The factors of the given expression are 5x², (x - 2), and (x - 2).
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
It is given that the polynomial expression 5x⁴ – 20x³ + 20x²
It is required to find its factor.
We have a polynomial expression let's denote it with f(x)
f(x) = 5x⁴ – 20x³ + 20x²
taking 5x² common
f(x) = (x²-4x +4) 5x²
from the formula (a -b)² = a² +b² -2ab
f(x) = (x -2)²*5x²
Thus, the factors of the given expression are 5x², (x - 2), and (x - 2).
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Which is a factor of x2 - 9x + 14?
X-9
x-2
x + 5
X +7
ANSWER
x-2
b
Answer:
(x - 2)
Step-by-step explanation:
Given
x² - 9x + 14
Consider the factors of the constant term (+ 14) which sum to give the coefficient of the x- term (- 9)
The factors are - 2 and - 7, since
- 2 × - 7 = + 14 and - 2 - 7 = - 9, thus
x² - 9x + 14 = (x - 2)(x - 7) ← in factored form
Thus (x - 2) is a factor of the expression
Please answer quicky!!
A ____________ is sometimes a rhombus
1. parallelogram
2. rectangle
3. square
4. trapezoid
Answer:
The answer is 1. parallelogram
Step-by-step explanation:
There's a fact said that a rhombus is just a special paralleogram.
=> So that's means the answer is 1. parallelogram
The volume of a cone is 48π cubic inches. The cone has a height of 36 inches. Mark is finding the radius of the cone. Complete his work. 1. Rewrite the formula including the area of the base: 2. Substitute the values into the formula: 3. Simplify the right side: 4. Divide 12π to both sides: Step 5 is to . The radius of the cone is . V = 1 3 πr²h 48π = 1 3 πr²(36) 48π = 12πr² 4 = r²
Answer:
C and A
Step-by-step explanation:
Step 5 is to ( C ) take the Square root of both sides
The radius of the cone is ( A ) 2 inches
The radius of the cone is 2 inches.
The volume of cone:The volume of a cone is determined by the amount of space occupied by the cone. A three-dimensional figure having a single circular base is known as a cone. The base and the vertex are connected by a curved surface. A cone with a radius of r has a volume V that is one-third the area of the base B times the height h.
[tex]V=\frac{1}{3} \pi r^{2} h[/tex] or [tex]V=\frac{1}{3} Bh[/tex],
Since, [tex]B=\pi r^{2}[/tex]
How to determine the volume of cone?Given that the volume of cone V is 48π cubic inches and Height of the cone h=36 inches.Volume of cone [tex]V=\frac{1}{3} \pi r^{2} h[/tex] -------1
Here, the base of the cone is circular in shape and the area of circle is [tex]\pi r^{2}[/tex]. Consider [tex]B=\pi r^{2}[/tex]
Substituting the area of base in the equation (1).
[tex]V=\frac{1}{3} \pi r^{2}[/tex]
[tex]= \frac{1}{3} Bh[/tex]
Substitute the given values in the equation (1).
⇒ [tex]48\pi =\frac{1}{3} \pi r^{2} 36[/tex]
⇒ [tex]\frac{48\pi }{36\pi } =\frac{r^{2} }{3}[/tex]
⇒ [tex]\frac{12(3)}{9}=r^{2}[/tex]
⇒[tex]4=r^{2}[/tex]
⇒ [tex]r=2[/tex]
Thus, the radius of the cone is 2 inches.
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PLEASE PLEASE PLEASE The graph of g(x), shown below, resembles the graph of f(x) = x^4-x^2 but it has been changed somewhat. Which of the following could be the equation
of g(x)?
Step-by-step explanation:
The equation of the given graph for the function g(x) is [tex]f(x) = x^4 - x^2 -2[/tex]. so option D is correct. The graph of f(x) is shifted down by a factor of 2 on the y-axis.
How to shift the graph vertically up or down?To shift the graph upwards vertically, add a factor(according to the shift) to the y-coordinate.To shift the graph downwards vertically, subtract a factor(according to the shift) from the y-coordinate.How the given graph is shifted?The given graph [tex]f(x)=x^4 -x^2[/tex] is shifted downwards on the y-axis.
And named g(x)
The shift in the y-axis is by 2 units
So,
g(x) = f(x) - 2
= [tex]x^4-x^2-2[/tex]
Therefore, the equation of the given graph when shifted is [tex]g(x)=x^4-x^2-2[/tex]
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Time (in years)
Dan bought a new computer for $900. Each year, the value of
the computer decreased by 25% of the previous year's value. At
this rate, what can Dan expect the approximate value of the
computer to be after 8 years?
