The complete factorization of the original expression is:
4x² (x + 1)²
We have,
First, we can factor out 4x².
4x² (x² + 2x + 1)
Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:
4x² (x + 1)²
Thus,
The complete factorization of the original expression is:
4x² (x + 1)²
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Which parent function is represented by the graph?
-10
10
-10
A. Quadratic parent function
B. An exponential parent function
O C. Absolute value parent function
OD. Linear parent function
10
SUBM
The requried function represents an absolute value parent function.
A graph is shown,
When we see at the points on the curve,
On x = -10 we have y = 10
simultaneously,
On x = 10 again we have y = 10
This implies that the function is an absolute value parent function.
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The area of a square garden is the same as the area of a rectangular garden that is 8 ft long and 2 ft wide. Write and solve an equation to find the side length of the square garden. Show your work.
The side length of the square garden is 4 feet if the area of a square garden is the same as the area of a rectangular garden that is 8 ft long and 2 ft wide.
Length of the rectangular garden = 8 ft
Width of the rectangular garden = 2 ft
Area of rectangular garden = length x width
Area of rectangle = 8 ft x 2 ft
Area of rectangular garden = 16 square feet
It is given that the area of the square garden is the same as the area of the rectangular garden. The area of the square garden is calculated as:
Area of square garden = side length x side length
Area of square garden = side length x side length = 16
To solve the equation, we need to make isolate it on one side of the equation.
Taking root on both sides:
[tex]\sqrt{(side length * side length)}[/tex] = [tex]\sqrt{16}[/tex]
side length = ± [tex]\sqrt{16}[/tex]
We need to take the positive root value:
side length = [tex]\sqrt{16}[/tex]
side length = 4 ft
Therefore, we can conclude that the side length of the square garden is 4 feet.
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NEED ANWSER ASAP PLS
a horizontal translation only
a horizontal translation and a 180° rotation
a horizontal translation and a glide reflection
a horizontal translation and a reflection across a vertical line
The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.
Here, we have,
the conditions for mapping the strip transformation pattern onto itself:
The strip pattern can be mapped onto itself in two different ways.
The first way is to translate the strip pattern horizontally and then rotate it by 180° degrees.
The second way is to reflect the strip pattern across a vertical line.
Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.
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complete question:
Which transformations map the strip pattern onto itself?
a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°
a horizontal translation only
a horizontal translation, a reflection across a horizontal line, and a glide reflection only
a horizontal translation and a 180° rotation only
PLEASE HELP ME ANSWER (b) REFER TO PICTURE
The standard deviation of the sampling distribution of p is 0.028284
How to calculate the standard deviationThe mean of the sampling distribution of p can be found using the formula:
μp = p = 0.2
The standard deviation of the sampling distribution of p can be found using the formula.
Plugging in the given values, we get:
σp = ✓[(0.2*(1-0.2))/200 * (25000-200)/(25000-1)]
= ✓[(0.16/200) * (24800/24999)]
= ✓[0.0008 * 0.99204]
= ✓(0.0007936)
= 0.028284
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Help out, Algebra 1 Math Nation Section 8
The function g(x)=3a²-4x-1 given represents the quadratic function family.
A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
Prior to the twentieth century, the distinction between a polynomial and its related polynomial function was hazy, therefore "quadratic polynomial" and "quadratic function" were nearly equivalent.
This is still the case in many elementary courses, where both names are sometimes shortened as "quadratic". A quadratic equation is formed when a quadratic function is equated with zero.
The zeros of the appropriate quadratic function are the solutions of a quadratic equation. A quadratic function may have an infinite number of variables.
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PLEASE ANSWER I NEED HELP WILL MARK BRAINLIST!!!!!
f(x) = x² and g(x) = 3(x + 1)² have the same minimum y-value and axis of symmetry, but they have different y-values at x = -2.
We have the function:
f(x) = x² and g(x) = 3(x + 1)² are both quadratic functions.
1. Minimum y-value:
For f(x) = x², the minimum y-value occurs at the vertex of the parabola, which is at (0, 0). The minimum y-value is 0.
For g(x) = 3(x + 1)², the minimum y-value occurs at the vertex of the parabola, which is at (-1, 0). The minimum y-value is also 0.
