The resulting expression for the factor of the provided polynomial with the help of grouping method is,
[tex](4x^2-3)(x^2-5)[/tex]
What is polynomial equation?Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
Factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The given polynomial equation is,
[tex]4x^4 - 20x^2 -3x^2 +15[/tex]
Make the groups of the above equation by taking out, 4x^2 from first two terms and -3 from second equation.
[tex]4x^4 - 20x^2 -3x^2 +15\\4x^2(x^2- 5) -3(x^2 -5)[/tex]
Take out the common group to simplify further.
[tex](x^2-5)(4x^2-3)\\(4x^2-3)(x^2-5)[/tex]
Thus, the resulting expression for the factor of the provided polynomial with the help of grouping method is,
[tex](4x^2-3)(x^2-5)[/tex]
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The Swinger family recycles about 15 pounds of waste a week. This is 2/3 of the total waste for the week. How many pounds of waste does the family produce each week?
The answer 37.5 lbs
than paid $40 for 5 cardio dance workout classes. He’s trying to set up an equation to help him find the cost of each class. What should Nathan put in the blank of the following equation? c=$40÷___ ?
Answer:
$40/5
Step-by-step explanation:
If you're trying to figure out the cost of each class divide the amount of money you pay in all ($40 dollars) by 5. Once you do that you should get 8, so $8 per class.
What is the pattern for this sequence? 2 , 0 , -2 , -4 , -6 , ... A. Each number in the sequence is 3 less than the previous number. B. The sequence decreases by multiples of 3: first by 3, then 6, then 9, then 12. C. The sequence decreases by multiples of 2: first by 2, then 4, then 6, then 8. D. Each number in the sequence is 2 less than the previous number.
Answer:
I believe the correct answer is D
Please someone help me out!!!!! Bill is bying a pair of jeans that costs $20. He has to pay 5% sales tax. How much will he pay in all?
Answer:
21
Step-by-step explanation:
First determine the amount of tax
20 * .05
1
Add this to the original amount
20+1
21
He will pay 21 dollars
what is the are of triangle ABC with vertices A(-2,1),B(-2,3),C(2,1)?
Answer:
A. 4 square units
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
Your triangle has a base of 4 units and a height of 2 units. Its area is ...
A = 1/2(4)(2) = 4 . . . . square units
__
The triangle dimensions are easily found from your diagram by counting grid squares. If you like, you can subtract the x-coordinates of the points on the horizontal line y=1 to find the base length: 2 -(-2) = 4. And you can subtract the y-coordinates of the points on the vertical line x=-2 to find the height: 3 -1 = 2.
© ? Jordan invests £2100 into his bank account. He receives 5.1% per year simple interest. How much will Jordan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer:
£2314.20
Step-by-step explanation:
Simple interest formula: A = P(1 + rt)
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)t = time (in years)Given:
P = £2100r = 5.1% = 0.051t = 2 years⇒ A = 2100(1 + 0.051 · 2)
⇒ A = 2100(1.102)
⇒ A = £2314.20
An isosceles triangle has a perimeter of 28cm and sides of integer length.
How many different such triangles can be made?
Answer:
over 18716271717161626cm
To solve this question, we have to:
Understand the concept of an isosceles triangle.Understand the perimeter concept.Understand the constraint needed to represent a triangle.Doing this, we get that: 6 different such triangles can be made.
Isosceles triangle:
In an isosceles triangle, two sides have the same measure. An example is given by the picture at the end of this answer.
Perimeter:
The perimeter of a polygon, in this case a triangle, is the sum of all it's sides.
Constraint:
The sum of the lengths of the two smaller sides of a triangle has to be greater than the length of the greater side.
This triangle:
Perimeter of 28.Two sides of x.One side yThus, the perimeter is:
[tex]P = 2x + y = 28[/tex]
Now, for the values of x, we find if the values of y generate a triangle, respecting the constraint.
x = 1
[tex]2 + y = 28 \rigtharrow y = 26[/tex]
1 + 1 < 26, thus, the constraint is not respected.
x = 2
[tex]4 + y = 28 \rightarrow y = 24[/tex]
2 + 2 < 24, thus, the constraint is not respected.
x = 3
[tex]6 + y = 28 \rightarrow y = 22[/tex]
3 + 3 < 22, thus, the constraint is not respected.
x = 4
[tex]8 + y = 28 \rightarrow y = 20[/tex]
4 + 4 < 20, thus, the constraint is not respected.
x = 5
[tex]10 + y = 28 \rightarrow y = 18[/tex]
5 + 5 < 18, thus, the constraint is not respected.
x = 6
[tex]12 + y = 28 \rightarrow y = 16[/tex]
6 + 6 < 16, thus, the constraint is not respected.
