Answers
For y, we can remove the parenthesis and just multiply it all together using the Associative Property of Multiplication. Next, we can combine like terms, adding all the exponents relating to x and all the exponents relating to y, as well as multiplying all of the straight-up numbers, resulting in (2*-6*1/3)(x^(-2-5-1))(y^(-5+3+6))=-4*x^(-8)*y^(4)
For 11, we can start with the parenthesis and exponents from PEMDAS, expanding -a³ to -a^6 (we multiply exponents when making an exponent to the power of something!) and 2b to 4b². Next, we can do the same for (4a²b)^4 , resulting in our expression then being
[tex]4a^{8} b^{4} * \frac{-a^{6}}{4b^{2}}=-4a^{14}*4b^{2}[/tex]
We got 4b² by noticing that 1/b²=b^(-2) and could add 4 and -2 to get 2
Related Questions
Find the area of a trapezoid with bases of 8 and 16 and a height of 10. A)1,280 sq. Units B) 240 sq. units C)120 sq. units
Answers
=[(8+10)/2]10
= 120
Answer: The answer is (C) 120 sq. units.
Step-by-step explanation: We are given to find the area of a trapezoid with bases of lengths 8 units and 16 units and height of 10 units.
We know that the area of the trapezoid with 'a' and 'b' as lengths of the bases and height 'h' is given by
[tex]A=\dfrac{1}{2}(a+b)h.[/tex]
Here, a = 8 units, B = 16 units and h = 10 units.
Therefore, the area of the given trapezoid will be
[tex]a\\\\=\dfrac{1}{2}(a+b)h\\\\=\dfrac{1}{2}\times(8+16)\times 10\\\\=24\times 5\\\\=120~\textup{sq. units.}[/tex]
Thus, the correct option is (C).
If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years
Answers
Answer:
If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.
35.36
atoms
Find the nth term of this sequence: 1,5,9,13,17
Answers
Just add four.
How to find the quadratic equation when given the vertex and y intercept?
Answers
The vertex form of a quadratic equation is given by:
[tex]y=a(x-h)^2+k=ax^2-2ahx+ah^2+k[/tex]
y-intercept is the value of y when x is 0.
Thus, given a y-intercept, c, we have:
[tex]c=ah^2+k \\ \\ \Rightarrow ah^2=c-k \\ \\ \Rightarrow a= \frac{c-k}{h^2} [/tex]
Therefore, given a vertex (h, k) and y-intercept, c, the quadratic equation is given by
[tex]y=\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h^2}\right)hx+\left(\frac{c-k}{h^2}\right)h^2+k \\ \\ =\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h}\right)x+c-k+k \\ \\ =\bold{\left(\frac{c-k}{h^2}\right)x^2-2\left(\frac{c-k}{h}\right)x+c}[/tex]
A radio station is having a promotion in which every 12th caller receives a free concert ticket and every 15th caller receives a limo ride. Which caller will be first one to win both?
Answers
common multiples of 12 : 12,24,36,48,60
common multiples of 15 : 15,30,45,60
LCM = 60
the caller that will be the first to win both is the 60th caller
Answer: Every 60th caller would win both.
Step-by-step explanation:
Since we have given that
every 12th caller receives a free concert ticket.
And
every 15th caller receives a limo ride.
We need to find the first caller who would win.
So, for this we would find L.C.M. of 12 and 15.
And we know the least common multiple of 12 and 15 is 60.
Hence , every 60 th caller would win both.
a golfer needs to hit a ball a distance of 500 feet, but there is a 60-foot tall tree that is 100 feet in front of the point where the shot needs to land. given that the maximum height of the shot is 120 feet, and that the intended distance of 500 feet is reached, by how much did the ball clear the tree?