Therefore, both functions have the same minimum y-value.
2. Axis of symmetry:
For f(x) = x², the axis of symmetry is the vertical line that passes through the vertex of the parabola, which is x = 0.
For g(x) = 3(x + 1)², the axis of symmetry is also the vertical line that passes through the vertex of the parabola, which is x = -1.
Therefore, both functions have different equations but share the same axis of symmetry.
3. Y-value at x = -2:
For f(x) = x², the y-value at x = -2 is f(-2) = (-2)² = 4.
For g(x) = 3(x + 1)², the y-value at x = -2 is g(-2) = 3(-2 + 1)² = 3.
Therefore, the two functions have different y-values at x = -2.
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Suppose we want to choose 6 letters, without replacement, from 14 distinct letters. If the order of the choices is taken into consideration, how many ways can this be done?
As per the combination method, there are 2,162,880 ways to choose 6 letters from 14 distinct letters, taking into account the order of the choices.
Since we are choosing 6 letters from 14 distinct letters, the number of ways to do this without taking into account the order is given by the combination formula:
C(14, 6) = 3003.
However, since we are also taking into account the order of the choices, we need to multiply the number of choices by the number of ways to arrange those choices.
The number of ways to arrange 6 letters is given by 6!, which represents the number of permutations of 6 objects.
Therefore, the total number of ways to choose 6 letters, with order taken into account, is given by the product of the number of combinations and the number of permutations:
C(14, 6) x 6! = 3003 x 720 = 2,162,880.
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f(x)=x^2-10x+1 in the form a(x-h)^2+k
Answer:
[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]
Step-by-step explanation:
Given the function:
[tex]\displaystyle{f(x)=x^2-10x+1}[/tex]
Separate 1 out of the terms:
[tex]\displaystyle{f(x)=(x^2-10x)+1}[/tex]
Convert parentheses-terms to perfect square:
[tex]\displaystyle{f(x)=(x^2-10x+25)+1-25}[/tex]
Evaluate and/or simplify:
[tex]\displaystyle{f(x)=(x-5)^2-24}[/tex]
A $5000 investment pays 3% interest compounded monthly. To the nearest cent, what will be the value of the investment after 10 years?
Answer:
We can use the formula for compound interest to solve this problem. The formula is:
A = P * (1 + r/n)^(n*t)
where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:
A = 5000 * (1 + 0.03/12)^(12*10)
A = 5000 * (1.0025)^120
A ≈ $6,621.36
So the investment will be worth approximately $6,621.36 after 10 years.
Please help me with number 11 please show work
Answer:
B. (1,7)
Step-by-step explanation:
if you answer it i will give you 100 points and brainlist
The correct expression that shows the slope of the line that passes through (3, 6) and (-7, -4) is -4 - 6 / -7 - 3.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore, the slope of a line is the change in y variable with respect to the change in x variable.
Hence,
m = slope = y₂ - y₁ / x₂ - x₁
Therefore, the line passes through (3, 6) and (-7, -4).
where
x₁ = 3
x₂ = -7
y₁ = 6
y₂ = -4
Therefore, the expression is -4 - 6 / -7 - 3.
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What is the range of this function?
74
A.
B.
O C.
all real numbers where 2 + n
all real numbers where
+ nn
(-∞0, ∞0)
21
Answer:
[tex](- \infty, \infty)[/tex]
Third answer choice
Step-by-step explanation:
This is the graph of the function f(x) = tan(x)
We can see that the minimum value of f(x) tends to - ∞ and the maximum value tends to + ∞
So the range of f(x) is [tex](- \infty, \infty)[/tex]
This is the third answer choice (the one that is highlighted in orange)
Enter the exact values of the trigonometric ratios in the boxes.
sin 45°
cos 30
tan 60
=
The required value of trigonometric ratios is,
sin 45° = 1/[tex]\sqrt{2}[/tex]
cos 30 = [tex]\sqrt{3}[/tex]/2
tan 60 = 1/ √3
We know that,
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Therefore,
sin 45° = 1/[tex]\sqrt{2}[/tex]
cos 30 = [tex]\sqrt{3}[/tex]/2
tan 60 = 1/ √3
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Ira’s Craft and Hobby Shoppe sells the items shown below. (AKA the image that I put) London has $7.00. She buys one of each item. How much money does she have left?