x = 7
[tex]14 + y = 28 \rightarrow y = 14[/tex]
7 + 7 = 14, thus, the constraint is not respected.
x = 8
[tex]16 + y = 28 \rightarrow y = 12[/tex]
8 + 8 > 12, thus, the constraint is respected, and this is the first possible triangle.
x = 9
[tex]18 + y = 28 \rightarrow y = 10[/tex]
9 + 9 > 10, thus, the constraint is respected, and this is the second possible triangle.
x = 10
[tex]20 + y = 28 \rightarrow y = 8[/tex]
8 + 10 > 10, the constraint is respected, and this is the third possible triangle.
x = 11
[tex]22 + y = 28 \rightarrow y = 6[/tex]
11 + 6 > 11, the constraint is respected, and this is the fourth possible triangle.
x = 12
[tex]24 + y = 28 \rightarrow y = 4[/tex]
4 + 12 > 12, the constraint is respected, and this is the fifth possible triangle.
x = 13
[tex]26 + y = 28 \rightarrow y = 2[/tex]
13 + 2 > 13, the constraint is respected, and this is the sixth possible triangle.
x = 14
[tex]28 + y = 28 \rightarrow y = 0[/tex]
Cannot have a triangle with a side of 0, so this is not possible.
After the tests, we have that 6 different such triangles can be made.
A similar question is given at https://brainly.com/question/6139098
Find the total amount of an investment of $413.99 compounded at 4.25% for 8.5 years
Answer:
Present Value = $413.99
Interest rate = 4.25%
Years = 8.5 years
Future value = P(1+I)^n
Future value = $413.99*(1+0.425)^8.5
Future value = $413.99*(1.0425)^8.5
Future value = $413.99*1.4244478
Future value = $589.707144722
Future value = $589.71
The total amount to be earned as a result of the investment for 8.5 years is $589.71.
If y=2x+3 and 2x+5=9, then y =
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Suppose that the relation I is defined as follov T= {(-3.3), (0.7). (7.-9).(-3.-4)} at Give the domain and range of T
Answer:
The domain is the set of all the values of x. The range is the set of all the values of y.
Domain:
{−3,0,7}
Range:
{3,7,−9,−4}
pee
HELP ASAP!!
which is greater AC or 4 or neither or both are equal
Simplify 4.2^2 x 5.1^2 x 4.2^4 x 5.1^3
Answer:
=18938545.55220... x^3
Step-by-step explanation:
A boat is trying to determine its speed, in feet per second. The boat spots a 245 foot tall lighthouse at point A at an angle of elevation of 12°. Five minutes later it arrives at point B after traveling in a straight line towards the light house. The angle of elevation is now 28°. What is the boat’s speed to the nearest foot per minute.
Using the slope concept, it is found that the boat traveled at a speed of 138 feet per minute.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
At point A, we have that the vertical change is of 245 ft with an angle of 12º, hence the position in feet is given by:
[tex]\tan{12^\circ} = \frac{245}{x_A}[/tex]
[tex]x_A = \frac{245}{\tan{12^\circ}}[/tex]
[tex]x_A = 1152.6[/tex]
At point B, we have an angle of 28º, hence:
[tex]\tan{28^\circ} = \frac{245}{x_B}[/tex]
[tex]x_B = \frac{245}{\tan{28^\circ}}[/tex]
[tex]x_B = 460.7[/tex]
The distance in feet the boat traveled in 5 minutes was of:
[tex]d = x_A - x_B = 1152.6 - 460.8 = 691.8[/tex]
Velocity is distance divided by time, hence:
v = 691.8/5 = 138.
The boat traveled at a speed of 138 feet per minute.
More can be learned about the slope concept at https://brainly.com/question/18090623
a toy which was bought for rupees 100 was sold at rupees 90. what was the loss in percentage
Answer:
Step-by-step explanation:
Cost of toy =100
Selling price = 90
Loss = 100
Loss in percentage = 10/90*100
Loss in %= 11.11
Nisha did the work below to solve an equation.
Step 1
Step 2
Step 3
Step 4.
7b+3.2b-5-18.92
10.2b-5-18.92
5.2b- 18.92
D=3.64
In which step did Nisha make her first error?
O Step 1
O Step 2
O
Step 3
Step 4
Answer:step 3
Step-by-step explanation:
Answer:
Step 3.
Step-by-step explanation:
She subtracted the 5 from 10.2b even though 5 did not have the variable b.