Answers
We can create a parabola equation of the trajectory using the vertex form:
y = a (x – h)^2 + k
The center is at h and k, where h and k are the points at the maximum height so:
h = 250
k = 120
Therefore:
y = a (x – 250)^2 + 120
At the initial point, x = 0, y = 0, so we can solve for a:
0 = a (0 – 250)^2 + 120
0 = a (62,500) + 120
a = -0.00192
So the whole equation is:
y = -0.00192 (x – 250)^2 + 120
So find for y when the golf ball is above the tree, x = 400:
y = -0.00192 (400 - 250)^2 + 120
y = 76.8 ft
So the ball cleared the tree by:
76.8 ft – 60 ft = 16.8 ft
Answer:
16.8 ft
Rounded to the nearest 3 decimal places, what is the value of r for this data set?
Answers
Answer: 0.989
Side Note: The fact that r is very close to +1 means the data set has strong positive linear correlation. The points all fall very close to a line with positive slope.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
h=2x+9
l= x+2
w= 3x
A) 2x^2+13x+18
B) 6x^3+27x^2+54x
C) 6x^3+39x^2+54x
D) 18x^4+117x^3+162x^2
Answers
Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.
also , h=2x+9
l= x+2
w= 3 x
So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property
=3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab
= 3 x [ 2 x²+ 4 x+ 9 x+18]
= 3 x[ 2 x² +13 x+18]
= (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property
= 6 x³+ 39 x² + 54 x → [ use [tex]x^{m} \times x^{n}= x^{m+n}[/tex]
Option (C) is correct.
The expression which represents the volume of the rectangular prism is; Choice C: 6x³+39x²+54x
Volume of a rectangular prismThe volume of the rectangular prism as given is;
V = lwhwhere, h=2x+9, l= x+2, and w= 3x
Therefore, Volume;
V = (2x+9) (x+2)(3x)V = (2x² +13x +18)(3x)V = 6x³+39x²+54xRead more on volume of rectangular prism;
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Solve the system by elimination.
-2x + 2y + 3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5
Please go step by step, thanks!
Answers
equation 2 plus equation 3, you will get: 2y+4z=2
Now focus on these two new equation you've just got; Let's eliminate y next. To eliminate y, we first have to make the coefficient the same.
multiple 5y+6z=5 by 2 and multiple 2y+4z=2 by 5, we'll get:
10y+12z=10
10y+20z=10
subtract the second of these two equations from the first, you'll get: -8z=0, therefore z=o
Plug z=0 into either one of these two equations, you'll get y=1
plug z=0, y=1 into any of the original three equations, you will get x=1
When writing a two column proof you should always start with ________ Information.
Answers
I hope its right
And i hope it helps
Between what two consecutive positive integers is the square root of 85
Answers
A number system is defined as a system of writing to express numbers. between 9 and 10 positive integers is the square root of 85 is there.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the two consecutive positive integers which have square root of 85 in between.
Firstly we need to know meaning of consecutive numbers.
Numbers which follow each other continuously in the order from smallest to largest are consecutive numbers.
Let us take some perfect square numbers
1,4,16,25,36,49,64,81,100
We know that square root of 81 is 9
square root of 100 is 10
square root of 85 is in between 9 and 10
Hence between 9 and 10 positive integers is the square root of 85 is there.
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How many square feet of carpeting are needed to carpet a 12-foot by 12-foot room
Answers
Area of a rectangle = length × width
Length = 12 ft
Width = 12 ft
A = l×w
= 12 ft × 12 ft
= 144 sq. ft
Thus, you would need 144 square feet of carpeting.
Realize income is ____.
A .The amount of income on hand
B.Income already spent
C. Income that comes from future investment
D. The amount of income you anticipate having
Answers
Realized income refers to the amount of income you expect to have, not yet received, including anticipated earnings and future investments.
Realized income represents the income an individual or entity expects to receive but has not yet received. It encompasses anticipated earnings, future investments, and any other income sources that have not yet materialized.
This includes income from salaries, investments, rental properties, or any other sources.
Unlike earned income, which refers to income already received, realized income is a forward-looking concept, reflecting the anticipated financial gains.
It plays a crucial role in financial planning and budgeting, guiding individuals and organizations in making decisions about expenditures, savings, and investment strategies based on expected future income streams.
Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro delivered 5 newspapers and earned $37.50. This week, he delivered 20 newspapers and earned $75. Let x equal the number of newspapers Pedro delivers and y be the earnings he receives in dollars. Which linear function models the scenario? g(x) = 0.4x + 35.5 g(x) = 0.4x + 67 g(x) = 2.5x + 25 g(x) = 2.5x + 50
Answers
g(x) = 2.5x + 25
5 newspapers, 2.5(5) + 25 = 12.5 + 25 = 37.5
20 newspapers, 2.5(20) + 25 = 50 + 25 = 75
The linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered.
x = the number of newspapers Pedro delivers
y = the earnings he receives in dollars.
From the data given the linear function can be framed as follows:
y = mx + b
Plug x = 5
y = 37.50
37.50 = 5m + b ...(I)
Plug x = 20, and y = 75
75 = 20m + b ...(II)
After solving equation (I) and equation (II):
m = 2.5
b = 25
y = 2.5x + 25
Replace y with g(x)
g(x) = 2.5x + 25
Thus, the linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.
Learn more about the function here:
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Which of the quadratic functions has the widest graph? y = 0.3x2 y = –4x2
Answers
A vertical compression is the squeezing of the graph towards the x-axis.
A compression is a stretch by a factor less than 1.
For the parent function y = f(x), the vertical stretching or compression of the function is a f(x).
If | a | < 1 (a fraction between 0 and 1), then the graph is compressed vertically by a factor of a units.
If | a | > 1, then the graph is stretched vertically by a factor of a units.
For values of a that are negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
Thus, the equation with the widest graph is 0.3x^2.Yes, Y = 0.3x^2 is correct!!
jack purchases 12 gallons of gas on monday .he uses 2/3 of amount purchased communting to and from work during the week additional 2 gallons running errands. how many gallons of gas does john juse for work and errands
Answers
12 * (2 / 3)
= 8 ----- he uses 8 gallons to and from work
+ 2 additinal for errands
therefore gallons for work + gallons for errand = *8 + 2
= 10
your answer is 10
MATH HELP
WILL AWARD BRAINILEST
Graham uses a 10 by 10 grid to model a decreasing pattern. He cuts off a section representing a percent of the current area so that the remaining area represents the next term in the pattern, rounded to nearest whole centimeter. The area after each cut is shown on the graph. After each cut, the remaining area is % of the previous area.
I think its 25% but idk
Answers
Hope this Helps!
Edit: Since I misread the question, I want to reframe my previous explanation instead in terms of what percent of the area of the previous point is left.
Looking again at the areas plotted, what percent of 100 sq. cm is 80 sq. cm? We want to translate the question into math, and our first indicator of where to start is the phrase "what percent of 100 sq. cm." When we talk about taking a fraction or percent of another quantity, we're usually referring to multiplying that fraction by that quantity. In this case, we have our unknown percent, [tex] \frac{x}{100}[/tex], multiplied by 100, which, of course, just leaves you with x. And we're told that this quantity is equal to 80, so we have our answer. x = 80, so we're going to be taking 80% of the area each step.
Leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. How many servings of espresso did he drink?
Answers
Answer:
Hope it helps
Step-by-step explanation:
5u - 5u =u -u help please
Answers
Answer:
it would cancel eachother out so infinite
Step-by-step explanation:
a function is represented by the set of ordered pairs shown below.
{(-4,3), (-1,3), (0,3), (1,5), (3,7)}
what is the range of this function
Answers
---------------------------------------
---------------------------------------
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input. The output values are y = 3, y = 3, y = 3, y = 5, y = 7. So we simply list these outputs without the "y=" portion. Toss out any duplicates. Only write the unique output values.
The curly braces surrounding the list of values tells us that we have a set.
Final answer:
The range of the given function is {3, 5, 7}.
Explanation:
The range of a function refers to the set of all possible output values (y-values) it can produce. Given the function represented by the set of ordered pairs {(-4,3), (-1,3), (0,3), (1,5), (3,7)}, to determine its range, we look at the second elements in each ordered pair since they correspond to the y-values produced by the function.
The y-values in the given set are 3, 3, 3, 5, and 7. Even though the value 3 is repeated, it is only counted once in the range. Thus, the range of this function is the set {3, 5, 7}.
Remember, the range includes all unique y-values that the function outputs. This set contains the different y-values that the function produces according to the given ordered pairs, which means these are the possible values that we can get as outputs from this function.
How would I graph and solve this inequality?? Help please! Press question to view image.
Answers
negative 3 times a number = less than negative 12. so, the higher the number, but negative, is less than. (example:-52<-3) so, |x| is x=4>y
sorry if unclear...
[tex]\bf |x|-3\le 4\implies |x|\le 7\implies \boxed{-7\le x\le 7} \\\\\\ -3|x|\ \textless \ -12\implies |x|\ \textgreater \ \cfrac{-12}{-3}\implies |x|\ \textgreater \ 4\implies \boxed{4\ \textless \ x\ \textless \ -4}[/tex]
A scalene triangle has side side lengths of 12 feet, 8 feet, and 15 feet. what is the perimeter of the triangle
Answers
P= 35 ft
The answer is 35 ft
Answer:
gh
Step-by-step explanation:
Find to slope of the line passing through the points 0,4 -8,-1
A,-8/5
B,-5/8
C, 5/8
D, 8/5
Answers
First, find the slope.
m=(y₂-y₁)/(x₂-x₁)
m=(-1-4)/(-8-0)
m=(-5)/(-8)
m=5/8 <--- this is positive because a negative divided by a negative is positive)
The correct solution is B.
Hope I helped :)
What is the value of X in the isosceles trapezoid below?
Answers
Answer:
D. 13Step-by-step explanation:
Remember that in a isosceles trapezoid, its angles on the base are always congruent.
Also, we know by definition that the sum of interior angles of a trapezoid is equal to 360°, so
[tex]2(2x)+2(10x+24)=360\\4x+20x+48=360\\24x=360-48\\x=\frac{312}{24}\\ x=13[/tex]
Therefore, the right answer is D.
Answer: 13
a p e x confirmed
the equation y= -5.131x^2 +31.821x -3.333 approximates the number of people standing in line to catch a commuter train x hours after 5 a.m.
What is the best estimate for the number of people in line at 8 a.m?
A. 77
B. 46
C. 40
D. 32
Answers
Answer:
The answer is 42!!! I just took test.
Step-by-step explanation:
What is the factored form of the expression? 4x2 – 81y2
Answers
4x^2-81y^2
(2x)^2-(9y)^2
(2x-9y)(2x+9y).
Charles has read 180 pages of book. This isn’t 3/4 of the total number of pages in the book. If p represents the number of pages in the book, what is p?
a.135
b.240
c.320
d. 420
Answers
3p = 720
p= 720÷3 = 240
p= 240
The product of two consecutive odd integers is 143. find all such pairs of integers.
Answers
x^2+2x-143=0
(x+13)(x-11)=0
x=-13
x=11 solution
x+2=13 solution
proof
11*13=143
143=143
l=w+4
thus (w+4)w=117
w^2+4w-117=0
(w+13)(w-9)=0
w-9=0
w=8 for the width
l=9+4=13 for the length.
proof
9*13=117
117=117
How many pairs of triangles appear congruent? The triangles may overlap
Answers
Answer:
4. If i know the picture you're talking about it would be 4.
Step-by-step explanation:
Please help!!
Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.
Answers
Final answer:
The standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3 is x² = -12y.
Explanation:
To find the standard form of the equation of a parabola with a given focus and directrix, we use the definition of a parabola: the locus of points equidistant from the focus and the directrix. Since the focus is at (0, -3) and the directrix is y = 3, the vertex is halfway between the focus and directrix, at (0, 0). The distance from the vertex to the focus (and to the directrix) is 3 units. The standard form of the parabola opening downwards is
(x - h)² = -4p(y - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus, when the parabola opens upwards or downwards.
Substituting the values for the vertex and p, we get
(x - 0)² = -4(3)(y - 0)
which simplifies to
x² = -12y
This is the standard form of the parabola with the given focus and directrix.