A. $4.90
B. $4.10
C. $3.10
D $2.10
Answer:
A. $4.90
Step-by-step explanation:
In one to two sentences, describe one similarity and one difference between a quota and an embargo.
A quota is a limit on the number of goods that a country can import or export during a specific time period, while an embargo is an official ban on trade with a particular country or good or service. Unlike a quota, an embargo is much more strict as it completely shuts down the trade, but a quota simply limits the amount of trade.
A quota limits the quantity of a specific product that can be imported, while an embargo prohibits the import or export of a particular product entirely.
The primary similarity between quotas and embargoes is that they both restrict the flow of goods between countries. Both policies are designed to protect domestic industries by limiting foreign competition and promoting local production.
The main difference between quotas and embargoes is the way they achieve their objectives. A quota sets a limit on the quantity of a particular product that can be imported into a country during a specified period. In contrast, an embargo prohibits the import or export of specific goods altogether, typically for political reasons such as national security concerns or human rights violations.
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A preformed piece of coal weighs 100 g correct to the nearest 5 g. A bag contains 30 pieces of preformed coal. Complete the sticker to attach to this bag of coal. (4 marks) This bag of coal weighs at least This bag of coal weighs at least kg kg
This coal bag has a minimum weight of 2.925 kilograms.
To find the minimum weight of the bag of coalWe must determine the coal's minimum weight, which is 30 pieces.
One piece of coal weighs 100 g, accurate to the closest 5 g. As a result, the actual weight of a piece of coal may range between 97.5 g to 102.5 g.
We can multiply the minimum weight of one piece of coal (97.5 g) by 30 to determine the minimum weight of 30 pieces of coal:
Minimum weight of 30 pieces of coal = 97.5 g x 30 = 2925 g
Therefore, The sticker can be finished as follows:
This coal bag has a minimum weight of 2.925 kilograms.
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what is a sales discount
Answer: A sales discount is a reduced price offered by a business on a product or service.
Step-by-step explanation:
Answer:
when the original selling price of a product does down. You'll be getting the same product at a lower price
Step-by-step explanation:
you can calculate the discount % by
NEW PRICE MULTIPLIED BY 100 DIVIDED BY OLD PRICE
Three thousand tickets are sold for $5 each. There is a $500
prize, a $250 prize, a $125 prize and a $50 prize. What is the
expected value for a person that buys a ticket? Round to the
nearest cent.
Step-by-step explanation:
The total amount of money collected from the ticket sales is:
$5/ticket x 3000 tickets = $15,000
The expected value for a person that buys a ticket can be calculated by adding up the probabilities of winning each prize multiplied by the amount of money for each prize:
E(X) = (1/3000) x $500 + (1/3000) x $250 + (1/3000) x $125 + (1/3000) x $50 - (2996/3000) x $5
Simplifying this expression:
E(X) = $0.1666667 + $0.0833333 + $0.0416667 + $0.0166667 - $4.9833333
E(X) = -$4.65
Therefore, the expected value for a person that buys a ticket is -$4.65, which means that on average, a person can expect to lose $4.65 for every ticket they buy.
Answer: $0.31
Step-by-step explanation:
1/3000 tickets will be worth $500.
1/3000 tickets will be worth $250.
1/3000 tickets will be worth $125.
1/3000 tickets will be worth $50.
The remaining 2996/3000 tickets will be worth $0. (Nobody else wins.)
So (1/3000)x500 + (1/3000)x250 + (1/3000)x125 + (1/3000)x50 + (2996/3000)x0 = $0.31.
Please note: This question asks for expected value. Expected value is a measure of what you should expect to get per game. The payoff of a game is the expected value of the game minus the cost.
*WILL GIVE BRAINLIEST*
Unit 5 circles unit test
What is mST?
i didnt get what you need but i assume you want the angle so it will be 360-130-80-70 = 80⁰
Work out the area of the parallelogram. 79⁰ angle 13cm left side 21cm down along
The area of parallelogram is calculated as, 267.54 cm²
Now, The area of parallelogram can be found by product of its base and height. The calculations are shown below:
We know that,
Area of parallelogram = base × height
Here, We can assume base to be 21 cm.