What is the inverse of the given coordinates: (-2, 2) (3, 0) (7,7) *
Answer:
[tex]2. - 2 \\ - 3.0 \\ - 7. - 7[/tex]
Write the midpoint of the segment as an ordered pair (-3,2),(4,-5)
Answer:
[tex] \huge{ \bold{ \boxed{ \tt{( \frac{1}{2} \: ,\: \: \frac{ - 3}{2} )}}}}[/tex]
Step-by-step explanation:
[tex] \text{Let \: the \: points \: be \: A \: and \: B}[/tex]
[tex] \text{A( - 3 \: 2) } \longrightarrow \text{(x1 \: , y1)}[/tex]
[tex] \text{B(4 \: - 5)} \longrightarrow \text{(x2 \:, y2)}[/tex]
[tex] \underline{ \text{Finding \: the \: midpoint}} : [/tex]
[tex] \boxed{ \sf{Midpoint = ( \frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )}}[/tex]
[tex] \sf{Midpoint = ( \frac{ - 3 + 4}{2} \: , \frac{2 + ( - 5)}{2} })[/tex]
[tex] \underline{ \text{Remember}} : [/tex]
[tex] \text{( + ) * ( - ) = ( - )}[/tex]
[tex] \text{( + ) \: * \: ( + ) = ( + )}[/tex]
[tex] \text{( - ) \: * \: ( + ) = ( - )}[/tex]
[tex] \text{( - ) \: * \: ( - ) = ( + )}[/tex]
[tex] \sf{Midpoint = ( \frac{ - 3 + 4}{2} \:, \frac{2 - 5}{2}) }[/tex]
[tex] \underline{ \text{Remember}}: [/tex]
The positive integers are always added but posses the positive ( + ) sign.The negative integers are always added but posses the negative ( - ) sign.The negative and positive integers are always subtracted but posses the sign of the bigger integer[tex] \sf{Midpoint = ( \frac{1}{2} \: , \frac{ - 3}{2} )}[/tex]
[tex] \text{Hope \: I \: helped}[/tex]!
[tex] \text{Best \: regards}[/tex]!
~[tex] \text{TheAnimeGirl}[/tex]
Can someone please help me? :(
Answer: 4 units, 3 units
Step-by-step explanation:
The side length of the square is measured to be 4 units on the graph
The height can be seen to be 3 units on the graph
4 units on each side
Height is 3 units
Step-by-step explanation:
Perpendicular height is 3 squares up, from the base of the square, to the top of the triangles.
The square measures 4 by 4 on each side.
Hope this helps!
Gabrielle is 11 years younger than Mikhail. The sum of their ages is 77 What is Mikhail's age?
Answer:
44
Step-by-step explanation:
The relations can be written using one variable to represent Mikhail's age: m. Gabrielle's age is (m-11), so the sum of their ages is ...
m +(m -11) = 77
2m = 88 . . . . . . add 11
m = 44 . . . . . . . divide by 2
Mikhail's age is 44.
__
Additional comment
Gabrielle is 33.
You could solve this using two variables:
m - g = 11m + g = 77Adding these two equations gives the one we have above:
2m = 88
m = 44
__
You may have noticed we are given the sum and the difference of the two ages. The older Mikhail's age is half the sum of those two numbers. The younger Gabrielle's age is half their difference: (77 -11)/2 = 33. This "half the sum, half the difference" solution is the generic solution to a "sum and difference" problem.
Gabrielle : 33
Mikhail : 44
Explanation:
Let Mikhail's age be x
And Gabrielle's age be y.
======================
Gabrielle is 11 years younger than Mikhail
y = x - 11 [ equation 1 ]
sum of their ages is 77
x + y = 77 [ equation 2 ]
Insert equation 1 into 2
x + x - 11 = 77
2x = 77 + 11
2x = 88
x = 44
Therefore, the age of Mikhail is 44
Find Gabrielle's age:
y = x - 11
y = 44 - 11
y = 33
Therefore, the age of Gabrielle is 33
Can you find the perimeter of each rectangle and type the correct code? Please remember to type in ALL CAPS with no spaces. *
Answer:
CEFA
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides. A rectangle has two lengths of equal size and two width of equal size. To find the perimeter, add the length and width and multiply by 2.
1. perimeter = 2(3x + 2 + 2x) = 2(5x + 2) = 10x + 4
2. perimeter = 2(4x + 1 + x) = 2(5x + 1) = 10x + 2
3. perimeter = 2(x + 5 + 7) = 2(x + 12) = 2x + 24
4. perimeter = 2(4x - 3 + 5) = 2(4x + 2) = 8x + 4
Codes:
1. C
2. E
3. F
4. A
The slope of the line shown in the graph is
and the y-intercept of the line is
Answer:
y-intercept is 6, the slope is 2/3
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
3.
