The answer to question 13 is (B). [tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]
The answer to question 14 is (A). [tex]\(x - 9\) and \(x + 3\)[/tex]
The answer to question 15 is (A). [tex]\((x - 6)\) and \((x - 5)\).[/tex]
The answer to question 16 is (A). [tex]\((x + 6y)(x + 4y)\).[/tex]
The answer to question 17 is (A).[tex]\(2x - 5\) and \(3x + 4\).[/tex]
The answer to question 18 is (B). [tex]\((5x + 7)\) and \((x - 2)\).[/tex]
To find a simpler form of the product [tex]\((4x - 6y^3)^2\)[/tex], we apply the formula for squaring a binomial, which is [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]. Here, [tex]\(a = 4x\)[/tex] and [tex]\(b = 6y^3\).[/tex]
So, [tex]\((4x - 6y^3)^2 = (4x)^2 - 2(4x)(6y^3) + (6y^3)^2\).[/tex]
Calculating each term, we get:
[tex]\((4x)^2 = 16x^2\),[/tex]
[tex]\(-2(4x)(6y^3) = -48xy^3\),[/tex]
[tex]\((6y^3)^2 = 36y^6\).[/tex]
Putting it all together, we have:
[tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]
To find the possible dimensions of the rectangle, we need to factor the trinomial [tex]\(x^2 + 6x - 27\).[/tex] We look for two numbers that multiply to -27 and add up to 6. These numbers are 9 and -3.
So, [tex]\(x^2 + 6x - 27 = (x + 9)(x - 3)\).[/tex]
We factor the trinomial [tex]\(x^2 + x - 30\)[/tex] by finding two numbers that multiply to -30 and add up to 1. These numbers are 6 and -5.
So, [tex]\(x^2 + x - 30 = (x - 6)(x + 5)\).[/tex]
To factor [tex]\(x^2 - 10xy + 24y^2\)[/tex], we look for two numbers that multiply to \[tex](24y^2\)[/tex] and add up to -10y. These numbers are -6y and -4y.
So, [tex]\(x^2 - 10xy + 24y^2 = (x - 6y)(x - 4y)\)[/tex].
To find the possible dimensions of the barnyard, we factor the trinomial [tex]\(6x^2 + 7x - 20\).[/tex] We need two numbers that multiply to [tex]\(6 \times -20 = -120\)[/tex] and add up to 7. These numbers are 15 and -8. We then split the middle term accordingly and factor by grouping:
[tex]\(6x^2 + 15x - 8x - 20 = 0\),[/tex]
[tex]\(3x(2x + 5) - 4(2x + 5) = 0\),[/tex]
[tex]\((3x - 4)(2x + 5)\).[/tex]
We factor the trinomial [tex]\(5x^2 - 3x - 14\)[/tex] by finding two numbers that multiply to [tex]\(5 \times -14 = -70\)[/tex] and add up to -3. These numbers are -10 and 7. We then split the middle term accordingly and factor by grouping:
[tex]\(5x^2 - 10x + 7x - 14 = 0\),[/tex]
[tex]\(5x(x - 2) + 7(x - 2) = 0\),[/tex]
[tex]\((5x + 7)(x - 2)\).[/tex]
Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem. Jack makes a mosaic out of glass tiles. The mosaic covers a parallelogram-shaped piece of wood. The area of the wood piece is 456 in² and its base is 24 inches. What is the height of the wood piece?
Help I need this ASAP 99 points!!!
What is the coefficient of x4y4 in the expansion of (x + y)8?
Answer:
70
Step-by-step explanation:
If you use Pascal's Triangle, you will need 9 lines, since there are 9 terms in a binomial raised to the 8th power. Those 9 terms are:
1, 8, 28, 56, 70, 56, 28, 8, 1
The first expansion through the one we need are below (I hope you know how to use Pascal's Triangle!):
[tex]1(x^8)(y^0)+8(x^7)(y^1)+28(x^6)(y^2)+56(x^5)(y^3)+70(x^4)(y^4)+...[/tex]
Answer:
70
Step-by-step explanation:
apex
PLEASE HELP ME! I keep getting the wrong answer.
Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?
g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x − 10 − 5x
g(x) − f(x) = −2x − 8 − 3x
g(x) − f(x) = −2x − 10 − 3x,
Write 58 1/2 in radical form
Find x so that the slope of the roof is one third 1/3.
A survey with a two-point scale was conducted in an organization. It concluded that 85% of the respondents were unsatisfied with the career guidance they were provided. If 2,000 people participated in the survey, people were satisfied with the career guidance.
Answer:
See image
Step-by-step explanation:
Plato
If 12 is added to the square of a positive integer, the result is 133. Find the positive integer
11___________________________
A chemist weighed out 101. g of potassium. Calculate the number of moles of potassium she weighed out.
Round your answer to 3 significant digits.
Answer:
101 g of Potassium is equivalent to 2.583 moles of Potassium.
Step-by-step explanation:
As per definition of moles, molecular weight of a substance = 1 mole
So molecular weight of Potassium = 39.0983 g
∵ 39.0983 g weight of Potassium = 1 mole
∴ 1 g weight of Potassium = [tex]\frac{1}{39.0983}[/tex] g
∴ 101 g of Potassium = [tex]\frac{101}{39.0983}[/tex] g
= 2.583 moles
Therefore, 101 g of Potassium is equivalent to 2.583 moles of Potassium.
If your credit reports shows different scores, what should you do?
A) Nothing, the credit bureaus will recognize the mistake and fix it for you.
B) Get in touch with credit bureaus to see if they have different or inaccurate information on your credit history.
C) Research online to see how you can get into the system and fix it yourself.
D) Visit your local bank and have them fix it for you.
Answer:
(B) is correct
Step-by-step explanation:
As the credit reports shows different scores so it will be resolved by credit bureaus and the report only shows different scores in case they have incorrect or different info about our credit history so we should contact the credit bureaus and ask them to correct the information of our credit history.
So, the right answer is (B).
25 POINTS!
Which of the following ordered pairs is a possible solution to the equation y = 3x - 2?
A: (0, 2)
B: (1, 1)
C: (-3, 1)
D: (2, 0)
The only ordered pair that is a possible solution to the equation y = 3x - 2 is B: (1, 1).
To determine if an ordered pair is a possible solution to the equation y = 3x - 2, we need to check if the x and y values satisfy the equation when substituted into it.
Let's check each option:
A: (0, 2)
Substitute x = 0 and y = 2 into the equation:
2 = 3(0) - 2
2 = -2
This is not true, so (0, 2) is not a possible solution.
B: (1, 1)
Substitute x = 1 and y = 1 into the equation:
1 = 3(1) - 2
1 = 1
This is true, so (1, 1) is a possible solution.
C: (-3, 1)
Substitute x = -3 and y = 1 into the equation:
1 = 3(-3) - 2
1 = -11
This is not true, so (-3, 1) is not a possible solution.
D: (2, 0)
Substitute x = 2 and y = 0 into the equation:
0 = 3(2) - 2
0 = 4
This is not true, so (2, 0) is not a possible solution.
The only ordered pair that is a possible solution to the equation y = 3x - 2 is B: (1, 1).
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What is a quartic function with only the two real zeroes given?
x=5 and x=1
The answer is
Y=x^4-6x^3 +6x^2 -6x+5
The quartic function with only two real zeroes given as; x=5 and x=1 is; x⁴ -12x³ +46x²-60x +25
With two zeroes given for a quartic equation;
The zeroes must appear twice each such that the factors of the function are;
(x-5), (x-5) , (x -1) and (x- 1)The quartic function is therefore:
(x² -10x +25) (x² -2x +1)(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25= x⁴ -12x³ +46x²-60x +25
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Use the identity below to complete the tasks: a3 + b3 = (a + b)(a2 - ab + b2) Use the identity for the sum of two cubes to factor 8q6r3 + 27s6t3. What is a? What is b? Factor the expression. es003-1.jpg es003-2.jpg es004-1.jpg es005-1.jpg es006-1.jpg
a is 2q^2r
b is 3s^2t
the expression factored is...
(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)
The given expression is a sum of two cubes. The factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
Given:
The given identity is, [tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex].
It is required to factorize [tex]8q^6r^3 + 27s^6t^3[/tex] using the given identity.
The given expression can be written in the form of sum of two cubes as,
[tex]8q^6r^3 + 27s^6t^3=2^3q^6r^3 + 3^3s^6t^3\\=(2q^2r)^3+(3s^2t)^3[/tex]
Here, a and b are [tex]2q^2r[/tex] and [tex]3s^2t[/tex] respectively.
Now, the factorization of the given expression can be one as,
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex]
Therefore, the factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
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A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?
A. 1/3x^2 in.2
B. 1/4x^2 in.2
C. x2 in.2
D. 1/2x^2 in.2
Also...
A solid right pyramid has a square base with an edge length of x cm and a heigt of y cm. Which expression represents the volume of the pyramid?
A. 1/3x2y cm3
B. 1/2xy2 cm3
C. 1/3xy cm3
D. 1/2x2y cm3
This is all the info I am given HELP
Answer: Th answer is A
The area of the base of each pyramid, if divided from a square base of entire length x inches and made of 8 pyramids, should be 1/8 x[tex]^[/tex] in.2, but among given options, B. 1/4 x[tex]^[/tex] in.2 is closest. The volume of a solid right pyramid with square base edge length x cm and height y cm is correctly given by A. 1/3 x[tex]^[/tex]y cm3.
Explanation:To find the area of the base of each pyramid in a soundproofing tile made of 8 identical solid right pyramids with square bases, we will calculate the area of the entire square base of the tile and then divide by the number of pyramids. If the length of the whole tile is x inches, the area of the whole base is x[tex]^[/tex] square inches. Since there are 8 pyramids, the area of the base of each pyramid is x^2 divided by 8, which simplifies to 1/8 x[tex]^[/tex] square inches. However, this option is not listed, suggesting there may have been an error in the question or choices provided. Regardless, among the given options, the closest would be B. 1/4 x[tex]^[/tex] in.2, considering the whole square is likely split into quarters for each pyramid.
For the volume of a solid right pyramid with a square base with an edge length of x cm and a height of y cm, the formula for the volume of the pyramid is 1/3 times the area of the base times the height. The area of the base, which is a square, is x[tex]^[/tex], so the volume is 1/3 x[tex]^[/tex]y cm3. Therefore, the correct answer is A. 1/3 x[tex]^[/tex]y cm3.
Suppose a population of 40 crickets doubles in size every month. the function gives the population after x months. how many crickets will there be after 3 years?
Answer:
2,880
Step-by-step explanation:
just trust me, it's that one
Which diagram represents rx ◦ RO,180°?
Answer:
the correct answer is B
Three consecutive odd integers are such that the square of the third integer is 1515 greater than greater than the sum of the squares of the first two. one solution is 33, 55, and 77. find three other consecutive odd integers that also satisfy the given conditions.
Answer:
Step-by-step explanation:
PLEASE HELP ASAP! TONS OF POINTS
Answer:
I would say it's B!
To be honest I got confused at a point but I think B is the correct answer.
Hope this helped
a triangle has verices at (4,-2), (-3,0) and (1,3). what is the approximate perimeter of the triangle?
1. 17 units
2.18 units
3.19 units
4.20 units
The reference angle for an angle whose measure is 260 degrees is
50 POINTS!!!!! HELP Soybean meal is 16% protein; cornmeal is 8% protein.How many pounds of each should be mixed together in order to get 320-lb mixture that is 9% protein?
How many pounds of cornmeal should be in the mixture? How many pounds of soybean should be in the mixture?
The diagram represents the enlargement of a rectangle by using a scale factor of 6
5*1 is the dimension of the original rectangle.