Then,
sin 79° = h / 13
height = 13 × 0.98 = 12.74
Hence, Area of parallelogram = 21 × 12.74
= 267.54
Thus, The area of parallelogram is calculated as, 267.54 cm²
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A packaging company prints 200,000 boxes per day. They determine that their printing machines are making a mistake on an average of 0.11% of boxes per day with a margin of error of ‡0.01%. How many boxes will need to be recycled due to a printing error in 5 days? boxes
Answer:1100 it is 220 every day
Which of the following shows that the decimal expansion of 12/44 eventually repeats? What did you do to solve for the answer?
Answer:
answer A
Step-by-step explanation:
since 12/44 = 0.2727272727
make v the subject of the formula
T=v/6+5
The formula for v in terms of T is in the equation T = v/6 + 5 is v = 6T - 30.
How to make v the subject of the formula?Given the formula in the question:
T = v/6 + 5
To make v the subject of the formula T = v/6 + 5, we need to isolate v on one side of the equation.
First, we can subtract 5 from both sides of the equation to get:
T = v/6 + 5
T - 5 = v/6 + 5 - 5
T - 5 = v/6
Next, we can multiply both sides by 6 to eliminate the fraction:
6(T - 5) = 6(v/6)
6(T - 5) = v
Simplifying the right-hand side, we get:
6×T 6×-5 = v
6T - 30 = v
v = 6T - 30
Therefore, v as the subject of the formula is v = 6T - 30.
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A human hair was measured to be 8.0•10-4 inch thick. A cat hair is measured to be 4.0•10^-1. How much greater is the thickness of the cat hair than the human hair? Writ this in standard form.
Whoever gets this right I will mark brainiest and 60 points!!
Answer:
500 times
Step-by-step explanation:
Divide the thickness of a cat hair by the thickness of a human hair.
4.0 × 10^-1 / 8.0 × 10^-4 =
= 0.5 × 10^3
= 500
500 times
Hi can someone who is great at math please help me with these math questions. I'm struggling with them!!
The value of x will be 18.67 for the given data of the triangle.
We have,
Thale's theorem:
When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.
Given that the sides of the triangle are divided into two parts,
For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.
The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-
x / ( x + 7 ) = 16 / 22
22x = 16x + 112
6x = 112
x = 112 / 6
x = 18.67
Therefore, the value of x will be 18.67.
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complete question;
Find the values of x and y. Find value of x.
A flat-screen television has a diagonal length of 40 inches. The length of the screen is 175% of its height. What is the length, in inches, of the screen?
The length of the flat-screen television is approximately 40.01 inches.
Let's assume that the height of the flat-screen television is "h" inches.
From the problem statement, we know that the length of the screen is 175% of its height.
Mathematically, we can write:
Length = 1.75 x Height
We can substitute the value of "h" in this equation to find the length of the screen:
Length = 1.75 x h
Now, we also know that the diagonal length of the screen is 40 inches. Using the Pythagorean, we can write:
(Length)² + (Height)² = (Diagonal)²
Substituting the values we have, we get:
(1.75h)² + h² = (40)²
Expanding and simplifying:
3.0625h² = 1600
Dividing both sides by 3.0625:
h² = 522.24
Taking the square root of both sides (and ignoring the negative root since we're dealing with lengths):
h = 22.86 inches
Now we can use the equation we derived earlier to find the length:
Length = 1.75 x h
Length = 1.75 x 22.86
Length = 40.01 inches (rounded to two decimal places)
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Yavonne has $15.90 in her checking account. She needs to buy items that cost $3.18 each. How many of these items can she buy?
a
4
b
5
c
6
d
7
Answer:
5.
Step-by-step explanation:
15.90 / 3.18 =
Please help me show work
Answer:
Part A: 13440ft³
Part B: 2940ft³
Step-by-step explanation:
box volume:
20 x 28 = 560
560 x 24 = 13440ft³
Subtract gift volume:
13440 - 10500 = 2940ft³
What is the square root of 64 in exponential notation
Answer: 64 1/2
Step-by-step explanation:
Answer:
2³
Step-by-step explanation:
Square root of 64 = 8
exponential notation = 2×2×2 = 2³
What is the sum, in degrees, of the interior angles of a regular icosagon