A
$84
B
$90
C
$100
D
$113
Answer:
B) $90
Step-by-step explanation:
To work out the value of the computer after 8 years you would first have to convert the percentage into a decimal. To achieve this you would divide the percentage of 25 by 100, which gives you 0.25. This is because percentages are out of 100. The next step is to minus 0.25 from 1, which gives you 0.75. This is because the value of the computer is diminishing. Then you would multiply 900 by 0.75 to the power of 8, which gives you 90. You would multiply to the power of 8 as the percentage decrease will need to take place 8 times due to it being annual.
1) Divide 25 by 100.
[tex]25/100=0.25[/tex]
2) Minus 0.25 from 1.
[tex]1-0.25=0.75[/tex]
3) Multiply 900 by 0.75 by the power of 8.
[tex]900*0.75^{8} =90.1[/tex]
4) Round to the nearest whole number.
90
Final answer:
Using the exponential decay formula, the value of Dan's computer after 8 years, with a 25% annual decline, is approximately $90, corresponding to option B.
Explanation:
The question asks about the depreciation of the value of a computer over time. To calculate the approximate value of Dan's computer after 8 years, with a 25% annual decrease in value, we can use the formula for exponential decay - V = P(1 - r)^t, where V is the final value, P is the initial value, r is the rate of decay, and t is the time in years.
The annual rate of decay, r, is 25% or 0.25.
The time in years, t, is 8 years.
Substituting these values into the formula gives us:
V = 900 (1 - 0.25)^8 = 900 (0.75)^8 = 900 * 0.10011291504 ≈ $90.10
After rounding, Dan can expect the approximate value of the computer to be about $90 after 8 years, which corresponds to option B.
A gift box is 4 inches long, 3 inches wide, and 2 inches high. What is the volume of the gift box
Answer:
24"
Step-by-step explanation:
Volume= length*width*height
4*3= 12
12*2= 24
Final answer:
To find the volume of a gift box, multiply its length, width, and height. For a box with dimensions 4x3x2 inches, the volume is 24 cubic inches.
Explanation:
Volume formula: Volume = length x width x height
Given dimensions: Length = 4 inches, Width = 3 inches, Height = 2 inches
Calculation: Volume = 4 inches x 3 inches x 2 inches = 24 cubic inches
WILL GIVE 20 POINTS
write an equation parallel to the function y=-4x+1 and goes through the point (1,1)
Y=???
Answer:
-4x + 5
Step-by-step explanation:
to be parallel, you need the same slope,
so it has to be -4x
and to go through the point (1,1) the y intercept has to be 5
because if you are using that slope, going down four and over one starting at (0,5) will connect the line to (1,1)
If it helps to draw it out or somehow visually see it, that would be a great idea
but in sum, the only answer is y = -4x + 5
(i didn't see someone had already answered)
(but the answer above uses the slope of 2x and I am unsure why because it says -4x on your question)
(so I guess you could just look at both and see what you need :))
The walls and ceiling of a hotel room are to be painted. The floor is a 14-foot square and the ceiling is 8 feet high. Ignoring any doors or windows, what is the surface area of the walls and the ceiling to be painted
The total surface area to be painted in the hotel room is 644 square feet.
To calculate the surface area of the walls and the ceiling to be painted in a room, we separate the two calculations since the walls and the ceiling have separate dimensions. The floor of the room is a 14-foot square, which means that each side of the wall is 14 feet long. The ceiling also has the same dimensions as the floor. The room has a height of 8 feet.
The area of the ceiling is equal to the area of the floor since they are both squares with the same side length, which is calculated as follows:
Area of ceiling = Side length × Side length
Area of ceiling = 14 feet × 14 feet = 196 square feet
Next, we calculate the surface area of the walls. There are four walls in the room, and each wall has the same height of 8 feet. The wall area is calculated as follows:
Area of one wall = Side length × Height
Area of one wall = 14 feet × 8 feet = 112 square feet
Since there are four walls, total wall area = 4 × 112 square feet = 448 square feet
Finally, we add the area of the ceiling to the total wall area to get the total surface area to be painted:
Total surface area = Ceiling area + Wall area
Total surface area = 196 square feet + 448 square feet = 644 square feet
Therefore, the total surface area of the walls and ceiling of the room that will be painted is 644 square feet, ignoring any doors or windows.
find the equation of the line in slope-intercept form containing the points (6,-1) and (-3,2)
Answer:
y= -1/3x + 1
Step-by-step explanation:
m= (-1-2)/(6-(-3)) = -1/3
-1= -1/3(6) + c
c=1
thus
y= -1/3x + 1
will give the brainliest!!!!!
Find the probability of this event. Enter the answer as a fraction in simplest form, as a decimal, and as a percent.
You choose a marble at random from a bag containing 12 red, 4 blue, 5 green, 7 yellow, and 32 black marbles.
