the trinomial is prime (cannot be factored), or it would require the quadratic formula to solve for factors involving irrational or complex numbers.
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A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
A) 43 minutes
B) 45 minutes
C) 280 minutes
D) 602 minutes
15 is what percent of 56
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
In 2000 Michigan had a population of 9,938,444. The number of people living in Michigan decreased by 0.6% in 2010. What was Michigan’s approximate population in 2010?
Answer:
9,878,813
Step-by-step explanation:
First, make 0.6% into a decimal
0.6 / 100 = 0.006
Then, multiply the number of people living in Michigan in 2000 by the number of people decreased (the percentage decrease) in 2010
9,938,444 x 0.006 = 59630.664
Last, subtract the percentage decrease by the original population in 2000
9,938,444 – 59630.664 = 9,878,813
In 2010 the approximate population in Michigan was about 9,878,813 (to the nearest whole person)
cell phone company A charges $20 per month plus $0.05 per text message. Cell phone company B charges $10 per month plus $0.07 per text message. Is there any number of text messages that will result in the exact same charge from both companies?
Answer : The number of text messages that will result in the exact same charge from both companies is, 500
Step-by-step explanation :
Let the number of text messages be, 'x'
Cell phone company A charges $20 per month plus $0.05 per text message. Thus, the equation will be:
[tex]20+0.05x=0[/tex] ............(1)
Cell phone company B charges $10 per month plus $0.07 per text message. Thus, the equation will be:
[tex]10+0.07x=0[/tex] ............(2)
Now equating equation 1 and 2, we get:
[tex]20+0.05x=10+0.07x[/tex]
[tex]20-10=0.07x-0.05x[/tex]
[tex]10=0.02x[/tex]
[tex]x=\frac{10}{0.02}[/tex]
[tex]x=500[/tex]
Thus, the number of text messages that will result in the exact same charge from both companies is, 500
For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 9, then x2 = 81.
a)If x2 = 81, then x = 9.
b)If x2 = 81, then x = 9.
x2 = 81 if and only if x = 9.
c)If x2 = 9, then x = 81.
d)If x2 = 81, then x = 9.
x = 9 if and only if x2 = 81
The converse statement interchange the hypothesis and the conclusion.
The converse of x=9 then [tex]x^{2} =81.[/tex] is [tex]x^{2} = 81 then x=9.[/tex] is true.
A biconditional statement is defined to be true whenever both parts have the same truth value . combining the statements as a biconditional we have
If [tex]x^{2}[/tex]. = 81, then x = 9.
x = 9 if and only if [tex]x^{2} .[/tex] = 81
Option D is the right answer.
A 16-inch cheese pizza at Fine Dough Pizza costs $10.00 and each additional topping is $1.50. The same size pizza at Johnson's Pizza costs $8.00 and each additional topping is $2.00. After how many toppings do the pizzas cost the same? Which pizza costs more with additional toppings?
To find the number of toppings at which the pizzas cost the same, we can set the total cost expressions for both pizzas equal to each other and solve for 'x'. After 4 additional toppings, the pizzas will cost the same. With 5 additional toppings, Johnson's Pizza costs more.
Explanation:To find the point at which the pizzas cost the same, we need to determine the number of toppings that will make the total cost equal for both pizzas. Let's denote the number of additional toppings as 'x', and the cost of each additional topping at Fine Dough Pizza as $1.50, and at Johnson's Pizza as $2.00. The total cost for Fine Dough Pizza will be $10.00 + $1.50x, and the total cost for Johnson's Pizza will be $8.00 + $2.00x. To find the number of toppings at which the pizzas cost the same, we can set the two total cost expressions equal to each other and solve for 'x':
$10.00 + $1.50x = $8.00 + $2.00x
To solve the equation, we can subtract $1.50x from both sides:
$10.00 = $8.00 + $0.50x
Next, we subtract $8.00 from both sides:
$2.00 = $0.50x
To isolate 'x', we divide both sides by $0.50:
x = 4
Therefore, after 4 additional toppings, the pizzas will cost the same.
To determine which pizza costs more with additional toppings, we can compare the total cost expressions for both pizzas for a specific number of toppings. For example, let's consider 5 additional toppings:
Total cost at Fine Dough Pizza = $10.00 + $1.50(5) = $10.00 + $7.50 = $17.50
Total cost at Johnson's Pizza = $8.00 + $2.00(5) = $8.00 + $10.00 = $18.00
Therefore, with 5 additional toppings, Johnson's Pizza costs more.