(a)
Expand and simplify 3(x - 3y) + 6y - 8x
SOME1 PLSS HELPP
Answer:
3(x - 3y) + 6y - 8x
Perform the distributive property;
3x - 9y + 6y - 8x ← Expanded form
Group like terms:
(3x - 8x) (-9y + 6y)
-5x - 3y ← Simplified form
Answer:
I believe it is -5x - 3y
Which of the following items would be considered an asset? Select all that apply.
gaming system
stereo equipment
camera
computer
cell phone
Eight out of 32 students in the class wear
glasses. What is the probability that the first
student who walks out of the class will be
wearing glasses?
Answer:
[tex]\dfrac14[/tex]
Step-by-step explanation:
[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]
If 8 students in a class of 32 wear glasses, then the probability of the first student who walks out of class wearing glasses will be:
[tex]\dfrac{8}{32}[/tex]
Simplifying:
[tex]\dfrac14[/tex]
Which graph below represents a functional relationship? A. 10 10 8 8 6 6 4 2 2 X 10864 6 8 10 10 8 6 4 4 6 8 10 -21 4 -61 -8 -8 10. -10 B. OD. 107 101 8 8 6 6 108 4 2 6 8 10 2. -2) 108 -64 2
Answer:
Graph (C)
Step-by-step explanation:
To find whether the graph\table represents a relationship or a function we have to analyze the input-output values given.
Graph A.
In this graph for every input value (x-value) there are two output values (y-values).
For x = -2, y = -2, 2
So the graph doesn't represent a function.
Graph B.
For every x value there are two y-values
For x = -5, y = -3, 3
So the graph doesn't represent a function.
Graph C.
For every input value there is a different y-value.
Therefore, graph represents a function.
Graph D.
In this graph for x = 3, y = 1, 2, 3, 4
For one value of x, there are four values of y.
Therefore, graph doesn't show the relationship.
Graph C has exactly one output (y-value) corresponding to each input (x-value), therefore, the graph that represents a functional relationship is: Graph C.
What is a Functional Relationship?A functional relationship is a relationship whereby every input in the relation has exactly one possible output.
In other words, a functional relationship must have exactly one output that corresponds to each of the input values.
Thus, graph C has exactly one output (y-value) corresponding to each input (x-value), therefore, the graph that represents a functional relationship is: Graph C.
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17 Mia wants to compare the 100-meter
dash times of 14.084 seconds and
14.102 seconds. Which is the correct
way to compare these two times?
A. 14.084 > 14.102
B. 14.084 < 14.102
C. 14.102 = 14.084
D. 14.102 < 14.084
B. 14.084 < 14.102
< means : less than - smaller than
Johnathan has 30 chocolates.He gives some chocklage to his friend David. He then gives Sarah half the number of chocolates he gave David and gives Lily two thirds of what he gave David. After giving away the chocolates,Johnathan has 4 chocolates left. If the number of chocolates Johnathan gives David is x, which equation represents the situation? How many soultiona does this equation have?
x+1/2x+2/3x+4=30, which has one solution
Which expression is equivalent to 3(v + 8)? (3 + v)8 8(v + 3), (v + 8)3, or 11v
Answer:
the answer is (v+8)3
(my answer needs to be longer so I'm writing this)
a map has a scale of 1/2 inches:12 miles if the actual distance between the cities is 480 miles how far apart are they on the map
Answer:
20 inches
Step-by-step explanation:
Since there are 480 miles in total, we have to divide it by 12 so we can see how many half inches that would be.
480÷12 = 40
That would mean you can fit forty 12's in 480. Since 12 miles equals 1/2, you would multiply it by 40.
1/2 × 40 =20
This means that the distance between the cities on the map would be 20 inches.
Connie has two credit cards, u and v. card u has a balance of $414.55, and card v has a balance of $751.81. the minimum monthly payment on card u is 2.82% of the balance, and the minimum monthly payment on card v is 3.09% of the total balance. how much greater is the minimum payment on card v than on card u? a. $8.70 b. $10.73 c. $9.51 d. $11.54 please select the best answer from the choices provided a b c d
The minimum payment of card u of Connie is $11.54 is greater than the minimum payment of credit cart v.
What is percentage ?Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
Connie has two credit cards, u and v. The card u has a balance of $414.55 and the minimum monthly payment on card u is 2.82% of the balance. Thus, the minimum payment for card u is,
[tex]P_u=\dfrac{2.82}{100}\times414.55\\P_u=11.69[/tex]
Card v has a balance of $751.81 and the minimum monthly payment on card v is 3.09% of the total balance. Thus, the minimum payment for card v is,
[tex]P_v=\dfrac{3.09}{100}\times751.81\\P_v=23.23[/tex]
The difference between the minimum payment of both the cards is,
[tex]d=23.23-11.69\\d=11.54[/tex]
Thus, the minimum payment of card u of Connie is $11.54 is greater than the minimum payment of credit cart v.
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