The marble is red.
The probability expressed as a fraction is:___
The probability expressed as a decimal is:___
The probability expressed as a percent is:___
Answer:
12/60, 0.2, 20%
hope i was helpful :)
Find the distance between the points (10, 12) and (10, -8).
units
pt1= (10,12)
pt2= (10,-8)
_________________
distance = √ (x1 - x2)² + (y2 - y1)²
_________________
=√ (0)² + (-20)²
______
=√400
=20 units
Answer:
Step-by-step explanation:
evaluate the expression for p=2
81-p
Answer:
79
Step-by-step explanation:
substitute 2 in for p in the equation 81-2
solve. 81-2=79
Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the
prism expressed as a fraction in simplest form is.
Answer:
Is there a Picture or something to see
Step-by-step explanation:
Which rule represents the table's values?
A)
y = 3x + 1
y = 2x + 11
y = 3x - 1
y = 4x - 15
Answer:
There is no table given to match the values
A dot plot titled Age of Eagles going from 7 to 12. 7 has 1 dot, 8 has 2 dots, 9 has 4 dots, 10 has 2 dots, 11 has 3 dots, 12 has 2 dots. A dot plot titled Age of Lions going from 7 to 12. 7 has 0 dots, 8 has 0 dots, 9 has 2 dots, 10 has 2 dots, 11 has 5 dots, 12 has 4 dots.
The dot plots show the ages of players on two soccer teams. Which statements are true? Check all that apply.
The Lions have more variability in the ages of their players.
The Eagles have more variability in the ages of their players.
The Lions have more players.
The Eagles have more players.
The mean of the ages of Lions is less than the mean of the ages of Eagles.
Answer:
2 and 4
Step-by-step explanation:
nice try though
The true statements about the dot plots are:
B. Eagles have more variability (5)
D. The Eagles have more players (14)
What is the Variability of a Data?Variability is a measure of the degree to which the data values vary from the average value. In a dot plot, the range (max value - min value) is a measure of variability. The larger the range, the more the variability.
Range for age of the 14 players of eagles = 12 - 7 = 5
Range for age of the 13 players of lions = 12 - 9 = 3
The true statement are:
B. Eagles have more variability (5)
D. The Eagles have more players (14)
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5x + 8 = 2x + 14
Need a little bit of help would be thankful xxx
Answer: x = 2
Step-by-step explanation: 5x + 8 = 2x + 14
5x + 8 - 2x = 2x + 14 - 2x
3x + 8 - 8 = 14 - 8
3x = 6
3x/3 = 6/3
x = 2
For this problem, x would equal 2.
x=2
-Dhruva;)
natalie read 10 books in 5 months. what was her rate of reading in books per month?
Answer:
2 books per month.
Step-by-step explanation:
For this, you will simply need to divide the total number of books by the amount of months.
10÷5= 2 books per month.
Natalie read two books for five months.
Divide.
Ten books divided by 5 months.
Find the answer. You get 2.
10 ÷ 5 = 2.
So, her rate of reading books per month was 2.
Hope this helps!
Find the value of x in the triangle shown below.
5.7
66
Answer:
x = 48°
Step-by-step explanation:
Since the triangle is an isosceles triangle, the two base angels will have the same measure.
So..
66 +66 = 132
And since all triangles have a sum of 180°, then..
180 - 132 = 48
On a coordinate plane, a line goes through (0, 4) and (2, 0). The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations. y = −2x + 4, y = − 1 3 x − 1 What is the solution to the system?
Answer:
{3,-2}
Step-by-step explanation:
ITS CORRECT
Answer: third option
Step-by-step explanation:
Rebecca said that the graph is NOT a function. What is the BEST reason she could give to Mr. Bradley to support her statement?
Answer:
Multiple y values for any x
Step-by-step explanation:
A function is a relationship in which every input has a unique output
She can show that there is an x which has multiple (two or more) y values
The width of a rectangle is 5 x minus 7.5 feet and the length is 7.5 x plus 8 feet. Find the perimeter of the rectangle. (help please :) )
Answer:
-2.5+(-2.5)+15.5+15.5=26
Step-by-step explanation:
26 i think
Find the area of the shaded figure in the diagram below. Use 3.14 for π and round your answer to the nearest tenth.
Hurry Please! I need this ASAP
Answer: 38.5
Step by Step:
First you need to find the radius of the smaller circle. 2
Add 2 to 1 and 1 half which gives you 3.5
Next multiply 3.5 by 3.5 that equals 12.25
Lastly times 12.25 by 3.14 and you get 38.5
Answer:
yes that the right answer
pls help! will give brainlist!
find each angle measure in the regular polygon
a. 144°
b. 135°
c. 180°
d. 140°
=====================================================
Work Shown:
E = exterior angle
n = number of sides
For any regular polygon, E = 360/n.