Find the circumference of the circle if the square has an area of 144 m2. Give your answer to the nearest tenth. Use 3.14 form
The circumference of the circle is found by first determining the side length of the square, then using that to calculate the diameter and radius of the circle. Using 3.14 as an approximation for pi, the circumference is calculated to be 37.7 meters when rounded to the nearest tenth.
To find the circumference of the circle when the square has an area of 144 m², we first determine the side length of the square using the formula for the area of a square, A = a², where A is the area and a is the side length.
A = 144m²
a = 12m
Since the area is 144 m², the side length of the square is "12 m (since 12 x 12 = 144).
Since the circle fits perfectly within the square, the diameter D of the circle is equal to the side length of the square. Therefore, D = 12 m. The radius r is half the diameter, so in this case, r = 6 m.
The formula for the circumference C of a circle is C = 2πr.
C = 2 x 3.14 x 6 m = 37.68 m
The circumference is 37.7 m.
Why is a larger down payment beneficial to a home investor?
a.
A larger down payment would only be beneficial to an investor if they intended on renting out the house.
b.
A larger down payment would enable an investor to get a loan with a higher interest rate and lower monthly payments.
c.
A larger down payment would enable an investor to get a loan with a lower interest rate and lower monthly payments.
d.
A larger down payment is essentially a larger bribe to the lending institution and gets the investor in their good favor.
The larger down payment beneficial to a home investor is because of option C.
The following information should be considered:
The large down payment could enables the investor for getting out the loan that have the less interest payment and less monthly payment. So that it is easy for the investor to pay off.Learn more: https://brainly.com/question/537797?referrer=searchResults
The diagram below shows a square inside a regular octagon. The apothem of the octagon is 13.28 units. To the nearest square unit, what is the area of the shaded region?
Area of shaded region is 463 square units.
What is area of octagon?Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height
What is apothem of octagon?The apothem of any polygon is equal to the line that connects the center of the polygon with one of its sides perpendicularly. Using the apothem, we can calculate the area of the polygons in an easier way.
Given
Apothem of the octagon = 13.28 units
Base of octagon = 11 units
Area of octagon = [tex]\frac{1}{2}[/tex] × [tex]8[/tex] × base × height
= [tex]\frac{1}{2}[/tex] × [tex]11[/tex] × [tex]13.28[/tex] × [tex]8[/tex]
= 584.32
Area of square = side × side
= 11 × 11
= 121
Area of shaded region = Area of octagon - Area of square
= 84.32 - 121
= 463.32
≅ 463 square units.
Hence, area of shaded region is 463 square units.
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If 7 units represent 98 liters find the value of 15 units
Final answer:
To find the value of 15 units when 7 units represent 98 liters, set up a proportion, cross multiply, and divide to find the value of 15 units, which is 210 liters.
Explanation:
To find the value of 15 units when 7 units represent 98 liters:
Set up a proportion: 7 units = 98 liters and determine the value of 15 units.Cross multiply to solve for the unknown value: 7 units * x liters = 15 units * 98 liters.Divide to find the value of 15 units: x = (15 * 98) / 7 = 210 liters. a1,a2,a3....a30-each of these 30 sets has 5 elements.b1,b2,....bn-each of these n sets has 3 elements.union of a1,a2...a30=union of b1,b2....bn=S.
if each elements of S is in 10 a sets and 9 bsets.then n=?
If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x? x units x units x units 2x units
the picture in the attached figure
we know that
if ABC is an isosceles triangle
then
AB=BC
angle A=angle C=45 degrees
and
triangle ABD and triangle BDC also are isosceles triangles
AD=BD=x
DC=BD=x
the hypotenuse AC is equal to
[tex] AC=AD+DC\\ AC=x+x\\ AC=2x [/tex]
To find the length AB applying the Pythagorean Theorem
[tex] AC^{2} =AB^{2} +BC^{2} [/tex]
remember that AB=BC
[tex] AC^{2} =2AB^{2} [/tex]
[tex] AC^{2} =2AB^{2}\\\\ AB=\frac{AC}{\sqrt{2}}\\\\ AB=\frac{2x}{\sqrt{2}}\\\\ AB=x\sqrt{2} [/tex]
therefore
the answer is
the length of one leg of the large right triangle in terms of x is equal to [tex] x\sqrt{2} [/tex]
Answer:
b)x/2
Step-by-step explanation:
took the test
Decide whether y is a function of x.
y=-3x-4
solve.
5m + 7/2 = -2m + 5/2
Solve for b. ab + c = d b = a + c/d b = a/(c - d) b = (d - c)/a
Answer: im sorry if im wrong but i think the answer is 0.3
Step-by-step explanation:
What is the coefficient of the term 43yz ? A. 1/3 B.4 C.4/3 D.4yz
The price of a gallon of milk is 3.70 5 dollars what is the price that is rounded to the nearest dollar
In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old are they now?
If x + 5 is Jill's age five years from now, which of the following equations could be used to solve the problem?
a.3x + 5 = 55 - x
b.3x + 15 = 55 - x
c.3x + 15 = 45 - x ...?
From net earnings of $740 per month for the rent on an apartment she says the two friends what percent of income is her rent payment
write 33/72 in simplest form
11/72
33/24
33/72
11/24
please explain ...?
For the function f(x) = x2 -12, find (f o f-1)(4)
Plane ABC and plane BCE ____ be the same plane.
A. must
B. may
C. cannot
Jordan’s job is located 67 miles from his home. His car’s gas mileage is 21 miles to the gallon. Approximately how many gallons of gasoline does Jordan need each day?
I think the answer is 6.381 gallons or 3.2?
The number of gallons of gasoline Jordan need each day is:
3.190476 gallons.
Step-by-step explanation:It is given that:
Jordan’s job is located 67 miles from his home.
His car’s gas mileage is 21 miles to the gallon.
i.e. for 21 miles he need 1 gallon of gas.
This means in order to cover 1 mile he needs 1/21 gallon of gas.
Hence,
In order to cover 67 miles he needs 67/21 gallon of gas
i.e.
for 67 miles he needs 3.190476 gallons of gas.
If t = -2π/3, evaluate (if possible) sin t, cos t, tan t
Before 1995, three-digit area codes for the united states had the following restrictions:
(a) neither 0 nor 1 could be used as the first digit.
(b) 0 or 1 had to be used for the second digit.
(c) there were no restrictions on the third digit.
How many different area codes were possible?
8y + 9
What is the variable term in the expression?
Answer:
8y
Step-by-step explanation:I took the test
8y contain the variable term where the variable is 'y'.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
expression: 8y + 9
As, we know a symbol without a set value is referred to as a variable.
So, 8y contain the variable term where the variable is 'y'.
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P is the midpoint of QN, MP is perpendicular to to QN prove rectangle MRQ is congruent to rectangle MRN
By using the rules of geometry, we can determine that if P is the midpoint of QN and MP is perpendicular to QN, then rectangles MRQ and MRN are congruent. The congruency is due to the properties of rectangles, triangles, midpoints, and the Hypotenuse-Leg Theorem.
Explanation:The proof of the congruence of rectangles MRQ and MRN involves geometry rules, particularly the properties of rectangles, triangles, and midpoints. Let's consider rectangle MRQ and MRN. We know that in a rectangle, diagonals are congruent. If P is the midpoint of QN, that means QP = PN. Additionally, if MP is perpendicular to QN, PMQR and PMNR are right triangles with the same hypotenuse.
Using the properties of triangles, we can say that if two right triangles have a congruent hypotenuse and one leg (which is MP in both cases), then these triangles are congruent. Therefore, ∆PMQR is congruent to ∆ PMNR by the Hypotenuse-Leg (HL) Theorem.
Considering that ∆ PMQR ≅ ∆ PMNR and QP = PN, we can say that quadrilaterals MRQN and MRNP are each a parallelogram. Additionally, since MP is perpendicular to QN, quadrilaterals MRQN and MRNP are actually rectangles based on the definition of a rectangle (a parallelogram with a right angle). Therefore, rectangle MRQ is congruent to rectangle MRN.
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A convention center rents a meeting room for $250 per day. There is a $30 one-time fee to make a reservation.
What function equation represents the total cost to rent a meeting room for d days?
A. c(d) = 250d + 30
B. c(d) = 30d − 250
C. c(d) = 30d + 250
D. c(d) = 250d − 30