What is Scale?The scale is the proportion that is used to show how the dimensions of a model or scaled figure compare to the equivalent dimensions of the real figure or item. In contrast, a scale factor is a number that is multiplied by each component of an item to create an expanded or reduced figure.
Given With a scale factor of 6, the diagram depicts the expansion of a rectangle.
and the new rectangle is 30*6 in size.
The scaling factor is 6
thus,
the length of the original rectangle = 30/6
the length of the original rectangle = 5
the width of the original rectangle = 6/6
the width of the original rectangle = 1
therefore, the dimension of the original rectangle is 5*1.
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Complete question:
What measurements did the initial rectangle have?
the difference of a number t and 7 is greater than 10 and less than 20....show me how to write this as an inequality.,
Please help, Picture included.
Jason jumps from a plane at an altitude of 1000m. his parachute opens after 10 seconds. The graph shows the relationship between his altitude and time. How far does he fall in the first 40 seconds?
A) 400m
B) 500m
C) 600m
D) 700m
Jason falls 800m in the first 40 seconds.
To find how far Jason falls in the first 40 seconds, we need to look at the graph provided. The graph shows that for the first 10 seconds, his altitude decreases from 1000m to 200m. So, in the first 10 seconds, he falls 1000m - 200m = 800m. Then, from 10 seconds to 40 seconds, his altitude stays constant at 200m, so he does not fall any further. Therefore, Jason falls a total of 800m in the first 40 seconds.
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You are buying a $24.50 item that has 6% sales tax. You give the cashier $40 to pay for the item. How much change do you get back?
Answer:
14.03
Step-by-step explanation:
I took a test
There are $14.03 get change do you get back.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
You are buying a $24.50 item that has 6% sales tax.
And, You give the cashier $40 to pay for the item.
Here, You are buying a $24.50 item that has 6% sales tax.
Hence, The amount of sales tax = 6% of $24.50
= 6/100 × $24.50
= $1.47
Thus, The amount of charge = $40 - ($24.50 + $1.47)
= $40 - $25.97
= $14.03
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You are asked to draw a triangle with side lengths of 6 inches and 8 inches. What is the longest whole number length that your third side can be?
@iGreen,
What is the median of the following set of data?
78, 92, 98, 87, 86, 72, 92, 81, 86, 92
Answer:
86.5
Explanation:
If you list these numbers in order from least to greatest, you get 10 numbers. Since there are isn't a number in the middle, you have to find the value between 86 and 87 which gives you 86.5. Sorry for the late response and have a great day!
N the construction of a new building, a landscape architect determined that he had a plot 810 feet by 35 feet, to be filled to a depth of 6 inches with loam. how many cubic yards of loam would he require?
What type of graph is useful when depicting piece rates?
A. Bar graph
B. Scatterplot
C. Slope
D. Linear graph
A linear graph is most useful when depicting piece rates as it clearly shows the continuous relationship and trend between the number of items produced and the pay received, represented by a positive, negative, or zero slope.
When depicting piece rates, which relate the payment an individual receives to the number of pieces produced or tasks completed, a linear graph or line graph is often most useful. Linear graphs effectively illustrate relationships between two variables, such as the number of items produced (on the x-axis) and the amount of money earned (on the y-axis), highlighting trends and changes over a range of values. A bar graph may be best to illustrate comparisons when showing the relationship of separate and distinct categories. However, in the context of piece rates, where there is a continuous relationship between work done and pay received, the connected data points in a line graph provide a clear visual of the rate of payment as it changes with the number of pieces.
Understanding the appearance of slopes is essential in reading graphs. A positive slope indicates an increase or upward trend in the relationship between the two variables, a negative slope represents a decrease or downward trend, and a zero slope indicates a consistent, flat relationship with no change over time.
What percent of 170 is 68?
393 is 60% of what number?
Write and simplify the equation you would use to solve the problem below. Scott has a jar of quarters and dimes. If there is $4.15 in the jar, and there are 4 dimes, how many quarters are in the jar?
A. x(25 + 10) = 415
B. 25x + 40 = 415
C. 25x + 10 = 415
D. 4 * 10x + 25x = 415