In this case, n = 10 as there are 10 sides, so E = 360/n = 360/10 = 36 degrees is the measure of each exterior angle.
Each interior angle is 180-E = 180-36 = 144 degrees
--------------
An alternative is to plug n = 10 into the formula below to get the measure of each interior angle i
i = 180(n-2)/n
i = 180(10-2)/10
i = 180(8)/10
i = 1440/10
i = 144
note: S = 180(n-2) is the sum of all the interior angles of any convex polygon. Dividing this sum over n will evenly divide the angle total to each interior angle.
The green area in the figure above represents a section of grass for a putting green. Find the area of the sector of grass.
complete question:
The green area in the figure above represents a section of grass for a putting green. Find the area of the sector of grass.
A. A= 32π ft²
B. A= 6π ft²
C. A= 36π ft²
D. A= 72π ft²
Answer:
C. A= 36π ft²
Step-by-step explanation:
The image below is where your question emanated. The area of the sector of grass can be calculated below.
Area of a sector = ∅/360 × πr²
where
∅ = angle from the center of the circle
r = radius
Area of a sector = ∅/360 × πr²
r = 12 ft
∅ = 90°
Area of a sector = 90/360 × π × 12²
Area of a sector = 90/360 × π × 144
Area of a sector = 1/4 × 144π
Area of a sector = 144π/4
Area of a sector = 36π ft²
Each Saturday, a store reduces the price of any unsold item by
10%. If an item was priced at $80, on Saturday of the first week it
is marked down to $72. At the end of the second week, it drops
to $64.80, and at the end of the third week the price is decreased
to $58.32. If this continues for 10 weeks, what should be the
selling price for an item that was originally priced at $80?
Answer:
8 dollars
Step-by-step explanation:
The required selling price of an item that has originally price $80 is $27.89.
Given that,
Each Saturday, a store reduces the price of any unsold item by 10%.
An item was priced at $80, on Saturday of the first week it is marked down to $72.
At the end of the second week, it drops to $64.80, and at the end of the third week, the price is decreases to $58.32.
This continues for 10 weeks.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From the given,
The relation is given as,
Selling price = original price [1 - 0.10]ˣ
Substitute the value in the above equation,
selling price = 80 [0.9]¹⁰
The selling price = $27.89
Thus, the required selling price of an item that has an original price $80 is $27.89.
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1 x (-4) - 8 x 9/-3
Answer: I'm sure it's 20
A cathedral has a large, circular stained-glass window. A visitor measures the window and calculates that it has an area of 50.24 square feet. What is the window's circumference?
Use 3.14 for .
Answer:
25.133
Step-by-step explanation:
area is pi*r^2. divide area by 3.14 and then sqrt to find radius. 6.28*radius= circumference, so 6.28*4=25.133
Answer:
25.12
Step-by-step explanation:
1. Use the formula for the area of a circle to find the radius
[tex]A=\pi r^2[/tex]
[tex]50.24=\pi r^2[/tex]
[tex]16=r^2[/tex]
[tex]\sqrt{16} =r[/tex]
[tex]4=r[/tex]
2. Use this value to find the circumference
[tex]C=2\pi r[/tex]
[tex]C=2\pi 4[/tex]
[tex]C=2(12.56)[/tex]
[tex]C=25.12[/tex]
Your family plays a money game where the first person chosen wins $1, the second person chosen wins $5, the third person chosen wins $10, and the fourth person chosen wins $50. Since you won the $50 prize during the last game, you are in charge of the choosing this time (so you cannot win). How many different winning scenarios are possible in this play of the money game?
Final answer:
There are 24 different winning scenarios possible in the family money game, calculated using permutations since the person in charge of choosing cannot win and there are three distinct prizes to be distributed among four participants.
Explanation:
The family money game presents a probability problem where one must calculate the number of different winning scenarios. Since there are five people including you, and you cannot win because you are the one choosing, you only need to consider the remaining four participants. Each person can win one of the three prizes - $1, $5 or $10 - since you won the $50 prize last time and you are exempt from winning again.
We need to look at the number of ways to arrange three distinct prizes among four people. This can be calculated using permutations where the order of assignment is important.
The formula for permutations is given as P(n, k) = n! / (n-k)!, where n is the total number, and k is the number to choose. In this case, n=4 (people) and k=3 (prizes). Hence, the calculation for permutations would be P(4, 3) = 4! / (4-3)! = (4 x 3 x 2 x 1) / 1 = 24.
Therefore, there are 24 different winning scenarios possible in this play of the money game.
Use the ratios above to make a conclusion about the angles measures of triangle ABC and triangle JKL
Answer:
One is bigget
Step-by-step explanation: