1. Which expression can be factored into the form (ax + b)(ax - b), where
a and b are rational numbers?
4n2 - 81
2n2 - 49
2n2 + 49
4n2 + 81
Answers
The expression that can be factored into the form (ax + b)(ax - b), where a and b are rational numbers, is 4n² - 81.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
A.
4n² - 81,
This can be factored as (2n - 9)(2n + 9), which is of the form (ax + b)(ax - b).
B.
2n² - 49,
This can be factored as (n - 7√2)(n + 7√2), but not in the form (ax + b)(ax - b).
C.
2n² + 49:
This cannot be factored into the form (ax + b)(ax - b) using rational numbers. We can factor it over the complex numbers as (n + i√49/2)(n - i√49/2), where i is the imaginary unit, but this does not satisfy the conditions of the problem.
D.
4n² + 81,
This cannot be factored into the form (ax + b)(ax - b)
Therefore, the expression that can be factored into the form (ax + b)(ax - b), where a and b are rational numbers, is 4n2 + 81.
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Related Questions
Petra’s electricity supply company charges her a fixed quarterly sum plus a rate per unit for electricity used. In the most expensive quarter last year (January to March), she used 2 000 units and her bill was $250. In the least expensive quarter (July to September), she used 600 units and her bill was $138. She is now adding extra insulation to her home which is expected to reduce her overall electricity consumption by 25%. What can she expect her January to March bill to be next year (if there are no increases in overall tariffs)? *
Answers
Answer:
$210
Step-by-step explanation:
(January - March) charge last year :
Unit consumed = 2000
Bill = $250
(July - September) charge last year:
Unit consumed = 600 units
Bill = $138
Billing :
Fixed charge + rate per unit ;
Let fixed charge = c ; rate per unit = m
Billing can be represented by the equation :
mx + c = y
x = unit consumed ; y = total charge
Expensive quarter:
2000x + c = 250 - - - (1)
Least expensive quarter:
600x + c = 138 - - - (2)
From (2)
c = 138 - 600x ; plug into (1)
2000x + 138 - 600x = 250
1400x = 250 - 138
1400x = 112
x = 0.08
0.08 = x = rate per unit
From ; c = 138 - 600x
c = 138 - 600(0.08)
c = 90
Fixed charge = 90
Billing equation :
y = 0.08x + 90
If insulation will reduce unit consumption by 25%
Then, consumption in most expensive quarter will be :
(100 - 25)% * 2000
0.75 * 2000 = 1500 units
Charge will be :
(0.08*1500) + 90
= $210
Imagine that you live near a skatepark. As part of some park renovations, the city plans to make the square skatepark 5 meters shorter in one direction and 6 meters longer in the other. What is the area of the new skatepark?
(please include the solving steps in your answer)
Answers
Answer:
x² + x - 30Step-by-step explanation:
Let the initial side be x
New skatepark has dimensions:
x - 5 and x + 6Its area is:
(x - 5)(x + 6) = x² + 6x - 5x - 30 = x² + x - 30Help me please I realy need help
Answers
Answer:
sry i cant help u and your jumping horses
Step-by-step explanation:
free branliest and points question is so easy :) :) :) :) :) :) :) :) :) :):| :) :) :) :) :) :) :P Ryan is shopping for barrels of concrete. After looking at different stores, he decides to purchase them from Construction and Us. The cost of their concrete barrels is listed in the table below:
Answers
Answer:
$23 per bag
Step-by-step explanation:
Ryan Is shopping for barrels of concrete
After looking at different stores he decides to purchase at construction and Us
Therefore the price of a bag can be calculated as follows
= 46/2
= 23
Hence the price of a bag is $23
Answer:
$23 per bag
Step-by-step explanation:
i got this frm the previous answer but im trying to stock up on points since i have alot of test coming up </3
guys I'm stuck plz help!!!!
Answers
Answer:
I believe 70
Step-by-step explanation:
What is x in 8x - 5 = -37
Answers
Answer:
If i'm doing this correctly it is 6?
Step-by-step explanation:
Answer:
x= -4
Step-by-step explanation:
8x - 5 = -37
+ 5 +5 add five to both sides of the equation so you can isolate the x
8x = -32
/8 /8 then divide 8 by both sides of the equation
x = -4
and then you get ur answer
Hope this helps :)
Calvin is planning to go snow skiing. He went shopping for a jacket. The jacket was
originally priced at $90 and was on sale 50% off. What is the price of the jacket now?
O A. $30.00
O B. $60.00
O C. $75.00
O D. $45.00
Answers
90*.50=45
90-45=45
Answer:
D. $45.00
Step-by-step explanation:
Half of $90.00
Use the distributive property to simplify the expression and then evaluate. Let x= 4 and y= -2
-6(-2x + 3y + 8)
Answers
Answer:
12v-18y-48
Step-by-step explanation:
-6(-2v+3y+8)
12v-18y-48
Need help again ASAP
Answers
Answer:
According to my calculator, the answer should be A) 5/6
Which equation matches the relationship shown in the table
Answers
Answer:
it is the second answer check that answer I'm pretty sure its correct
The sum is 12. The difference is 5
Answers
Solve for the variable. 4/2=3/x
A.2/3
B.1.5
C.6
D.12
Answers
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{4}{2}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
4x = 6 ( divide both sides by 4 )
x = 1.5 → B
Answer:
3/2 0r B. 1 1/2
Step-by-step explanation:
Step 1: Cross-multiply.
4/2=3/x
4*x=(3)*(2)
4x=6
Step 2: Divide both sides by 4.
4x/4=6/4
x=3/2
Answer:
x=3/2
3/2 is an equivilant to B 1.5 or 1 1/2
find the cube root of 27a
Answers
Answer:
3a
Step-by-step explanation:
27a ÷ 3 (number of cube root) = 3a
Answer:
3 a
Step-by-step explanation:
is the right answer you welcome
I need help with a math problem
Answers
18 erasers cost $0.90, how much would 3 erasers cost?
Answers
Answer:
$0.15
Step-by-step explanation:
0.90/18=0.05
0.05x 3=0.15
Answer:
$0.15
Step-by-step explanation:
0.90/18=0.05
0.05x 3=0.15
If the length of leg x is 12 feet, what is the length in feet of the hypotenuse of each triangle? Record your answer in the boxes below. Be sure to use the correct place value .
Answers
Answer:15.00
Step-by-step explanation:
Answer:
The length of the hypotenuse of each triangle is 13 feet. Below is the explanation
Step-by-step explanation:
Given:
In the middle, there is a square with 10 ft as the side length.
An Isosceles triangle formed on each side of the square which height as 12 feet.
To find:
The hypotenuse measure of the right triangle.
Let's use the Pythagoras theorem to find hypotenuse measures.
I'll attach the file to find the hypotenuse measure.
Hypotenuse measures 13 feet.
You can learn more:
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please help all of it, tysm
Answers
2. 0.001
3. Email, Chores, homework
As in email the least and homework the most
4. The least portion of the class is the amount of people that walk to school. The 18% of people is the least.
5. Work: the number of pets people have is LESS than the number of people on a sports team
6. It is LESS than the portion of students that don’t live within a mile radius, for 11/50 is equivalent to 22% and 100-22 is equivalent to 78. 78% don’t live within a mile. So the answer is LESS.
7. 60
8. 0.8 which is 80%
9. 4
10. 12.8
The last four problems are up to you, it was a bit difficult for me
A)distributive property of multiplication over subtraction
B)subtraction property of equality
C)associative property of multiplication
D)multiplication property of equality
Answers
Answer: sup brendalys it’s me Timotheus
Step-by-step explanation:
The answer is c I think
whos prettier? doja cat or megan thee stallion
Answers
Answer:
The Stallion
Step-by-step explanation:
Answer:
megan thee stallion
Step-by-step explanation:
what is the slope of the line containing points (1,-3) and (4,2)
Answers
Answer:
5/3 is the slope
Step-by-step explanation:
Which graph represents the function f(x)=-|x|-2?
Answers
Answer:
ind the absolute value vertex. In this case, the vertex for y=−|x|−2 is (0,−2).
(0,−2)
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(−∞,∞)
Set-Builder Notation: {x|x ∈ R}
For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.
x y
−2 −4
−1 −3
0 −2
1 −3
2 −4
Step-by-step explanation:
Answer:
The answer is C.
I hope this helps you!
The perimeter of a triangle is 120. If the ratio of the triangle's side is 4:5:6, what is the length of the shortest side?
Answers
Hey there ☺️
Please mark me as brainliest and follow me ..
here is ur answer ..
What is the measure of angle x? (Brainly + Bonus points for the best correct answer and explain)
Answers
Answer: 76
Step-by-step explanation:
If a pair of parallel lines are cut by a line, the alternate angles are equal to each other. The angles 76 and x are alternate angles, so that means they are equal.
work out the equation of the line which has a gradient of 2 and passes through the point (1,4)
please answer quick
i will mark you brainiest
Answers
gradient is 2
Step-by-step explanation:
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Which expression correctly sets up the quadratic formula with x^2+1=2x-3
Answers
Given:
The quadratic equation is
[tex]x^2+1=2x-3[/tex]
To find:
The expression that correctly sets up the quadratic formula with the given equation.
Solution:
We have,
[tex]x^2+1=2x-3[/tex]
[tex]x^2+1-2x+3=0[/tex]
[tex]x^2-2x+4=0[/tex]
On comparing with [tex]ax^2+bx+c=0[/tex], we get
[tex]a=1,b=-2,c=4[/tex]
The quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Putting [tex]a=1,b=-2,c=4[/tex], we get
[tex]x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex]
Therefore, the required expression is [tex]\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex].
4(6x-4)=8(3x-2) equations with special cases
Answers
Answer:
Infinite solutions
Step-by-step explanation:
4(6x-4)=8(3x-2)
24x - 16 = 24x - 16 ^ Distribute
Infinite solutions (they equal each other)
Step-by-step explanation:
4(6x−4)=8(3x−2)4(6x-4)=8(3x-2)
Simplifica 4(6x−4)4(6x-4).
Pulsa para ver menos pasos...
Aplicar al propiedad distributiva.
4(6x)+4⋅−4=8(3x−2)4(6x)+4⋅-4=8(3x-2)
Multiplicar.
Toca para ver más pasos...
24x−16=8(3x−2)24x-16=8(3x-2)
Simplifica 8(3x−2)8(3x-2).
Pulsa para ver menos pasos...
Aplicar al propiedad distributiva.
24x−16=8(3x)+8⋅−224x-16=8(3x)+8⋅-2
Multiplicar.
Pulsa para ver menos pasos...
Multiplicar 33 por 88.
24x−16=24x+8⋅−224x-16=24x+8⋅-2
Multiplicar 88 por −2-2.
24x−16=24x−1624x-16=24x-16
Mover todos los términos que contengan xx al lado izquierdo de la ecuación.
Pulsa para ver menos pasos...
Restar 24x24x a ambos lados de la ecuación.
24x−16−24x=−1624x-16-24x=-16
Combine los términos opuestos en 24x−16−24x24x-16-24x.
Pulsa para ver menos pasos...
Reste 24x24x de 24x24x.
0−16=−160-16=-16
Reste 1616 de 00.
−16=−16-16=-16
Dado que −16=−16-16=-16, la ecuación siempre será verdad para cualquier valor de xx.
Todos los números reales
El resultado se puede mostrar en múltiples formas.
Todos los números reales
Notación de intervalos:
(−∞,∞)
The diagram shows two congruent equilateral triangles whose overlap is a hexagon. The areas of the smaller triangles, which are also equilateral, are 1 , 1 , 9 , 9 , 16 and 16 , as shown. What is the area of the inner hexagon?
Answers
Answer:
Step-by-step explanation:
Answer:
38
Step-by-step explanation:
hiii pls help i’ll give brainliest if you give a correct answer
Answers
Answer:
الجملة الاسميةالجملة الاسميةالجملة الاسميةالجملة الاسميةالجملة الاسميةالجملة الاسميةالجملة الاسميةvالجملة الاسميةالجملة الاسميةالجملة الاسميةالجملة الاسميةv
gkgkhhkStep-by-step explanation:
$213 ski jacket with a 30% discount and a 6% tax
Answers
Take the discount off first, 213*.70=149.10, then multiply 149.10*1.06= $158.046
158.04$.
What is discount?A discount is a decrease in the cost of a commodity or service. If the item is broken, you can ask the manager for a discount.
Given the Written price of the ski jacket is 213$ on that there is a discount of 30% and 6% of tax. Hence,
discounted price of jacket = 213 (1- 30%)
discounted price of jacket = 149 approx.
Total price of the jacket after-tax = 149 (1 + 6%)
The total price of the jacket after-tax = 158.04$
Therefore, the price of a $213 ski jacket with a 30% discount and a 6% tax is 158.04$.
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What is a decimal that is equivalent to the fraction 6/10
Answers
Answer:
0.60 or 0.6
Step-by-step explanation:
To convert you devide the two 6/10 is 0.6
0.6 is a decimal that is equivalent to the fraction 6/10
What is Number system?A number system is defined as a system of writing to express numbers.
A fraction represents a part of a whole.
The given fraction is 6/10.
The fraction is six by ten
In the given fraction is six and denominator is ten.
We need to convert 6/10 to the decimal which is equivalent.
10 is the divisor and 6 is the dividend.
6/10=0.60
Six by ten equal to zero point six
Hence, 0.6 is a decimal that is equivalent to the fraction 6/10
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